Corporate finance [9 ed.] 9780073382333, 0073382337, 9780077337629, 007733762X

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Corporate Finance

The McGraw-Hill/Irwin Series in Finance, Insurance, and Real Estate Stephen A. Ross Franco Modigliani Professor of Finance and Economics Sloan School of Management Massachusetts Institute of Technology ConsultingE ditor Financial Management Adair Excel Applications for Corporate Finance First Edition Block, Hirt, and Danielsen Foundations of Financial Management Thirteenth Edition Brealey, Myers, and Allen Principles of Corporate Finance Ninth Edition Brealey, Myers, and Allen Principles of Corporate Finance, Concise First Edition Brealey, Myers, and Marcus Fundamentals of Corporate Finance Sixth Edition

Ross, Westerfield, and Jaffe Corporate Finance Ninth Edition Ross, Westerfield, Jaffe, and Jordan Corporate Finance: Core Principles and Applications Second Edition Ross, Westerfield, and Jordan Essentials of Corporate Finance Sixth Edition

Shefrin Behavioral Corporate Finance: Decisions that Create Value First Edition

Kuemmerle Case Studies in International Entrepreneurship: Managing and Financing Ventures in the Global Economy First Edition

Bruner Case Studies in Finance: Managing for Corporate Value Creation Sixth Edition

Investments

DeMello Cases in Finance Second Edition Grinblatt (editor) Stephen A. Ross, Mentor: Influence through Generations Grinblatt and Titman Financial Markets and Corporate Strategy Second Edition Higgins Analysis for Financial Management Ninth Edition Kellison Theory of Interest Third Edition Kester, Ruback, and Tufano Case Problems in Finance Twelfth Edition

International Finance Eun and Resnick International Financial Management Fifth Edition

White Financial Analysis with an Electronic Calculator Sixth Edition

Cornett, Adair, and Nofsinger Finance: Applications and Theory First Edition

Saunders and Cornett Financial Markets and Institutions Fourth Edition

Ross, Westerfield, and Jordan Fundamentals of Corporate Finance Ninth Edition

Brooks FinGame Online 5.0

Chew The New Corporate Finance: Where Theory Meets Practice Third Edition

Saunders and Cornett Financial Institutions Management: A Risk Management Approach Sixth Edition

Bodie, Kane, and Marcus Essentials of Investments Eighth Edition Bodie, Kane, and Marcus Investments Eighth Edition Hirt and Block Fundamentals of Investment Management Ninth Edition Hirschey and Nofsinger Investments: Analysis and Behavior Second Edition

Real Estate Brueggeman and Fisher Real Estate Finance and Investments Thirteenth Edition Ling and Archer Real Estate Principles: A Value Approach Third Edition

Financial Planning and Insurance Allen, Melone, Rosenbloom, and Mahoney Retirement Plans: 401(k)s, IRAs, and Other Deferred Compensation Approaches Tenth Edition Altfest Personal Financial Planning First Edition

Jordan and Miller Fundamentals of Investments: Valuation and Management Fifth Edition

Harrington and Niehaus Risk Management and Insurance Second Edition

Financial Institutions and Markets

Kapoor, Dlabay, and Hughes Focus on Personal Finance: An active approach to help you develop successful financial skills Third Edition

Rose and Hudgins Bank Management and Financial Services Eighth Edition Rose and Marquis Money and Capital Markets: Financial Institutions and Instruments in a Global Marketplace Tenth Edition

Kapoor, Dlabay, and Hughes Personal Finance Ninth Edition

Corporate Finance NinthE dition

Stephen A. Ross Sloan School of Management Massachusetts Institute of Technology

Randolph W. Westerfield Marshall School of Business University of Southern California

Jeffrey Jaffe Wharton School of Business University of Pennsylvania

CORPORATEF INANCE Published by McGraw-Hill/Irwin, a business unit of The McGraw-Hill Companies, Inc., 1221 Avenue of the Americas, New York, NY, 10020. Copyright © 2010, 2008, 2005, 2002, 1999, 1996, 1993, 1990, 1988 by The McGraw-Hill Companies, Inc. All rights reserved. No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written consent of The McGraw-Hill Companies, Inc., including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning. Some ancillaries, including electronic and print components, may not be available to customers outside the United States. This book is printed on acid-free paper. 1 2 3 4 5 6 7 8 9 0 DOW/DOW 0 9 ISBN978-0-07-338233-3 MHID0-07-338233-7 Vicep residentan de ditor-in-chief: Brent Gordon Publisher: Douglas Reiner Executivee ditor: Michele Janicek Directoro f d evelopment: Ann Torbert Developmente ditor: Elizabeth Hughes Vice president and director of marketing: Robin J. Zwettler Marketingd irector: Sankha Basu Seniormar ketingman ager: Melissa S. Caughlin Vice president of editing, design and production: Sesha Bolisetty Leadp rojectman ager: Christine A. Vaughan Productionsu pervisor: Michael R. McCormick Interiord esigner: Pam Verros Leadme diap rojectman ager: Brian Nacik Coverima ge: © Veer Typeface: 10/12 Times Roman Compositor: Macmillan Publishing Solutions Printer: R. R. Donnelley Library of Congress Cataloging-in-Publication Data Ross, Stephen A. Corporate finance / Stephen A. Ross, Randolph W. Westerfield, Jeffrey Jaffe. -- 9th ed. p. cm. -- (The McGraw-Hill/Irwin series in finance, insurance and real estate) Includes index. ISBN-13: 978-0-07-338233-3 (alk. paper) ISBN-10: 0-07-338233-7 (alk. paper) 1. Corporations—Finance. I. W esterfield, Randolph. II. Jaffe, Jeffrey F., 1946- III. Title. HG4026.R675 2010 658.15 -- dc22 2009028916

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To our family and friends with love and gratitude.

About the Authors STEPHEN A. ROSS Sloan School of Management, Massachusetts Institute of Tech-

nology Stephen A. Ross is the Franco Modigliani Professor of Financial Economics at the Sloan School of Management, Massachusetts Institute of Technology. One of the most widely published authors in finance and economics, Professor Ross is recognized for his work in developing the arbitrage pricing theory, as well as for having made substantial contributions to the discipline through his research in signaling, agency theory, option pricing, and the theory of the term structure of interest rates, among other topics. A past president of the American Finance Association, he currently serves as an associate editor of several academic and practitioner journals and is a trustee of CalTech. RANDOLPH W. WESTERFIELD Marshall School of Business, University of Southern California Randolph W. Westerfield is Dean Emeritus of the University of Southern California’s Marshall School of Business and is the Charles B. Thornton Professor of Finance. Professor Westerfield came to USC from the Wharton School, University of Pennsylvania, where he was the chairman of the finance department and member of the finance faculty for 20 years. He was also elected to membership in the Financial Economists Roundtable. He has been a member of several public company boards of directors, including Health Management Associates, Inc., William Lyon Homes, and the Nicholas Applegate Growth Fund. His areas of expertise include corporate financial policy, investment management, and stock market price behavior. JEFFREY F. JAFFE Wharton School of Business, University of Pennsylvania Jeffrey F. Jaffe has been a frequent contributor to the finance and economics literatures in such journals as the Quarterly Economic Journal, The Journal of Finance, The Journal of Financial and Quantitative Analysis, The Journal of Financial Economics, and The Financial Analysts Journal. His best-known work concerns insider trading, where he showed both that corporate insiders earn abnormal profits from their trades and that regulation has little effect on these profits. He has also made contributions concerning initial public offerings, regulation of utilities, the behavior of market makers, the fluctuation of gold prices, the theoretical effect of inflation on interest rates, the empirical effect of inflation on capital asset prices, the relationship between small-capitalization stocks and the January effect, and the capital structure decision.

vi

Preface

T

he teaching and the practice of corporate finance are more challenging and exciting than ever before. The last decade has seen fundamental changes in financial markets and financial instruments. In the early years of the 21st century, we still see announcements in the financial press about takeovers, junk bonds, financial restructuring, initial public offerings, bankruptcies, and derivatives. In addition, there are the new recognitions of “real” options, private equity and venture capital, subprime mortgages, bailouts, and credit spreads. As we have learned in the recent global credit crisis and stock market collapse, the world’s financial markets are more integrated than ever before. Both the theory and practice of corporate finance have been moving ahead with uncommon speed, and our teaching must keep pace. These developments have placed new burdens on the teaching of corporate finance. On one hand, the changing world of finance makes it more difficult to keep materials up to date. On the other hand, the teacher must distinguish the permanent from the temporary and avoid the temptation to follow fads. Our solution to this problem is to emphasize the modern fundamentals of the theory of finance and make the theory come to life with contemporary examples. Increasingly, many of these examples are outside the United States. All too often the beginning student views corporate finance as a collection of unrelated topics that are unified largely because they are bound together between the covers of one book. As in the previous editions, our aim is to present corporate finance as the working of a few integrated and powerful institutions.

The Intended Audience of This Book This book has been written for the introductory courses in corporate finance at the MBA level and for the intermediate courses in many undergraduate programs. Some instructors will find our text appropriate for the introductory course at the undergraduate level as well. We assume that most students either will have taken, or will be concurrently enrolled in, courses in accounting, statistics, and economics. This exposure will help students understand some of the more difficult material. However, the book is self-contained, and a prior knowledge of these areas is not essential. The only mathematics prerequisite is basic algebra.

New to Ninth Edition • • • • •

Separate chapters on bonds and stocks. Expanded material on bonds and stocks moved after capital budgeting for better flow. Integrated short-term finance, credit, and cash management. An introduction to integrated long-term debt and long-term finance. More Excel example problems integrated into the chapters. Chapter 1

Chapter 3

Introduction to Corporate Finance • New material on corporate governance and regulation, including Sarbanes-Oxley. Financial Statements Analysis and Financial Models • Updated and modernized financial statement analysis information, including EBITDAan de nterprisev alue(E V). vii

viii

Preface

Chapter 4

Discounted Cash Flow Valuation • Several new spreadsheet applications. • Appendix 4B on using financial calculators (on Web site).

Chapter 8

New chapter, Interest Rates and Bond Valuation • Added coverage of TIPS. • Added coverage of term structure of interest rates. • New material on credit risk. • Updated coverage on how bonds are bought and sold.

Chapter 9

New chapter, Stock Valuation • More on the link between dividends, cash flow, and value. • More applications using real-world companies. • New section on the retention decision and shareholder value. • New material on stock market trading and reporting.

Chapter 10

Risk and Return: Lessons from Market History • New material on the global stock market collapse of 2008.

Chapter 11

Return and Risk: The Capital Asset Pricing Model • Improved and expanded discussion of diversification and unsystematican dsyste maticr isk.

Chapter 12

An Alternative View of Risk & Return: The Arbitrage Pricing Model • New box feature on factor models by Kenneth French.

Chapter 13

Risk, Cost of Capital, and Capital Budgeting • Added material on the market risk premium. • Expanded coverage of flotation cost. • Added material on preferred stock. • New section discussing the case of non-dividend–paying stocks andth ec osto f c apital.

Chapter 14

Efficient Capital Markets and Behavioral Challenges • More material on current global market collapse.

Chapter 15

Long-Term Financing: An Introduction • Expanded and updated coverage of common stock and longterm corporate debt. • Updatedtr endsin c apitalstru cture.

Chapter 25

Derivatives and Hedging Risk • Added credit default swaps (CDS) material.

Chapter30

FinancialDistr ess • Addedth eZ -model.

In this edition of Corporate Finance, we have

Pedagogy

updated and improved our features to present material in a way that makes it coherent and easy to understand. In addition, Corporate Finance is rich in valuable learning tools and support, to help students succeed in learning

PART III

the fundamentals of financial management.

CHAPTER 10

Risk and Return Lessons from Market History

Chapter Opening Vignettes

With the S&P 500 Index down about 39 percent and the NASDAQ Index down about 41 percent in 2008, stock market performance overall was not very good. In fact, the loss on the S&P 500 was the worst since 1937, and the loss for the NASDAQ was the worst in its relatively short history. Overall, the declines in U.S. stock markets wiped out about $6.9 trillion in equity during 2008. Of course, some stocks did worse than others. For example, stock

Each chapter begins with a contemporary vignette that highlights the concepts in the chapter and their relevance to real-world examples.

in insurance giant American International Group (AIG) fell over 97 percent during the year, and stock in mortgage giants Fannie Mae and Freddie Mac both dropped about 98 percent. Even so, it was a great year for investors in biopharmaceutical company Emergent BioSolutions, Inc., whose stock gained a whopping 461 percent. And investors in gas and oil company Mexco Energy Corp., had to be energized by the 211 percent gain of the stock. These examples show that there were tremendous potential profits to be made during 2008, but there was also the risk of losing money—and lots of it. So what should you, as a stock market investor, expect when you invest your own money? In this chapter, we study more than eight decades of market history to find out.

10.1 Returns Dollar Returns

How did the market do today? Find out at finance.yahoo.com.

Suppose the Video Concept Company has several thousand shares of stock outstanding and you are a shareholder. Further suppose that you purchased some of the shares of stock in the company at the beginning of the year; it is now year-end and you want to figure out how well you have done on your investment. The return you get on an investment in stocks, like that in bonds or any other investment, comes in two forms. As the owner of stock in the Video Concept Company, you are a part owner of the company. If the company is profitable, it generally could distribute some of its profits to the shareholders. Therefore, as the owner of shares of stock, you could receive some cash, called a dividend, during the year. This cash is the income component of your return. In addition to the dividends, the other part of your return is the capital gain—or, if it is negative, the capital loss (negative capital gain)—on the investment. For example, suppose we are considering the cash flows of the investment in Figure 10.1, showing that you purchased 100 shares of stock at the beginning of the year at a price of $37 per share. Your total investment, then, was: C0 = $37 × 100 = $3,700

300

x

Figure 8.2 Interest Rate Risk and Time to Maturity

2,000

Bond value ($)

$1,768.62 30-year bond

1,500

1,000

$1,047.62

1-year bond $916.67

$502.11

500

5

10 15 Interest rate (%)

20

Value of a Bond with a 10 Percent Coupon Rate for Different Interest Rates and Maturities Time to Maturity

EXAMPLE 9.5

Interest Rate

1 Year

30 Years

5% 10 15 20

$1,047.62 1,000.00 956.52 916.67

$1,768.62 1,000.00 671.70 502.11

Calculating the Required Return Pagemaster Enterprises, the company examined in the previous example, has 1,000,000 shares of stock outstanding. The stock is selling at $10. What is the required return on the stock? Because the retention ratio is 40 percent, the payout ratio is 60 percent (1 − Retention ratio). The payout ratio is the ratio of dividends ∕earnings. Because earnings a year from now will be $2,128,000 ($2,000,000 × 1.064), dividends will be $1,276,800 (.60 × $2,128,000). Dividends per share will be $1.28 ($1,276,800 1,000,000). Given our previous result that g = .064, we calculate R from (9.9) as follows: $1.28 .192 = ______ $10.00 + .064

Figures and Tables This text makes extensive use of real data and presents them in various figures and tables. Explanations in the narrative, examples, and end-of-chapter problems will refer to many of these exhibits.

Examples E S Separate called-out examples are integrated throughout the cchapters. Each example illustrates an intuitive or mathematiccal application in a step-by-step format.There is enough detail in the explanations so students don’t have to look elsewhere for additional information. fo

In Their Own Words

“In Their Own Words” Boxes Located throughout the chapters, this unique series consists of articles written by distinguished scholars or practitioners about key topics in the text. Boxes include essays by Edward I. Altman, Robert S. Hansen, Robert C. Higgins, Michael C. Jensen, Richard M. Levich, Merton Miller, and Jay R. Ritter.

ROBERT C. HIGGINS ON SUSTAINABLE GROWTH Most financial officers know intuitively that it takes money to make money. Rapid sales growth requires increased assets in the form of accounts receivable, inventory, and fixed plant, which, in turn, require money to pay for assets. They also know that if their company does not have the money when needed, it can literally “grow broke.” The sustainable growth equation states these intuitive truths explicitly. Sustainable growth is often used by bankers and other external analysts to assess a company’s creditworthiness. They are aided in this exercise by several sophisticated computer software packages that provide detailed analyses of the company’s past financial performance, including its annual sustainable growth rate. Bankers use this information in several ways. Quick comparison of a company’s actual growth rate to its sustainable rate tells the banker what issues will be at the top of management’s financial agenda. If actual growth consistently exceeds sustainable growth, management’s problem will be where to get the cash to finance growth. The banker thus can anticipate interti l d t C l if t i bl th

prepared to talk about investment products because management’s problem will be what to do with all the cash that keeps piling up in the till. Bankers also find the sustainable growth equation useful for explaining to financially inexperienced small business owners and overly optimistic entrepreneurs that, for the long-run viability of their business, it is necessary to keep growth and profitability in proper balance. Finally, comparison of actual to sustainable growth rates helps a banker understand why a loan applicant needs money and for how long the need might continue. In one instance, a loan applicant requested $100,000 to pay off several insistent suppliers and promised to repay in a few months when he collected some accounts receivable that were coming due. A sustainable growth analysis revealed that the firm had been growing at four to six times its sustainable growth rate and that this pattern was likely to continue in the foreseeable future. This alerted the banker that impatient suppliers were only a symptom of the much more fundamental disease of overly rapid growth, and that a $100,000 loan would likely prove to be only the down payment on a much larger, multiyear commitment.

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SPREADSHEET APPLICATIONS

Using a Spreadsheet for Time Value of Money Calculations More and more, businesspeople from many different areas (not just finance and accounting) rely on spreadsheets to do all the different types of calculations that come up in the real world. As a result, in this section, we will show you how to use a spreadsheet to handle the various time value of money problems we present in this chapter. We will use Microsoft Excel™, but the commands are similar for other types of software. We assume you are already familiar with basic spreadsheet operations. As we have seen, you can solve for any one of the following four potential unknowns: future value, present value, the discount rate, or the number of periods. With a spreadsheet, there is a separate formula for each. In Excel, these are shown in a nearby box. In these formulas, pv and fv are present and To Find Enter This Formula future value, nper is the number of periods, and rate is the discount, or interest, rate. Future value = FV (rate,nper,pmt,pv) Two things are a little tricky here. First, unlike Present value = PV (rate,nper,pmt,fv) a financial calculator, the spreadsheet requires Discount rate = RATE (nper,pmt,pv,fv) that the rate be entered as a decimal. Second, Number of periods as with most financial calculators, you have to = NPER (rate,pmt,pv,fv) put a negative sign on either the present value or the future value to solve for the rate or the number of periods. For the same reason, if you solve for a present value, the a negative l h answer will ill have h i sign i unless you input a negative future value. The same is true when you compute a future value. To illustrate how you might use these formulas, we will go back to an example in the chapter. If you invest $25,000 at 12 percent per year, how long until you have $50,000? You might set up a spreadsheet like this:

Spreadsheet Applications Now integrated into select chapters, Spreadsheet Application boxes reintroduce students to Excel, demonstrating how to set up spreadsheets in order to analyze common financial problems—a vital part of every business student’s education. (For even more spreadsheet example problems, check out Excel Master on the OLC!).

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14

B

D

E

F

G

H

If we invest $25,000 at 12 percent, how long until we have $50,000? We need to solve for the unknown number of periods, so we use the formula NPER(rate, pmt, pv, fv). Present value (pv): Future value (fv): Rate (rate):

$25,000 $50,000 .12

Periods: 6.1162554 The formula entered in cell B11 is =NPER(B9,0,-B7,B8); notice that pmt is zero and that pv has a negative sign on it. Also notice that rate is entered as a decimal, not a percentage.

Explanatory Web site Links

Stock Market Reporting You can get real-time stock quotes on the Web. See finance.yahoo.com for details.

C

Using a spreadsheet for time value of money calculations

In recent years, stock price quotes and related information have increasingly moved from traditional print media, such as The Wall Street Journal, to various Web sites. Yahoo! Finance (finance.yahoo.com) is a good example. We went there and requested a stock quote on wholesale club Costco, which is listed on the NASDAQ. Here is a portion of what we found:

These Web links are specifically selected to accompany text material and provide students and instructors with a quick reference to additional information on the Internet.

25.5 Interest Rate Futures Contracts In this section we consider interest rate futures contracts. Our examples deal with futures contracts on Treasury bonds because of their high popularity. We first price Treasury bonds and Treasury bond forward contracts. Differences between futures and forward contracts are explored. Hedging examples are provided next.

Pricing of Treasury Bonds As mentioned earlier in the text, a Treasury bond pays semiannual interest over its life. In addition, the face value of the bond is paid at maturity. Consider a 20-year, 8 percent coupon bond that was issued on March 1. The first payment is to occur in six months—that is, on September 1. The value of the bond can be determined as follows: Pricing of Treasury Bond PTB =

$40 ______ 1 + R1

$1,040 $40 $40 $40 + ________ + ________ + . . . + _________ + _________ (1 + R2)2

(1 + R3)3

(1 + R39)39

(1 + R40)40

(25.1)

Because an 8 percent coupon bond pays interest of $80 a year, the semiannual coupon is $40. Principal and the semiannual coupons are both paid at maturity. As we i di i h h i f h T b d P i d i d

xii

Numbered Equations Key equations are numbered and listed on the back endsheets for easy reference.

End-of-Chapter Material Summary and Conclusions

Concept Questions

Financial Statements Analysis and Financial Models

The end-of-chapter material reflects and builds upon the

77

concepts learned from the chapter and study features.

This chapter focuses on working with information contained in financial statements. Specifically, we studied standardized financial statements, ratio analysis, and long-term financial planning. 1. We explained that differences in firm size make it difficult to compare financial statements, and we discussed how to form common-size statements to make comparisons easier and more meaningful. 2. Evaluating ratios of accounting numbers is another way of comparing financial statement information. We defined a number of the most commonly used ratios, and we discussed the famous Du Pont identity. 3. We showed how pro forma financial statements can be generated and used to plan for future financing needs. After you have studied this chapter, we hope that you have some perspective on the uses and abuses of financial statement information. You should also find that your vocabulary of business and financial terms has grown substantially.

1.

3. 4.

5.

6.

7.

The summary provides a quick review of key concepts in the chapter.

Questions and Problems www.mhhe.com/rwj

2.

Financial Ratio Analysis A financial ratio by itself tells us little about a company because financial ratios vary a great deal across industries. There are two basic methods for analyzing financial ratios for a company: Time trend analysis and peer group analysis. In time trend analysis, you find the ratios for the company over some period, say five years, and examine how each ratio has changed over this period. In peer group analysis, you compare a company’s financial ratios to those of its peers. Why might each of these analysis methods be useful? What does each tell you about the company’s financial health? Industry-Specific Ratios So-called “same-store sales” are a very important measure for companies as diverse as McDonald’s and Sears. As the name suggests, examining same-store sales means comparing revenues from the same stores or restaurants at two different points in time. Why might companies focus on same-store sales rather than total sales? Sales Forecast Why do you think most long-term financial planning begins with sales forecasts? Put differently, why are future sales the key input? Sustainable Growth In the chapter, we used Rosengarten Corporation to demonstrate how to calculate EFN. The ROE for Rosengarten is about 7.3 percent, and the plowback ratio is about 67 percent. If you calculate the sustainable growth rate for Rosengarten, you will find it is only 5.14 percent. In our calculation for EFN, we used a growth rate of 25 percent. Is this possible? (Hint: Yes. How?) EFN and Growth Rate Broslofski Co. maintains a positive retention ratio and keeps its debt–equity ratio constant every year. When sales grow by 20 percent, the firm has a negative projected EFN. What does this tell you about the firm’s sustainable growth rate? Do you know, with certainty, if the internal growth rate is greater than or less than 20 percent? Why? What happens to the projected EFN if the retention ratio is increased? What if the retention ratio is decreased? What if the retention ratio is zero? Common-Size Financials One tool of financial analysis is common-size financial statements. Why do you think common-size income statements and balance sheets are used? Note that the accounting statement of cash flows is not converted into a common-size statement. Why do you think this is? Asset Utilization and EFN One of the implicit assumptions we made in calculating the external funds needed was that the company was operating at full capacity. If the company is operating at less than full capacity, how will this affect the external funds needed?

Summary and Conclusions

Because solving problems is so critical to a student’s learning, new questions and problems have been added, and existing questions and problems have been revised. All problems have also been thoroughly reviewed and checked for accuracy. Problems have been grouped according to level of difficulty with the levels listed in the margin: Basic, Intermediate, and Challenge. Additionally, we have tried to make the problems in the critical “concept” chapters, such as those on value, risk, and capital structure, especially challenging and interesting. We provide answers to selected problems in Appendix B at the end of the book.

S&P Problems

S&P Problems

15.

16.

17.

Ratios and Fixed Assets The Le Bleu Company has a ratio of long-term debt to total assets of .40 and a current ratio of 1.30. Current liabilities are $900, sales are $5,320, profit margin is 9.4 percent, and ROE is 18.2 percent. What is the amount of the firm’s net fixed assets? Calculating the Cash Coverage Ratio Titan Inc.’s net income for the most recent year was $9,450. The tax rate was 34 percent. The firm paid $2,360 in total interest expense and deducted $3,480 in depreciation expense. What was Titan’s cash coverage ratio for the year? Cost of Goods Sold Guthrie Corp. has current liabilities of $270,000, a quick ratio of 1.1, inventory turnover of 4.2, and a current ratio of 2.3. What is the cost of goods sold for the company?

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Included in the end-of-chapter material are problems directly incorporating the Educational Version of Market Insight, a service based on Standard & Poor’s renowned Compustat database.These problems provide you with an easy method of including current real-world data in your course.

www.mhhe.com/edumarketinsight 1. Calculating the Du Pont Identity Find the annual income statements and balance sheets for Dow Chemical (DOW) and AutoZone (AZO). Calculate the Du Pont identity for each company for the most recent three years. Comment on the changes in each component of the Du Pont identity for each company over this period and compare the components between the two companies. Are the results what you expected? Why or why not? 2. Ratio Analysis Find and download the “Profitability” spreadsheet for Southwest Airlines (LUV) and Continental Airlines (CAL). Find the ROA (Net ROA), ROE (Net ROE), PE ratio (P/E—high and P/E—low), and the market-to-book ratio (Price/Book—high and Price/Book—low) for each company. Because stock prices change daily, PE and market-to-book ratios are often reported as the highest and lowest values over the year, as is done in this instance. Look at these ratios for both companies over the past five years. Do you notice any trends in these ratios? Which company appears to be operating at a more efficient level based on these four ratios? f i i i i li hi h (if i h ) f h i

Excel Problems Indicated by the Excel icon in the margin, these problems can be found at the end of almost all chapters. Located on the book’s Web site (see Online Resources), Excel templates have been created for each of these problems, where students can use the data in the problem to work out the solution using Excel skills.

End-of-Chapter Cases Located at the end of almost every chapter, these mini cases focus on common company situations that embody important corporate finance topics. Each case presents a new scenario, data, and a dilemma. Several questions at the end of each case require students to analyze and focus on all of the material they learned in that chapter.

Mini Case

Chapter 3

FINANCING EAST COAST YACHTS’S EXPANSION PLANS WITH A BOND ISSUE After Dan’s EFN analysis for East Coast Yachts (see the Mini Case in Chapter 3), Larissa has decided to expand the company’s operations. She has asked Dan to enlist an underwriter to help sell $40 million in new 20-year bonds to finance new construction. Dan has entered into discussions with Kim McKenzie, an underwriter from the firm of Crowe & Mallard, about which bond features East Coast Yachts should consider and also what coupon rate the issue will likely have. Although Dan is aware of bond features, he is uncertain as to the costs and benefits of some of them, so he isn’t clear on how each feature would affect the coupon rate of the bond issue. 1. You are Kim’s assistant, and she has asked you to prepare a memo to Dan describing the effect of each of the following bond features on the coupon rate of the bond. She would also like you to list any advantages or disadvantages of each feature. a. The security of the bond, that is, whether or not the bond has collateral. b. The seniority of the bond. c. The presence of a sinking fund. d. A call provision with specified call dates and call prices. Ad f d ll i h b ll ii

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Comprehensive Teaching CorporateF inance has many options in terms of the textbook, instructor supplements, student supplements, and multimedia products. Mix and match to create a package that is perfect for yourcours e.

OnlineL earningCen ter Instructor Support The Online Learning Center (OLC) contains all the necessary supplements—Instructor’s Manual, Test Bank, Computerized Test Bank, and PowerPoint—all in one place. Go to www.mhhe.com/rwj to find: • Instructor’s Manual Prepared by Steven Dolvin, Butler University. This is a great place to find new lecture ideas. The IM has three main sections. The first section contains a chapter outline and other lecture materials. The annotated outline for each chapter includes lecture tips, real-world tips, ethics notes, suggested PowerPoint slides, and, when appropriate, a video synopsis. • Solutions Manual Prepared by Joseph Smolira, Belmont University. This manual contains detailed, worked-out solutions for all of the problems in the end-of-chapter material. It has been reviewed for accuracy by multiple sources. The Solutions Manual is also available for purchase by your students. (ISBN: 0-07-724609-8) • Test Bank Prepared by Patricia Ryan, Colorado State University. Here’s a great format for a better testing process. The Test Bank has well over 100 questions per chapter that closely link with the text material and provide a variety of question formats (multiple-choice questions/problems and essay questions) and levels of difficulty (basic, intermediate, and challenge) to meet every instructor’s testing needs. Problems are detailed enough to make them intuitive for students, and solutions are provided for the instructor. • Computerized Test Bank (Windows) These additional questions are found in a computerized test bank utilizing McGraw-Hill’s EZ Test testing software to quickly create customized exams. This user-friendly program allows instructors to sort questions by format; edit existing questions or add new ones; and scramble questions for multiple versions of the same test. • PowerPoint Presentation System Prepared by Steven Dolvin, Butler University. Customize our content for your course. This presentation has been thoroughly revised to include more lecture-oriented slides, as well as exhibits and examples both from the book and from outside sources. Applicable slides have Web links that take you directly to specific Internet sites, or a spreadsheet link to show an example in Excel. You can also go to the Notes Page function for more tips on presenting the slides. If you already have PowerPoint installed on your PC, you can edit, print, or rearrange the complete presentation to meet your specific needs. xiv

and Learning Package • Videos Now available in DVD format: a current set of videos about hot topics! McGraw-Hill/Irwin has produced a series of finance videos that are 10-minute case studies of topics such as financial markets, careers, rightsizing, capital budgeting, EVA (economic value added), mergers and acquisitions, and foreign exchange. Discussion questions for these videos are available in the Instructor’s Center at www.mhhe.com/rwj.

Student Support • Narrated PowerPoint Examples Developed by Bruce Costa, University of Montana, exclusively for students as part of the premium content package of this book. Each chapter’s slides follow the chapter topics and provide steps and explanations showing how to solve key problems. Because each student learns differently, a quick click on each slide will “talk through” its contents with you! • Interactive FinSims Created by Eric Sandburg, Interactive Media, each module highlights a key concept of the book and simulates how to solve its problems, asking the student to input certain variables. This hands-on approach guides students through difficult and important corporate finance topics and is part of the premium content package for this book. • Excel Templates Corresponding to most end-of-chapter problems, each template allows the student to work through the problem using Excel. Each end-of-chapter problem with a template is indicated by an Excel icon in the margin beside it. • More Be sure to check out the other helpful features on the OLC, including self-study quizzes and chapter appendices.

Standard & Poor’s Educational Version of Market Insight McGraw-Hill/Irwin and the Institutional Market Services division of Standard & Poor’s are pleased to announce an exclusive partnership that offers instructors and students FREE access to the educational version of Standard & Poor’s Market Insight with each new textbook. The educational version of Market Insight is a rich online resource that provides six years of fundamental financial data for over 1,000 companies in the database. S&P–specific problems can be found at the end of almost all chapters in this text and ask students to solve problems by using research found on this site. For more details, please see the bound-in card inside the front cover of this text or visit www.mhhe.com/edumarketinsight.

Options Available for Purchase & Packaging You may also package either version of the text with a variety of additional learning tools that are available for your students.

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SolutionsMa nual ISBN-10: 0-07-724609-8 / ISBN-13: 978-0-07-724609-9 Prepared by Joseph Smolira, Belmont University. This manual contains detailed, worked-out solutions for all of the problems in the end-of-chapter material. It has also been reviewed for accuracy by multiple sources. The Solutions Manual is also available for purchase by your students.

FinGameOnl ine4.0 ISBN-10: 0-07-292219-2 / ISBN-13: 978-0-07-292219-6 By LeRoy Brooks, John Carroll University. Just $15.00 when packaged with this text. In this comprehensive simulation game, students control a hypothetical company over numerous periods of operation. The game is now tied to the text by exercises found at the Online Learning Center. As students make major financial and operating decisions for their company, they will develop and enhance skills in financial management and financial accounting statement analysis. Financial Analysis with an Electronic Calculator, Sixth Edition ISBN-10: 0-07-321709-3 / ISBN-13: 978-0-07-321709-3 By Mark A. White, University of Virginia, McIntire School of Commerce. The information and procedures in this supplementary text enable students to master the use of financial calculators and develop a working knowledge of financial mathematics and problem solving. Complete instructions are included for solving all major problem types on three popular models: HP 10-B and 12-C, TI BA II Plus, and TI-84. Hands-on problems with detailed solutions allow students to practice the skills outlined in the text and obtain instant reinforcement. Financial Analysis with an Electronic Calculator is a self-contained supplement to the introductory financial management course.

McGraw-Hill Connect Finance Less Managing. More Teaching. Greater Learning. TM

McGraw-Hill’s Connect Finance is an online assignment and assessment solution that connects students with the tools and resources they’ll need to achieve success. Connect helps prepare students for their future by enabling faster learning, more efficient studying, and higher retention of knowledge.

McGraw-Hill Connect Finance Features Connect Finance offers a number of powerful tools and features to make managing assignments easier, so faculty can spend more time teaching. With Connect Finance, students can engage with their coursework anytime and anywhere, making the learning process more accessible and efficient. Connect Finance offers you the features described below. Simple assignment management With Connect Finance, creating assignments is easier than ever, so you can spend more time teaching and less time managing. The assignment management function enables you to: • Create and deliver assignments easily with selectable end-of-chapter questions and test bank items. • Streamline lesson planning, student progress reporting, and assignment grading to make classroom management more efficient than ever. • Go paperless with the eBook and online submission and grading of student assignments.

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Smart grading When it comes to studying, time is precious. Connect Finance helps students learn more efficiently by providing feedback and practice material when they need it, where they need it. When it comes to teaching, your time is also precious. The grading function enables you to: • Have assignments scored automatically, giving students immediate feedback on their work and side-byside comparisons with correct answers. • Access and review each response; manually change grades or leave comments for students to review. • Reinforce classroom concepts with practice tests and instant quizzes. Instructor library The Connect Finance Instructor Library is your repository for additional resources to improve student engagement in and out of class. You can select and use any asset that enhances your lecture. Student study center The Connect Finance Student Study Center is the place for students to access additional resources. The Student Study Center: • Offers students quick access to lectures, practice materials, eBooks, and more. • Provides instant practice material and study questions, easily accessible on the go. • Gives students access to the Personal Learning Plan described below. Personal Learning Plan The Personal Learning Plan (PLP) connects each student to the learning resources needed for success in the course. For each chapter, students: • Take a practice test to initiate the Personal Learning Plan. • Immediately upon completing the practice test, see how their performance compares to the chapter objectives to be achieved within each section of the chapters. • Receive a Personal Learning Plan that recommends specific readings from the text, supplemental study material, and practice work that will improve their understanding and mastery of each learning objective. Student progress tracking Connect Finance keeps instructors informed about how each student, section, and class is performing, allowing for more productive use of lecture and office hours. The progress-tracking function enables you to: • View scored work immediately and track individual or group performance with assignment and grade reports. • Access an instant view of student or class performance relative to learning objectives. Lecture capture through Tegrity Campus For an additional charge Lecture Capture offers new ways for students to focus on the in-class discussion, knowing they can revisit important topics later. This can be delivered through Connect or separately. See below for more details.

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McGraw-Hill Connect Plus Finance McGraw-Hill reinvents the textbook learning experience for the modern student with Connect Plus Finance. A seamless integration of an eBook and Connect Finance, Connect Plus Finance provides all of the Connect Finance features plus the following: • An integrated eBook, allowing for anytime, anywhere access to the textbook. • Dynamic links between the problems or questions you assign to your students and the location in the eBook where that problem or question is covered. • A powerful search function to pinpoint and connect key concepts in a snap. In short, Connect Finance offers you and your students powerful tools and features that optimize your time and energies, enabling you to focus on course content, teaching, and student learning. Connect Finance also offers a wealth of content resources for both instructors and students. This state-of-the-art, thoroughly tested system supports you in preparing students for the world that awaits. For more information about Connect, go to www.mcgrawhillconnect.com, or contact your local McGrawHill sales representative.

Tegrity Campus: Lectures 24/7 Tegrity Campus is a service that makes class time available 24/7 by automatically capturing every lecture in a searchable format for students to review when they study and complete assignments. With a simple one-click start-and-stop process, you capture all computer screens and corresponding audio. Students can replay any part of any class with easy-to-use browser-based viewing on a PC or Mac. Educators know that the more students can see, hear, and experience class resources, the better they learn. In fact, studies prove it. With Tegrity Campus, students quickly recall key moments by using Tegrity Campus’s unique search feature. This search helps students efficiently find what they need, when they need it, across an entire semester of class recordings. Help turn all your students’ study time into learning moments immediately supported by your lecture. To learn more about Tegrity, watch a 2-minute Flash demo at http://tegritycampus.mhhe.com.

McGraw-Hill Customer Care Contact Information At McGraw-Hill, we understand that getting the most from new technology can be challenging. That’s why our services don’t stop after you purchase our products. You can e-mail our product specialists 24 hours a day to get product-training online. Or you can search our knowledge bank of Frequently Asked Questions on our support Web site. For Customer Support, call 800-331-5094, e-mail [email protected], or visit www.mhhe.com/support. One of our Technical Support Analysts will be able to assist you in a timely fashion.

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Acknowledgments The plan for developing this edition began with a number of our colleagues who had an interest in the book and regularly teach the MBA introductory course. We integrated their comments and recommendations throughout the ninth edition. Contributors to this edition include the following: Lucy Ackert Kennesaw State University Anne Anderson Lehigh University Kevin Chiang University of Vermont Jonathan Clarke Georgia Institute of Technology Ted Day University of Texas, Dallas Marcos de Arruda Drexel University Eliezer Fich Drexel University Partha Gangopadhyay St. Cloud University Stuart Gillan Texas Technical University

Ann Gillette Kennesaw State University Re-Jin Guo University of Illinois at Chicago Qing Hao University of Missouri-Columbia Robert Hauswald American University Thadavilil Jithendranathan University of St. Thomas Brian Kluger University of Cincinnati Gregory LeBlanc University of California, Berkeley Vassil Mihov Texas Christian University James Nelson East Carolina University

Darshana Palker Minnesota State University, Mankato Kimberly Rodgers American University Raghavendra Rau Purdue University Bill Reese Tulane University Ray Sant St. Edwards University Kevin Schieuer Bellevue University Joeseph Stokes University of Massachusetts, Amherst Sue White University of Maryland John Zietlow Malone College

Over the years, many others have contributed their time and expertise to the development and writing of this text. We extend our thanks once again for their assistance and countless insights: R.Ag garwal JohnC arrollUni versity ChristopherAnde rson Universityof M issouri–Columbia JamesJ .Ange l GeorgetownUni versity NasserAr shadi Universityof M issouri–St.L ouis KevinB ahr Universityof W isconsin–Milwaukee RobertB alik WesternM ichiganUni versity John W.B allantine BabsonColle ge ThomasB ankston AngeloS tateUni versity BradB arber Universityof Calif ornia–Davis MichaelB arry BostonColle ge SwatiB hatt RutgersUni versity

RogerB olton WilliamsColle ge GordonB onner Universityof De laware OswaldB owlin TexasT echnicalUni versity RonaldB raswell FloridaS tateUni versity WilliamO .B rown ClaremontM cKennaColle ge KirtB utler MichiganS tateUni versity BillCallahan SouthernM ethodistUni versity StevenCar vell CornellUni versity IndudeepS .Chhac hhi WesternK entuckyUni versity AndreasChr istofi MonmouthUni versity JeffreyL .Cole s ArizonaS tateUni versity

MarkCoppe r WayneS tateUni versity JamesCot ter Universityof I owa JayCoughe nour Universityof M assachusetts–Boston ArnoldCo wan IowaS tateUni versity RaymondCo x CentralM ichiganUni versity JohnCr ockett GeorgeM asonUn iversity MarkCr oss LouisianaT echnicalUni versity RonCr owe JacksonvilleUni versity WilliamDamon VanderbiltUni versity SudipDat ta BentleyColle ge AnandDe sai Universityof F lorida

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MirandaL amDe tzler Universityof M assachusetts–Boston DavidDista d Universityof Calif ornia–Berkeley DennisDr aper Universityof S outhernCalif ornia Jean-FrancoisDr eyfus NewY orkUni versity GeneDrz ycimski Universityof W isconsin–Oshkosh RobertDuv ic TheUni versityof T exasat A ustin DemissewE jara Universityof M assachusetts–Boston RobertE ldridge FairfieldUni versity GaryE mery Universityof Ok lahoma TheodoreE ytan City University of New York–Baruch College DonF ehrs Universityof Notr eDame StevenF erraro PepperdineU niversity AndrewF ields Universityof De laware PaigeF ields TexasA&M Uni versity AdlaiF isher NewY orkUni versity MichaelF ishman NorthwesternUni versity Yee-TienF u StanfordUn iversity BrunoGe rard Universityof S outhernCalif ornia FrankGhannadian MercerUni versity–Atlanta MichaelGoldste in Universityof Color ado IndraGue rtler BabsonColle ge JamesHalti ner Collegeof W illiamandM ary JanetHami lton PortlandS tateUni versity RobertHau swald AmericanUni versity

DelvinHa wley Universityof M ississippi HalHe aton BrighamY oungUni versity JohnA.He lmuth Universityof M ichigan–Dearborn JohnHe lmuth RochesterI nstituteof T echnology MichaelHe mler Universityof Not reDame StephenHe ston WashingtonUni versity AndreaHe uson Universityof M iami EdithHot chkiss BostonColle ge CharlesHu ClaremontM cKennaColle ge HughHunt er EasternW ashingtonUni versity JamesJ ackson OklahomaS tateUni versity RaymondJ ackson Universityof Massachusetts–Dartmouth PremJ ain TulaneUni versity NarayananJ ayaraman GeorgiaI nstituteof T echnology Jarl Kallberg NewY orkUni versity JonathanK arpoff Universityof W ashington PaulK eat AmericanGr aduateS choolof InternationalM anagement DollyKing Universityof W isconsin–Milwaukee NarayanaK ocherlakota Universityof I owa RobertKr ell GeorgeM asonUni versity RonaldK udla TheUni versityof Ak ron YoungsikK wak DelawareS tateUni versity NelsonL acey Universityof M assachusetts GeneL ai Universityof Rhode I sland

Josef L akonishok Universityof I llinois DennisL asser StateUni versityof Ne w York–Binghamton PaulL aux CaseW esternR eserveUni versity Bong-SuL ee Universityof M innesota YounghoL ee HowardUni versity ThomasL egg Universityof M innesota JamesT .L indley Universityof S outhernM ississippi DennisL ogue DartmouthColle ge MichaelL ong RutgersUni versity YulongM a CalS tate–LongB each IleenM alitz FairleighDic kinsonUni versity TerryM aness BaylorUni versity SurendraM ansinghka SanF ranciscoS tateUni versity MichaelM azzco MichiganS tateUni versity RobertI .M cDonald NorthwesternUni versity HughM cLaughlin BentleyColle ge JosephM eredith ElonUni versity LarryM erville Universityof T exas–Richardson JoeM essina SanF ranciscoS tateUni versity RogerM esznik City College of New York–Baruch College RickM eyer Universityof S outhF lorida RichardM iller WesleyanUni versity NavalM odani Universityof Ce ntralF lorida EdwardM orris LindenwoodUni versity

Acknowledgments

RichardM ull NewM exicoS tateUni versity Jim Musumeci Southern Illinois University–Carbondale RobertNac htmann Universityof P ittsburgh EdwardNe lling GeorgiaT ech GregoryNie haus Universityof S outhCar olina PederNie lsen OregonS tateUni versity IngmarNyman HunterColle ge DennisOf ficer Universityof K entucky JosephOgde n State Universityof Ne wY ork VenkyP anchapagesan WashingtonUni versity–St.L ouis BulentP arker Universityof W isconsin–Madison AjayP atel Universityof M issouri–Columbia Dilip KumarP atro RutgersUni versity Gary Patterson Universityof S outhF lorida GlennN .P ettengill EmporiaS tateUni versity PegaretP ichler Universityof M aryland ChristoP irinsky Ohio StateUni versity JeffreyP ontiff Universityof W ashington FranklinP otts BaylorUni versity AnnetteP oulsen Universityof Ge orgia N.P rabhala YaleU niversity Mao Qiu Universityof Utah–S altL akeCit y LathaRamc hand Universityof Hou ston GabrielRamir ez VirginiaCommonw ealthUni versity

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NarendarRao NortheasternI llinoisUni versity StevenRa ymar IndianaUni versity StuartR osenstein EastCar olinaUni versity BruceR ubin OldDominionUni versity PatriciaR yan DrakeUni versity JaimeS abal NewY orkUni versity AnthonyS anders OhioS tateUni versity AndyS aporoschenko Universityof Ak ron WilliamS artoris IndianaUni versity JamesS challheim Universityof Ut ah MaryJ eanS cheuer CaliforniaS tateU niversityat Northridge FarukS elcuk Universityof B ridgeport LemmaS enbet Universityof M aryland KuldeepS hastri Universityof P ittsburgh BettyS imkins OklahomaS tateUni versity SudhirS ingh FrostburgS tateU niversity ScottS mart IndianaUni versity JackieS o SouthernI llinoisUni versity JohnS tansfield ColumbiaColle ge JohnS .S trong Collegeo f W illiamandM ary A.Char leneS ullivan PurdueUni versity MichaelS ullivan Universityof Ne vada–LasV egas TimothyS ullivan BentleyColle ge

R.B ruceS wensen AdelphiUni versity ErnestS wift GeorgiaS tateUni versity AlexT ang MorganS tateUni versity RichardT aylor ArkansasS tateUni versity AndrewC .T hompson VirginiaP olytechnicI nstitute TimothyT hompson NorthwesternUni versity KarinT horburn DartmouthColle ge SatishT hosar University of Massachusetts–Dorchester CharlesT rzcinka StateUni versityof Ne wY ork–Buffalo HalukUnal Universityof M aryland–CollegeP ark OscarV arela Universityof Ne wOr leans StevenV enti DartmouthColle ge AvinashV erma WashingtonUni versity LankfordW alker EasternI llinoisUni versity RalphW alkling OhioS tateUni versity F.K atherineW arne SouthernB ellColle ge SusanW hite Universityof T exas–Austin RobertW hitelaw NewY orkUni versity BerryW ilson GeorgetownUni versity RobertW ood TennesseeT echUni versity DonaldW ort California State University, East Bay ThomasZor n Universityof Ne braska–Lincoln KentZumw alt ColoradoS tateUni versity

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For their help on the ninth edition, we would like to thank Stephen Dolvin, Butler University; Patricia Ryan, Colorado State University; Joe Smolira, Belmont University, and Bruce Costa, University of Montana for their work developing the supplements. We also owe a debt of gratitude to Bradford D. Jordan of the University of Kentucky; Edward I. Altman of New York University; Robert S. Hansen of Virginia Tech; and Jay R. Ritter of the University of Florida, who have provided several thoughtful comments and immeasurable help. We thank Laura Coogan, Steve Hailey, Jacob Prewitt, and Angela Sundin for their extensive proofing and problem-checking efforts. Over the past three years readers have provided assistance by detecting and reporting errors. Our goal is to offer the best textbook available on the subject, so this information was invaluable as we prepared the ninth edition. We want to ensure that all future editions are error-free—and therefore we offer $10 per arithmetic error to the first individual reporting it. Any arithmetic error resulting in subsequent errors will be counted double. All errors should be reported using the Feedback Form on the Corporate Finance Online Learning Center at www.mhhe.com/rwj. Many talented professionals at McGraw-Hill/Irwin have contributed to the development of Corporate Finance, Ninth Edition. We would especially like to thank Michele Janicek, Elizabeth Hughes, Melissa Caughlin, Christine Vaughan, Pam Verros, Michael McCormick, and Brian Nacik. Finally, we wish to thank our families and friends, Carol, Kate, Jon, Jan, Mark, and Lynne, for their forbearance and help. Stephen A. Ross Randolph W. Westerfield Jeffrey F. Jaffe

Brief Contents PA R T I Overview

PA R T I V Capital Structure and Dividend Policy

1 Introduction to Corporate Finance

1

2 Financial Statements and Cash Flow

20

3 Financial Statements Analysis and Financial Models

44

14 Efficient Capital Markets and Behavioral Challenges 428 15 Long-Term Financing: An Introduction 16 Capital Structure: Basic Concepts

PA R T I I Valuation and Capital Budgeting 4 Discounted Cash Flow Valuation

18

Valuation and Capital Budgeting for the Levered Firm 553

19 Dividends and Other Payouts

575

135

171

7 Risk Analysis, Real Options, and Capital Budgeting

PA R T Risk

520

87

6 Making Capital Investment Decisions

9 Stock Valuation

488

17 Capital Structure: Limits to the Use of Debt

5 Net Present Value and Other Investment Rules

8 Interest Rates and Bond Valuation

467

206

234

20 Issuing Securities to the Public

268

21 Leasing

III

10 Risk and Return: Lessons from Market History

300

11 Return and Risk: The Capital Asset Pricing Model (CAPM) 329 12 An Alternative View of Risk and Return: The Arbitrage Pricing Theory 371 13 Risk, Cost of Capital, and Capital Budgeting

PA R T V Long-Term Financing

392

616

652

P A R T VI Options, Futures, and Corporate Finance 22 Options and Corporate Finance

676

23 Options and Corporate Finance: Extensions and Applications 719 24 Warrants and Convertibles 25 Derivatives and Hedging Risk

744 763

xxiii

xxiv

Brief Contents

Appendix A: Mathematical Tables 963

P A R T VII Short-Term Finance

Appendix B: Solutions to Selected End-of-Chapter Problems 972 Name Index

26 Short-Term Finance and Planning 795 27 Cash Management

Subject Index

824

28 Credit and Inventory Management

846

P A R T VIII Special Topics 29 Mergers, Acquisitions, and Divestitures 30 Financial Distress

917

31 International Corporate Finance 933

875

975 978

Contents PA R T

I Overview

2.4 2.5 2.6

Chapter 1 Introduction to Corporate Finance 1.1

1.2

1.3 1.4

1.5

1.6

What Is Corporate Finance? The Balance Sheet Model of the Firm The Financial Manager The Corporate Firm The Sole Proprietorship The Partnership The Corporation A Corporation by Another Name . . . The Importance of Cash Flows The Goal of Financial Management Possible Goals The Goal of Financial Management A More General Goal The Agency Problem and Control of the Corporation Agency Relationships Management Goals Do Managers Act in the Stockholders’ Interests? Stakeholders Regulation The Securities Act of 1933 and the Securities Exchange Act of 1934 Sarbanes-Oxley Summary and Conclusions Concept Questions S&P Problems

1 1 1 3 4 4 4 5 7 7 10 11 11 12 13 13 14 14 15 16 16 17 18 18 19

2.7

2.1

2.2

2.3

The Balance Sheet Liquidity Debt versus Equity Value versus Cost The Income Statement Generally Accepted Accounting Principles Noncash Items Time and Costs Taxes Corporate Tax Ra tes Average versus Marginal Tax Rates

20 20 21 22 22 23 24 25 25 26 26 26

28 28 32 32 32 33 34 35 35 35 41 41

Chapter 3 Financial Statements Analysis and Financial Models 3.1

3.2

3.3

3.4

Chapter 2 Financial Statements and Cash Flow

Net Working Capital Financial Cash Flow The Accounting Statement of Cash Flows Cash Flow from Operating Activities Cash Flow from Investing Activities Cash Flow from Financing Activities Cash Flow Management Summary and Conclusions Concept Questions Questions and Problems S&P Problems Mini Case: Cash Flows at Warf Computers, Inc.

3.5

3.6

Financial Statements Analysis Standardizing Statements Common-Size Balance Sheets Common-Size Income Statements Ratio Analysis Short-Term Solvency or Liquidity Measures Long-Term Solvency Measures Asset Management or Turnover Measures Profitability Measures Market Value Measures The Du Pont Identity A Closer Look at ROE Problems with Financial Statement Analysis Financial Models A Simple Financial Planning Model The Percentage of Sales Approach External Financing and Growth EFN and Growth Financial Policy and Growth A Note about Sustainable Growth Rate Calculations Some Caveats Regarding Financial Planning Models Summary and Conclusions Concept Questions Questions and Problems S&P Problems Mini Case: Ratios and Financial Planning at East Coast Yachts

44 44 44 45 46 48 49 51 52 54 55 59 59 61 62 62 63 68 68 71 74 75 77 77 78 84 84 xxv

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Contents

PA R T

I I Valuation and

Capital Budgeting Chapter 4 Discounted Cash Flow Valuation 4.1 4.2

4.3

4.4

4.5 4.6

Valuation: The One-Period Case The Multiperiod Case Future Value and Compounding The Power of Compounding: A Digression Present Value and Discounting Finding the Number of Periods The Algebraic Formula Compounding Periods Distinction between Stated Annual Interest Rate and Effective Annual Rate Compounding over Many Years Continuous Compounding Simplifications Perpetuity Growing Perpetuity Annuity Growing Annuity Loan Amortization What Is a Firm Worth? Summary and Conclusions Concept Questions Questions and Problems S&P Problems

87 87 91 91 94 95 98 101 101 103 104 104 106 106 107 109 115 116 120 122 123 123 133

Appendix 4A: Net Present Value: First Principles of Finance

133

Appendix 4B: Using Financial Calculators

133

Mini Case: The MBA Decision

134

Chapter 5 Net Present Value and Other Investment Rules 5.1 5.2

5.3 5.4 5.5

Why Use Net Present Value? The Payback Period Method Defining the Rule Problems with the Payback Method Managerial Perspective Summary of Payback The Discounted Payback Period Method The Internal Rate of Return Problems with the IRR Approach

5.6 5.7

144 145 149 154 154 155 155 157 159 160 162 169

Chapter 6 Making Capital Investment Decisions 6.1

6.2

6.3

6.4

135 135 138 138 139 140 141 141 141 144

Definition of Independent and Mutually Exclusive Projects Two General Problems Affecting Both Independent and Mutually Exclusive Projects Problems Specific to Mutually Exclusive Projects Redeeming Qualities of IRR A Test The Profitability Index Calculation of Profitability Index The Practice of Capital Budgeting Summary and Conclusions Concept Questions Questions and Problems Mini Case: Bullock Gold Mining

6.5

Incremental Cash Flows: The Key to Capital Budgeting Cash Flows—Not Accounting Income Sunk Costs Opportunity Costs Side Effects Allocated Costs The Baldwin Company: An Example An Analysis of the Project Which Set of Books? A Note about Net Working Capital A Note about Depreciation Interest Expense Inflation and Capital Budgeting Interest Rates and Inflation Cash Flow and Inflation Discounting: Nominal or Real? Alternative Definitions of Operating Cash Flow The Top-Down Approach The Bottom-Up Approach The Tax Shield Approach Conclusion Investments of Unequal Lives: The Equivalent Annual Cost Method The General Decision to Replace Summary and Conclusions Concept Questions Questions and Problems Mini Cases: Bethesda Mining Company Goodweek Tires, Inc.

171 171 171 172 172 173 173 174 176 179 179 180 181 181 181 183 184 186 187 187 188 189 189 191 193 194 195 203 204

Contents

xxvii

Conclusion Summary and Conclusions Concept Questions Questions and Problems S&P Problem Mini Case: Financing East Coast Yachts’s Expansion Plans with a Bond Issue

Chapter 7 Risk Analysis, Real Options, and Capital Budgeting 7.1

7.2

7.3

7.4

Sensitivity Analysis, Scenario Analysis, and Break-Even Analysis Sensitivity Analysis and Scenario Analysis Break-Even Analysis Monte Carlo Simulation Step 1: Specify the Basic Model Step 2: Specify a Distribution for Each Variable in the Model Step 3: The Computer Draws One Outcome Step 4: Repeat the Procedure Step 5: Calculate NPV Real Options The Option to Expand The Option to Abandon Timing Options Decision Trees Summary and Conclusions Concept Questions Questions and Problems Mini Case: Bunyan Lumber, LLC

206 206 206 210 214 214 214 217 217 218 218 219 220 222 223 225 225 226 232

8.1

8.2

8.3

8.4

8.5

Bonds and Bond Valuation Bond Features and Prices Bond Values and Yields Interest Rate Risk Finding the Yield to Maturity: More Trial and Error Zero Coupon Bonds Government and Corporate Bonds Government Bonds Corporate Bonds Bond Ratings Bond Markets How Bonds Are Bought and Sold Bond Price Reporting A Note on Bond Price Quotes Inflation and Interest Rates Real versus Nominal Rates Inflation Risk and Inflation-Linked Bonds The Fisher Effect Determinants of Bond Yields The Term Structure of Interest Rates Bond Yields and the Yield Curve: Putting It All Together

Stock Valuation 9.1

9.2

9.3

234 234 234 235 238 240 242 244 244 245 247 248 248 249 252 253 253 254 255 257 257 260

266

Chapter 9

Chapter 8 Interest Rates and Bond Valuation

261 261 261 263 266

9.4 9.5

The Present Value of Common Stocks Dividends versus Capital Gains Valuation of Different Types of Stocks Estimates of Parameters in the Dividend Discount Model Where Does g Come From? Where Does R Come From? A Healthy Sense of Skepticism A Note on the Link between Dividends and Corporate Cash Flows Growth Opportunities NPVGOs of Real-World Companies Growth in Earnings and Dividends versus Growth Opportunities Does a Higher Retention Ratio Benefit Shareholders? Dividends or Earnings: Which to Discount? The No-Dividend Firm Price–Earnings Ratio The Stock Markets Dealers and Brokers Organization of the NYSE NASDAQ Operations Stock Market Reporting Summary and Conclusions Concept Questions Questions and Problems S&P Problems Mini Case: Stock Valuation at Ragan Engines

PA R T

268 268 268 269 273 273 275 276 277 278 280 281 282 284 284 285 287 287 288 290 291 292 293 293 297 298

III Risk

Chapter 10 Risk and Return: Lessons from Market History 10.1 Returns Dollar Returns Percentage Returns

300 300 300 302

xxviii

Contents

Holding Period Returns Return Statistics Average Stock Returns and Risk-Free Returns Risk Statistics Variance Normal Distribution and Its Implications for Standard Deviation 10.6 More on Average Returns Arithmetic versus Geometric Averages Calculating Geometric Average Returns Arithmetic Average Return or Geometric Average Return? 10.7 The U.S. Equity Risk Premium: Historical and International Perspectives 10.8 2008: A Year of Financial Crisis Summary and Conclusions Concept Questions Questions and Problems S&P Problems 10.2 10.3 10.4 10.5

Appendix 10A: The Historical Market Risk Premium: The Very Long Run Mini Case: A Job at East Coast Yachts

304 307 311 312 313 314 315 315 316 317 318 321 322 322 323 326 326 327

Chapter 11 Return and Risk: The Capital Asset Pricing Model (CAPM) 11.1 Individual Securities 11.2 Expected Return,Variance, and Covariance Expected Return and Variance Covariance and Correlation 11.3 The Return and Risk for Portfolios The Expected Return on a Portfolio Variance and Standard Deviation of a Portfolio 11.4 The Efficient Set for Two Assets 11.5 The Efficient Set for Many Securities Variance and Standard Deviation in a Portfolio of Many Assets 11.6 Diversification The Anticipated and Unanticipated Components of News Risk: Systematic and Unsystematic The Essence of Diversification 11.7 Riskless Borrowing and Lending The Optimal Portfolio 11.8 Market Equilibrium Definition of the Market Equilibrium Portfolio Definition of Risk When Investors Hold the Market Portfolio

329 329 330 330 332 335 335 336 339 344

The Formula for Beta A Test 11.9 Relationship between Risk and Expected Return (CAPM) Expected Return on Market Expected Return on Individual Security Summary and Conclusions Concept Questions Questions and Problems S&P Problem

357 357 358 361 362 363 369

Appendix 11A: Is Beta Dead?

369

Mini Case: A Job at East Coast Yachts, Part 2

369

Chapter 12 An Alternative View of Risk and Return: The Arbitrage Pricing Theory 12.1 Introduction 12.2 Systematic Risk and Betas 12.3 Portfolios and Factor Models Portfolios and Diversification 12.4 Betas, Arbitrage, and Expected Returns The Linear Relationship The Market Portfolio and the Single Factor 12.5 The Capital Asset Pricing Model and the Arbitrage Pricing Theory Differences in Pedagogy Differences in Application 12.6 Empirical Approaches to Asset Pricing Empirical Models Style Portfolios Summary and Conclusions Concept Questions Questions and Problems Mini Case: The Fama–French Multifactor Model and Mutual Fund Returns

371 371 371 374 376 379 379 380 381 381 381 383 383 384 386 386 387 391

Chapter 13

345 347

Risk, Cost of Capital, and Capital Budgeting

347 347 348 350 352 353 353

13.1 The Cost of Equity Capital 13.2 Estimating the Cost of Equity Capital with the CAPM The Risk-Free Rate Market Risk Premium 13.3 Estimation of Beta Real-World Betas Stability of Beta Using an Industry Beta

354

356 357

392 392 393 396 396 398 398 399 400

Contents

xxix

13.4 Beta, Covariance, and Correlation Beta and Covariance Beta and Correlation 13.5 Determinants of Beta Cyclicality of Revenues Operating Leverage Financial Leverage and Beta 13.6 Dividend Discount Model Comparison of DDM and CAPM Can a Low-Dividend or a No-Dividend Stock Have a High Cost of Capital? 13.7 Cost of Capital for Divisions and Projects 13.8 Cost of Fixed Income Securities Cost of Debt Cost of Preferred Stock 13.9 The Weighted Average Cost of Capital 13.10 Estimating Eastman Chemical’s Cost of Capital 13.11 Flotation Costs and the Weighted Average Cost of Capital The Basic Approach Flotation Costs and NPV Internal Equity and Flotation Costs Summary and Conclusions Concept Questions Questions and Problems

401 402 402 404 404 404 404 406 406 407 408 410 410 412 412 415 417 417 418 419 419 420 421

Appendix 13A: Economic Value Added and the Measurement of Financial Performance

426

Mini Case: The Cost of Capital for Goff Computer, Inc.

PA R T

426

I V Capital Structure

and Dividend Policy Chapter 14 Efficient Capital Markets and Behavioral Challenges

428

14.1 Can Financing Decisions Create Value? 14.2 A Description of Efficient Capital Markets Foundations of Market Efficiency 14.3 The Different Types of Efficiency The Weak Form The Semistrong and Strong Forms Some Common Misconceptions about the Efficient Market Hypothesis 14.4 The Evidence The Weak Form

428 430 432 433 433 435 436 437 437

14.5 14.6 14.7

14.8

The Semistrong Form The Strong Form The Behavioral Challenge to Market Efficiency Empirical Challenges to Market Efficiency Reviewing the Differences Representativeness Conservatism The Academic Viewpoints Implications for Corporate Finance 1. Accounting Choices, Financial Choices, and Market Efficiency 2. The Timing Decision 3. Speculation and Efficient Markets 4. Information in Market Prices Summary and Conclusions Concept Questions Questions and Problems Mini Case: Your 401(k) Account at East Coast Yachts

439 443 443 445 451 451 452 452 453 453 454 455 457 460 460 463 465

Chapter 15 Long-Term Financing: An Introduction 467 15.1 Some Features of Common and Preferred Stocks Common Stock Features Preferred Stock Features 15.2 Corporate Long-Term Debt Is It Debt or Equity? Long-Term Debt: The Basics The Indenture 15.3 Some Different Types of Bonds Floating-Rate Bonds Other Types of Bonds 15.4 Long-Term Syndicated Bank Loans 15.5 International Bonds 15.6 Patterns of Financing 15.7 Recent Trends in Capital Structure Which Are Best: Book or Market Values? Summary and Conclusions Concept Questions Questions and Problems

467 467 470 472 472 472 474 477 477 478 479 480 480 482 483 484 484 485

Chapter 16 Capital Structure: Basic Concepts 16.1 The Capital Structure Question and the Pie Theory 16.2 Maximizing Firm Value versus Maximizing Stockholder Interests

488 488 489

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Contents

16.3 Financial Leverage and Firm Value: An Example Leverage and Returns to Shareholders The Choice between Debt and Equity A Key Assumption 16.4 Modigliani and Miller: Proposition II (No Taxes) Risk to Equityholders Rises with Leverage Proposition II: Required Return to Equityholders Rises with Leverage MM: An Interpretation 16.5 Taxes The Basic Insight Present Value of the Tax Shield Value of the Levered Firm Expected Return and Leverage under Corporate Taxes The Weighted Average Cost of Capital, RWACC , and Corporate Taxes Stock Price and Leverage under Corporate Taxes Summary and Conclusions Concept Questions Questions and Problems S&P Problems Mini Case: Stephenson Real Estate Recapitalization

491 491 493 495 495 495 496 502 504 504 506 506 508 510 511 513 513 514 518 519

Chapter 17 Capital Structure: Limits to the Use of Debt 17.1 Costs of Financial Distress Bankruptcy Risk or Bankruptcy Cost? 17.2 Description of Financial Distress Costs Direct Costs of Financial Distress: Legal and Administrative Costs of Liquidation or Reorganization Indirect Costs of Financial Distress Agency Costs 17.3 Can Costs of Debt Be Reduced? Protective Covenants Consolidation of Debt 17.4 Integration of Tax Effects and Financial Distress Costs Pie Again 17.5 Signaling 17.6 Shirking, Perquisites, and Bad Investments: A Note on Agency Cost of Equity Effect of Agency Costs of Equity on Debt–Equity Financing Free Cash Flow 17.7 The Pecking-Order Theory Rules of the Pecking Order Implications

520 520 520 523

523 524 525 528 528 529 530 531 533 534 536 536 537 538 539

17.8 Growth and the Debt–Equity Ratio No Growth Growth 17.9 Personal Taxes The Basics of Personal Taxes The Effect of Personal Taxes on Capital Structure 17.10 How Firms Establish Capital Structure Summary and Conclusions Concept Questions Questions and Problems

540 540 541 542 542 543 544 548 548 549

Appendix 17A: Some Useful Formulas of Financial Structure

552

Appendix 17B: The Miller Model and the Graduated Income Tax

552

Mini Case: McKenzie Corporation’s Capital Budgeting

552

Chapter 18 Valuation and Capital Budgeting for the Levered Firm 18.1 Adjusted Present Value Approach 18.2 Flow to Equity Approach Step 1: Calculating Levered Cash Flow (LCF) Step 2: Calculating RS Step 3: Valuation 18.3 Weighted Average Cost of Capital Method 18.4 A Comparison of the APV, FTE, and WACC Approaches A Suggested Guideline 18.5 Capital Budgeting When the Discount Rate Must Be Estimated 18.6 APV Example 18.7 Beta and Leverage The Project Is Not Scale Enhancing Summary and Conclusions Concept Questions Questions and Problems S&P Problem Appendix 18A: The Adjusted Present Value Approach to Valuing Leveraged Buyouts Mini Case: The Leveraged Buyout of Cheek Products, Inc.

553 553 555 555 556 556 556 557 558 560 562 565 567 568 568 569 572 573 573

Chapter 19 Dividends and Other Payouts 19.1 Different Types of Payouts 19.2 Standard Method of Cash Dividend Payment

575 575 575

Contents

19.3 The Benchmark Case: An Illustration of the Irrelevance of Dividend Policy Current Policy: Dividends Set Equal to Cash Flow Alternative Policy: Initial Dividend Is Greater Than Cash Flow The Indifference Proposition Homemade Dividends A Test Dividends and Investment Policy 19.4 Repurchase of Stock Dividend versus Repurchase: Conceptual Example Dividends versus Repurchases: Real-World Considerations 19.5 Personal Taxes, Dividends, and Stock Repurchases Firms without Sufficient Cash to Pay a Dividend Firms with Sufficient Cash to Pay a Dividend Summary of Personal Taxes 19.6 Real-World Factors Favoring a High-Dividend Policy Desire for Current Income Behavioral Finance Agency Costs Information Content of Dividends and Dividend Signaling 19.7 The Clientele Effect: A Resolution of Real-World Factors? 19.8 What We Know and Do Not Know about Dividend Policy Corporate Dividends Are Substantial Fewer Companies Pay Dividends Corporations Smooth Dividends Some Survey Evidence about Dividends 19.9 Putting It All Together 19.10 Stock Dividends and Stock Splits Some Details about Stock Splits and Stock Dividends Value of Stock Splits and Stock Dividends Reverse Splits Summary and Conclusions Concept Questions Questions and Problems S&P Problem Mini Case: Electronic Timing, Inc.

xxxi

578

PA R T

V Long-Term

Financing

578

Chapter 20

578 579 580 581 582 582

Issuing Securities to the Public

583 584 586 586 587 589 590 590 590 591 592 595 597 597 598 599 600 602 604 604 606 607 608 608 610 614 614

20.1 The Public Issue The Basic Procedure for a New Issue 20.2 Alternative Issue Methods 20.3 The Cash Offer Investment Banks The Offering Price Underpricing: A Possible Explanation 20.4 What CFOs Say about the IPO Process 20.5 The Announcement of New Equity and the Value of the Firm 20.6 The Cost of New Issues The Costs of Going Public: The Case of Symbion 20.7 Rights The Mechanics of a Rights Offering Subscription Price Number of Rights Needed to Purchase a Share Effect of Rights Offering on Price of Stock Effects on Shareholders The Underwriting Arrangements 20.8 The Rights Puzzle 20.9 Dilution Dilution of Proportionate Ownership Dilution of Value: Book versus Market Values 20.10 Shelf Registration 20.11 The Private Equity Market Private Placement The Private Equity Firm Suppliers of Venture Capital Stages of Financing Summary and Conclusions Concept Questions Questions and Problems Mini Case: East Coast Yachts Goes Public

616 616 616 617 619 622 623 624 627 628 629 632 633 633 634 634 635 636 637 637 639 639 640 641 642 642 643 643 644 646 646 648 651

Chapter 21 Leasing 21.1 Types of Leases The Basics Operating Leases Financial Leases

652 652 652 652 653

xxxii

Contents

Accounting and Leasing Taxes, the IRS, and Leases The Cash Flows of Leasing A Detour for Discounting and Debt Capacity with Corporate Taxes Present Value of Riskless Cash Flows Optimal Debt Level and Riskless Cash Flows 21.6 NPV Analysis of the Lease-versus-Buy Decision The Discount Rate 21.7 Debt Displacement and Lease Valuation The Basic Concept of Debt Displacement Optimal Debt Level in the Xomox Example 21.8 Does Leasing Ever Pay? The Base Case 21.9 Reasons for Leasing Good Reasons for Leasing Bad Reasons for Leasing 21.10 Some Unanswered Questions Are the Uses of Leases and Debt Complementary? Why Are Leases Offered by Both Manufacturers and Third-Party Lessors? Why Are Some Assets Leased More Than Others? Summary and Conclusions Concept Questions Questions and Problems

654 656 656

670 670 671 671 672

Appendix 21A: APV Approach to Leasing

674

21.2 21.3 21.4 21.5

658 659 660 660 661 661 661 662 665 666 666 669 670 670

Mini Case: The Decision to Lease or Buy at Warf Computers

PA R T

675

VI Options, Futures,

and Corporate Finance Chapter 22 Options and Corporate Finance 22.1 Options 22.2 Call Options The Value of a Call Option at Expiration 22.3 Put Options The Value of a Put Option at Expiration 22.4 Selling Options 22.5 Option Quotes 22.6 Combinations of Options 22.7 Valuing Options Bounding the Value of a Call The Factors Determining Call Option Values

676 676 677 677 678 678 680 681 682 685 685 687

A Quick Discussion of Factors Determining Put Option Values 22.8 An Option Pricing Formula A Two-State Option Model The Black–Scholes Model 22.9 Stocks and Bonds as Options The Firm Expressed in Terms of Call Options The Firm Expressed in Terms of Put Options A Resolution of the Two Views A Note about Loan Guarantees 22.10 Options and Corporate Decisions: Some Applications Mergers and Diversification Options and Capital Budgeting 22.11 Investment in Real Projects and Options Summary and Conclusions Concept Questions Questions and Problems Mini Case: Clissold Industries Options

690 690 691 693 698 699 700 701 702 703 703 705 707 709 710 711 718

Chapter 23 Options and Corporate Finance: Extensions and Applications 23.1 Executive Stock Options Why Options? Valuing Executive Compensation 23.2 Valuing a Start-Up 23.3 More about the Binomial Model Heating Oil 23.4 Shutdown and Reopening Decisions Valuing a Gold Mine The Abandonment and Opening Decisions Valuing the Simple Gold Mine Summary and Conclusions Concept Questions Questions and Problems Mini Case: Exotic Cuisines Employee Stock Options

719 719 719 720 723 726 727 733 733 734 735 740 740 741 742

Chapter 24 Warrants and Convertibles 24.1 Warrants 24.2 The Difference between Warrants and Call Options How the Firm Can Hurt Warrant Holders 24.3 Warrant Pricing and the Black–Scholes Model 24.4 Convertible Bonds

744 744 745 748 748 749

Contents

24.5 The Value of Convertible Bonds Straight B ond Value Conversion Value Option Value 24.6 Reasons for Issuing Warrants and Convertibles Convertible Debt versus Straight Debt Convertible Debt versus Common Stock The “Free Lunch” Story The “Expensive Lunch” Story A Reconciliation 24.7 Why Are Warrants and Convertibles Issued? Matching Cash Flows Risk Synergy Agency Costs Backdoor Equity 24.8 Conversion Policy Summary and Conclusions Concept Questions Questions and Problems Mini Case: S&S Air’s Convertible Bond

xxxiii

750 750 750 751 753 753 753 754 755 755 755 756 756 756 757 757 758 759 759 762

Chapter 25 Derivatives and Hedging Risk Derivatives, Hedging, and Risk Forward Contracts Futures Contracts Hedging Interest Rate Futures Contracts Pricing of Treasury Bonds Pricing of Forward Contracts Futures Contracts Hedging in Interest Rate Futures 25.6 Duration Hedging The Case of Zero Coupon Bonds The Case of Two Bonds with the Same Maturity but with Different Coupons Duration Matching Liabilities with Assets 25.7 Swaps Contracts Interest Rate Swaps Currency Swaps Credit Default Swap (CDS) Exotics 25.8 Actual Use of Derivatives Summary and Conclusions Concept Questions Questions and Problems Mini Case: Williamson Mortgage, Inc. 25.1 25.2 25.3 25.4 25.5

763 763 764 765 769 771 771 772 773 774 778 778 779 780 782 784 784 786 786 787 789 790 790 792 794

PA R T

VII Short-Term

Finance Chapter 26 Short-Term Finance and Planning 26.1 Tracing Cash and Net Working Capital 26.2 The Operating Cycle and the Cash Cycle Defining the Operating and Cash Cycles The Operating Cycle and the Firm’s Organization Chart Calculating the Operating and Cash Cycles Interpreting the Cash Cycle A Look at Operating and Cash Cycles 26.3 Some Aspects of Short-Term Financial Policy The Size of the Firm’s Investment in Current Assets Alternative Financing Policies for Current Assets Which Is Best? 26.4 Cash Budgeting Cash Outflow The Cash Balance 26.5 The Short-Term Financial Plan Unsecured Loans Secured Loans Other Sources Summary and Conclusions Concept Questions Questions and Problems S&P Problems Mini Case: Keafer Manufacturing Working Capital Management

795 796 797 798 800 800 803 803 804 805 808 809 810 811 812 812 812 813 813 813 814 814 822 822

Chapter 27 Cash Management 27.1 Reasons for Holding Cash The Speculative and Precautionary Motives The Transaction Motive Compensating Balances Costs of Holding Cash Cash Management versus Liquidity Management 27.2 Understanding Float Disbursement Float Collection Float and Net Float Float Management Electronic Data Interchange and Check 21: The End of Float?

824 824 824 825 825 825 825 826 826 827 828 831

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Contents

27.3 Cash Collection and Concentration Components of Collection Time Cash Collection Lockboxes Cash Concentration Accelerating Collections: An Example 27.4 Managing Cash Disbursements Increasing Disbursement Float Controlling Disbursements 27.5 Investing Idle Cash Temporary Cash Surpluses Characteristics of Short-Term Securities Some Different Types of Money Market Securities Summary and Conclusions Concept Questions Questions and Problems Appendix 27A: Determining the Target Cash Balance Appendix 27B: Adjustable Rate Preferred Stock, Auction Rate Preferred Stock, and Floating-Rate Certificates of Deposit Mini Case: Cash Management at Richmond Corporation

832 832 833 833 834 835 837 837 838 839 839 840 840 841 842 843

28.1 Credit and Receivables Components of Credit Policy The Cash Flows from Granting Credit The Investment in Receivables 28.2 Terms of the Sale The Basic Form The Credit Period Cash Discounts Credit Instruments 28.3 Analyzing Credit Policy Credit Policy Effects Evaluating a Proposed Credit Policy 28.4 Optimal Credit Policy The Total Credit Cost Curve Organizing the Credit Function 28.5 Credit Analysis When Should Credit Be Granted? Credit Information Credit Evaluation and Scoring

859 859 860 861 861 861 862 862 863 863 867 869 870 870 871

Appendix 28A: More about Credit Policy Analysis

874

Mini Case: Credit Policy at Braam Industries

874

845

PA R T 845 845

Chapter 28 Credit and Inventory Management

28.6 Collection Policy Monitoring Receivables Collection Effort 28.7 Inventory Management The Financial Manager and Inventory Policy Inventory Types Inventory Costs 28.8 Inventory Management Techniques The ABC Approach The Economic Order Quantity Model Extensions to the EOQ Model Managing Derived-Demand Inventories Summary and Conclusions Concept Questions Questions and Problems

846 846 846 847 847 848 848 848 850 851 852 852 852 854 855 856 856 857 858 859

VIII Special Topics

Chapter 29 Mergers, Acquisitions, and Divestitures 875 29.1 The Basic Forms of Acquisitions Merger or Consolidation Acquisition of Stock Acquisition of Assets A Classification Scheme A Note about Takeovers 29.2 Synergy 29.3 Sources of Synergy Revenue Enhancement Cost Reduction Tax Gains Reduced Capital Requirements 29.4 Two Financial Side Effects of Acquisitions Earnings Growth Diversification 29.5 A Cost to Stockholders from Reduction in Risk The Base Case Both Firms Have Debt How Can Shareholders Reduce Their Losses from the Coinsurance Effect? 29.6 The NPV of a Merger Cash Common Stock Cash versus Common Stock

875 875 876 876 877 877 878 879 879 880 882 884 885 885 886 887 887 887 889 889 889 891 892

Contents

29.7 Friendly versus Hostile Takeovers 29.8 Defensive Tactics Deterring Takeovers before Being in Play Deterring a Takeover after the Company Is in Play 29.9 Do M ergers Add Value? Returns to Bidders Target Companies The Managers versus the Stockholders 29.10 The Tax Forms of Acquisitions 29.11 Accounting for Acquisitions 29.12 Going Private and Leveraged Buyouts 29.13 Divestitures Sale Spin-Off Carve-Out Tracking Stocks Summary and Conclusions Concept Questions Questions and Problems Mini Case: The Birdie Golf–Hybrid Golf Merger

xxxv

893 895 895 896 898 899 900 901 903 904 905 906 906 907 907 908 908 909 910 915

Chapter 30 Financial Distress 30.1 What Is Financial Distress? 30.2 What Happens in Financial Distress? 30.3 Bankruptcy Liquidation and Reorganization Bankruptcy Liquidation Bankruptcy Reorganization 30.4 Private Workout or Bankruptcy: Which Is Best? The Marginal Firm Holdouts Complexity Lack of Information 30.5 Prepackaged Bankruptcy 30.6 Predicting Corporate Bankruptcy: The Z-Score Model Summary and Conclusions Concept Questions Questions and Problems

917 917 918 921 921 924 926 927 927 927 928 928 929 931 931 932

Chapter 31 International Corporate Finance 31.1 Terminology 31.2 Foreign Exchange Markets and Exchange Rates Exchange Rates 31.3 Purchasing Power Parity Absolute Purchasing Power Parity Relative Purchasing Power Parity 31.4 Interest Rate Parity, Unbiased Forward Rates, and the International Fisher Effect Covered Interest Arbitrage Interest Rate Parity Forward Rates and Future Spot Rates Putting It All Together 31.5 International Capital Budgeting Method 1: The Home Currency Approach Method 2: The Foreign Currency Approach Unremitted Cash Flows The Cost of Capital for International Firms 31.6 Exchange Rate Risk Short-Term Exposure Long-Term Exposure Translation Exposure Managing Exchange Rate Risk 31.7 Political Risk Summary and Conclusions Concept Questions Questions and Problems S&P Problem Mini Case: East Coast Yachts Goes International

933 934 934 935 939 940 943 945 945 946 947 948 949 950 950 951 951 952 952 953 954 955 955 956 957 958 961 961

Appendix A: Mathematical Tables

963

Appendix B: Solutions to Selected End-of-Chapter Problems

972

Name Index

975

Subject Index

978

PART I

CHAPTER 1

Introduction to Corporate Finance Compensation of corporate executives in the United States continues to be a hot-button issue. It is widely viewed that CEO pay has grown to exorbitant levels (at least in some cases). In response, in April 2007, the U.S. House of Representatives passed the “Say on Pay” bill. The bill requires corporations to allow a nonbinding shareholder vote on executive pay. (Note that because the bill applies to corporations, it does not give voters a “say on pay” for U.S. Representatives.) Specifically, the measure allows shareholders to approve or disapprove a company’s executive compensation plan. Because the vote is nonbinding, it does not permit shareholders to veto a compensation package and does not place limits on executive pay. Some companies had actually already begun initiatives to allow shareholders a say on pay before Congress got involved. On May 5, 2008, Aflac, the insurance company with the well-known “spokesduck,” held the first shareholder vote on executive pay in the United States. Understanding how a corporation sets executive pay, and the role of shareholders in that process, takes us into issues involving the corporate form of organization, corporate goals, and corporate control, all of which we cover in this chapter.

1.1 What Is Corporate Finance? Suppose you decide to start a firm to make tennis balls. To do this you hire managers to buy raw materials, and you assemble a workforce that will produce and sell finished tennis balls. In the language of finance, you make an investment in assets such as inventory, machinery, land, and labor. The amount of cash you invest in assets must be matched by an equal amount of cash raised by financing. When you begin to sell tennis balls, your firm will generate cash. This is the basis of value creation. The purpose of the firm is to create value for you, the owner. The value is reflected in the framework of the simple balance sheet model of the firm.

The Balance Sheet Model of the Firm Suppose we take a financial snapshot of the firm and its activities at a single point in time. Figure 1.1 shows a graphic conceptualization of the balance sheet, and it will help introduce you to corporate finance. The assets of the firm are on the left side of the balance sheet. These assets can be thought of as current and fixed. Fixed assets are those that will last a long time, such as buildings. Some fixed assets are tangible, such as machinery and equipment. Other fixed assets are intangible, such as patents and trademarks. The other category of assets, current assets, comprises those that have short lives, such as inventory. The

1

2

Part I

Overview

Figure 1.1 TheB alanceS heet ModeloftheF irm

Current assets

Net working capital

Current liabilities

Long-term debt Fixed assets 1. Tangible fixed assets 2. Intangible fixed assets

Total Value of Assets

Shareholders' equity

Total Value of the Firm to Investors

tennis balls that your firm has made, but has not yet sold, are part of its inventory. Unless you have overproduced, they will leave the firm shortly. Before a company can invest in an asset, it must obtain financing, which means that it must raise the money to pay for the investment. The forms of financing are represented on the right side of the balance sheet. A firm will issue (sell) pieces of paper called debt (loan agreements) or equity shares (stock certificates). Just as assets are classified as long-lived or short-lived, so too are liabilities. A short-term debt is called a current liability. Short-term debt represents loans and other obligations that must be repaid within one year. Long-term debt is debt that does not have to be repaid within one year. Shareholders’ equity represents the difference between the value of the assets and the debt of the firm. In this sense, it is a residual claim on the firm’s assets. From the balance sheet model of the firm, it is easy to see why finance can be thought of as the study of the following three questions: 1. In what long-lived assets should the firm invest? This question concerns the left side of the balance sheet. Of course the types and proportions of assets the firm needs tend to be set by the nature of the business. We use the term capital budgeting to describe the process of making and managing expenditures on long-lived assets. 2. How can the firm raise cash for required capital expenditures? This question concerns the right side of the balance sheet. The answer to this question involves the firm’s capital structure, which represents the proportions of the firm’s financing from current and long-term debt and equity. 3. How should short-term operating cash flows be managed? This question concerns the upper portion of the balance sheet. There is often a mismatch between the timing of cash inflows and cash outflows during operating activities. Furthermore, the amount and timing of operating cash flows are not known with certainty. Financial managers must attempt to manage the gaps in cash flow. From a balance sheet perspective, short-term management of cash flow is

Chapter 1

Introduction to Corporate Finance

3

associated with a firm’s net working capital. Net working capital is defined as current assets minus current liabilities. From a financial perspective, short-term cash flow problems come from the mismatching of cash inflows and outflows. This is the subject of short-term finance.

TheF inancialMa nager For current issues facing CFOs, see www.cfo.com.

In large firms, the finance activity is usually associated with a top officer of the firm, such as the vice president and chief financial officer, and some lesser officers. Figure 1.2 depicts a general organizational structure emphasizing the finance activity within the firm. Reporting to the chief financial officer are the treasurer and the controller. The treasurer is responsible for handling cash flows, managing capital expenditure decisions, and making financial plans. The controller handles the accounting function, which includes taxes, cost and financial accounting, and information systems.

Figure 1.2 Hypothetical OrganizationC hart

Board of Directors

Chairman of the Board and Chief Executive Officer (CEO)

President and Chief Operations Officer (COO)

Vice President and Chief Financial Officer (CFO)

Treasurer

Controller

Cash Manager

Credit Manager

Tax Manager

Cost Accounting Manager

Capital Expenditures

Financial Planning

Financial Accounting Manager

Information Systems Manager

4

Part I

Overview

1.2 TheCo rporate Firm The firm is a way of organizing the economic activity of many individuals. A basic problem of the firm is how to raise cash. The corporate form of business—that is, organizing the firm as a corporation—is the standard method for solving problems encountered in raising large amounts of cash. However, businesses can take other forms. In this section we consider the three basic legal forms of organizing firms, and we see how firms go about the task of raising large amounts of money under each form.

TheSo leP roprietorship

For more about small business organization, see the “Business and Human Resources” section at www.nolo.com.

A sole proprietorship is a business owned by one person. Suppose you decide to start a business to produce mousetraps. Going into business is simple: You announce to all who will listen, “Today, I am going to build a better mousetrap.” Most large cities require that you obtain a business license. Afterward, you can begin to hire as many people as you need and borrow whatever money you need. At year-end all the profits and the losses will be yours. Here are some factors that are important in considering a sole proprietorship: 1. The sole proprietorship is the cheapest business to form. No formal charter is required, and few government regulations must be satisfied for most industries. 2. A sole proprietorship pays no corporate income taxes. All profits of the business are taxed as individual income. 3. The sole proprietorship has unlimited liability for business debts and obligations. No distinction is made between personal and business assets. 4. The life of the sole proprietorship is limited by the life of the sole proprietor. 5. Because the only money invested in the firm is the proprietor’s, the equity money that can be raised by the sole proprietor is limited to the proprietor’s personal wealth.

TheP artnership Any two or more people can get together and form a partnership. Partnerships fall into two categories: (1) general partnerships and (2) limited partnerships. In a general partnership all partners agree to provide some fraction of the work and cash and to share the profits and losses. Each partner is liable for all of the debts of the partnership. A partnership agreement specifies the nature of the arrangement. The partnership agreement may be an oral agreement or a formal document setting forth the understanding. Limited partnerships permit the liability of some of the partners to be limited to the amount of cash each has contributed to the partnership. Limited partnerships usually require that (1) at least one partner be a general partner and (2) the limited partners do not participate in managing the business. Here are some things that are important when considering a partnership: 1. Partnerships are usually inexpensive and easy to form. Written documents are required in complicated arrangements. Business licenses and filing fees may be necessary. 2. General partners have unlimited liability for all debts. The liability of limited partners is usually limited to the contribution each has made to the partnership. If one general partner is unable to meet his or her commitment, the shortfall must be made up by the other general partners.

Chapter 1

Introduction to Corporate Finance

5

3. The general partnership is terminated when a general partner dies or withdraws (but this is not so for a limited partner). It is difficult for a partnership to transfer ownership without dissolving. Usually all general partners must agree. However, limited partners may sell their interest in a business. 4. It is difficult for a partnership to raise large amounts of cash. Equity contributions are usually limited to a partner’s ability and desire to contribute to the partnership. Many companies, such as Apple Computer, start life as a proprietorship or partnership, but at some point they choose to convert to corporate form. 5. Income from a partnership is taxed as personal income to the partners. 6. Management control resides with the general partners. Usually a majority vote is required on important matters, such as the amount of profit to be retained in the business. It is difficult for large business organizations to exist as sole proprietorships or partnerships. The main advantage to a sole proprietorship or partnership is the cost of getting started. Afterward, the disadvantages, which may become severe, are (1) unlimited liability, (2) limited life of the enterprise, and (3) difficulty of transferring ownership. These three disadvantages lead to (4) difficulty in raising cash.

TheCo rporation Of the forms of business enterprises, the corporation is by far the most important. It is a distinct legal entity. As such, a corporation can have a name and enjoy many of the legal powers of natural persons. For example, corporations can acquire and exchange property. Corporations can enter contracts and may sue and be sued. For jurisdictional purposes the corporation is a citizen of its state of incorporation (it cannot vote, however). Starting a corporation is more complicated than starting a proprietorship or partnership. The incorporators must prepare articles of incorporation and a set of bylaws. The articles of incorporation must include the following: 1. Nameo f th ec orporation. 2. Intended life of the corporation (it may be forever). 3. Businessp urpose. 4. Number of shares of stock that the corporation is authorized to issue, with a statement of limitations and rights of different classes of shares. 5. Nature of the rights granted to shareholders. 6. Number of members of the initial board of directors. The bylaws are the rules to be used by the corporation to regulate its own existence, and they concern its shareholders, directors, and officers. Bylaws range from the briefest possible statement of rules for the corporation’s management to hundreds of pages of text. In its simplest form, the corporation comprises three sets of distinct interests: the shareholders (the owners), the directors, and the corporation officers (the top management). Traditionally, the shareholders control the corporation’s direction, policies, and activities. The shareholders elect a board of directors, who in turn select top management. Members of top management serve as corporate officers and manage the operations of the corporation in the best interest of the shareholders. In closely held corporations with few shareholders, there may be a large overlap among the

6

Part I

Overview

shareholders, the directors, and the top management. However, in larger corporations, the shareholders, directors, and the top management are likely to be distinct groups. The potential separation of ownership from management gives the corporation several advantages over proprietorships and partnerships: 1. Because ownership in a corporation is represented by shares of stock, ownership can be readily transferred to new owners. Because the corporation exists independently of those who own its shares, there is no limit to the transferability of shares as there is in partnerships. 2. The corporation has unlimited life. Because the corporation is separate from its owners, the death or withdrawal of an owner does not affect the corporation’s legal existence. The corporation can continue on after the original owners have withdrawn. 3. The shareholders’ liability is limited to the amount invested in the ownership shares. For example, if a shareholder purchased $1,000 in shares of a corporation, the potential loss would be $1,000. In a partnership, a general partner with a $1,000 contribution could lose the $1,000 plus any other indebtedness of the partnership. Limited liability, ease of ownership transfer, and perpetual succession are the major advantages of the corporate form of business organization. These give the corporation an enhanced ability to raise cash. There is, however, one great disadvantage to incorporation. The federal government taxes corporate income (the states do as well). This tax is in addition to the personal income tax that shareholders pay on dividend income they receive. This is double taxation for shareholders when compared to taxation on proprietorships and partnerships. Table 1.1 summarizes our discussion of partnerships and corporations.

Table 1.1

A Comparison of Partnerships and Corporations

Liquidity and marketability Voting rights

Taxation

Reinvestment and dividend payout

Corporation

Partnership

Shares can be exchanged without termination of the corporation. Common stock can be listed on a stock exchange. Usually each share of common stock entitles the holder to one vote per share on matters requiring a vote and on the election of the directors. Directors determine top management. Corporations have double taxation: Corporate income is taxable, and dividends to shareholders are also taxable. Corporations have broad latitude on dividend payout decisions.

Units are subject to substantial restrictions on transferability. There is usually no established trading market for partnership units. Some voting rights by limited partners. However, general partners have exclusive control and management of operations.

Liability

Shareholders are not personally liable for obligations of the corporation.

Continuity of existence

Corporations may have a perpetual life.

Partnerships are not taxable. Partners pay personal taxes on partnership profits. Partnerships are generally prohibited from reinvesting partnership profits. All profits are distributed to partners. Limited partners are not liable for obligations of partnerships. General partners may have unlimited liability. Partnerships have limited life.

Chapter 1

Table 1.2

Introduction to Corporate Finance

7

International Corporations

Type of Company Company

Country of Origin

In Original Language

Interpretation

Bayerische Motoren Werke (BMW) AG Dornier GmBH

Germany

Aktiengesellschaft

Corporation

Germany

Rolls-Royce PLC Shell UK Ltd. Unilever NV Fiat SpA Volvo AB Peugeot SA

United Kingdom United Kingdom Netherlands Italy Sweden France

Gesellschaft mit Beschränkter Haftung Public limited company Limited Naamloze Vennootschap Società per Azioni Aktiebolag Société Anonyme

Limited liability company Public Ltd. Company Corporation Joint stock company Joint stock company Joint stock company Joint stock company

To find out more about LLCs, visit www.incorporate.com.

Today all 50 states have enacted laws allowing for the creation of a relatively new form of business organization, the limited liability company (LLC). The goal of this entity is to operate and be taxed like a partnership but retain limited liability for owners, so an LLC is essentially a hybrid of partnership and corporation. Although states have differing definitions for LLCs, the more important scorekeeper is the Internal Revenue Service (IRS). The IRS will consider an LLC a corporation, thereby subjecting it to double taxation, unless it meets certain specific criteria. In essence, an LLC cannot be too corporation-like, or it will be treated as one by the IRS. LLCs have become common. For example, Goldman, Sachs and Co., one of Wall Street’s last remaining partnerships, decided to convert from a private partnership to an LLC (it later “went public,” becoming a publicly held corporation). Large accounting firms and law firms by the score have converted to LLCs.

A Corporation by Another Name . . . The corporate form of organization has many variations around the world. The exact laws and regulations differ from country to country, of course, but the essential features of public ownership and limited liability remain. These firms are often called joint stock companies, public limited companies, or limited liability companies, depending on the specific nature of the firm and the country of origin. Table 1.2 gives the names of a few well-known international corporations, their countries of origin, and a translation of the abbreviation that follows each company name.

1.3 TheIm portance of Cash Flows The most important job of a financial manager is to create value from the firm’s capital budgeting, financing, and net working capital activities. How do financial managers create value? The answer is that the firm should: 1. Try to buy assets that generate more cash than they cost. 2. Sell bonds and stocks and other financial instruments that raise more cash than theyc ost.

In Their Own Words SKILLS NEEDED FOR THE CHIEF FINANCIAL OFFICERS OF eFINANCE.COM

Chief risk officer: Limiting risk will be even more important as markets become more global and hedging instruments become more complex.

Chief strategist: CFOs will need to use real-time financial information to make crucial decisions fast.

Chief communicator: Gaining the confidence of Wall Street and the media will be essential.

Chief deal maker: CFOs must be adept at venture capital, mergers and acquisitions, and strategic partnerships.

SOURCE: BusinessWeek, August 28, 2000, p. 120.

Thus, the firm must create more cash flow than it uses. The cash flows paid to bondholders and stockholders of the firm should be greater than the cash flows put into the firm by the bondholders and stockholders. To see how this is done, we can trace the cash flows from the firm to the financial markets and back again. The interplay of the firm’s activities with the financial markets is illustrated in Figure 1.3. The arrows in Figure 1.3 trace cash flow from the firm to the financial markets and back again. Suppose we begin with the firm’s financing activities. To raise money, the firm sells debt and equity shares to investors in the financial markets. This results in cash flows from the financial markets to the firm (A). This cash is invested in the investment activities (assets) of the firm (B) by the firm’s management. The cash generated by the firm (C) is paid to shareholders and bondholders (F). The shareholders receive cash in the form of dividends; the bondholders who lent funds to the firm receive interest and, when the initial loan is repaid, principal. Not all of the firm’s cash is paid out. Some is retained (E ), and some is paid to the government as taxes (D). Over time, if the cash paid to shareholders and bondholders (F) is greater than the cash raised in the financial markets (A), value will be created.

Figure 1.3 CashFlo wsbetw een the Firm and the FinancialMar kets

Cash for securities issued by the firm (A) Firm invests in assets (B)

Retained cash flows (E) Cash flow from firm (C)

Dividends and debt payments (F )

Short-term debt Long-term debt Equity shares

Taxes

Current assets Fixed assets

Financial markets

Total Value of Assets

8

Government (D)

Total Value of the Firm to Investors in the Financial Markets

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9

Identification of Cash Flows Unfortunately, it is sometimes not easy to observe cash flows directly. Much of the information we obtain is in the form of accounting statements, and much of the work of financial analysis is to extract cash flow information from accounting statements. The following example illustrates how this is done.

EXAMPLE 1.1

Accounting Profit versus Cash Flows The Midland Company refines and trades gold. At the end of the year, it sold 2,500 ounces of gold for $1 million. The company had acquired the gold for $900,000 at the beginning of the year. The company paid cash for the gold when it was purchased. Unfortunately it has yet to collect from the customer to whom the gold was sold. The following is a standard accounting of Midland’s financial circumstances at year-end: The Midland Company Accounting View Income Statement Year Ended December 31 Sales −Costs Profit

$1,000,000 −900,000 $ 100,000

By generally accepted accounting principles (GAAP), the sale is recorded even though the customer has yet to pay. It is assumed that the customer will pay soon. From the accounting perspective, Midland seems to be profitable. However, the perspective of corporate finance is different. It focuses on cash flows: The Midland Company Financial View Income Statement Year Ended December 31 Cash inflow Cash outflow

$ 0 −900,000 −$ 900,000

The perspective of corporate finance is interested in whether cash flows are being created by the gold trading operations of Midland. Value creation depends on cash flows. For Midland, value creation depends on whether and when it actually receives $1 million.

Timing of Cash Flows The value of an investment made by a firm depends on the timing of cash flows. One of the most important principles of finance is that individuals prefer to receive cash flows earlier rather than later. One dollar received today is worth more than one dollar received next year.

10

Part I

EXAMPLE 1.2

Overview

Cash Flow Timing The Midland Company is attempting to choose between two proposals for new products. Both proposals will provide additional cash flows over a four-year period and will initially cost $10,000. The cash flows from the proposals are as follows: Year 1 2 3 4 Total

New Product A

New Product B

$

0 0 0 20,000 $20,000

$ 4,000 4,000 4,000 4,000 $16,000

At first it appears that new product A would be best. However, the cash flows from proposal B come earlier than those of A. Without more information, we cannot decide which set of cash flows would create the most value for the bondholders and shareholders. It depends on whether the value of getting cash from B up front outweighs the extra total cash from A. Bond and stock prices reflect this preference for earlier cash, and we will see how to use them to decide between A and B.

Risk of Cash Flows The firm must consider risk. The amount and timing of cash flows are not usually known with certainty. Most investors have an aversion to risk.

EXAMPLE 1.3

Risk The Midland Company is considering expanding operations overseas. It is evaluating Europe and Japan as possible sites. Europe is considered to be relatively safe, whereas operating in Japan is seen as very risky. In both cases the company would close down operations after one year. After doing a complete financial analysis, Midland has come up with the following cash flows of the alternative plans for expansion under three scenarios—pessimistic, most likely, and optimistic:

Europe Japan

Pessimistic

Most Likely

Optimistic

$75,000 0

$100,000 150,000

$125,000 200,000

If we ignore the pessimistic scenario, perhaps Japan is the best alternative. When we take the pessimistic scenario into account, the choice is unclear. Japan appears to be riskier, but it also offers a higher expected level of cash flow. What is risk and how can it be defined? We must try to answer this important question. Corporate finance cannot avoid coping with risky alternatives, and much of our book is devoted to developing methods for evaluating risky opportunities.

1.4 The Goal of Financial Management Assuming that we restrict our discussion to for-profit businesses, the goal of financial management is to make money or add value for the owners. This goal is a little vague, of course, so we examine some different ways of formulating it to come up with a more

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11

precise definition. Such a definition is important because it leads to an objective basis for making and evaluating financial decisions.

PossibleG oals If we were to consider possible financial goals, we might come up with some ideas like thef ollowing: • • • • • • •

Survive. Avoid financial distress and bankruptcy. Beatth ec ompetition. Maximize sales or market share. Minimizec osts. Maximizep rofits. Maintainste adye arningsgr owth.

These are only a few of the goals we could list. Furthermore, each of these possibilities presents problems as a goal for the financial manager. For example, it’s easy to increase market share or unit sales: All we have to do is lower our prices or relax our credit terms. Similarly, we can always cut costs simply by doing away with things such as research and development. We can avoid bankruptcy by never borrowing any money or never taking any risks, and so on. It’s not clear that any of these actions are in the stockholders’ best interests. Profit maximization would probably be the most commonly cited goal, but even this is not a precise objective. Do we mean profits this year? If so, then we should note that actions such as deferring maintenance, letting inventories run down, and taking other short-run cost-cutting measures will tend to increase profits now, but these activities aren’t necessarily desirable. The goal of maximizing profits may refer to some sort of “long-run” or “average” profits, but it’s still unclear exactly what this means. First, do we mean something like accounting net income or earnings per share? As we will see in more detail in the next chapter, these accounting numbers may have little to do with what is good or bad for the firm. We are actually more interested in cash flows. Second, what do we mean by the long run? As a famous economist once remarked, in the long run, we’re all dead! More to the point, this goal doesn’t tell us what the appropriate trade-off is between current and future profits. The goals we’ve listed here are all different, but they tend to fall into two classes. The first of these relates to profitability. The goals involving sales, market share, and cost control all relate, at least potentially, to different ways of earning or increasing profits. The goals in the second group, involving bankruptcy avoidance, stability, and safety, relate in some way to controlling risk. Unfortunately, these two types of goals are somewhat contradictory. The pursuit of profit normally involves some element of risk, so it isn’t really possible to maximize both safety and profit. What we need, therefore, is a goal that encompasses both factors.

The Goal of Financial Management The financial manager in a corporation makes decisions for the stockholders of the firm. So, instead of listing possible goals for the financial manager, we really need to answer a more fundamental question: From the stockholders’ point of view, what is a good financial management decision?

12

Part I

Overview

If we assume that stockholders buy stock because they seek to gain financially, then the answer is obvious: Good decisions increase the value of the stock, and poor decisions decrease the value of the stock. From our observations, it follows that the financial manager acts in the shareholders’ best interests by making decisions that increase the value of the stock. The appropriate goal for the financial manager can thus be stated quite easily: The goal of financial management is to maximize the current value per share of the existing stock.

The goal of maximizing the value of the stock avoids the problems associated with the different goals we listed earlier. There is no ambiguity in the criterion, and there is no short-run versus long-run issue. We explicitly mean that our goal is to maximize the current stock value. If this goal seems a little strong or one-dimensional to you, keep in mind that the stockholders in a firm are residual owners. By this we mean that they are entitled only to what is left after employees, suppliers, and creditors (and everyone else with legitimate claims) are paid their due. If any of these groups go unpaid, the stockholders get nothing. So if the stockholders are winning in the sense that the leftover, residual portion is growing, it must be true that everyone else is winning also. Because the goal of financial management is to maximize the value of the stock, we need to learn how to identify investments and financing arrangements that favorably impact the value of the stock. This is precisely what we will be studying. In the previous section we emphasized the importance of cash flows in value creation. In fact, we could have defined corporate finance as the study of the relationship between business decisions, cash flows, and the value of the stock in the business.

A More General Goal

Business ethics are considered at www.business-ethics .com.

If our goal is as stated in the preceding section (to maximize the value of the stock), an obvious question comes up: What is the appropriate goal when the firm has no traded stock? Corporations are certainly not the only type of business; and the stock in many corporations rarely changes hands, so it’s difficult to say what the value per share is at any particular time. As long as we are considering for-profit businesses, only a slight modification is needed. The total value of the stock in a corporation is simply equal to the value of the owners’ equity. Therefore, a more general way of stating our goal is as follows: Maximize the value of the existing owners’ equity. With this in mind, we don’t care whether the business is a proprietorship, a partnership, or a corporation. For each of these, good financial decisions increase the market value of the owners’ equity, and poor financial decisions decrease it. In fact, although we choose to focus on corporations in the chapters ahead, the principles we develop apply to all forms of business. Many of them even apply to the not-for-profit sector. Finally, our goal does not imply that the financial manager should take illegal or unethical actions in the hope of increasing the value of the equity in the firm. What we mean is that the financial manager best serves the owners of the business by identifying goods and services that add value to the firm because they are desired and valued inth efr eemar ketplace.

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13

1.5 The Agency Problem and Control of the Corporation We’ve seen that the financial manager acts in the best interests of the stockholders by taking actions that increase the value of the stock. However, in large corporations ownership can be spread over a huge number of stockholders.1 This dispersion of ownership arguably means that management effectively controls the firm. In this case, will management necessarily act in the best interests of the stockholders? Put another way, might not management pursue its own goals at the stockholders’ expense? In the following pages we briefly consider some of the arguments relating to this question.

AgencyR elationships The relationship between stockholders and management is called an agency relationship. Such a relationship exists whenever someone (the principal) hires another (the agent) to represent his or her interests. For example, you might hire someone (an agent) to sell a car that you own while you are away at school. In all such relationships there is a possibility of a conflict of interest between the principal and the agent. Such a conflict is called an agency problem. Suppose you hire someone to sell your car and you agree to pay that person a flat fee when he or she sells the car. The agent’s incentive in this case is to make the sale, not necessarily to get you the best price. If you offer a commission of, say, 10 percent of the sales price instead of a flat fee, then this problem might not exist. This example illustrates that the way in which an agent is compensated is one factor that affects agencyp roblems.

1

This is a bit of an overstatement. Actually, in most countries other than the U.S. and the U.K., publicly traded companies are usually controlled by one or more large shareholders. Moreover, in countries with limited shareholder protection, when compared to countries with strong shareholder protection like the U.S. and the U.K., large shareholders may have a greater opportunity to impose agency costs on the minority shareholders. See, for example, “Investor Protection and Corporate Valuation,” by Rafael La Porta, Florencio Lopez-De-Silanes, Andrei Shleifer, and Robert Vishny, Journal of Finance 57 (2002), pp. 1147–1170; and “Cash Holdings, Dividend Policy, and Corporate Governance: A Cross-Country Analysis,” by Lee Pinkowitz, René M. Stulz, and Rohan Williamson, Journal of Applied Corporate Finance, Vol. 19, No. 1 (2007), pp. 81–87. They show that a country’s investor protection framework is important to understanding firm cash holdings and dividend payout. For example, they find that shareholders do not highly value cash holdings in firms in countries with low investor protection when compared to firms in the U.S. where investor protection is high. In the basic corporate governance setup, the shareholders elect the board of directors who in turn appoint the top corporate managers, such as the CEO. The CEO is usually a member of the board of directors. One aspect of corporate governance we do not talk much about is the issue of an independent chair of a firm’s board of directors. However, in a large number of U.S. corporations, the CEO and the board chair are the same person. In “U.S. Corporate Governance: Accomplishments and Failings, A Discussion with Michael Jensen and Robert Monks” (moderated by Ralph Walkling), Journal of Applied Corporate Finance, Vol. 20, No. 1 (Winter 2008), the point is made that combining the CEO and board chair positions can contribute to poor corporate governance. Both Jensen and Monks give an edge to the U.K. in governance partially because over 90 percent of U.K. companies are chaired by outside directors and not the CEO. This is a contentious issue confronting many U.S. corporations. For example, in May 2008, 19 institutional investors, including some of ExxonMobil’s largest shareholders and members of the founding Rockefeller family, supported a resolution to split the jobs of CEO and board chair. About 40 percent of the shareholders voted for the split.

14

Part I

Overview

ManagementG oals To see how management and stockholder interests might differ, imagine that a firm is considering a new investment. The new investment is expected to favorably impact the share value, but it is also a relatively risky venture. The owners of the firm will wish to take the investment (because the stock value will rise), but management may not because there is the possibility that things will turn out badly and management jobs will be lost. If management does not take the investment, then the stockholders may lose a valuable opportunity. This is one example of an agency cost. More generally, the term agency costs refers to the costs of the conflict of interest between stockholders and management. These costs can be indirect or direct. An indirect agency cost is a lost opportunity, such as the one we have just described. Direct agency costs come in two forms. The first type is a corporate expenditure that benefits management but costs the stockholders. Perhaps the purchase of a luxurious and unneeded corporate jet would fall under this heading. The second type of direct agency cost is an expense that arises from the need to monitor management actions. Paying outside auditors to assess the accuracy of financial statement information could be one example. It is sometimes argued that, left to themselves, managers would tend to maximize the amount of resources over which they have control or, more generally, corporate power or wealth. This goal could lead to an overemphasis on corporate size or growth. For example, cases in which management is accused of overpaying to buy up another company just to increase the size of the business or to demonstrate corporate power are not uncommon. Obviously, if overpayment does take place, such a purchase does not benefit the stockholders of the purchasing company. Our discussion indicates that management may tend to overemphasize organizational survival to protect job security. Also, management may dislike outside interference, so independence and corporate self-sufficiency may be important goals.

Do Managers Act in the Stockholders’ Interests? Whether managers will, in fact, act in the best interests of stockholders depends on two factors. First, how closely are management goals aligned with stockholder goals? This question relates, at least in part, to the way managers are compensated. Second, can managers be replaced if they do not pursue stockholder goals? This issue relates to control of the firm. As we will discuss, there are a number of reasons to think that, even in the largest firms, management has a significant incentive to act in the interests of stockholders. Managerial Compensation Management will frequently have a significant economic incentive to increase share value for two reasons. First, managerial compensation, particularly at the top, is usually tied to financial performance in general and often to share value in particular. For example, managers are frequently given the option to buy stock at a bargain price. The more the stock is worth, the more valuable is this option. In fact, options are often used to motivate employees of all types, not just top management. According to The Wall Street Journal, in 2007, Lloyd L. Blankfein, CEO of Goldman Sachs, made $600,000 in salary and $67.9 million in bonuses tied to financial performance. As mentioned, many firms also give managers an ownership stake in the company by granting stock or stock options. In 2007, the total compensation of Nicholas D. Chabraja, CEO of General Dynamics, was reported by The Wall Street Journal to be $15.1 million. His base salary was $1.3 million with bonuses of $3.5 million, stock option grants of $6.9 million, and restricted

Chapter 1

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15

stock grants of $3.4 million. Although there are many critics of the high level of CEO compensation, from the stockholders’ point of view, sensitivity of compensation to firm performance is usually more important. The second incentive managers have relates to job prospects. Better performers within the firm will tend to get promoted. More generally, managers who are successful in pursuing stockholder goals will be in greater demand in the labor market and thus command higher salaries. In fact, managers who are successful in pursuing stockholder goals can reap enormous rewards. For example, the best-paid executive in 2008 was Larry Ellison, the CEO of Oracle; according to Forbes magazine, he made about $193 million. By way of comparison, J. K. Rowling made $300 million and Oprah Winfrey made about $275 million. Over the period of 2004–2008, Ellison made $429 million.2 Control of the Firm Control of the firm ultimately rests with stockholders. They elect the board of directors, who, in turn, hire and fire management. An important mechanism by which unhappy stockholders can replace existing management is called a proxy fight. A proxy is the authority to vote someone else’s stock. A proxy fight develops when a group solicits proxies in order to replace the existing board and thereby replace existing management. In 2002, the proposed merger between HP and Compaq triggered one of the most widely followed, bitterly contested, and expensive proxy fights in history, with an estimated price tag of well over $100 million. Another way that management can be replaced is by takeover. Firms that are poorly managed are more attractive as acquisitions than well-managed firms because a greater profit potential exists. Thus, avoiding a takeover by another firm gives management another incentive to act in the stockholders’ interests. Unhappy prominent shareholders can suggest different business strategies to a firm’s top management. This was the case with Carl Icahn and Motorola. Carl Icahn specializes in takeovers. His stake in Motorola reached 7.6 percent ownership in 2008, so he was a particularly important and unhappy shareholder. This large stake made the threat of a shareholder vote for new board membership and a takeover more credible. His advice was for Motorola to split its poorly performing handset mobile phone unit from its home and networks business and create two publicly traded companies—a strategy the company adopted. Conclusion The available theory and evidence are consistent with the view that stockholders control the firm and that stockholder wealth maximization is the relevant goal of the corporation. Even so, there will undoubtedly be times when management goals are pursued at the expense of the stockholders, at least temporarily.

Stakeholders Our discussion thus far implies that management and stockholders are the only parties with an interest in the firm’s decisions. This is an oversimplification, of course. Employees, customers, suppliers, and even the government all have a financial interest in the firm.

2

This raises the issue of the level of top management pay and its relationship to other employees. According to The New York Times, the average CEO compensation was greater than 180 times the average employee compensation in 2007 and only 90 times in 1994. However, there is no precise formula that governs the gap between top management compensation and that of employees.

16

Part I

Overview

Taken together, these various groups are called stakeholders in the firm. In general, a stakeholder is someone other than a stockholder or creditor who potentially has a claim on the cash flows of the firm. Such groups will also attempt to exert control over the firm, perhaps to the detriment of the owners.

1.6 Regulation Until now, we have talked mostly about the actions that shareholders and boards of directors can take to reduce the conflicts of interest between themselves and management. We have not talked about regulation.3 Until recently the main thrust of federal regulation has been to require that companies disclose all relevant information to investors and potential investors. Disclosure of relevant information by corporations is intended to put all investors on a level information playing field and, thereby to reduce conflicts of interest. Of course, regulation imposes costs on corporations and any analysis of regulation must include both benefits and costs.

The Securities Act of 1933 and the Securities Exchange Act of 1934 The Securities Act of 1933 (the 1933 Act) and the Securities Exchange Act of 1934 (the 1934 Act) provide the basic regulatory framework in the United States for the public trading of securities. The 1933 Act focuses on the issuing of new securities. Basically, the 1933 Act requires a corporation to file a registration statement with the Securities and Exchange Commission (SEC) that must be made available to every buyer of a new security. The intent of the registration statement is to provide potential stockholders with all the necessary information to make a reasonable decision. The 1934 Act extends the disclosure requirements of the 1933 Act to securities trading in markets after they have been issued. The 1934 Act establishes the SEC and covers a large number of issues including corporate reporting, tender offers, and insider trading. The 1934 Act requires corporations to file reports to the SEC on an annual basis (Form 10K), on a quarterly basis (Form 10Q), and on a monthly basis (Form 8K). As mentioned, the 1934 Act deals with the important issue of insider trading. Illegal insider trading occurs when any person who has acquired nonpublic, special information (i.e., inside information) buys or sells securities based upon that information. One section of the 1934 Act deals with insiders such as directors, officers, and large shareholders, while another deals with any person who has acquired inside information. The intent of these sections of the 1934 Act is to prevent insiders or persons with inside information from taking unfair advantage of this information when trading with outsiders. To illustrate, suppose you learned that ABC firm was about to publicly announce that it had agreed to be acquired by another firm at a price significantly greater than its current price. This is an example of inside information. The 1934 Act prohibits you from buying ABC stock from shareholders who do not have this information. This 3

At this stage in our book, we focus on the regulation of corporate governance. We do not talk about many other regulators in financial markets such as the Federal Reserve Board. In Chapter 8, we discuss the nationally recognized statistical rating organizations (NRSROs) in the U.S. They are Fitch Ratings, Moody’s, and Standard & Poor’s. Their ratings are used by market participants to help value securities such as corporate bonds. Many critics of the rating agencies blame the 2007–2009 subprime credit crisis on weak regulatory oversight of these agencies.

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17

prohibition would be especially strong if you were the CEO of the ABC firm. Other kinds of a firm’s inside information could be knowledge of an initial dividend about to be paid, the discovery of a drug to cure cancer, or the default of a debt obligation. A recent example of insider trading involved Samuel Waksal, the founder and CEO of ImClone Systems, a biopharmaceutical company. He was charged with learning that the U.S. Food and Drug Administration was going to reject an application for ImClone’s cancer drug, Erbitrux. What made this an insider trading case was Waksal’s allegedly trying to sell shares of ImClone stock before release of the Erbitrux information, as well as his family and friends also selling the stock. He was arrested in June 2002 and in October 2002 pleaded guilty to securities fraud among other things. In 2003, Waksal was sentenced to more than seven years in prison.

Sarbanes-Oxley In response to corporate scandals at companies such as Enron, WorldCom, Tyco, and Adelphia, Congress enacted the Sarbanes-Oxley Act in 2002. The act, better known as “Sarbox,” is intended to protect investors from corporate abuses. For example, one section of Sarbox prohibits personal loans from a company to its officers, such as the ones that were received by WorldCom CEO Bernie Ebbers. One of the key sections of Sarbox took effect on November 15, 2004. Section 404 requires, among other things, that each company’s annual report must have an assessment of the company’s internal control structure and financial reporting. The auditor must then evaluate and attest to management’s assessment of these issues. Sarbox also creates the Public Companies Accounting Oversight Board (PCAOB) to establish new audit guidelines and ethical standards. It requires public companies’ audit committees of corporate boards to include only independent, outside directors to oversee the annual audits and disclose if the committees have a financial expert (and if not, why not). Sarbox contains other key requirements. For example, the officers of the corporation must review and sign the annual reports. They must explicitly declare that the annual report does not contain any false statements or material omissions; that the financial statements fairly represent the financial results; and that they are responsible for all internal controls. Finally, the annual report must list any deficiencies in internal controls. In essence, Sarbox makes company management responsible for the accuracy of the company’s financial statements. Of course, as with any law, there are costs. Sarbox has increased the expense of corporate audits, sometimes dramatically. In 2004, the average compliance cost for large firms was $4.51 million. By 2006, the average compliance cost had fallen to $2.92 million, so the burden seems to be dropping, but it is still not trivial, particularly for a smaller firm. This added expense has led to several unintended results. For example, in 2003, 198 firms delisted their shares from exchanges, or “went dark,” and about the same number delisted in 2004. Both numbers were up from 30 delistings in 1999. Many of the companies that delisted stated the reason was to avoid the cost of compliance withS arbox.4 A company that goes dark does not have to file quarterly or annual reports. Annual audits by independent auditors are not required, and executives do not have to certify

4

But in “Has New York Become Less Competitive in Global Markets? Evaluating Foreign Listing Choices Over Time” (NBER Working Paper No. 13029) 2008, Craig Doidge, Andrew Karolyi, and René Stulz find that the decline in delistings is not directly related to Sarbanes-Oxley. They conclude that most New York delisting was because of mergers and acquisitions, distress, and restructuring.

18

Part I

Overview

the accuracy of the financial statements, so the savings can be huge. Of course, there are costs. Stock prices typically fall when a company announces it is going dark. Further, such companies will typically have limited access to capital markets and usually will have a higher interest cost on bank loans. Sarbox has also probably affected the number of companies choosing to go public in the United States. For example, when Peach Holdings, based in Boynton Beach, Florida, decided to go public in 2006, it shunned the U.S. stock markets, instead choosing the London Stock Exchange’s Alternative Investment Market (AIM). To go public in the United States, the firm would have paid a $100,000 fee, plus about $2 million to comply with Sarbox. Instead, the company spent only $500,000 on its AIM stock offering. Overall, the European exchanges had a record year in 2006, with 651 companies going public, while the U.S. exchanges had a lackluster year, with 224c ompaniesgo ingp ublic.

www.mhhe.com/rwj

Summary and Conclusions

Concept Questions

This chapter introduced you to some of the basic ideas in corporate finance: 1. Corporate finance has three main areas of concern: a. Capital budgeting: What long-term investments should the firm take? b. Capital structure: Where will the firm get the long-term financing to pay for its investments? Also, what mixture of debt and equity should it use to fund operations? c. Working capital management: How should the firm manage its everyday financial activities? 2. The goal of financial management in a for-profit business is to make decisions that increase the value of the stock, or, more generally, increase the market value of the equity. 3. The corporate form of organization is superior to other forms when it comes to raising money and transferring ownership interests, but it has the significant disadvantage of doublet axation. 4. There is the possibility of conflicts between stockholders and management in a large corporation. We called these conflicts agency problems and discussed how they might be controlled and reduced. 5. The advantages of the corporate form are enhanced by the existence of financial markets. Of the topics we’ve discussed thus far, the most important is the goal of financial management: maximizing the value of the stock. Throughout the text we will be analyzing many different financial decisions, but we will always ask the same question: How does the decision under consideration affect the value of the stock?

1.

2.

Agency Problems Who owns a corporation? Describe the process whereby the owners control the firm’s management. What is the main reason that an agency relationship exists in the corporate form of organization? In this context, what kinds of problems can arise? Not-for-Profit Firm Goals Suppose you were the financial manager of a not-forprofit business (a not-for-profit hospital, perhaps). What kinds of goals do you think would be appropriate?

Chapter 1

3.

4.

5. 6.

7.

9.

10.

S&P Problems

19

Goal of the Firm Evaluate the following statement: Managers should not focus on the current stock value because doing so will lead to an overemphasis on short-term profits at the expense of long-term profits. Ethics and Firm Goals Can the goal of maximizing the value of the stock conflict with other goals, such as avoiding unethical or illegal behavior? In particular, do you think subjects like customer and employee safety, the environment, and the general good of society fit in this framework, or are they essentially ignored? Think of some specific scenarios to illustrate your answer. International Firm Goal Would the goal of maximizing the value of the stock differ for financial management in a foreign country? Why or why not? Agency Problems Suppose you own stock in a company. The current price per share is $25. Another company has just announced that it wants to buy your company and will pay $35 per share to acquire all the outstanding stock. Your company’s management immediately begins fighting off this hostile bid. Is management acting in the shareholders’ best interests? Why or why not? Agency Problems and Corporate Ownership Corporate ownership varies around the world. Historically, individuals have owned the majority of shares in public corporations in the United States. In Germany and Japan, however, banks, other large financial institutions, and other companies own most of the stock in public corporations. Do you think agency problems are likely to be more or less severe in Germany and Japan than in the United States? Agency Problems and Corporate Ownership In recent years, large financial institutions such as mutual funds and pension funds have become the dominant owners of stock in the United States, and these institutions are becoming more active in corporate affairs. What are the implications of this trend for agency problems and corporatec ontrol? Executive Compensation Critics have charged that compensation to top managers in the United States is simply too high and should be cut back. For example, focusing on large corporations, Larry Ellison of Oracle has been one of the best-compensated CEOs in the United States, earning about $193 million in 2008 alone and $429 million over the 2004–2008 period. Are such amounts excessive? In answering, it might be helpful to recognize that superstar athletes such as Tiger Woods, top entertainers such as Tom Hanks and Oprah Winfrey, and many others at the top of their respective fields earn at least as much, if not a great deal more. Goal of Financial Management Why is the goal of financial management to maximize the current share price of the company’s stock? In other words, why isn’t the goal to maximize the future share price?

www.mhhe.com/edumarketinsight 1. Industry Comparison On the Market Insight home page, follow the “Industry” link at the top of the page. You will be on the industry page. You can use the drop-down menu to select different industries. Answer the following questions for these industries: airlines, automobile manufacturers, biotechnology, computer hardware, homebuilding, marine, restaurants, soft drinks, and wireless telecommunications. a. How many companies are in each industry? b. What are the total sales for each industry? c. Do the industries with the largest total sales have the most companies in the industry?W hatd oest hist elly oua boutc ompetitionin t hev ariousin dustries?

www.mhhe.com/rwj

8.

Introduction to Corporate Finance

CHAPTER 2

FinancialSt atements and Cash Flow A write-off frequently means that the value of the company’s assets has declined. For example, in the first quarter of 2009, luxury homebuilder Toll Brothers said it was writing down $157 million in assets, much of which was a reflection of the reduced value of land the company owned. Of course, Toll Brothers was not the only homebuilder suffering. Hovnanian Enterprises announced it would take a $132 million write-off, and Centex Corp. announced a $590 million write-off. At the same time, D. R. Horton, Inc., the largest homebuilder by volume, had a much smaller write-off of only $56 million. However, D. R. Horton had already written off $1.15 billion in the fourth quarter of 2008. So did stockholders in these homebuilders lose hundreds of millions of dollars (or more) because of the write-offs? The answer is probably not. Understanding why ultimately leads us to the main subject of this chapter: that all-important substance known as cash fl ow.

2.1 TheBal anceS heet The balance sheet is an accountant’s snapshot of a firm’s accounting value on a particular date, as though the firm stood momentarily still. The balance sheet has two sides: On the left are the assets and on the right are the liabilities and stockholders’ equity. The balance sheet states what the firm owns and how it is financed. The accounting definition that underlies the balance sheet and describes the balance is: Assets ≡ Liabilities + Stockholders’ equity

Two excellent sources for company financial information are finance.yahoo.com and money.cnn.com.

20

We have put a three-line equality in the balance equation to indicate that it must always hold, by definition. In fact, the stockholders’ equity is defined to be the difference between the assets and the liabilities of the firm. In principle, equity is what the stockholders would have remaining after the firm discharged its obligations. Table 2.1 gives the 2010 and 2009 balance sheet for the fictitious U.S. Composite Corporation. The assets in the balance sheet are listed in order by the length of time it normally would take an ongoing firm to convert them into cash. The asset side depends on the nature of the business and how management chooses to conduct it. Management must make decisions about cash versus marketable securities, credit versus cash sales, whether to make or buy commodities, whether to lease or purchase items, the types of business in which to engage, and so on. The liabilities and the stockholders’ equity are listed in the order in which they would typically be paid over time.

Chapter 2

Table 2.1

Financial Statements and Cash Flow

21

The Balance Sheet of the U.S. Composite Corporation

U.S. COMPOSITE CORPORATION Balance Sheet 2010 and 2009 ($ in millions) Assets

2010

Current assets: Cash and equivalents Accounts receivable Inventories Other Total current assets Fixed assets: Property, plant, and equipment Less accumulated depreciation Net property, plant, and equipment Intangible assets and others Total fixed assets

Total assets

2009

$ 140 294 269 58 $ 761

$ 107 270 280 50 $ 707

$1,423 550 873

$1,274 460 814

245 $1,118

221 $1,035

$1,879

$1,742

Liabilities (Debt) and Stockholders’ Equity

2010

Current liabilities: Accounts payable Notes payable Accrued expenses Total current liabilities

$ 213 50 223 $ 486

$ 197 53 205 $ 455

Long-term liabilities: Deferred taxes Long-term debt* Total long-term liabilities

$ 117 471 $ 588

$ 104 458 $ 562

Stockholders’ equity: Preferred stock Common stock ($1 par value) Capital surplus Accumulated retained earnings Less treasury stock† Total equity

$ 39 55 347 390 26 $ 805

$

Total liabilities and stockholders’ equity‡

$ 1,879

$1,742

2009

39 32 327 347 20 $ 725

*

Long-term debt rose by $ 471 million – $ 458 million = $13 million. This is the difference between $ 86 million new debt and $ 73 million in retirement of old debt.

†

Treasury stock rose by $ 6 million. This reflects the repurchase of $ 6 million of U.S. Composite’s company stock.

‡

U.S. Composite reports $ 43 million in new equity. The company issued 23 million shares at a price of $1.87. The par value of common stock increased by $ 23 million, and capital surplus increased by $ 20 million.

The liabilities and stockholders’ equity side reflects the types and proportions of financing, which depend on management’s choice of capital structure, as between debt and equity and between current debt and long-term debt. When analyzing a balance sheet, the financial manager should be aware of three concerns: liquidity, debt versus equity, and value versus cost. Annual and quarterly financial statements for most public U.S. corporations can be found in the EDGAR database at www.sec.gov.

Liquidity Liquidity refers to the ease and quickness with which assets can be converted to cash (without significant loss in value). Current assets are the most liquid and include cash and assets that will be turned into cash within a year from the date of the balance sheet. Accounts receivable are amounts not yet collected from customers for goods or services sold to them (after adjustment for potential bad debts). Inventory is composed of raw materials to be used in production, work in process, and finished goods. Fixed assets are the least liquid kind of assets. Tangible fixed assets include property, plant,

22

Part I

Overview

and equipment. These assets do not convert to cash from normal business activity, and they are not usually used to pay expenses such as payroll. Some fixed assets are not tangible. Intangible assets have no physical existence but can be very valuable. Examples of intangible assets are the value of a trademark or the value of a patent. The more liquid a firm’s assets, the less likely the firm is to experience problems meeting short-term obligations. Thus, the probability that a firm will avoid financial distress can be linked to the firm’s liquidity. Unfortunately, liquid assets frequently have lower rates of return than fixed assets; for example, cash generates no investment income. To the extent a firm invests in liquid assets, it sacrifices an opportunity to invest in more profitable investment vehicles.

Debtve rsusE quity Liabilities are obligations of the firm that require a payout of cash within a stipulated period. Many liabilities involve contractual obligations to repay a stated amount and interest over a period. Thus, liabilities are debts and are frequently associated with nominally fixed cash burdens, called debt service, that put the firm in default of a contract if they are not paid. Stockholders’ equity is a claim against the firm’s assets that is residual and not fixed. In general terms, when the firm borrows, it gives the bondholders first claim on the firm’s cash flow.1 Bondholders can sue the firm if the firm defaults on its bond contracts. This may lead the firm to declare itself bankrupt. Stockholders’ equity is the residual difference between assets and liabilities: Assets − Liabilities ≡ Stockholders’ equity This is the stockholders’ share in the firm stated in accounting terms. The accounting value of stockholders’ equity increases when retained earnings are added. This occurs when the firm retains part of its earnings instead of paying them out as dividends.

The home page for the Financial Accounting Standards Board (FASB) is www.fasb.org.

Valueve rsusCo st The accounting value of a firm’s assets is frequently referred to as the carrying value or the book value of the assets.2 Under generally accepted accounting principles (GAAP), audited financial statements of firms in the United States carry the assets at cost.3 Thus the terms carrying value and book value are unfortunate. They specifically say “value,” when in fact the accounting numbers are based on cost. This misleads many readers of financial statements to think that the firm’s assets are recorded at true market values. Market value is the price at which willing buyers and sellers would trade the assets. It would be only a coincidence if accounting value and market value were the same. In fact, management’s job is to create value for the firm that exceeds its cost. Many people use the balance sheet, but the information each may wish to extract is not the same. A banker may look at a balance sheet for evidence of accounting

1

Bondholders are investors in the firm’s debt. They are creditors of the firm. In this discussion, the term bondholder means the same thing as creditor.

2

Confusion often arises because many financial accounting terms have the same meaning. This presents a problem with jargon for the reader of financial statements. For example, the following terms usually refer to the same thing: assets minus liabilities, net worth, stockholders’ equity, owners’ equity, book equity, and equity capitalization. 3 Generally, GAAP requires assets to be carried at the lower of cost or market value. In most instances, cost is lower than market value. However, in some cases when a fair market value can be readily determined, the assets have their value adjusted to the fair market value.

Chapter 2

Financial Statements and Cash Flow

23

liquidity and working capital. A supplier may also note the size of accounts payable and therefore the general promptness of payments. Many users of financial statements, including managers and investors, want to know the value of the firm, not its cost. This information is not found on the balance sheet. In fact, many of the true resources of the firm do not appear on the balance sheet: good management, proprietary assets, favorable economic conditions, and so on. Henceforth, whenever we speak of the value of an asset or the value of the firm, we will normally mean its market value. So, for example, when we say the goal of the financial manager is to increase the value of the stock, we usually mean the market value of the stock not the book value.

EXAMPLE 2.1

Market Value versus Book Value The Cooney Corporation has fixed assets with a book value of $700 and an appraised market value of about $1,000. Net working capital is $400 on the books, but approximately $600 would be realized if all the current accounts were liquidated. Cooney has $500 in long-term debt, both book value and market value. What is the book value of the equity? What is the market value? We can construct two simplified balance sheets, one in accounting (book value) terms and one in economic (market value) terms: COONEY CORPORATION Balance Sheets Market Value versus Book Value Assets

Net working capital Net fixed assets

Liabilities and Shareholders’ Equity

Book

Market

$ 400 700 $1,100

$ 600 1,000 $1,600

Long-term debt Shareholders’ equity

Book

Market

$ 500 600 $1,100

$ 500 1,100 $1,600

In this example, shareholders’ equity is actually worth almost twice as much as what is shown on the books. The distinction between book and market values is important precisely because book values can be so different from market values.

2.2 TheIn come Statement The income statement measures performance over a specific period—say a year. The accounting definition of income is: Revenue − Expenses ≡ Income If the balance sheet is like a snapshot, the income statement is like a video recording of what the people did between two snapshots. Table 2.2 gives the income statement for the U.S. Composite Corporation for 2010. The income statement usually includes several sections. The operations section reports the firm’s revenues and expenses from principal operations. One number of particular importance is earnings before interest and taxes (EBIT), which summarizes earnings before taxes and financing costs. Among other things, the nonoperating section of the income statement includes all financing costs, such as interest expense.

24

Table 2.2 The Income Statement of the U.S. Composite Corporation

Part I

Overview

U.S. COMPOSITE CORPORATION Income Statement 2010 ($ in millions) Total operating revenues Cost of goods sold Selling, general, and administrative expenses Depreciation Operating income Other income Earnings before interest and taxes (EBIT) Interest expense Pretax income Taxes Current: $71 Deferred: 13 Net income Addition to retained earnings: Dividends:

$2,262 1,655 327 90 $ 190 29 $ 219 49 $ 170 84

$ $

86 43 43

NOTE: There are 29 million shares outstanding. Earnings per share and dividends per share can be calculated as follows: Net income Earnings per share = ____________________ Total shares outstanding $86 = ____ 29 = $2.97 per share Dividends Dividends per share = ____________________ Total shares outstanding $43 = ____ 29 = $1.48 per share

Usually a second section reports as a separate item the amount of taxes levied on income. The last item on the income statement is the bottom line, or net income. Net income is frequently expressed per share of common stock—that is, earnings per share. When analyzing an income statement, the financial manager should keep in mind GAAP, noncash items, time, and costs.

Generally Accepted Accounting Principles Revenue is recognized on an income statement when the earnings process is virtually completed and an exchange of goods or services has occurred. Therefore, the unrealized appreciation from owning property will not be recognized as income. This provides a device for smoothing income by selling appreciated property at convenient times. For example, if the firm owns a tree farm that has doubled in value, then, in a year when its earnings from other businesses are down, it can raise overall earnings by selling some trees. The matching principle of GAAP dictates that revenues be matched with expenses. Thus, income is reported when it is earned, or accrued, even though no cash flow has necessarily occurred (for example, when goods are sold for credit, sales and profits are reported).

Chapter 2

Financial Statements and Cash Flow

25

NoncashI tems The economic value of assets is intimately connected to their future incremental cash flows. However, cash flow does not appear on an income statement. There are several noncash items that are expenses against revenues but do not affect cash flow. The most important of these is depreciation. Depreciation reflects the accountant’s estimate of the cost of equipment used up in the production process. For example, suppose an asset with a five-year life and no resale value is purchased for $1,000. According to accountants, the $1,000 cost must be expensed over the useful life of the asset. If straight-line depreciation is used, there will be five equal installments, and $200 of depreciation expense will be incurred each year. From a finance perspective, the cost of the asset is the actual negative cash flow incurred when the asset is acquired (that is, $1,000, not the accountant’s smoothed $200-per-year depreciation expense). Another noncash expense is deferred taxes. Deferred taxes result from differences between accounting income and true taxable income.4 Notice that the accounting tax shown on the income statement for the U.S. Composite Corporation is $84 million. It can be broken down as current taxes and deferred taxes. The current tax portion is actually sent to the tax authorities (for example, the Internal Revenue Service). The deferred tax portion is not. However, the theory is that if taxable income is less than accounting income in the current year, it will be more than accounting income later on. Consequently, the taxes that are not paid today will have to be paid in the future, and they represent a liability of the firm. This shows up on the balance sheet as deferred tax liability. From the cash flow perspective, though, deferred tax is not a cash outflow. In practice, the difference between cash flows and accounting income can be quite dramatic, so it is important to understand the difference. For example, in the first quarter of 2009, media giant Cablevision, whose holdings include the New York Knicks and New York Rangers, reported a loss of $321 million. Sounds bad, but Cablevision reported a positive operating cash flow of $498 million! In large part, the difference was due to noncash charges associated with Cablevision’s purchase of the Newsday newspaper the previous year.

Timea ndCo sts It is often useful to visualize all of future time as having two distinct parts, the short run and the long run. The short run is the period in which certain equipment, resources, and commitments of the firm are fixed; but the time is long enough for the firm to vary its output by using more labor and raw materials. The short run is not a precise period that will be the same for all industries. However, all firms making decisions in the short run have some fixed costs—that is, costs that will not change because of fixed commitments. In real business activity, examples of fixed costs are bond interest, overhead, and property taxes. Costs that are not fixed are variable. Variable costs change as the output of the firm changes; some examples are raw materials and wages for laborers on the production line. In the long run, all costs are variable. Financial accountants do not distinguish between variable costs and fixed costs. Instead, accounting costs usually fit into a classification that distinguishes product costs from period costs. Product costs are the total production costs incurred during a period—raw materials, direct labor, and 4

One situation in which taxable income may be lower than accounting income is when the firm uses accelerated depreciation expense procedures for the IRS but uses straight-line procedures allowed by GAAP for reporting purposes.

26

Part I

Overview

manufacturing overhead—and are reported on the income statement as cost of goods sold. Both variable and fixed costs are included in product costs. Period costs are costs that are allocated to a time period; they are called selling, general, and administrative expenses. One period cost would be the company president’s salary.

2.3 Taxes Taxes can be one of the largest cash outflows a firm experiences. In 2007, according to the Department of Commerce, total corporate profits before taxes in the United States were about $1.6 trillion, and taxes on corporate profits were about $450 billion or about 28 percent of pretax profits. The size of the firm’s tax bill is determined by the tax code, an often amended set of rules. In this section, we examine corporate tax rates and how taxes are calculated. If the various rules of taxation seem a little bizarre or convoluted to you, keep in mind that the tax code is the result of political, not economic, forces. As a result, there is no reason why it has to make economic sense. To put the complexity of corporate taxation into perspective, General Electric’s 2006 tax return required 24,000 pages, far too much to print. The electronically filed return ran 237 megabytes.

CorporateT axR ates Corporate tax rates in effect for 2008 are shown in Table 2.3. A peculiar feature of taxation instituted by the Tax Reform Act of 1986 and expanded in the 1993 Omnibus Budget Reconciliation Act is that corporate tax rates are not strictly increasing. As shown, corporate tax rates rise from 15 percent to 39 percent, but they drop back to 34 percent on income over $335,000. They then rise to 38 percent and subsequently fall to 35 percent. According to the originators of the current tax rules, there are only four corporate rates: 15 percent, 25 percent, 34 percent, and 35 percent. The 38 and 39 percent brackets arise because of “surcharges” applied on top of the 34 and 35 percent rates. A tax is a tax, however, so there are really six corporate tax brackets, as we have shown.

Average versus Marginal Tax Rates In making financial decisions, it is frequently important to distinguish between average and marginal tax rates. Your average tax rate is your tax bill divided by your taxable income—in other words, the percentage of your income that goes to pay taxes. Your marginal tax rate is the tax you would pay (in percent) if you earned one more dollar.

Table 2.3

Taxable Income

Tax Rate

0– 50,000 50,001– 75,000 75,001– 100,000 100,001– 335,000 335,001–10,000,000 10,000,001–15,000,000 15,000,001–18,333,333

15% 25 34 39 34 35 38 35

Corporate Tax R ates

$

18,333,334+

Chapter 2

Financial Statements and Cash Flow

27

The percentage tax rates shown in Table 2.3 are all marginal rates. Put another way, the tax rates apply to the part of income in the indicated range only, not all income. The difference between average and marginal tax rates can best be illustrated with a simple example. Suppose our corporation has a taxable income of $200,000. What is the tax bill? Using Table 2.3, we can figure our tax bill like this: .15($ 50,000) = $ 7,500 .25($ 75,000 − 50,000) = 6,250 .34($100,000 − 75,000) = 8,500 .39($200,000 − 100,000) = 39,000 $61,250

The IRS has a great Web site: www.irs.gov.

Our total tax is thus $61,250. In our example, what is the average tax rate? We had a taxable income of $200,000 and a tax bill of $61,250, so the average tax rate is $61,250/200,000 = 30.625%. What is the marginal tax rate? If we made one more dollar, the tax on that dollar would be 39 cents, so our marginal rate is 39 percent.

EXAMPLE 2.2 Deep in the Heart of Taxes Algernon, Inc., has a taxable income of $85,000. What is its tax bill? What is its average tax rate? Its marginal tax rate? From Table 2.3, we see that the tax rate applied to the first $50,000 is 15 percent; the rate applied to the next $25,000 is 25 percent; and the rate applied after that up to $100,000 is 34 percent. So Algernon must pay .15 × $50,000 + .25 × 25,000 + .34 × (85,000 − 75,000) = $17,150. The average tax rate is thus $17,150/85,000 = 20.18%. The marginal rate is 34 percent because Algernon’s taxes would rise by 34 cents if it had another dollar in taxable income.

Table 2.4 summarizes some different taxable incomes, marginal tax rates, and average tax rates for corporations. Notice how the average and marginal tax rates come together at 35 percent. With a flat-rate tax, there is only one tax rate, so the rate is the same for all income levels. With such a tax, the marginal tax rate is always the same as the average tax rate. As it stands now, corporate taxation in the United States is based on a modified flatrate tax, which becomes a true flat rate for the highest incomes. In looking at Table 2.4, notice that the more a corporation makes, the greater is the percentage of taxable income paid in taxes. Put another way, under current tax law, the

Table 2.4 Corporate Taxes and Tax Rates

(1) Taxable Income $

45,000 70,000 95,000 250,000 1,000,000 17,500,000 50,000,000 100,000,000

(2) Marginal Tax Rate 15% 25 34 39 34 38 35 35

(3) Total Tax $

6,750 12,500 20,550 80,750 340,000 6,100,000 17,500,000 35,000,000

(3)/(I) Average Tax Rate 15.00% 17.86 21.63 32.30 34.00 34.86 35.00 35.00

28

Part I

Overview

average tax rate never goes down, even though the marginal tax rate does. As illustrated, for corporations, average tax rates begin at 15 percent and rise to a maximum of 35 percent. Normally, the marginal tax rate will be relevant for financial decision making. The reason is that any new cash flows will be taxed at that marginal rate. Because financial decisions usually involve new cash flows or changes in existing ones, this rate will tell us the marginal effect of a decision on our tax bill. There is one last thing to notice about the tax code as it affects corporations. It’s easy to verify that the corporate tax bill is just a flat 35 percent of taxable income if our taxable income is more than $18.33 million. Also, for the many midsize corporations with taxable incomes in the range of $335,000 to $10,000,000, the tax rate is a flat 34 percent. Because we will usually be talking about large corporations, you can assume that the average and marginal tax rates are 35 percent unless we explicitly say otherwise. Before moving on, we should note that the tax rates we have discussed in this section relate to federal taxes only. Overall tax rates can be higher if state, local, and any othertax esar ec onsidered.

2.4 Net Working Capital Net working capital is current assets minus current liabilities. Net working capital is positive when current assets are greater than current liabilities. This means the cash that will become available over the next 12 months will be greater than the cash that must be paid out. The net working capital of the U.S. Composite Corporation is $275 million in 2010 and $252 million in 2009.

2010 2009

Current assets ($ millions) $761 707

− − −

Current liabilities ($ millions) $486 455

= = =

Net working capital ($ millions) $275 252

In addition to investing in fixed assets (i.e., capital spending), a firm can invest in net working capital. This is called the change in net working capital. The change in net working capital in 2010 is the difference between the net working capital in 2010 and 2009—that is, $275 million − $252 million = $23 million. The change in net working capital is usually positive in a growing firm.

2.5 FinancialCash F low Perhaps the most important item that can be extracted from financial statements is the actual cash flow of the firm. An official accounting statement called the statement of cash flows helps to explain the change in accounting cash and equivalents, which for U.S. Composite is $33 million in 2010. (See Section 2.6.) Notice in Table 2.1 that cash and equivalents increase from $107 million in 2009 to $140 million in 2010. However, we will look at cash flow from a different perspective: the perspective of finance. In finance, the value of the firm is its ability to generate financial cash flow. (We will talk more about financial cash flow in a later chapter.) The first point we should mention is that cash flow is not the same as net working capital. For example, increasing inventory requires using cash. Because both inventories and cash are current assets, this does not affect net working capital. In this case, an increase in inventory is associated with decreasing cash flow. Just as we established that the value of a firm’s assets is always equal to the combined value of the liabilities and the value of the equity, the cash flows received from

Chapter 2

Table 2.5 Financial Cash Flow of the U.S. Composite Corporation

Financial Statements and Cash Flow

29

U.S. COMPOSITE CORPORATION Financial Cash Flow 2010 ($ in millions) Cash flow of the firm Operating cash flow (Earnings before interest and taxes plus depreciation minus taxes) Capital spending (Acquisitions of fixed assets minus sales of fixed assets) Additions to net working capital Total Cash flow to investors in the firm Debt (Interest plus retirement of debt minus long-term debt financing) Equity (Dividends plus repurchase of equity minus new equity financing) Total

$238 −173 −23 $ 42 $ 36 6 $ 42

the firm’s assets (that is, its operating activities), CF(A), must equal the cash flows to the firm’s creditors, CF(B), and equity investors, CF(S): CF(A) ≡ CF(B) + CF(S ) The first step in determining cash flows of the firm is to figure out the cash flow from operations. As can be seen in Table 2.5, operating cash flow is the cash flow generated by business activities, including sales of goods and services. Operating cash flow reflects tax payments, but not financing, capital spending, or changes in net working capital: $ in millions Earnings before interest and taxes Depreciation Current taxes Operating cash flow

$219 90 −71 $238

Another important component of cash flow involves changes in fixed assets. For example, when U.S. Composite sold its power systems subsidiary in 2010, it generated $25 million in cash flow. The net change in fixed assets equals the acquisition of fixed assets minus the sales of fixed assets. The result is the cash flow used for capital spending: Acquisition of fixed assets Sales of fixed assets Capital spending

$198 −25 $173

($149 + 24 = Increase in property, plant, and equipment + Increase in intangible assets)

30

Part I

Overview

We can also calculate capital spending simply as: Capitalsp ending = Ending net fixed assets − Beginning net fixed assets + Depreciation = $1,118 − 1,035 + 90 =$173 Cash flows are also used for making investments in net working capital. In U.S. Composite Corporation in 2010, additions to net working capitalar e: Additions to net working capital

$23

Note that this $23 million is the change in net working capital we previously calculated. Total cash flows generated by the firm’s assets are then equal to: Operating cash flow Capital spending Additions to net working capital Total cash flow of the firm

$238 −173 − 23 $ 42

The total outgoing cash flow of the firm can be separated into cash flow paid to creditors and cash flow paid to stockholders. The cash flow paid to creditors represents a regrouping of the data in Table 2.5 and an explicit recording of interest expense. Creditors are paid an amount generally referred to as debt service. Debt service is interest payments plus repayments of principal (that is, retirement of debt). An important source of cash flow is the sale of new debt. U.S. Composite’s longterm debt increased by $13 million (the difference between $86 million in new debt and $73 million in retirement of old debt).5 Thus, an increase in long-term debt is the net effect of new borrowing and repayment of maturing obligations plus interest expense: Cash Flow Paid to Creditors ($ in millions) Interest Retirement of debt Debt service Proceeds from long-term debt sales Total

$ 49 73 122 −86 $ 36

Cash flow paid to creditors can also be calculated as: Cash flow paid to creditors = Interest paid − Net new borrowing = Interest paid − (Ending long-term debt − Beginning long-term debt) = $49 − (471 − 458) =$36 5

New debt and the retirement of old debt are usually found in the “notes” to the balance sheet.

Chapter 2

Financial Statements and Cash Flow

31

Cash flow of the firm also is paid to the stockholders. It is the net effect of paying dividends plus repurchasing outstanding shares of stock and issuing new shares of stock: Cash Flow to Stockholders ($ in millions) Dividends Repurchase of stock Cash to stockholders Proceeds from new stock issue Total

$43 6 49 −43 $ 6

In general, cash flow to stockholders can be determined as: Cashf lowto sto ckholders = Dividends paid − Net new equity raised = Dividends paid − (Stock sold −S tockr epurchased) To determine stock sold, first notice that the common stock and capital surplus accounts went up by a combined $23 + 20 = $43, which implies that the company sold $43 million worth of stock. Second, treasury stock went up by $6, indicating that the company bought back $6 million worth of stock. Net new equity is thus $43 − 6 = $37. Dividends paid were $43 million, so the cash flow to stockholders was: Cashf lowto sto ckholders = $43 − (43 − 6) =$6, which is what we previously calculated. Some important observations can be drawn from our discussion of cash flow: 1. Several types of cash flow are relevant to understanding the financial situation of the firm. Operating cash flow, defined as earnings before interest plus depreciation minus taxes, measures the cash generated from operations not counting capital spending or working capital requirements. It is usually positive; a firm is in trouble if operating cash flow is negative for a long time because the firm is not generating enough cash to pay operating costs. Total cash flow of the firm includes adjustments for capital spending and additions to net working capital. It will frequently be negative. When a firm is growing at a rapid rate, spending on inventory and fixed assets can be higher than operating cash flow. 2. Net income is not cash flow. The net income of the U.S. Composite Corporation in 2010 was $86 million, whereas cash flow was $42 million. The two numbers are not usually the same. In determining the economic and financial condition of a firm, cash flow is more revealing. A firm’s total cash flow sometimes goes by a different name, free cash flow. Of course, there is no such thing as “free” cash (we wish!). Instead, the name refers to cash that the firm is free to distribute to creditors and stockholders because it is not needed for working capital or fixed asset investments. We will stick with “total cash flow of the firm” as our label for this important concept because, in practice, there is some variation in exactly how free cash flow is computed. Nonetheless, whenever you hear the phrase “free cash flow,” you should understand that what is being discussed is cash flow from assets or something quite similar.

32

Part I

Overview

2.6 The Accounting Statement of Cash Flows As previously mentioned, there is an official accounting statement called the statement of cash flows. This statement helps explain the change in accounting cash, which for U.S. Composite is $33 million in 2010. It is very useful in understanding financial cash flow. The first step in determining the change in cash is to figure out cash flow from operating activities. This is the cash flow that results from the firm’s normal activities in producing and selling goods and services. The second step is to make an adjustment for cash flow from investing activities. The final step is to make an adjustment for cash flow from financing activities. Financing activities are the net payments to creditors and owners (excluding interest expense) made during the year. The three components of the statement of cash flows are determined next.

Cash Flow from Operating Activities To calculate cash flow from operating activities we start with net income. Net income can be found on the income statement and is equal to $86 million. We now need to add back noncash expenses and adjust for changes in current assets and liabilities (other than cash and notes payable). The result is cash flow from operating activities. Notes payable will be included in the financing activities section. U.S. COMPOSITE CORPORATION Cash Flow from Operating Activities 2010 ($ in millions) Net income Depreciation Deferred taxes Change in assets and liabilities Accounts receivable Inventories Accounts payable Accrued expense Other Cash flow from operating activities

$ 86 90 13 −24 11 16 18 −8 $202

Cash Flow from Investing Activities Cash flow from investing activities involves changes in capital assets: acquisition of fixed assets and sales of fixed assets (i.e., net capital expenditures). The result for U.S. Composite is shown here: U.S. COMPOSITE CORPORATION Cash Flow from Investing Activities 2010 ($ in millions) Acquisition of fixed assets Sales of fixed assets Cash flow from investing activities

−$198 25 −$173

Chapter 2

Financial Statements and Cash Flow

33

Cash Flow from Financing Activities Cash flows to and from creditors and owners include changes in equity and debt: U.S. COMPOSITE CORPORATION Cash Flow from Financing Activities 2010 ($ in millions) Retirement of long-term debt Proceeds from long-term debt sales Change in notes payable Dividends Repurchase of stock Proceeds from new stock issue Cash flow from financing activities

−$73 86 −3 −43 −6 43 $ 4

The statement of cash flows is the addition of cash flows from operations, cash flows from investing activities, and cash flows from financing activities, and is produced in Table 2.6. When we add all the cash flows together, we get the change in cash on the balance sheet of $33 million.

Table 2.6 Statement of Consolidated Cash Flows of the U.S. Composite Corporation

U.S. COMPOSITE CORPORATION Statement of Cash Flows 2010 ($ in millions) Operations Net income Depreciation Deferred taxes Changes in assets and liabilities Accounts receivable Inventories Accounts payable Accrued expenses Other Total cash flow from operations

$ 86 90 13 −24 11 16 18 −8 $202

Investing activities Acquisition of fixed assets Sales of fixed assets Total cash flow from investing activities

−$198 25 −$173

Financing activities Retirement of long-term debt Proceeds from long-term debt sales Change in notes payable Dividends Repurchase of stock Proceeds from new stock issue Total cash flow from financing activities Change in cash (on the balance sheet)

−$ 73 86 −3 −43 −6 43 $ 4 $ 33

34

Part I

Overview

There is a close relationship between the official accounting statement called the statement of cash flows and the total cash flow of the firm used in finance. Going back to the previous section, you should note a slight conceptual problem here. Interest paid should really go under financing activities, but unfortunately that is not how the accounting is handled. The reason is that interest is deducted as an expense when net income is computed. As a consequence, a primary difference between the accounting cash flow and the financial cash flow of the firm (see Table 2.5) is interest expense.

2.7 CashF lowMan agement One of the reasons why cash flow analysis is popular is the difficulty in manipulating, or spinning, cash flows. GAAP accounting principles allow for significant subjective decisions to be made regarding many key areas. The use of cash flow as a metric to evaluate a company comes from the idea that there is less subjectivity involved, and, therefore, it is harder to spin the numbers. But several recent examples have shown that companies can still find ways to do it. For example, in 2007, rental car company Avis Budget Group was forced to revise its first quarter 2007 operating cash flow by more than $45 million. The company had improperly classified the cash flow as an operating cash flow rather than an investing cash flow. This maneuver had the effect of decreasing investing cash flows and increasing operating cash flows by the same amount. In August 2007, Vail Resorts faced a similar problem when it was forced to restate cash flows resulting from its real estate investments as investment cash flow rather than operating cash flow. Tyco used several ploys to alter cash flows. For example, the company purchased more than $800 million of customer security alarm accounts from dealers. The cash flows from these transactions were reported in the financing activity section of the accounting statement of cash flows. When Tyco received payments from customers, the cash inflows were reported as operating cash flows. Another method used by Tyco was to have acquired companies prepay operating expenses. In other words, the company acquired by Tyco would pay vendors for items not yet received. In one case, the payments totaled more than $50 million. When the acquired company was consolidated with Tyco, the prepayments reduced Tyco’s cash outflows, thus increasing the operating cash flows. Dynegy, the energy giant, was accused of engaging in a number of complex “roundtrip trades.” The round-trip trades essentially involved the sale of natural resources to a counterparty, with the repurchase of the resources from the same party at the same price. In essence, Dynegy would sell an asset for $100, and immediately repurchase it from the buyer for $100. The problem arose with the treatment of the cash flows from the sale. Dynegy treated the cash from the sale of the asset as an operating cash flow, but classified the repurchase as an investing cash outflow. The total cash flows of the contracts traded by Dynegy in these round-trip trades totaled $300 million. Adelphia Communications was another company that apparently manipulated cash flows. In Adelphia’s case, the company capitalized the labor required to install cable. In other words, the company classified this labor expense as a fixed asset. While this practice is fairly common in the telecommunications industry, Adelphia capitalized a higher percentage of labor than is common. The effect of this classification was that the labor was treated as an investment cash flow, which increased the operating cash flow. In each of these examples, the companies were trying to boost operating cash flows by shifting cash flows to a different heading. The important thing to notice is that these movements don’t affect the total cash flow of the firm, which is why we recommend focusing on this number, not just operating cash flow.

Chapter 2

Summary and Conclusions

Concept Questions

1. 2.

5.

6. 7. 8.

9.

10.

1.

2.

Liquidity True or false: All assets are liquid at some price. Explain. Accounting and Cash Flows Why might the revenue and cost figures shown on a standard income statement not represent the actual cash inflows and outflows that occurred during a period? Accounting Statement of Cash Flows Looking at the accounting statement of cash flows, what does the bottom line number mean? How useful is this number for analyzing a company? Cash Flows How do financial cash flows and the accounting statement of cash flows differ? Which is more useful for analyzing a company? Book Values versus Market Values Under standard accounting rules, it is possible for a company’s liabilities to exceed its assets. When this occurs, the owners’ equity is negative. Can this happen with market values? Why or why not? Cash Flow from Assets Why is it not necessarily bad for the cash flow from assets to be negative for a particular period? Operating Cash Flow Why is it not necessarily bad for the operating cash flow to be negative for a particular period? Net Working Capital and Capital Spending Could a company’s change in net working capital be negative in a given year? (Hint: Yes.) Explain how this might come about. What about net capital spending? Cash Flow to Stockholders and Creditors Could a company’s cash flow to stockholders be negative in a given year? (Hint: Yes.) Explain how this might come about. What about cash flow to creditors? Firm Values Referring back to the D. R. Horton example at the beginning of the chapter, note that we suggested that D. R. Horton’s stockholders probably didn’t suffer as a result of the reported loss. What do you think was the basis for our conclusion?

Building a Balance Sheet Culligan, Inc., has current assets of $5,300, net fixed assets of $26,000, current liabilities of $3,900, and long-term debt of $14,200. What is the value of the shareholders’ equity account for this firm? How much is net workingc apital? Building an Income Statement Ragsdale, Inc., has sales of $493,000, costs of $210,000, depreciation expense of $35,000, interest expense of $19,000, and a tax rate of 35 percent. What is the net income for the firm? Suppose the company paid out $50,000 in cash dividends. What is the addition to retained earnings?

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4.

BASIC (Questions 1–10)

35

Besides introducing you to corporate accounting, the purpose of this chapter has been to teach you how to determine cash flow from the accounting statements of a typical company. 1. Cash flow is generated by the firm and paid to creditors and shareholders. It can be classified as: a. Cashf lowf romo perations. b. Cash flow from changes in fixed assets. c. Cashf lowf romc hangesin w orkingc apital. 2. Calculations of cash flow are not difficult, but they require care and particular attention to detail in properly accounting for noncash expenses such as depreciation and deferred taxes. It is especially important that you do not confuse cash flow with changes in net working capital and net income.

3.

Questions and Problems

Financial Statements and Cash Flow

36

Part I

3.

4.

5.

6.

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7.

Overview

Market Values and Book Values Klingon Cruisers, Inc., purchased new cloaking machinery three years ago for $9.5 million. The machinery can be sold to the Romulans today for $6.3 million. Klingon’s current balance sheet shows net fixed assets of $5 million, current liabilities of $2.1 million, and net working capital of $800,000. If all the current assets were liquidated today, the company would receive $2.8 million cash. What is the book value of Klingon’s assets today? What is the market value? Calculating Taxes The Herrera Co. had $246,000 in taxable income. Using the rates from Table 2.3 in the chapter, calculate the company’s income taxes. What is the average tax rate? What is the marginal tax rate? Calculating OCF Ranney, Inc., has sales of $14,900, costs of $5,800, depreciation expense of $1,300, and interest expense of $780. If the tax rate is 40 percent, what is the operating cash flow, or OCF? Calculating Net Capital Spending Gordon Driving School’s 2009 balance sheet showed net fixed assets of $1.65 million, and the 2010 balance sheet showed net fixed assets of $1.73 million. The company’s 2010 income statement showed a depreciation expense of $284,000. What was Gordon’s net capital spending for 2010? Building a Balance Sheet The following table presents the long-term liabilities and stockholders’ equity of Information Control Corp. one year ago:

Long-term debt Preferred stock Common stock ($1 par value) Accumulated retained earnings Capital surplus

8.

9.

10.

$72,000,000 9,000,000 20,000,000 97,000,000 43,000,000

During the past year, Information Control issued 10 million shares of new stock at a total price of $43 million, and issued $10 million in new long-term debt. The company generated $9 million in net income and paid $2 million in dividends. Construct the current balance sheet reflecting the changes that occurred at Information Control Corp. during the year. Cash Flow to Creditors The 2009 balance sheet of Anna’s Tennis Shop, Inc., showed long-term debt of $1.34 million, and the 2010 balance sheet showed long-term debt of $1.39 million. The 2010 income statement showed an interest expense of $118,000. What was the firm’s cash flow to creditors during 2010? Cash Flow to Stockholders The 2009 balance sheet of Anna’s Tennis Shop, Inc., showed $430,000 in the common stock account and $2.6 million in the additional paid-in surplus account. The 2010 balance sheet showed $450,000 and $3.05 million in the same two accounts, respectively. If the company paid out $385,000 in cash dividends during 2010, what was the cash flow to stockholders for the year? Calculating Cash Flows Given the information for Anna’s Tennis Shop, Inc., in the previous two problems, suppose you also know that the firm’s net capital spending for 2010 was $875,000 and that the firm reduced its net working capital investment by $69,000. What was the firm’s 2010 operating cash flow, or OCF?

Chapter 2

INTERMEDIATE (Questions 11–24)

11.

Financial Statements and Cash Flow

37

Cash Flows Ritter Corporation’s accountants prepared the following financial statements for year-end 2010: a. Explain the change in cash during 2010. b. Determine the change in net working capital in 2010. c. Determine the cash flow generated by the firm’s assets during 2010.

RITTER CORPORATION Income Statement 2010 Revenue Expenses Depreciation Net income Dividends

$600 405 90 $105 $ 45

RITTER CORPORATION Balance Sheets December 31 2009

Assets Cash Other current assets Net fixed assets Total assets

$ 50 155 340 $ 545

$ 35 140 290 $465

Liabilities and Equity Accounts payable Long-term debt Stockholders’ equity Total liabilities and equity

$ 85 135 325 $545

$ 95 105 265 $465

Financial Cash Flows information:

The Stancil Corporation provided the following current

Proceeds from long-term borrowing Proceeds from the sale of common stock Purchases of fixed assets Purchases of inventories Payment of dividends

$19,000 3,000 15,000 1,500 19,500

Determine the cash flows from the firm and the cash flows to investors of the firm.

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12.

2010

38

Part I

13.

14.

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15.

16.

17.

18.

19.

20.

21.

Overview

Building an Income Statement During the year, the Senbet Discount Tire Company had gross sales of $1.2 million. The firm’s cost of goods sold and selling expenses were $450,000 and $225,000, respectively. Senbet also had notes payable of $900,000. These notes carried an interest rate of 9 percent. Depreciation was $110,000. Senbet’s tax rate was 35 percent. a. What was Senbet’s net income? b. Whatw asS enbet’so peratingc ashf low? Calculating Total Cash Flows Schwert Corp. shows the following information on its 2010 income statement: sales = $167,000; costs = $91,000; other expenses = $5,400; depreciation expense = $8,000; interest expense = $11,000; taxes = $18,060; dividends = $9,500. In addition, you’re told that the firm issued $7,250 in new equity during 2010 and redeemed $7,100 in outstanding long-term debt. a. What is the 2010 operating cash flow? b. What is the 2010 cash flow to creditors? c. What is the 2010 cash flow to stockholders? d. If net fixed assets increased by $22,400 during the year, what was the addition to netw orkingc apital( NWC)? Using Income Statements Given the following information for O’Hara Marine Co., calculate the depreciation expense: sales = $43,000; costs = $27,500; addition to retained earnings = $5,300; dividends paid = $1,530; interest expense = $1,900; tax rate = 35 percent. Preparing a Balance Sheet Prepare a 2010 balance sheet for Jarrow Corp. based on the following information: cash = $183,000; patents and copyrights = $695,000; accounts payable = $465,000; accounts receivable = $138,000; tangible net fixed assets = $3,200,000; inventory = $297,000; notes payable = $145,000; accumulated retained earnings = $1,960,000; long-term debt =$1,550,000. Residual Claims Huang, Inc., is obligated to pay its creditors $9,700 very soon. a. What is the market value of the shareholders’ equity if assets have a market value of $10,500? b. Whatif as setse qual$6,800? Marginal versus Average Tax Rates (Refer to Table 2.3.) Corporation Growth has $78,000 in taxable income, and Corporation Income has $7,800,000 in taxable income. a. What is the tax bill for each firm? b. Suppose both firms have identified a new project that will increase taxable income by $10,000. How much in additional taxes will each firm pay? Why is this amount thes ame? Net Income and OCF During 2010, Raines Umbrella Corp. had sales of $740,000. Cost of goods sold, administrative and selling expenses, and depreciation expenses were $610,000, $105,000, and $140,000, respectively. In addition, the company had an interest expense of $70,000 and a tax rate of 35 percent. (Ignore any tax loss carryback or carryforward provisions.) a. What is Raines’s net income for 2010? b. What is its operating cash flow? c. Explain your results in (a) and (b). Accounting Values versus Cash Flows In Problem 19, suppose Raines Umbrella Corp. paid out $30,000 in cash dividends. Is this possible? If spending on net fixed assets and net working capital was zero, and if no new stock was issued during the year, what was the change in the firm’s long-term debt account? Calculating Cash Flows Cusic Industries had the following operating results for 2010: sales = $15,300; cost of goods sold = $10,900; depreciation expense = $2,100; interest expense = $520; dividends paid = $500. At the beginning of the year, net

Chapter 2

22.

Financial Statements and Cash Flow

39

fixed assets were $11,800, current assets were $3,400, and current liabilities were $1,900. At the end of the year, net fixed assets were $12,900, current assets were $3,950, and current liabilities were $1,950. The tax rate for 2010 was 40 percent. a. What is net income for 2010? b. What is the operating cash flow for 2010? c. What is the cash flow from assets for 2010? Is this possible? Explain. d. If no new debt was issued during the year, what is the cash flow to creditors? What is the cash flow to stockholders? Explain and interpret the positive and negative signs of your answers in (a) through (d). Calculating Cash Flows Consider the following abbreviated financial statements for WestonE nterprises:

WESTON ENTERPRISES 2010 Income Statement

WESTON ENTERPRISES 2009 and 2010 Partial Balance Sheets Assets Current assets Net fixed assets

Liabilities and Owners’ Equity

2009

2010

$ 780 3,480

$ 846 4,080

Current liabilities Long-term debt

2009

2010

$ 318 1,800

$ 348 2,064

SSales Costs C Depreciation D IInterest paid

$10,320 4,980 960 259

Sales Depreciation Cost of goods sold Other expenses Interest Cash Accounts receivable Short-term notes payable Long-term debt Net fixed assets Accounts payable Inventory Dividends

2009

2010

$ 5,223 750 1,797 426 350 2,739 3,626 529 9,173 22,970 2,877 6,447 637

$ 5,606 751 2,040 356 402 2,802 4,085 497 10,702 23,518 2,790 6,625 701

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a. What is owners’ equity for 2009 and 2010? b. What is the change in net working capital for 2010? c. In 2010, Weston Enterprises purchased $1,800 in new fixed assets. How much in fixed assets did Weston Enterprises sell? What is the cash flow from assets for the year? (The tax rate is 35 percent.) d. During 2010, Weston Enterprises raised $360 in new long-term debt. How much long-term debt must Weston Enterprises have paid off during the year? What is the cash flow to creditors? Use the following information for Ingersoll, Inc., for Problems 23 and 24 (assume the tax rate is 34 percent):

40

Part I

23. 24. CHALLENGE (Questions 25–27)

25.

Overview

Financial Statements Draw up an income statement and balance sheet for this company for 2009 and 2010. Calculating Cash Flow For 2010, calculate the cash flow from assets, cash flow to creditors,an dc ashf lowt os tockholders. Cash Flows You are researching Time Manufacturing and have found the following accounting statement of cash flows for the most recent year. You also know that the company paid $82 million in current taxes and had an interest expense of $43 million. Use the accounting statement of cash flows to construct the financial statement of cash flows.

TIME MANUFACTURING Statement of Cash Flows ($ in millions)

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Operations Net income Depreciation Deferred taxes Changes in assets and liabilities Accounts receivable Inventories Accounts payable Accrued expenses Other Total cash flow from operations

26.

$144 78 16 −15 18 14 −7 2 $250

Investing activities Acquisition of fixed assets Sale of fixed assets Total cash flow from investing activities

−$148 19 −$129

Financing activities Retirement of long-term debt Proceeds from long-term debt sales Change in notes payable Dividends Repurchase of stock Proceeds from new stock issue Total cash flow from financing activities Change in cash (on balance sheet)

−$135 97 5 −72 −11 37 −$ 79 $ 42

Net Fixed Assets and Depreciation On the balance sheet, the net fixed assets (NFA) account is equal to the gross fixed assets (FA) account, which records the acquisition cost of fixed assets, minus the accumulated depreciation (AD) account, which records the total depreciation taken by the firm against its fixed assets. Using the fact that NFA = FA − AD, show that the expression given in the chapter for net capital spending, NFAend − NFAbeg + D (where D is the depreciation expense during the year), is equivalent to FAend − FAbeg.

Chapter 2

27.

Mini Case

41

Tax Rates Refer to the corporate marginal tax rate information in Table 2.3. a. Why do you think the marginal tax rate jumps up from 34 percent to 39 percent at a taxable income of $100,001, and then falls back to a 34 percent marginal rate at a taxable income of $335,001? b. Compute the average tax rate for a corporation with exactly $335,001 in taxable income. Does this confirm your explanation in part (a)? What is the average tax rate for a corporation with exactly $18,333,334? Is the same thing happening here? c. The 39 percent and 38 percent tax rates both represent what is called a tax “bubble.” Suppose the government wanted to lower the upper threshold of the 39 percent marginal tax bracket from $335,000 to $200,000. What would the new 39p ercentb ubbler ateh avet ob e?

www.mhhe.com/edumarketinsight 1. Marginal and Average Tax Rates Download the annual income statements for Sharper Image (SHRP). Looking back at Table 2.3, what is the marginal income tax rate for Sharper Image? Using the total income tax and the pretax income numbers, calculate the average tax rate for Sharper Image. Is this number greater than 35 percent? Why or why not? 2. Net Working Capital Find the annual balance sheets for American Electric Power (AEP) and HJ Heinz (HNZ). Calculate the net working capital for each company. Is American Electric Power’s net working capital negative? If so, does this indicate potential financial difficulty for the company? What about Heinz? 3. Per Share Earnings and Dividends Find the annual income statements for HarleyDavidson (HOG), Hawaiian Electric Industries (HE), and Time Warner (TWX). What are the earnings per share (EPS Basic from operations) for each of these companies? What are the dividends per share for each company? Why do these companies pay out a different portion of income in the form of dividends? 4. Cash Flow Identity Download the annual balance sheets and income statements for Landrys Restaurants (LNY). Using the most recent year, calculate the cash flow identity for Landrys Restaurants. Explain your answer.

CASH FLOWS AT WARF COMPUTERS, INC. Warf Computers, Inc., was founded 15 years ago by Nick Warf, a computer programmer. The small initial investment to start the company was made by Nick and his friends. Over the years, this same group has supplied the limited additional investment needed by the company in the form of both equity and short- and long-term debt. Recently the company has developed a virtual keyboard (VK). The VK uses sophisticated artificial intelligence algorithms that allow the user to speak naturally and have the computer input the text, correct spelling and grammatical errors, and format the document according to preset user guidelines. The VK even suggests alternative phrasing and sentence structure, and it provides detailed stylistic diagnostics. Based on a proprietary, very advanced software/hardware hybrid technology, the system is a full generation beyond what is currently on the market. To introduce the VK, the company will require significant outside investment. Nick has made the decision to seek this outside financing in the form of new equity investments and bank loans. Naturally, new investors and the banks will require a detailed financial analysis. Your employer, Angus Jones & Partners, LLC, has asked you to examine

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S&P Problems

Financial Statements and Cash Flow

42

Part I

Overview

the financial statements provided by Nick. Here are the balance sheet for the two most recent years and the most recent income statement: WARF COMPUTERS Balance Sheet ($ in thousands) 2010

2009 $ 251

Accounts receivable

459

428

Notes payable

Inventories

411

425

59

50

$ 1,219

$1,154

Total current assets

$

Accounts payable

290

Other

Less accumulated depreciation Net property, plant, and equipment Intangible assets and others Total fixed assets

$ 245

71

66

Accrued expenses

158

257

Total current liabilities

$ 491

$ 568

$ 2,631

$2,038

$ 212

$ 103

Deferred taxes Long-term debt

859

700

$ 1,772

$1,338

508

454

$ 2,280

$1,792

Total long-term liabilities

Preferred stock Common stock Capital surplus

Less treasury stock Total equity $ 3,499

$2,946

756

736

$ 968

$ 839

$

$

Stockholders’ equity

Accumulated retained earnings

Total assets

$ 262

Long-term liabilities

Fixed assets Property, plant, and equipment

2009

Current liabilities

Current assets Cash and equivalents

2010

Total liabilities and shareholders’ equity

13 81

13 80

509

499

1,558

1,028

121

81

$2,040

$1,539

$3,499

$2,946

Nick has also provided the following information: During the year the company raised $118,000 in new long-term debt and retired $98,000 in long-term debt. The company also sold $11,000 in new stock and repurchased $40,000 in stock. The company purchased $786,000 in fixed assets and sold $139,000 in fixed assets.

Chapter 2

Financial Statements and Cash Flow

43

WARF COMPUTERS Income Statement ($ in thousands) Sales

$4,844

Cost of goods sold

2,858

Selling, general, and administrative expense

543

Depreciation

159

Operating income Other income

$1,284 48

Earnings before interest and taxes (EBIT) Interest expense Pretax income

$1,332 95 $1,237

Taxes

495

Current: $386 Deferred:

109

Net income

$ 742

Addition to retained earnings

$ 530

Dividends

$ 212

Angus has asked ked you to prepare the financial statement of cash flows and the accounting statement of cash flows. He has also asked you to answer the following questions: 1. How would you describe Warf Computers’ cash flows? 2. Which cash flow statement more accurately describes the cash flows at the company? 3. In light of your previous answers, comment on Nick’s expansion plans.

CHAPTER 3

FinancialSt atementsA nalysis and Financial Models The price of a share of common stock in Aeropostale, the trendy clothing retailer, closed at about $28 on April 2, 2009. At that price, Aeropostale had a price–earnings (PE) ratio of 12.7. That is, investors were willing to pay $12.7 for every dollar in income earned by Aeropostale. At the same time, investors were willing to pay $6.0, $18.2, and $27.2 for each dollar earned by Chevron, Coca-Cola, and Google, respectively. At the other extreme was the lumber company, Weyerhauser, which had negative earnings for the previous year, yet the stock was priced at about $30 per share. Because it had negative earnings, the PE ratio would have been negative, so it was not reported. At the same time, the typical stock in the S&P 500 Index of large company stocks was trading at a PE of about 12.4, or about 12.4 times earnings, as they say on Wall Street. Price-to-earnings comparisons are examples of the use of financial ratios. As we will see in this chapter, there are a wide variety of financial ratios, all designed to summarize specific aspects of a firm’s financial position. In addition to discussing how to analyze financial statements and compute financial ratios, we will have quite a bit to say about who uses this information and why.

3.1 Financial Statements Analysis In Chapter 2, we discussed some of the essential concepts of financial statements and cash flows. This chapter continues where our earlier discussion left off. Our goal here is to expand your understanding of the uses (and abuses) of financial statement information. A good working knowledge of financial statements is desirable simply because such statements, and numbers derived from those statements, are the primary means of communicating financial information both within the firm and outside the firm. In short, much of the language of business finance is rooted in the ideas we discuss in this chapter. Clearly, one important goal of the accountant is to report financial information to the user in a form useful for decision making. Ironically, the information frequently does not come to the user in such a form. In other words, financial statements don’t come with a user’s guide. This chapter is a first step in filling this gap.

StandardizingSta tements One obvious thing we might want to do with a company’s financial statements is to compare them to those of other, similar companies. We would immediately have a problem, however. It’s almost impossible to directly compare the financial statements for two companies because of differences in size. 44

Chapter 3

Financial Statements Analysis and Financial Models

45

For example, Ford and GM are obviously serious rivals in the auto market, but GM is larger, so it is difficult to compare them directly. For that matter, it’s difficult even to compare financial statements from different points in time for the same company if the company’s size has changed. The size problem is compounded if we try to compare GM and, say, Toyota. If Toyota’s financial statements are denominated in yen, then we have size and currency differences. To start making comparisons, one obvious thing we might try to do is to somehow standardize the financial statements. One common and useful way of doing this is to work with percentages instead of total dollars. The resulting financial statements are called common-size statements. We consider these next.

Common-SizeB alanceShe ets For easy reference, Prufrock Corporation’s 2009 and 2010 balance sheets are provided in Table 3.1. Using these, we construct common-size balance sheets by expressing each item as a percentage of total assets. Prufrock’s 2009 and 2010 common-size balance sheets are shown in Table 3.2. Notice that some of the totals don’t check exactly because of rounding errors. Also notice that the total change has to be zero because the beginning and ending numbers must add up to 100 percent. In this form, financial statements are relatively easy to read and compare. For example, just looking at the two balance sheets for Prufrock, we see that current assets were 19.7 percent of total assets in 2010, up from 19.1 percent in 2009. Current liabilities

Table 3.1

PRUFROCK CORPORATION Balance Sheets as of December 31, 2009 and 2010 ($ in millions) Assets Current assets Cash Accounts receivable Inventory Total Fixed assets Net plant and equipment Total assets Liabilities and Owners’ Equity Current liabilities Accounts payable Notes payable Total Long-term debt Owners’ equity Common stock and paid-in surplus Retained earnings Total Total liabilities and owners’ equity

2009

2010

$

84 165 393 $ 642

$

$2,731 $3,373

$2,880 $3,588

$ 312 231 $ 543 $ 531

$ 344 196 $ 540 $ 457

$ 500 1,799 $2,299 $3,373

$ 550 2,041 $2,591 $3,588

98 188 422 $ 708

46

Table 3.2

Part I

Overview

PRUFROCK CORPORATION Common-Size Balance Sheets December 31, 2009 and 2010 Assets Current assets Cash Accounts receivable Inventory Total Fixed assets Net plant and equipment Total assets Liabilities and Owners’ Equity Current liabilities Accounts payable Notes payable Total Long-term debt Owners’ equity Common stock and paid-in surplus Retained earnings Total Total liabilities and owners’ equity

2009

2010

2.5% 4.9 11.7 19.1

2.7% 5.2 11.8 19.7

80.9 100.0%

80.3 100.0%

− .6 .0%

9.2% 6.8 16.0 15.7

9.6% 5.5 15.1 12.7

+ .4% −1.3 − .9 −3.0

14.8 53.3 68.1 100.0%

15.3 56.9 72.2 100.0%

+ .5 +3.6 +4.1 .0%

Change + + + +

.2% .3 .1 .6

declined from 16.0 percent to 15.1 percent of total liabilities and equity over that same time. Similarly, total equity rose from 68.1 percent of total liabilities and equity to 72.2 percent. Overall, Prufrock’s liquidity, as measured by current assets compared to current liabilities, increased over the year. Simultaneously, Prufrock’s indebtedness diminished as a percentage of total assets. We might be tempted to conclude that the balance sheet has grown “stronger.”

Common-SizeI ncomeSta tements Table 3.3 describes some commonly used measures of earnings. A useful way of standardizing the income statement shown in Table 3.4 is to express each item as a percentage of total sales, as illustrated for Prufrock in Table 3.5. This income statement tells us what happens to each dollar in sales. For Prufrock, interest expense eats up $.061 out of every sales dollar, and taxes take another $.081. When all is said and done, $.157 of each dollar flows through to the bottom line (net income), and that amount is split into $.105 retained in the business and $.052 paid out in dividends. These percentages are useful in comparisons. For example, a relevant figure is the cost percentage. For Prufrock, $.582 of each $1.00 in sales goes to pay for goods sold. It would be interesting to compute the same percentage for Prufrock’s main competitors to see how Prufrock stacks up in terms of cost control.

Chapter 3

Table 3.3 Measures of Earnings

Table 3.4

Financial Statements Analysis and Financial Models

47

Investors and analysts look closely at the income statement for clues on how well a company has performed during a particular year. Here are some commonly used measures of earnings (numbers in millions). Net Income The so-called bottom line, defined as total revenue minus total expenses. Net income for Prufrock in the latest period is $363 million. Net income reflects differences in a firm’s capital structure and taxes as well as operating income. Interest expense and taxes are subtracted from operating income in computing net income. Shareholders look closely at net income because dividend payout and retained earnings are closely linked to net income. EPS Net income divided by the number of shares outstanding. It expresses net income on a per share basis. For Prufrock, the EPS = (Net income)/(Shares outstanding) = $363/33 = $11. EBIT Earnings before interest expense and taxes. EBIT is usually called “income from operations” on the income statement and is income before unusual items, discontinued operating or extraordinary items. To calculate EBIT, operating expenses are subtracted from total operations revenues. Analysts like EBIT because it abstracts from differences in earnings from a firm’s capital structure (interest expense) and taxes. For Prufrock, EBIT is $691 million. EBITDA Earnings before interest expense, taxes, depreciation, and amortization. EBITDA = EBIT + depreciation and amortization. Here amortization refers to a noncash expense similar to depreciation except it applies to an intangible asset (such as a patent), rather than a tangible asset (such as a machine). The word amortization here does not refer to the payment of debt. There is no amortization in Prufrock’s income statement. For Prufrock, EBITDA = $691 + $276 = $967 million. Analysts like to use EBITDA because it adds back two noncash items (depreciation and amortization) to EBIT and thus is a better measure of before-tax operating cash flow. Sometimes these measures of earnings are preceded by the letters LTM, meaning the last twelve months. For example, LTM EPS is the last twelve months of EPS and LTM EBITDA is the last twelve months of EBITDA. At other times, the letters TTM are used, meaning trailing twelve months. Needless to say, LTM is the same as TTM.

PRUFROCK CORPORATION 2010 Income Statement ($ in millions) Sales Cost of goods sold Depreciation Earnings before interest and taxes Interest paid Taxable income Taxes (34%) Net income Dividends Addition to retained earnings

$2,311 1,344 276 $ 691 141 $ 550 187 $ 363 $ 121 242

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Part I

Table 3.5

Overview

PRUFROCK CORPORATION Common-Size Income Statement 2010 Sales Cost of goods sold Depreciation Earnings before interest and taxes Interest paid Taxable income Taxes (34%) Net income Dividends Addition to retained earnings

100.0% 58.2 11.9 29.9 6.1 23.8 8.1 15.7% 5.2% 10.5

3.2 Ratio Analysis Another way of avoiding the problems involved in comparing companies of different sizes is to calculate and compare financial ratios. Such ratios are ways of comparing and investigating the relationships between different pieces of financial information. We cover some of the more common ratios next (there are many others we don’t discuss here). One problem with ratios is that different people and different sources frequently don’t compute them in exactly the same way, and this leads to much confusion. The specific definitions we use here may or may not be the same as ones you have seen or will see elsewhere. If you are using ratios as tools for analysis, you should be careful to document how you calculate each one; and, if you are comparing your numbers to those of another source, be sure you know how their numbers are computed. We will defer much of our discussion of how ratios are used and some problems that come up with using them until later in the chapter. For now, for each ratio we discuss, several questions come to mind: Go to www.reuters.com/ finance/stocks and find the ratios link to examine comparative ratios for a huge number of companies.

1. Howisitc omputed? 2. What is it intended to measure, and why might we be interested? 3. What is the unit of measurement? 4. What might a high or low value be telling us? How might such values be misleading? 5. How could this measure be improved? Financial ratios are traditionally grouped into the following categories: 1. 2. 3. 4. 5.

Short-term solvency, or liquidity, ratios. Long-term solvency, or financial leverage, ratios. Asset management, or turnover, ratios. Profitabilityr atios. Marketv aluer atios.

We will consider each of these in turn. In calculating these numbers for Prufrock, we will use the ending balance sheet (2010) figures unless we explicitly say otherwise.

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49

Short-Term Solvency or Liquidity Measures As the name suggests, short-term solvency ratios as a group are intended to provide information about a firm’s liquidity, and these ratios are sometimes called liquidity measures. The primary concern is the firm’s ability to pay its bills over the short run without undue stress. Consequently, these ratios focus on current assets and current liabilities. For obvious reasons, liquidity ratios are particularly interesting to short-term creditors. Because financial managers are constantly working with banks and other shortterm lenders, an understanding of these ratios is essential. One advantage of looking at current assets and liabilities is that their book values and market values are likely to be similar. Often (though not always), these assets and liabilities just don’t live long enough for the two to get seriously out of step. On the other hand, like any type of near-cash, current assets and liabilities can and do change fairly rapidly, so today’s amounts may not be a reliable guide to the future. Current Ratio One of the best-known and most widely used ratios is the current ratio. As you might guess, the current ratio is defined as: Current assets Currentr atio = _______________ Current liabilities

(3.1)

For Prufrock, the 2010 current ratio is: $708 Currentr atio = _____ =1.31time s $540 Because current assets and liabilities are, in principle, converted to cash over the following 12 months, the current ratio is a measure of short-term liquidity. The unit of measurement is either dollars or times. So, we could say Prufrock has $1.31 in current assets for every $1 in current liabilities, or we could say Prufrock has its current liabilities covered 1.31 times over. To a creditor, particularly a short-term creditor such as a supplier, the higher the current ratio, the better. To the firm, a high current ratio indicates liquidity, but it also may indicate an inefficient use of cash and other short-term assets. Absent some extraordinary circumstances, we would expect to see a current ratio of at least 1; a current ratio of less than 1 would mean that net working capital (current assets less current liabilities) is negative. This would be unusual in a healthy firm, at least for most types of businesses. The current ratio, like any ratio, is affected by various types of transactions. For example, suppose the firm borrows over the long term to raise money. The short-run effect would be an increase in cash from the issue proceeds and an increase in longterm debt. Current liabilities would not be affected, so the current ratio would rise.

EXAMPLE 3.1

Current Events Suppose a firm were to pay off some of its suppliers and short-term creditors. What would happen to the current ratio? Suppose a firm buys some inventory. What happens in this case? What happens if a firm sells some merchandise? The first case is a trick question. What happens is that the current ratio moves away from 1. If it is greater than 1 (the usual case), it will get bigger, but if it is less than 1, it will get smaller. To see this, suppose the firm has $4 in current assets and $2 in current liabilities for a current ratio of 2. If we use $1 in cash to reduce current liabilities, the new current ratio is ($4 − 1)/($2 − 1) = 3. (continued)

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If we reverse the original situation to $2 in current assets and $4 in current liabilities, the change will cause the current ratio to fall to 1/3 from 1/2. The second case is not quite as tricky. Nothing happens to the current ratio because cash goes down while inventory goes up—total current assets are unaffected. In the third case, the current ratio would usually rise because inventory is normally shown at cost and the sale would normally be at something greater than cost (the difference is the markup). The increase in either cash or receivables is therefore greater than the decrease in inventory. This increases current assets, and the current ratio rises.

Finally, note that an apparently low current ratio may not be a bad sign for a company with a large reserve of untapped borrowing power. Quick (or Acid-Test) Ratio Inventory is often the least liquid current asset. It’s also the one for which the book values are least reliable as measures of market value because the quality of the inventory isn’t considered. Some of the inventory may later turn out to be damaged, obsolete, or lost. More to the point, relatively large inventories are often a sign of short-term trouble. The firm may have overestimated sales and overbought or overproduced as a result. In this case, the firm may have a substantial portion of its liquidity tied up in slowmoving inventory. To further evaluate liquidity, the quick, or acid-test, ratio is computed just like the current ratio, except inventory is omitted: Current assets – Inventory Quickr atio = _______________________ Current liabilities

(3.2)

Notice that using cash to buy inventory does not affect the current ratio, but it reduces the quick ratio. Again, the idea is that inventory is relatively illiquid compared to cash. For Prufrock, this ratio in 2010 was: $708 − 422 Quickr atio = __________ =.53time s $540 The quick ratio here tells a somewhat different story than the current ratio because inventory accounts for more than half of Prufrock’s current assets. To exaggerate the point, if this inventory consisted of, say, unsold nuclear power plants, then this would be a cause for concern. To give an example of current versus quick ratios, based on recent financial statements, Wal-Mart and Manpower, Inc., had current ratios of .89 and 1.45, respectively. However, Manpower carries no inventory to speak of, whereas Wal-Mart’s current assets are virtually all inventory. As a result, Wal-Mart’s quick ratio was only .13, and Manpower’s was 1.37, almost the same as its current ratio. CashRatio

A very short-term creditor might be interested in the cash ratio: Cash Cashr atio = _______________ Current liabilities

You can verify that this works out to be .18 times for Prufrock.

(3.3)

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51

Long-TermSo lvencyMe asures Long-term solvency ratios are intended to address the firm’s long-run ability to meet its obligations or, more generally, its financial leverage. These ratios are sometimes called financial leverage ratios or just leverage ratios. We consider three commonly used measures and some variations. Total Debt Ratio The total debt ratio takes into account all debts of all maturities to all creditors. It can be defined in several ways, the easiest of which is this: Total assets – Total equity Totald ebtr atio = _______________________ Total assets $3,588 − 2,591 _____________ =.28time s = $3,588

The online Women’s Business Center has more information about financial statements, ratios, and small business topics at www.sba.gov.

(3.4)

In this case, an analyst might say that Prufrock uses 28 percent debt.1 Whether this is high or low or whether it even makes any difference depends on whether capital structure matters, a subject we discuss in a later chapter. Prufrock has $.28 in debt for every $1 in assets. Therefore, there is $.72 in equity (=$1 – .28) for every $.28 in debt. With this in mind, we can define two useful variations on the total debt ratio, the debt–equity ratio and the equitym ultiplier : Debt–equityr atio = Total debt/Total equity = $.28/$.72 =.39time s

(3.5)

Equitym ultiplier = Total assets/Total equity = $1/$.72 =1.39time s

(3.6)

The fact that the equity multiplier is 1 plus the debt–equity ratio is not a coincidence: Equitym ultiplier = Total assets/Total equity = $1/$.72 = 1.39 times = (Total equity + Total debt)/Total equity = 1 + Debt–equity ratio =1.39time s The thing to notice here is that given any one of these three ratios, you can immediately calculate the other two, so they all say exactly the same thing. Times Interest Earned Another common measure of long-term solvency is the times interest earned (TIE) ratio. Once again, there are several possible (and common) definitions, but we’ll stick with the most traditional: EBIT Timesin tereste arnedr atio = _______ Interest $691 = _____ =4.9time s $141

(3.7)

As the name suggests, this ratio measures how well a company has its interest obligations covered, and it is often called the interest coverage ratio. For Prufrock, the interest bill is covered 4.9 times over. Cash Coverage A problem with the TIE ratio is that it is based on EBIT, which is not really a measure of cash available to pay interest. The reason is that depreciation

1

Total equity here includes preferred stock, if there is any. An equivalent numerator in this ratio would be (Current liabilities + Long-term debt).

52

Part I

Overview

and amortization, noncash expenses, have been deducted out. Because interest is most definitely a cash outflow (to creditors), one way to define the cash coverage ratiois : EBIT + (Depreciation and amortization) Cashc overager atio = ____________________________________ Interest =

$691 + 276 __________ $141

=

$967 _____ $141

(3.8)

=6.9time s

The numerator here, EBIT plus depreciation and amortization, is often abbreviated EBITDA (earnings before interest, taxes, depreciation, and amortization). It is a basic measure of the firm’s ability to generate cash from operations, and it is frequently used as a measure of cash flow available to meet financial obligations. More recently another long-term solvency measure is increasingly seen in financial statement analysis and in debt covenants. It uses EBITDA and interest bearing debt. Specifically, for Prufrock: Interest bearing debt __________________ EBITDA

$196 million + 457 million = _______________________ =.68time s $967 million

Here we include notes payable (most likely notes payable is bank debt) and long-term debt in the numerator and EBITDA in the denominator. Values below 1 on this ratio are considered very strong and values below 5 are considered weak. However a careful comparison with other comparable firms is necessary to properly interpret the ratio.

Asset Management or Turnover Measures We next turn our attention to the efficiency with which Prufrock uses its assets. The measures in this section are sometimes called asset management or utilization ratios. The specific ratios we discuss can all be interpreted as measures of turnover. What they are intended to describe is how efficiently, or intensively, a firm uses its assets to generate sales. We first look at two important current assets: inventory and receivables. Inventory Turnover and Days’ Sales in Inventory During the year, Prufrock had a cost of goods sold of $1,344. Inventory at the end of the year was $422. With these numbers, inventory turnover can be calculated as: Cost of goods sold Inventorytu rnover = _________________ Inventory $1,344 = ______ =3.2time s $422

(3.9)

In a sense, we sold off, or turned over, the entire inventory 3.2 times during the year. As long as we are not running out of stock and thereby forgoing sales, the higher this ratio is, the more efficiently we are managing inventory. If we know that we turned our inventory over 3.2 times during the year, we can immediately figure out how long it took us to turn it over on average. The result is the average days’ sales in inventory: 365 days Days’sale sin in ventory = _________________ Inventory turnover 365 = ____ =114d ays 3.2

(3.10)

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53

This tells us that, roughly speaking, inventory sits 114 days on average before it is sold. Alternatively, assuming we used the most recent inventory and cost figures, it will take about 114 days to work off our current inventory. For example, in September 2007, sales of General Motors (GM) pickup trucks could have used a pickup. At that time, the company had a 120-day supply of the GMC Sierra and a 114-day supply of the Chevrolet Silverado. These numbers mean that at the then-current rate of sales, it would take GM 120 days to deplete the available supply of Sierras whereas a 60-day supply is considered normal in the industry. Of course, the days in inventory are lower for better-selling models, and, fortunately for GM, its crossover vehicles were a hit. The company had only a 22-day supply of Buick Enclaves and a 32-day supply of GMC Acadias. Receivables Turnover and Days’ Sales in Receivables Our inventory measures give some indication of how fast we can sell products. We now look at how fast we collect on those sales. The receivables turnover is defined in the same way as inventory turnover: Sales Receivablest urnover = _________________ Accounts receivable $2,311 = ______ =12.3time s $188

(3.11)

Loosely speaking, we collected our outstanding credit accounts and lent the money again 12.3 times during the year.2 This ratio makes more sense if we convert it to days, so the days’ sales in receivables is: 365 days Days’sale sin r eceivables = __________________ Receivables turnover 365 ____ = =30d ays 12.3

(3.12)

Therefore, on average, we collect on our credit sales in 30 days. For obvious reasons, this ratio is frequently called the average collection period (ACP). Also note that if we are using the most recent figures, we can also say that we have 30 days’ worth of sales currentlyu ncollected.

EXAMPLE 3.2

Payables Turnover Here is a variation on the receivables collection period. How long, on average, does it take for Prufrock Corporation to pay its bills? To answer, we need to calculate the accounts payable turnover rate using cost of goods sold. We will assume that Prufrock purchases everything on credit. The cost of goods sold is $1,344, and accounts payable are $344. The turnover is therefore $1,344/$344 = 3.9 times. So, payables turned over about every 365/3.9 = 94 days. On average, then, Prufrock takes 94 days to pay. As a potential creditor, we might take note of this fact.

2

Here we have implicitly assumed that all sales are credit sales. If they were not, we would simply use total credit sales in these calculations, not total sales.

54

Part I

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TotalA ssetT urnover Moving away from specific accounts like inventory or receivables, we can consider an important “big picture” ratio, the total asset turnover ratio. As the name suggests, total asset turnover is: Sales Totalasse ttu rnover = __________ Total assets $2,311 = ______ =.64time s $3,588

(3.13)

In other words, for every dollar in assets, we generated $.64 in sales.

EXAMPLE 3.3

More Turnover Suppose you find that a particular company generates $.40 in annual sales for every dollar in total assets. How often does this company turn over its total assets? The total asset turnover here is .40 times per year. It takes 1/.40 = 2.5 years to turn assets over completely.

ProfitabilityMe asures The three types of measures we discuss in this section are probably the best-known and most widely used of all financial ratios. In one form or another, they are intended to measure how efficiently the firm uses its assets and how efficiently the firm manages its operations. ProfitM argin

Companies pay a great deal of attention to their profit margin: Net income Profitmar gin = __________ Sales $363 = ______ =15.7% $2,311

(3.14)

This tells us that Prufrock, in an accounting sense, generates a little less than 16 cents in net income for every dollar in sales. EBITDA Margin Another commonly used measure of profitability is the EBITDA margin. As mentioned, EBITDA is a measure of before-tax operating cash flow. It adds back noncash expenses and does not include taxes or interest expense. As a consequence, EBITDA margin looks more directly at operating cash flows than does net income and does not include the effect of capital structure or taxes. For Prufrock, EBITDA margin is: EBITDA ________ Sales

$967 million = _____________ =41.8% $2,311 million

All other things being equal, a relatively high margin is obviously desirable. This situation corresponds to low expense ratios relative to sales. However, we hasten to add that other things are often not equal. For example, lowering our sales price will usually increase unit volume but will normally cause margins to shrink. Total profit (or, more importantly, operating cash flow) may go up or down, so the fact that margins are smaller isn’t necessarily bad. After all, isn’t it possible that, as the saying goes, “Our prices are so low that we lose money on everything we sell, but we make it up in volume”?3 3

No,it’ sn ot.

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55

Margins are very different for different industries. Grocery stores have a notoriously low profit margin, generally around 2 percent. In contrast, the profit margin for the pharmaceutical industry is about 18 percent. So, for example, it is not surprising that recent profit margins for Albertson’s and Pfizer were about 1.2 percent and 15.6 percent, respectively. Return on Assets Return on assets (ROA) is a measure of profit per dollar of assets. It can be defined several ways,4 but the most common is: Net income Returno nasse ts = ___________ Total assets $363 = ______ =10.12% $3,588

(3.15)

Return on Equity Return on equity (ROE) is a measure of how the stockholders fared during the year. Because benefiting shareholders is our goal, ROE is, in an accounting sense, the true bottom-line measure of performance. ROE is usually measured as: Net income Returno ne quity = ___________ Total equity $363 = ______ =14% $2,591

(3.16)

Therefore, for every dollar in equity, Prufrock generated 14 cents in profit; but, again, this is correct only in accounting terms. Because ROA and ROE are such commonly cited numbers, we stress that it is important to remember they are accounting rates of return. For this reason, these measures should properly be called return on book assets and return on book equity. In addition, ROE is sometimes called return on net worth. Whatever it’s called, it would be inappropriate to compare the result to, for example, an interest rate observed in the financial markets. The fact that ROE exceeds ROA reflects Prufrock’s use of financial leverage. We will examine the relationship between these two measures in the next section.

MarketV alueMe asures Our final group of measures is based, in part, on information not necessarily contained in financial statements—the market price per share of the stock. Obviously, these measures can be calculated directly only for publicly traded companies. We assume that Prufrock has 33 million shares outstanding and the stock sold for $88 per share at the end of the year. If we recall that Prufrock’s net income was $363 million, then we can calculate that its earnings per share were: $363 Net income EPS = _________________ = _____ =$11 33 Shares outstanding

(3.17)

4

For example, we might want a return on assets measure that is neutral with respect to capital structure (interest expense) and taxes. Such a measure for Prufrock would be: EBIT __________ Total assets

$691 = ______ =19.3% $3,588

This measure has a very natural interpretation. If 19.3 percent exceeds Prufrock’s borrowing rate, Prufrock will earn more money on its investments than it will pay out to its creditors. The surplus will be available to Prufrock’s shareholders after adjusting for taxes.

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Price–Earnings Ratio The first of our market value measures, the price–earnings or PE ratio (or multiple), is defined as: Price per share PEr atio = ________________ Earnings per share $88 = ____ =8time s $11

(3.18)

In the vernacular, we would say that Prufrock shares sell for eight times earnings, or we might say that Prufrock shares have, or “carry,” a PE multiple of 8. Because the PE ratio measures how much investors are willing to pay per dollar of current earnings, higher PEs are often taken to mean that the firm has significant prospects for future growth. Of course, if a firm had no or almost no earnings, its PE would probably be quite large; so, as always, care is needed in interpreting this ratio. Market-to-Book Ratio A second commonly quoted measure is the market-to-book ratio: Market value per share Market-to-bookr atio = ____________________ Book value per share $88 $88 _________ = = _____ =1.12time s $2,591/33 $78.5

(3.19)

Notice that book value per share is total equity (not just common stock) divided by the number of shares outstanding. Book value per share is an accounting number that reflects historical costs. In a loose sense, the market-to-book ratio therefore compares the market value of the firm’s investments to their cost. A value less than 1 could mean that the firm has not been successful overall in creating value for its stockholders. Market Capitalization The market capitalization of a public firm is equal to the firm’s stock market price per share multiplied by the number of shares outstanding. For Prufrock, this is: Pricep ersh are × Shares outstanding = $88 × 33 million =$2,904millio n This is a useful number for potential buyers of Prufrock. A prospective buyer of all of the outstanding shares of Prufrock (in a merger or acquisition) would need to come up with at least $2,904 million plus a premium. Enterprise Value Enterprise value is a measure of firm value that is very closely related to market capitalization. Instead of focusing on only the market value of outstanding shares of stock, it measures the market value of outstanding shares of stock plus the market value of outstanding interest bearing debt less cash on hand. We know the market capitalization of Prufrock but we do not know the market value of its outstanding interest bearing debt. In this situation, the common practice is to use the book value of outstanding interest bearing debt less cash on hand as an approximation. For Prufrock, enterprise value is (in millions): EV = Market capitalization + Market value of interest bearing debt − cash = $2,904 + ($196 + 457) − $98 =$3,459millio n (3.20)

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57

The purpose of the EV measure is to better estimate how much it would take to buy all of the outstanding stock of a firm and also to pay off the debt. The adjustment for cash is to recognize that if we were a buyer the cash could be used immediately to buy back debt or pay a dividend. Enterprise Value Multiples Financial analysts use valuation multiples based upon a firm’s enterprise value when the goal is to estimate the value of the firm’s total business rather than just focusing on the value of its equity. To form an appropriate multiple, enterprise value is divided by EBITDA. For Prufrock, the enterprise value multiple is: EV ________ EBITDA

$3,459 million = _____________ =3.6time s $967 million

The multiple is especially useful because it allows comparison of one firm with another when there are differences in capital structure (interest expense), taxes, or capital spending. The multiple is not directly affected by these differences. Similar to PE ratios, we would expect a firm with high growth opportunities to have high EV multiples. This completes our definition of some common ratios. We could tell you about more of them, but these are enough for now. We’ll leave it here and go on to discuss some ways of using these ratios instead of just how to calculate them. Table 3.6 summarizes some of the ratios we’ve discussed.

Table 3.6

Common Financial Ratios

I. Short-Term Solvency, or Liquidity, Ratios Current assets Current ratio = _______________ Current liabilities

365 days Days’ sales in receivables = __________________ Receivables turnover

Current assets − Inventory Quick ratio = _______________________ Current liabilities

Sales Total asset turnover = __________ Total assets

Cash Cash ratio = _______________ Current liabilities

Total assets Capital intensity = __________ Sales

II. Long-Term Solvency, or Financial Leverage, Ratios

IV. Profitability Ratios

Total assets − Total equity Total debt ratio = ______________________ Total assets

Net income Profit margin = __________ Sales

Debt–equity ratio = Total debt/Total equity

Net income Return on assets (ROA) = __________ Total assets

Equity multiplier = Total assets/Total equity EBIT Times interest earned ratio = _______ Interest EBITDA Cash coverage ratio = _______ Interest

Net income Return on equity (ROE) = __________ Total equity Sales Assets Net income ______ × Assets × ______ ROE = __________ Equity Sales V. Market Value Ratios

III. Asset Utilization, or Turnover, Ratios Inventory turnover =

Cost of goods sold ________________ Inventory

365 days Days’ sales in inventory = ________________ Inventory turnover Sales _________________

Receivables turnover = Accounts receivable

Price per share Price –earnings ratio = ________________ Earnings per share Market value per share Market-to-book ratio = ___________________ Book value per share Enterprise value EV multiple = ______________ EBITDA

58

EXAMPLE 3.4

Part I

Overview

Consider the following 2008 data for Lowe’s Companies and Home Depot (billions except for price per share):

Lowe’s Companies, Inc.

The Home Depot, Inc.

$48.3 $ 4.8 $ 2.8 $ .5 $ 1.5 $ 6.7 $30.9 $24 1.5 $16.1

$77.3 $ 7.3 $ 4.4 $ .5 $ 1.9 $13.4 $44.3 $27 1.7 $17.7

Sales EBIT Net income Cash Depreciation Interest bearing debt Total assets Price per share Shares outstanding Shareholder equity

1. Determine the profit margin, ROE, market capitalization, enterprise value, PE multiple, and EV multiple for both Lowe’s and Home Depot.

Lowe’s Companies, Inc.

The Home Depot, Inc.

Equity multiplier

30.9/16.1 =

1.9

44.3/17.7 =

2.5

Asset turnover

48.3/30.9 =

1.6

77.3/44.3 =

1.7

Profit margin ROE Market capitalization Enterprise value PE multiple EBITDA EV multiple

2.8/48.3 =

5.8%

2.8/16.1 = 1.5 × 24

4.4/77.3

= 5.7%

17.4%

4.4/17.7

= 24.9%

= $36 billion

1.7 × 27

= $45.9 billion

(1.5 × 24) + 6.7 − .5 = $42.2 billion (1.7 × 27) + 13.4 − .5 = $58.8 billion 24/1.87 =

12.8

27/2.6

4.8 + 1.5 =

$6.3

7.3 + 1.9

42.2/6.3 =

6.7

=

10.4

= $9.2

58.8/9.2 =

6.4

2. How would you describe these two companies from a financial point of view? These are similarly situated companies. In 2008, Home Depot had a higher ROE (partially because of using more debt and higher turnover), but Lowe’s had slightly higher PE and EV multiples. Both companies’ multiples were somewhat below the general market, raising questions about future growth prospects.

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3.3 TheD u Pont Identity As we mentioned in discussing ROA and ROE, the difference between these two profitability measures reflects the use of debt financing or financial leverage. We illustrate the relationship between these measures in this section by investigating a famous way of decomposing ROE into its component parts.

A Closer Look at ROE To begin, let’s recall the definition of ROE: Net income Returno ne quity = ___________ Total equity If we were so inclined, we could multiply this ratio by Assets/Assets without changing anything: Net income Net income Assets Returno ne quity = ___________ = ___________ × ______ Total equity Total equity Assets Assets Net income = __________ × ___________ Assets Total equity Notice that we have expressed the ROE as the product of two other ratios—ROA and the equity multiplier: ROE = ROA × Equity multiplier = ROA × (1 +De bt–equityr atio) Looking back at Prufrock, for example, we see that the debt–equity ratio was .39 and ROA was 10.12 percent. Our work here implies that Prufrock’s ROE, as we previously calculated, is: ROE = 10.12% × 1.39 =14% The difference between ROE and ROA can be substantial, particularly for certain businesses. For example, based on recent financial statements, U.S. Bancorp has an ROA of only 1.11 percent, which is actually fairly typical for a bank. However, banks tend to borrow a lot of money, and, as a result, have relatively large equity multipliers. For U.S. Bancorp, ROE is about 11.2 percent, implying an equity multiplier of 10.1. We can further decompose ROE by multiplying the top and bottom by total sales: Sales Net income Assets ROE = _____ × __________ × ___________ Sales Assets Total equity If we rearrange things a bit, ROE is: Sales Assets Net income ROE = __________ × ______ × ___________ Sales Assets Total equity

(3.21)

Return on assets = Profit margin × Total asset turnover ×E quitym ultiplier What we have now done is to partition ROA into its two component parts, profit margin and total asset turnover. The last expression of the preceding equation is called the Du Pont identity after the Du Pont Corporation, which popularized its use.

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We can check this relationship for Prufrock by noting that the profit margin was 15.7 percent and the total asset turnover was .64. ROE should thus be: ROE = Profit margin × Total asset turnover × Equity multiplier = 15.7% × .64 × 1.39 = 14% This 14 percent ROE is exactly what we had before. The Du Pont identity tells us that ROE is affected by three things: 1. Operating efficiency (as measured by profit margin). 2. Asset use efficiency (as measured by total asset turnover). 3. Financial leverage (as measured by the equity multiplier). Weakness in either operating or asset use efficiency (or both) will show up in a diminished return on assets, which will translate into a lower ROE. Considering the Du Pont identity, it appears that the ROE could be leveraged up by increasing the amount of debt in the firm. However, notice that increasing debt also increases interest expense, which reduces profit margins, which acts to reduce ROE. So, ROE could go up or down, depending. More important, the use of debt financing has a number of other effects, and, as we discuss at some length in later chapters, the amount of leverage a firm uses is governed by its capital structure policy. The decomposition of ROE we’ve discussed in this section is a convenient way of systematically approaching financial statement analysis. If ROE is unsatisfactory by some measure, then the Du Pont identity tells you where to start looking for the reasons.5 Yahoo! and Google are among the most important Internet companies in the world. In spring 2008, Yahoo! was being urged by a group of dissident investors to sell the company or some portion to Microsoft in Microsoft’s bid to bolster its online services to better compete with Google. Yahoo! and Google may be good examples of how Du Pont analysis can be useful in helping to ask the right questions about a firm’s financial performance. The Du Pont breakdowns for Yahoo! and Google are summarized in Table 3.7.

Table 3.7

The Du Pont Breakdown for Yahoo! and Google

Yahoo! Twelve Months Ending

ROE

=

Profit Margin

×

Total Asset Turnover

×

Equity Multiplier

12/07 12/06 12/05

6.9% 8.1 10.0

= = =

9.5% 11.7 16.4

× × ×

.570 .558 .485

× × ×

1.28 1.24 1.26

Google Twelve Months Ending

ROE

=

Profit Margin

×

Total Asset Turnover

×

Equity Multiplier

12/07 12/06 12/05

18.6% 18.0 17.7

= = =

25.3% 29.1 23.9

× × ×

.655 .574 .598

× × ×

1.12 1.08 1.24

5

Perhaps this is a time to mention Abraham Briloff, a well-known financial commentator who famously remarked that “financial statements are like fine perfume; to be sniffed but not swallowed.”

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As can be seen, in 2007, Yahoo! had an ROE of 6.9 percent, down from its ROE in 2005 of 10.0 percent. In contrast, in 2007, Google had an ROE of 18.6 percent, up from its ROE in 2005 of 17.7 percent. Given this information, how is it possible that Google’s ROE could be so much higher than the ROE of Yahoo! during this period of time, and what accounts for the decline in Yahoo!’s ROE? On close inspection of the Du Pont breakdown, we see that Yahoo!’s profit margin declined dramatically during this period of time from 16.4 percent to 9.5 percent. Meanwhile Google’s profit margin was 25.3 percent in 2007, about the same as the 2 years before. Yet Yahoo! and Google have very comparable asset turnover and financial leverage. What can account for Google’s advantage over Yahoo! in profit margin? Operating efficiencies can come from higher volumes, higher prices, and/or lower costs. It is clear that the big difference in ROE between the two firms can be attributed to the difference in profit margins.

Problems with Financial Statement Analysis We continue our chapter by discussing some additional problems that can arise in using financial statements. In one way or another, the basic problem with financial statement analysis is that there is no underlying theory to help us identify which quantities to look at and to guide us in establishing benchmarks. As we discuss in other chapters, there are many cases in which financial theory and economic logic provide guidance in making judgments about value and risk. Little such help exists with financial statements. This is why we can’t say which ratios matter the most and what a high or low value might be. One particularly severe problem is that many firms are conglomerates, owning more or less unrelated lines of business. GE is a well-known example. The consolidated financial statements for such firms don’t really fit any neat industry category. More generally, the kind of peer group analysis we have been describing is going to work best when the firms are strictly in the same line of business, the industry is competitive, and there is only one way of operating. Another problem that is becoming increasingly common is that major competitors and natural peer group members in an industry may be scattered around the globe. The automobile industry is an obvious example. The problem here is that financial statements from outside the United States do not necessarily conform to GAAP. The existence of different standards and procedures makes it difficult to compare financial statements across national borders. Even companies that are clearly in the same line of business may not be comparable. For example, electric utilities engaged primarily in power generation are all classified in the same group. This group is often thought to be relatively homogeneous. However, most utilities operate as regulated monopolies, so they don’t compete much with each other, at least not historically. Many have stockholders, and many are organized as cooperatives with no stockholders. There are several different ways of generating power, ranging from hydroelectric to nuclear, so the operating activities of these utilities can differ quite a bit. Finally, profitability is strongly affected by the regulatory environment, so utilities in different locations can be similar but show different profits. Several other general problems frequently crop up. First, different firms use different accounting procedures—for inventory, for example. This makes it difficult to compare statements. Second, different firms end their fiscal years at different times. For firms in seasonal businesses (such as a retailer with a large Christmas season), this can lead to difficulties in comparing balance sheets because of fluctuations in accounts

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during the year. Finally, for any particular firm, unusual or transient events, such as a one-time profit from an asset sale, may affect financial performance. Such events can give misleading signals as we compare firms.

3.4 Financial Models Financial planning is another important use of financial statements. Most financial planning models output pro forma financial statements, where pro forma means “as a matter of form.” In our case, this means that financial statements are the form we use to summarize the projected future financial status of a company.

A Simple Financial Planning Model We can begin our discussion of financial planning models with a relatively simple example. The Computerfield Corporation’s financial statements from the most recent year are shown below. Unless otherwise stated, the financial planners at Computerfield assume that all variables are tied directly to sales and current relationships are optimal. This means that all items will grow at exactly the same rate as sales. This is obviously oversimplified; we use this assumption only to make a point. COMPUTERFIELD CORPORATION Financial Statements Income Statement Sales Costs Net income

Balance Sheet

$1,000 800 $ 200

Assets

$500

Total

$500

Debt Equity Total

$250 250 $500

Suppose sales increase by 20 percent, rising from $1,000 to $1,200. Planners would then also forecast a 20 percent increase in costs, from $800 to $800 × 1.2 = $960. The pro forma income statement would thus look like this: Pro Forma Income Statement Sales Costs Net income

$1,200 960 $ 240

The assumption that all variables will grow by 20 percent lets us easily construct the pro forma balance sheet as well: Pro Forma Balance Sheet Assets

$600 (+100)

Total

$600 (+100)

Debt Equity Total

$300 (+50) 300 (+50) $600 (+100)

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Notice we have simply increased every item by 20 percent. The numbers in parentheses are the dollar changes for the different items. Now we have to reconcile these two pro forma statements. How, for example, can net income be equal to $240 and equity increase by only $50? The answer is that Computerfield must have paid out the difference of $240 – 50 = $190, possibly as a cash dividend. In this case dividends are the “plug” variable. Suppose Computerfield does not pay out the $190. In this case, the addition to retained earnings is the full $240. Computerfield’s equity will thus grow to $250 (the starting amount) plus $240 (net income), or $490, and debt must be retired to keep total assets equal to $600. With $600 in total assets and $490 in equity, debt will have to be $600 − 490 = $110. Because we started with $250 in debt, Computerfield will have to retire $250 − 110 = $140 in debt. The resulting pro forma balance sheet would look like this: Pro Forma Balance Sheet Assets

$600 (+100)

Total

$600 (+100)

Debt Equity Total

$110 (−140) 490 (+240) $600 (+100)

In this case, debt is the plug variable used to balance projected total assets and liabilities. This example shows the interaction between sales growth and financial policy. As sales increase, so do total assets. This occurs because the firm must invest in net working capital and fixed assets to support higher sales levels. Because assets are growing, total liabilities and equity, the right side of the balance sheet, will grow as well. The thing to notice from our simple example is that the way the liabilities and owners’ equity change depends on the firm’s financing policy and its dividend policy. The growth in assets requires that the firm decide on how to finance that growth. This is strictly a managerial decision. Note that in our example the firm needed no outside funds. This won’t usually be the case, so we explore a more detailed situation in the next section.

The Percentage of Sales Approach In the previous section, we described a simple planning model in which every item increased at the same rate as sales. This may be a reasonable assumption for some elements. For others, such as long-term borrowing, it probably is not: The amount of long-term borrowing is set by management, and it does not necessarily relate directly to the level of sales. In this section, we describe an extended version of our simple model. The basic idea is to separate the income statement and balance sheet accounts into two groups, those that vary directly with sales and those that do not. Given a sales forecast, we will then be able to calculate how much financing the firm will need to support the predicted sales level. The financial planning model we describe next is based on the percentage of sales approach. Our goal here is to develop a quick and practical way of generating pro forma statements. We defer discussion of some “bells and whistles” to a later section. The Income Statement We start out with the most recent income statement for the Rosengarten Corporation, as shown in Table 3.8. Notice that we have still simplified things by including costs, depreciation, and interest in a single cost figure.

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Table 3.8

Part I

Overview

ROSENGARTEN CORPORATION Income Statement Sales Costs Taxable income Taxes (34%) Net income Dividends Addition to retained earnings

Table 3.9

$1,000 800 $ 200 68 $ 132 $44 88

ROSENGARTEN CORPORATION Pro Forma Income Statement Sales (projected) Costs (80% of sales) Taxable income Taxes (34%) Net income

$1,250 1,000 $ 250 85 $ 165

Rosengarten has projected a 25 percent increase in sales for the coming year, so we are anticipating sales of $1,000 × 1.25 = $1,250. To generate a pro forma income statement, we assume that total costs will continue to run at $800/1,000 = 80 percent of sales. With this assumption, Rosengarten’s pro forma income statement is as shown in Table 3.9. The effect here of assuming that costs are a constant percentage of sales is to assume that the profit margin is constant. To check this, notice that the profit margin was $132/1,000 = 13.2 percent. In our pro forma statement, the profit margin is $165/1,250 = 13.2 percent; so it is unchanged. Next, we need to project the dividend payment. This amount is up to Rosengarten’s management. We will assume Rosengarten has a policy of paying out a constant fraction of net income in the form of a cash dividend. For the most recent year, the dividend payout ratiow as: Dividendp ayoutr atio = Cash dividends/Net income = $44/132 = 33 1/3%

(3.22)

We can also calculate the ratio of the addition to retained earnings to net income: Additionto r etainede arnings/Netin come = $88/132 = 66 2/3% This ratio is called the retention ratio or plowback ratio, and it is equal to 1 minus the dividend payout ratio because everything not paid out is retained. Assuming that the payout ratio is constant, the projected dividends and addition to retained earnings will be: Projected dividends paid to shareholders = $165 × 1/3 = $ 55 Projected addition to retained earnings = $165 × 2/3 = 110 $165

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Table 3.10 ROSENGARTEN CORPORATION Balance Sheet Assets

Current assets Cash Accounts receivable Inventory Total Fixed assets Net plant and equipment

Total assets

$

Percentage of Sales

$ 160 440 600 $1,200

16% 44 60 120

$1,800

180

$3,000

300%

Liabilities and Owners’ Equity Percentage $ of Sales Current liabilities Accounts payable Notes payable Total Long-term debt Owners’ equity Common stock and paid-in surplus Retained earnings Total Total liabilities and owners’ equity

$ 300 100 $ 400 $ 800

30% n/a n/a n/a

$ 800

n/a

1,000 $1,800 $3,000

n/a n/a n/a

The Balance Sheet To T generate t a pro fforma b balance l sheet, h t we start t t with ith th the mostt recent statement, as shown in Table 3.10. On our balance sheet, we assume that some items vary directly with sales and others do not. For those items that vary with sales, we express each as a percentage of sales for the year just completed. When an item does not vary directly with sales, we write “n/a” for “not applicable.” For example, on the asset side, inventory is equal to 60 percent of sales (=$600/1,000) for the year just ended. We assume this percentage applies to the coming year, so for each $1 increase in sales, inventory will rise by $.60. More generally, the ratio of total assets to sales for the year just ended is $3,000/1,000 = 3, or 300 percent. This ratio of total assets to sales is sometimes called the capital intensity ratio. It tells us the amount of assets needed to generate $1 in sales; the higher the ratio is, the more capital intensive is the firm. Notice also that this ratio is just the reciprocal of the total asset turnover ratio we defined previously. For Rosengarten, assuming that this ratio is constant, it takes $3 in total assets to generate $1 in sales (apparently Rosengarten is in a relatively capital-intensive business). Therefore, if sales are to increase by $100, Rosengarten will have to increase total assets by three times this amount, or $300. On the liability side of the balance sheet, we show accounts payable varying with sales. The reason is that we expect to place more orders with our suppliers as sales volume increases, so payables will change “spontaneously” with sales. Notes payable, on the other hand, represents short-term debt such as bank borrowing. This will not vary unless we take specific actions to change the amount, so we mark this item as “n/a.” Similarly, we use “n/a” for long-term debt because it won’t automatically change with sales. The same is true for common stock and paid-in surplus. The last item on the right side, retained earnings, will vary with sales, but it won’t be a simple percentage of sales. Instead, we will explicitly calculate the change in retained earnings based on our projected net income and dividends. We can now construct a partial pro forma balance sheet for Rosengarten. We do this by using the percentages we have just calculated wherever possible to calculate the projected

66

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Table 3.11 ROSENGARTEN CORPORATION Partial Pro Forma Balance Sheet Assets

Current assets Cash Accounts receivable Inventory Total Fixed assets Net plant and equipment

Total assets

Liabilities and Owners’ Equity

Next Year

Change from Current Year

$ 200 550 750 $1,500

$ 40 110 150 $300

$2,250

$450

$3,750

$750

Current liabilities Accounts payable Notes payable Total Long-term debt Owners’ equity Common stock and paid-in surplus Retained earnings Total Total liabilities and owners’ equity External financing needed

Next Year

Change from Current Year

$ 375 100 $ 475 $ 800

$ 75 0 $ 75 $ 0

$ 800

$ 0

1,110 $1,910 $3,185 $ 565

110 $110 $185 $565

amounts. For example, net fixed assets are 180 percent of sales; so, with a new sales level of $1,250, the net fixed asset amount will be 1.80 × $1,250 = $2,250, representing an increase of $2,250 – 1,800 = $450 in plant and equipment. It is important to note that for items that don’t vary directly with sales, we initially assume no change and simply write in the original amounts. The result is shown in Table 3.11. Notice that the change in retained earnings is equal to the $110 addition to retained earnings we calculated earlier. Inspecting our pro forma balance sheet, we notice that assets are projected to increase by $750. However, without additional financing, liabilities and equity will increase by only $185, leaving a shortfall of $750 – 185 = $565. We label this amount external financing needed(E FN). Rather than create pro forma statements, if we were so inclined, we could calculate EFNd irectlyasf ollows: Spontaneous liabilities Assets EFN = ______ × ∆Sales − ____________________ × ∆Sales − PM Sales Sales × Projected sales × (1 − d )

(3.23)

In this expression, “∆Sales” is the projected change in sales (in dollars). In our example projected sales for next year are $1,250, an increase of $250 over the previous year, so ∆Sales = $250. By “Spontaneous liabilities,” we mean liabilities that naturally move up and down with sales. For Rosengarten, the spontaneous liabilities are the $300 in accounts payable. Finally, PM and d are the profit margin and dividend payout ratios, which we previously calculated as 13.2 percent and 33 1/3 percent, respectively. Total assets and sales are $3,000 and $1,000, respectively, so we have: $3,000 $300 1 =$565 EFN = ______ × $250 – _____ × $250 – .132 × $1,250 × 1 – __ 1,000 1,000 3

(

)

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67

In this calculation, notice that there are three parts. The first part is the projected increase in assets, which is calculated using the capital intensity ratio. The second is the spontaneous increase in liabilities. The third part is the product of profit margin and projected sales, which is projected net income, multiplied by the retention ratio. Thus, the third part is the projected addition to retained earnings. A Particular Scenario Our financial planning model now reminds us of one of those good news–bad news jokes. The good news is we’re projecting a 25 percent increase in sales. The bad news is this isn’t going to happen unless Rosengarten can somehow raise $565 in new financing. This is a good example of how the planning process can point out problems and potential conflicts. If, for example, Rosengarten has a goal of not borrowing any additional funds and not selling any new equity, then a 25 percent increase in sales is probably not feasible. If we take the need for $565 in new financing as given, we know that Rosengarten has three possible sources: short-term borrowing, long-term borrowing, and new equity. The choice of some combination among these three is up to management; we will illustrate only one of the many possibilities. Suppose Rosengarten decides to borrow the needed funds. In this case, the firm might choose to borrow some over the short term and some over the long term. For example, current assets increased by $300 whereas current liabilities rose by only $75. Rosengarten could borrow $300 − 75 = $225 in short-term notes payable and leave total net working capital unchanged. With $565 needed, the remaining $565 – 225 = $340 would have to come from long-term debt. Table 3.12 shows the completed pro forma balance sheet for Rosengarten.

Table 3.12 ROSENGARTEN CORPORATION Pro Forma Balance Sheet Assets

Current assets Cash Accounts receivable Inventory Total Fixed assets Net plant and equipment

Total assets

Liabilities and Owners’ Equity

Next Year

Change from Current Year

$ 200 550 750 $1,500

$ 40 110 150 $300

$2,250

$450

$3,750

$750

Current liabilities Accounts payable Notes payable Total Long-term debt Owners’ equity Common stock and paid-in surplus Retained earnings Total Total liabilities and owners’ equity

Next Year

Change from Current Year

$ 375 325 $ 700 $1,140

$ 75 225 $300 $340

$ 800

$ 0

1,110 $1,910 $3,750

110 $110 $750

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We have used a combination of short- and long-term debt as the plug here, but we emphasize that this is just one possible strategy; it is not necessarily the best one by any means. We could (and should) investigate many other scenarios. The various ratios we discussed earlier come in handy here. For example, with the scenario we have just examined, we would surely want to examine the current ratio and the total debt ratio to see if we were comfortable with the new projected debt levels.

3.5 External Financing and Growth External financing needed and growth are obviously related. All other things staying the same, the higher the rate of growth in sales or assets, the greater will be the need for external financing. In the previous section, we took a growth rate as given, and then we determined the amount of external financing needed to support that growth. In this section, we turn things around a bit. We will take the firm’s financial policy as given and then examine the relationship between that financial policy and the firm’s ability to finance new investments and thereby grow. We emphasize that we are focusing on growth not because growth is an appropriate goal; instead, for our purposes, growth is simply a convenient means of examining the interactions between investment and financing decisions. In effect, we assume that the use of growth as a basis for planning is just a reflection of the very high level of aggregation used in the planning process.

EFNa ndG rowth The first thing we need to do is establish the relationship between EFN and growth. To do this, we introduce the simplified income statement and balance sheet for the Hoffman Company in Table 3.13. Notice that we have simplified the balance sheet by combining

Table 3.13 HOFFMAN COMPANY Income Statement and Balance Sheet Income Statement Sales Costs Taxable income Taxes (34%) Net income Dividends Addition to retained earnings

$500 400 $100 34 $ 66 $22 44

Balance Sheet Assets

Current assets Net fixed assets Total assets

Liabilities and Owners’ Equity

$

Percentage of Sales

$200 300 $500

40% 60 100%

Total debt Owners’ equity Total liabilities and owners’ equity

$

Percentage of Sales

$250 250 $500

n/a n/a n/a

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Table 3.14 HOFFMAN COMPANY Pro Forma Income Statement and Balance Sheet Income Statement Sales (projected) Costs (80% of sales) Taxable income Taxes (34%) Net income Dividends Addition to retained earnings

$600.0 480.0 $120.0 40.8 $ 79.2 $26.4 52.8

Balance Sheet Assets

Current assets Net fixed assets Total assets

Liabilities and Owners’ Equity

$

Percentage of Sales

$240.0 360.0 $600.0

40% 60 100%

Total debt Owners’ equity Total liabilities and owners’ equity External financing needed

$

Percentage of Sales

$250.0 302.8 $552.8

n/a n/a n/a

$ 47.2

n/a

short-term and long-term debt into a single total debt figure. Effectively, we are assuming that none of the current liabilities vary spontaneously with sales. This assumption isn’t as restrictive as it sounds. If any current liabilities (such as accounts payable) vary with sales, we can assume that any such accounts have been netted out in current assets. Also, we continue to combine depreciation, interest, and costs on the income statement. Suppose the Hoffman Company is forecasting next year’s sales level at $600, a $100 increase. Notice that the percentage increase in sales is $100/500 = 20 percent. Using the percentage of sales approach and the figures in Table 3.13, we can prepare a pro forma income statement and balance sheet as in Table 3.14. As Table 3.14 illustrates, at a 20 percent growth rate, Hoffman needs $100 in new assets. The projected addition to retained earnings is $52.8, so the external financing needed, EFN, is $100 − 52.8 = $47.2. Notice that the debt–equity ratio for Hoffman was originally (from Table 3.13) equal to $250/250 = 1.0. We will assume that the Hoffman Company does not wish to sell new equity. In this case, the $47.2 in EFN will have to be borrowed. What will the new debt–equity ratio be? From Table 3.14, we know that total owners’ equity is projected at $302.8. The new total debt will be the original $250 plus $47.2 in new borrowing, or $297.2 total. The debt–equity ratio thus falls slightly from 1.0 to $297.2/302.8 = .98. Table 3.15 shows EFN for several different growth rates. The projected addition to retained earnings and the projected debt–equity ratio for each scenario are also given (you should probably calculate a few of these for practice). In determining the debt–equity ratios, we assumed that any needed funds were borrowed, and we also assumed any surplus funds were used to pay off debt. Thus, for the zero growth case the debt falls by $44, from $250 to $206. In Table 3.15, notice that the increase in assets

70

Table 3.15 Growth and Projected EFN for the Hoffman Company

Part I

Overview

Projected Sales Growth

Increase in Assets Required $ 0 25 50 75 100 125

0% 5 10 15 20 25

Addition to Retained Earnings

External Financing Needed, EFN

Projected Debt– Equity Ratio

$44.0 46.2 48.4 50.6 52.8 55.0

–$44.0 –21.2 1.6 24.4 47.2 70.0

.70 .77 .84 .91 .98 1.05

required is simply equal to the original assets of $500 multiplied by the growth rate. Similarly, the addition to retained earnings is equal to the original $44 plus $44 times the growth rate. Table 3.15 shows that for relatively low growth rates, Hoffman will run a surplus, and its debt–equity ratio will decline. Once the growth rate increases to about 10 percent, however, the surplus becomes a deficit. Furthermore, as the growth rate exceeds approximately 20 percent, the debt–equity ratio passes its original value of 1.0. Figure 3.1 illustrates the connection between growth in sales and external financing needed in more detail by plotting asset needs and additions to retained earnings from Table 3.15 against the growth rates. As shown, the need for new assets grows at a much faster rate than the addition to retained earnings, so the internal financing provided by the addition to retained earnings rapidly disappears. As this discussion shows, whether a firm runs a cash surplus or deficit depends on growth. Microsoft is a good example. Its revenue growth in the 1990s was amazing, averaging well over 30 percent per year for the decade. Growth slowed down noticeably over the 2000–2006 period, but, nonetheless, Microsoft’s combination of growth and

GrowthandR elated Financing Needed for the Hoffman Company

Asset needs and retained earnings ($)

Figure 3.1 Increase in assets required

125 100

EFN ⬎ 0 (deficit)

75 50 44 25

EFN ⬍ 0 (surplus)

5

Projected addition to retained earnings

15 20 10 Projected growth in sales (%)

25

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substantial profit margins led to enormous cash surpluses. In part because Microsoft paid few dividends, the cash really piled up; in 2008, Microsoft’s cash and short-term investment horde exceeded $21 billion.

Financial Policy and Growth Based on our discussion just preceding, we see that there is a direct link between growth and external financing. In this section, we discuss two growth rates that are particularly useful in long-range planning.

The Internal Growth Rate The first growth rate of interest is the maximum growth rate that can be achieved with no external financing of any kind. We will call this the internal growth rate because this is the rate the firm can maintain with internal financing only. In Figure 3.1, this internal growth rate is represented by the point where the two lines cross. At this point, the required increase in assets is exactly equal to the addition to retained earnings, and EFN is therefore zero. We have seen that this happens when the growth rate is slightly less than 10 percent. With a little algebra (see Problem 28 at the end of the chapter), we can define this growth rate more precisely as: ROA × b Internalgr owthr ate = ____________ 1 − ROA × b

(3.24)

where ROA is the return on assets we discussed earlier, and b is the plowback, or retention, ratio also defined earlier in this chapter. For the Hoffman Company, net income was $66 and total assets were $500. ROA is thus $66/500 = 13.2 percent. Of the $66 net income, $44 was retained, so the plowback ratio, b, is $44/66 = 2/3. With these numbers, we can calculate the internal growth rate as: ROA × b Internalgr owthr ate = ____________ 1 – ROA × b .132 × (2/3) = ______________ 1 – .132 × (2/3) =9.65% Thus, the Hoffman Company can expand at a maximum rate of 9.65 percent per year without external financing. The Sustainable Growth Rate We have seen that if the Hoffman Company wishes to grow more rapidly than at a rate of 9.65 percent per year, external financing must be arranged. The second growth rate of interest is the maximum growth rate a firm can achieve with no external equity financing while it maintains a constant debt–equity ratio. This rate is commonly called the sustainable growth rate because it is the maximum rate of growth a firm can maintain without increasing its financial leverage. There are various reasons why a firm might wish to avoid equity sales. For example, new equity sales can be expensive because of the substantial fees that may be involved. Alternatively, the current owners may not wish to bring in new owners or contribute additional equity. Why a firm might view a particular debt–equity ratio as optimal is discussed in later chapters; for now, we will take it as given.

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Based on Table 3.15, the sustainable growth rate for Hoffman is approximately 20 percent because the debt–equity ratio is near 1.0 at that growth rate. The precise value can be calculated as follows (see Problem 28 at the end of the chapter): ROE × b Sustainablegr owthr ate = ____________ 1 – ROE × b

(3.25)

This is identical to the internal growth rate except that ROE, return on equity, is used instead of ROA. For the Hoffman Company, net income was $66 and total equity was $250; ROE is thus $66/250 = 26.4 percent. The plowback ratio, b, is still 2/3, so we can calculate the sustainable growth rate as: ROE × b Sustainablegr owthr ate = ____________ 1 – ROE × b .264 × (2/3) = ______________ 1 – .264 × (2/3) =21.36% Thus, the Hoffman Company can expand at a maximum rate of 21.36 percent per year without external equity financing.

EXAMPLE 3.5 S Sustainable Growth Suppose Hoffman grows at exactly the sustainable growth rate of 21.36 ppercent. What will the pro forma statements look like? At a 21.36 percent growth rate, sales will rise from $500 to $606.8.The pro forma income statement will look like this:

HOFFMAN COMPANY Pro Forma Income Statement Sales (projected) Costs (80% of sales) Taxable income Taxes (34%) Net income Dividends Addition to retained earnings

$606.8 485.4 $121.4 41.3 $ 80.1 $26.7 53.4

We construct the balance sheet just as we did before. Notice, in this case, that owners’ equity will rise from $250 to $303.4 because the addition to retained earnings is $53.4.

Chapter 3

Financial Statements Analysis and Financial Models

73

HOFFMAN COMPANY Pro Forma Balance Sheet Assets

Current assets Net fixed assets Total assets

Liabilities and Owners’ Equity

$

Percentage of Sales

$242.7 364.1 $606.8

40% 60 100%

Total debt Owners’ equity Total liabilities and owners’ equity External financing needed

$

Percentage of Sales

$250.0 303.4 $553.4

n/a n/a n/a

$ 53.4

n/a

As illustrated, EFN is $53.4. If Hoffman borrows this amount, then total debt will rise to $303.4, and the debt–equity ratio will be exactly 1.0, which verifies our earlier calculation. At any other growth rate, something would have to change.

Determinants of Growth Earlier in this chapter, we saw that the return on equity, ROE, could be decomposed into its various components using the Du Pont identity. Because ROE appears so prominently in the determination of the sustainable growth rate, it is obvious that the factors important in determining ROE are also important determinants of growth. From our previous discussions, we know that ROE can be written as the product of three factors: ROE = Profit margin × Total asset turnover ×E quitym ultiplier If we examine our expression for the sustainable growth rate, we see that anything that increases ROE will increase the sustainable growth rate by making the top bigger and the bottom smaller. Increasing the plowback ratio will have the same effect. Putting it all together, what we have is that a firm’s ability to sustain growth depends explicitly on the following four factors: 1. Profit margin: An increase in profit margin will increase the firm’s ability to generate funds internally and thereby increase its sustainable growth. 2. Dividend policy: A decrease in the percentage of net income paid out as dividends will increase the retention ratio. This increases internally generated equity and thus increases sustainable growth. 3. Financial policy: An increase in the debt–equity ratio increases the firm’s financial leverage. Because this makes additional debt financing available, it increases the sustainable growth rate. 4. Total asset turnover: An increase in the firm’s total asset turnover increases the sales generated for each dollar in assets. This decreases the firm’s need for new assets as sales grow and thereby increases the sustainable growth rate. Notice that increasing total asset turnover is the same thing as decreasing capital intensity.

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The sustainable growth rate is a very useful planning number. What it illustrates is the explicit relationship between the firm’s four major areas of concern: its operating efficiency as measured by profit margin, its asset use efficiency as measured by total asset turnover, its dividend policy as measured by the retention ratio, and its financial policy as measured by the debt–equity ratio.

EXAMPLE 3.6

Profit Margins and Sustainable Growth The Sandar Co. has a debt–equity ratio of .5, a profit margin of 3 percent, a dividend payout ratio of 40 percent, and a capital intensity ratio of 1. What is its sustainable growth rate? If Sandar desired a 10 percent sustainable growth rate and planned to achieve this goal by improving profit margins, what would you think? ROEis.03 × 1 × 1.5 = 4.5 percent. The retention ratio is 1 – .40 = .60. Sustainable growth is thus .045(.60)/[1 – .045(.60)] = 2.77 percent. For the company to achieve a 10 percent growth rate, the profit margin will have to rise. To see this, assume that sustainable growth is equal to 10 percent and then solve for profit margin, PM: .10 = PM(1.5)(.6)/[1 – PM(1.5)(.6)] PM = .1/.99 = 10.1% For the plan to succeed, the necessary increase in profit margin is substantial, from 3 percent to about 10 percent. This may not be feasible.

Given values for all four of these, there is only one growth rate that can be achieved. This is an important point, so it bears restating: If a firm does not wish to sell new equity and its profit margin, dividend policy, financial policy, and total asset turnover (or capital intensity) are all fixed, then there is only one possible growth rate.

One of the primary benefits of financial planning is that it ensures internal consistency among the firm’s various goals. The concept of the sustainable growth rate captures this element nicely. Also, we now see how a financial planning model can be used to test the feasibility of a planned growth rate. If sales are to grow at a rate higher than the sustainable growth rate, the firm must increase profit margins, increase total asset turnover, increase financial leverage, increase earnings retention, or sell new shares. The two growth rates, internal and sustainable, are summarized in Table 3.16.

A Note about Sustainable Growth Rate Calculations Very commonly, the sustainable growth rate is calculated using just the numerator in our expression, ROE × b. This causes some confusion, which we can clear up here. The issue has to do with how ROE is computed. Recall that ROE is calculated as net income divided by total equity. If total equity is taken from an ending balance sheet (as we have done consistently, and is commonly done in practice), then our formula is the right one. However, if total equity is from the beginning of the period, then the simpler formula is the correct one. In principle, you’ll get exactly the same sustainable growth rate regardless of which way you calculate it (as long as you match up the ROE calculation with the right

Chapter 3

Table 3.16 Summary of Internal and Sustainable Growth Rates

Financial Statements Analysis and Financial Models

75

I. Internal Growth Rate

ROA × b Internalg rowth rate = ____________ 1 − ROA × b where ROA = Return on assets = Net income/Total assets b = Plowback (retention) ratio = Addition to retained earnings/Net income The internal growth rate is the maximum growth rate that can be achieved with no external financing of any kind. II. Sustainable Growth Rate

ROE × b Sustainable growth rate = ___________ 1 – ROE × b where ROE = Return on equity = Net income/Total equity b = Plowback (retention) ratio = Addition to retained earnings/Net income The sustainable growth rate is the maximum growth rate that can be achieved with no external equity financing while maintaining a constant debt–equity ratio.

formula). In reality, you may see some differences because of accounting-related complications. By the way, if you use the average of beginning and ending equity (as some advocate), yet another formula is needed. Also, all of our comments here apply to the internal growth rate as well.

3.6 Some Caveats Regarding Financial PlanningMo dels Financial planning models do not always ask the right questions. A primary reason is that they tend to rely on accounting relationships and not financial relationships. In particular, the three basic elements of firm value tend to get left out—namely, cash flow size, risk, and timing. Because of this, financial planning models sometimes do not produce output that gives the user many meaningful clues about what strategies will lead to increases in value. Instead, they divert the user’s attention to questions concerning the association of, say, the debt–equity ratio and firm growth. The financial model we used for the Hoffman Company was simple—in fact, too simple. Our model, like many in use today, is really an accounting statement generator at heart. Such models are useful for pointing out inconsistencies and reminding us of financial needs, but they offer little guidance concerning what to do about these problems. In closing our discussion, we should add that financial planning is an iterative process. Plans are created, examined, and modified over and over. The final plan will be a result negotiated between all the different parties to the process. In fact, long-term

In Their Own Words ROBERT C. HIGGINS ON SUSTAINABLE GROWTH Most financial officers know intuitively that it takes money to make money. Rapid sales growth requires increased assets in the form of accounts receivable, inventory, and fixed plant, which, in turn, require money to pay for assets. They also know that if their company does not have the money when needed, it can literally “grow broke.” The sustainable growth equation states these intuitive truths explicitly. Sustainable growth is often used by bankers and other external analysts to assess a company’s creditworthiness. They are aided in this exercise by several sophisticated computer software packages that provide detailed analyses of the company’s past financial performance, including its annual sustainable growth rate. Bankers use this information in several ways. Quick comparison of a company’s actual growth rate to its sustainable rate tells the banker what issues will be at the top of management’s financial agenda. If actual growth consistently exceeds sustainable growth, management’s problem will be where to get the cash to finance growth. The banker thus can anticipate interest in loan products. Conversely, if sustainable growth consistently exceeds actual, the banker had best be

prepared to talk about investment products because management’s problem will be what to do with all the cash that keeps piling up in the till. Bankers also find the sustainable growth equation useful for explaining to financially inexperienced small business owners and overly optimistic entrepreneurs that, for the long-run viability of their business, it is necessary to keep growth and profitability in proper balance. Finally, comparison of actual to sustainable growth rates helps a banker understand why a loan applicant needs money and for how long the need might continue. In one instance, a loan applicant requested $100,000 to pay off several insistent suppliers and promised to repay in a few months when he collected some accounts receivable that were coming due. A sustainable growth analysis revealed that the firm had been growing at four to six times its sustainable growth rate and that this pattern was likely to continue in the foreseeable future. This alerted the banker that impatient suppliers were only a symptom of the much more fundamental disease of overly rapid growth, and that a $100,000 loan would likely prove to be only the down payment on a much larger, multiyear commitment. Robert C. Higgins is Professor of Finance at the University of Washington. He pioneered the use of sustainable growth as a tool for financial analysis.

financial planning in most corporations relies on what might be called the Procrustes approach.6 Upper-level management has a goal in mind, and it is up to the planning staff to rework and to ultimately deliver a feasible plan that meets that goal. The final plan will therefore implicitly contain different goals in different areas and also satisfy many constraints. For this reason, such a plan need not be a dispassionate assessment of what we think the future will bring; it may instead be a means of reconciling the planned activities of different groups and a way of setting common goals for the future. However it is done, the important thing to remember is that financial planning should not become a purely mechanical exercise. If it does, it will probably focus on the wrong things. Nevertheless, the alternative to planning is stumbling into the future. Perhaps the immortal Yogi Berra (the baseball catcher, not the cartoon character), said it best: “Ya gotta watch out if you don’t know where you’re goin’. You just might notge tth ere.”7

6

In Greek mythology, Procrustes is a giant who seizes travelers and ties them to an iron bed. He stretches them or cuts off their legs as needed to make them fit the bed.

7

We’re not exactly sure what this means, either, but we like the sound of it.

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Chapter 3

Summary and Conclusions

Concept Questions

Financial Statements Analysis and Financial Models

77

This chapter focuses on working with information contained in financial statements. Specifically, we studied standardized financial statements, ratio analysis, and long-term financial planning. 1. We explained that differences in firm size make it difficult to compare financial statements, and we discussed how to form common-size statements to make comparisons easier and more meaningful. 2. Evaluating ratios of accounting numbers is another way of comparing financial statement information. We defined a number of the most commonly used ratios, and we discussed the famous Du Pont identity. 3. We showed how pro forma financial statements can be generated and used to plan for future financing needs. After you have studied this chapter, we hope that you have some perspective on the uses and abuses of financial statement information. You should also find that your vocabulary of business and financial terms has grown substantially.

1.

3. 4.

5.

6.

7.

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2.

Financial Ratio Analysis A financial ratio by itself tells us little about a company because financial ratios vary a great deal across industries. There are two basic methods for analyzing financial ratios for a company: Time trend analysis and peer group analysis. In time trend analysis, you find the ratios for the company over some period, say five years, and examine how each ratio has changed over this period. In peer group analysis, you compare a company’s financial ratios to those of its peers. Why might each of these analysis methods be useful? What does each tell you about the company’s financial health? Industry-Specific Ratios So-called “same-store sales” are a very important measure for companies as diverse as McDonald’s and Sears. As the name suggests, examining same-store sales means comparing revenues from the same stores or restaurants at two different points in time. Why might companies focus on same-store sales rather than total sales? Sales Forecast Why do you think most long-term financial planning begins with sales forecasts? Put differently, why are future sales the key input? Sustainable Growth In the chapter, we used Rosengarten Corporation to demonstrate how to calculate EFN. The ROE for Rosengarten is about 7.3 percent, and the plowback ratio is about 67 percent. If you calculate the sustainable growth rate for Rosengarten, you will find it is only 5.14 percent. In our calculation for EFN, we used a growth rate of 25 percent. Is this possible? (Hint: Yes. How?) EFN and Growth Rate Broslofski Co. maintains a positive retention ratio and keeps its debt–equity ratio constant every year. When sales grow by 20 percent, the firm has a negative projected EFN. What does this tell you about the firm’s sustainable growth rate? Do you know, with certainty, if the internal growth rate is greater than or less than 20 percent? Why? What happens to the projected EFN if the retention ratio is increased? What if the retention ratio is decreased? What if the retention ratio is zero? Common-Size Financials One tool of financial analysis is common-size financial statements. Why do you think common-size income statements and balance sheets are used? Note that the accounting statement of cash flows is not converted into a common-size statement. Why do you think this is? Asset Utilization and EFN One of the implicit assumptions we made in calculating the external funds needed was that the company was operating at full capacity. If the company is operating at less than full capacity, how will this affect the external funds needed?

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Comparing ROE and ROA Both ROA and ROE measure profitability. Which one is more useful for comparing two companies? Why? 9. Ratio Analysis Consider the ratio EBITD/Assets. What does this ratio tell us? Why might it be more useful than ROA in comparing two companies? 10. Return on Investment A ratio that is becoming more widely used is return on investment. Return on investment is calculated as net income divided by long-term liabilities plus equity. What do you think return on investment is intended to measure? What is the relationship between return on investment and return on assets? Use the following information to answer the next five questions: A small business called The Grandmother Calendar Company began selling personalized photo calendar kits. The kits were a hit, and sales soon sharply exceeded forecasts. The rush of orders created a huge backlog, so the company leased more space and expanded capacity, but it still could not keep up with demand. Equipment failed from overuse and quality suffered. Working capital was drained to expand production, and, at the same time, payments from customers were often delayed until the product was shipped. Unable to deliver on orders, the company became so strapped for cash that employee paychecks began to bounce. Finally, out of cash, the company ceased operations entirely three years later. 11. Product Sales Do you think the company would have suffered the same fate if its product had been less popular? Why or why not? 12. Cash Flow The Grandmother Calendar Company clearly had a cash flow problem. In the context of the cash flow analysis we developed in Chapter 2, what was the impact of customers not paying until orders were shipped? 13. Corporate Borrowing If the firm was so successful at selling, why wouldn’t a bank or some other lender step in and provide it with the cash it needed to continue? 14. Cash Flow Which was the biggest culprit here: Too many orders, too little cash, or too little production capacity? 15. Cash Flow What are some actions a small company like The Grandmother Calendar Company can take (besides expansion of capacity) if it finds itself in a situation in which growth in sales outstrips production?

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8.

Questions and Problems

1. 2.

3. BASIC (Questions 1–10)

4.

Du Pont Identity If Roten, Inc., has an equity multiplier of 1.35, total asset turnover of 2.15, and a profit margin of 5.8 percent, what is its ROE? Equity Multiplier and Return on Equity Thomsen Company has a debt–equity ratio of .90. Return on assets is 10.1 percent, and total equity is $645,000. What is the equity multiplier? Return on equity? Net income? Using the Du Pont Identity Y3K, Inc., has sales of $3,100, total assets of $1,580, and a debt–equity ratio of 1.20. If its return on equity is 16 percent, what is its net income? EFN The most recent financial statements for Martin, Inc., are shown here: Income Statement Sales Costs Taxable income Taxes (34%) Net income

$25,800 16,500 $ 9,300 3,162 $ 6,138

Balance Sheet Assets

$113,000

Total

$113,000

Debt Equity Total

$ 20,500 92,500 $113,000

Chapter 3

5.

Financial Statements Analysis and Financial Models

Assets and costs are proportional to sales. Debt and equity are not. A dividend of $1,841.40 was paid, and Martin wishes to maintain a constant payout ratio. Next year’s sales are projected to be $30,960. What external financing is needed? Sales and Growth The most recent financial statements for Fontenot Co. are shown here:

Income Statement Sales Costs Taxable income Taxes (34%) Net income

6.

8.

Balance Sheet Current assets Fixed assets Total

$67,000 43,800 $23,200 7,888 $15,312

Long-term debt Equity Total

$ 68,000 81,000 $149,000

Assets and costs are proportional to sales. The company maintains a constant 30 percent dividend payout ratio and a constant debt–equity ratio. What is the maximum increase in sales that can be sustained assuming no new equity is issued? Sustainable Growth If the Layla Corp. has a 15 percent ROE and a 10 percent payout ratio, what is its sustainable growth rate? Sustainable Growth Assuming the following ratios are constant, what is the sustainable growth rate? Totalas sett urnover =1.90 Profitmar gin = 8.1% Equitym ultiplier = 1.25 Payoutr atio = 30% Calculating EFN The most recent financial statements for Bradley, Inc., are shown here (assuming no income taxes): Income Statement Sales Costs Net income

9.

$ 31,000 118,000 $149,000

$5,700 3,820 $1,880

Balance Sheet Assets

$14,100

Total

$14,100

Debt Equity Total

$ 6,300 7,800 $14,100

Assets and costs are proportional to sales. Debt and equity are not. No dividends are paid. Next year’s sales are projected to be $6,669. What is the external financing needed? External Funds Needed Cheryl Colby, CFO of Charming Florist Ltd., has created the firm’s pro forma balance sheet for the next fiscal year. Sales are projected to grow by 10 percent to $390 million. Current assets, fixed assets, and short-term debt are 20 percent, 120 percent, and 15 percent of sales, respectively. Charming Florist pays out 30 percent of its net income in dividends. The company currently has $130 million of long-term debt and $48 million in common stock par value. The profit margin is 12 percent. a. Construct the current balance sheet for the firm using the projected sales figure. b. Based on Ms. Colby’s sales growth forecast, how much does Charming Florist need in external funds for the upcoming fiscal year? c. Construct the firm’s pro forma balance sheet for the next fiscal year and confirm the external funds needed that you calculated in part (b).

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7.

79

80

Part I

10.

INTERMEDIATE (Questions 11–23)

11.

12.

13.

Overview

Sustainable Growth Rate The Steiben Company has an ROE of 10.5 percent and a payout ratio of 40 percent. a. What is the company’s sustainable growth rate? b. Can the company’s actual growth rate be different from its sustainable growth rate? Why or why not? c. Howc ant hec ompanyin creaseit ss ustainablegr owthr ate? Return on Equity Firm A and Firm B have debt–total asset ratios of 40 percent and 30 percent and returns on total assets of 12 percent and 15 percent, respectively. Which firm has a greater return on equity? Ratios and Foreign Companies Prince Albert Canning PLC had a net loss of £15,834 on sales of £167,983. What was the company’s profit margin? Does the fact that these figures are quoted in a foreign currency make any difference? Why? In dollars, sales were $251,257. What was the net loss in dollars? External Funds Needed The Optical Scam Company has forecast a 20 percent sales growth rate for next year. The current financial statements are shown here:

Income Statement

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Sales Costs Taxable income Taxes Net income Dividends Addition to retained earnings

$30,400,000 26,720,000 $ 3,680,000 1,288,000 $ 2,392,000 $ 956,800 1,435,200

Balance Sheet Assets

Current assets Fixed assets

Total assets

14.

$ 7,200,000

Liabilities and Equity

Short-term debt Long-term debt

$ 6,400,000 4,800,000

Common stock Accumulated retained earnings

$ 3,200,000 10,400,000

Total equity Total liabilities and equity

$13,600,000 $24,800,000

17,600,000

$24,800,000

a. Using the equation from the chapter, calculate the external funds needed for next year. b. Construct the firm’s pro forma balance sheet for next year and confirm the external funds needed that you calculated in part (a). c. Calculate the sustainable growth rate for the company. d. Can Optical Scam eliminate the need for external funds by changing its dividend policy? What other options are available to the company to meet its growth objectives? Days’ Sales in Receivables A company has net income of $205,000, a profit margin of 9.3 percent, and an accounts receivable balance of $162,500. Assuming 80 percent of sales are on credit, what is the company’s days’ sales in receivables?

Chapter 3

15.

16.

17.

18.

Financial Statements Analysis and Financial Models

81

Ratios and Fixed Assets The Le Bleu Company has a ratio of long-term debt to total assets of .40 and a current ratio of 1.30. Current liabilities are $900, sales are $5,320, profit margin is 9.4 percent, and ROE is 18.2 percent. What is the amount of thef irm’sn etf ixedas sets? Calculating the Cash Coverage Ratio Titan Inc.’s net income for the most recent year was $9,450. The tax rate was 34 percent. The firm paid $2,360 in total interest expense and deducted $3,480 in depreciation expense. What was Titan’s cash coverage ratio for the year? Cost of Goods Sold Guthrie Corp. has current liabilities of $270,000, a quick ratio of 1.1, inventory turnover of 4.2, and a current ratio of 2.3. What is the cost of goods sold for the company? Common-Size and Common–Base Year Financial Statements In addition to commonsize financial statements, common–base year financial statements are often used. Common–base year financial statements are constructed by dividing the current year account value by the base year account value. Thus, the result shows the growth rate in the account. Using the following financial statements, construct the common-size balance sheet and common–base year balance sheet for the company. Use 2009 as the base year.

Assets

Liabilities and Owners’ Equity 2009

Current assets Cash Accounts receivable Inventory Total Fixed assets Net plant and equipment

Total assets

2010

$ 8,436 21,530 38,760 $ 68,726

$ 10,157 23,406 42,650 $ 76,213

$226,706

$248,306

$295,432

$324,519

Current liabilities Accounts payable Notes payable Total Long-term debt Owners’ equity Common stock and paid-in surplus Accumulated retained earnings Total Total liabilities and owners’ equity

2009

2010

$ 43,050 18,384 $ 61,434 $ 25,000

$ 46,821 17,382 $ 64,203 $ 32,000

$ 40,000

$ 40,000

168,998

188,316

$208,998 $295,432

$228,316 $324,519

Use the following information for Problems 19, 20, and 22: The discussion of EFN in the chapter implicitly assumed that the company was operating at full capacity. Often, this is not the case. For example, assume that Rosengarten was operating at 90 percent capacity. Full-capacity sales would be $1,000/.90 = $1,111. The balance sheet shows $1,800 in fixed assets. The capital intensity ratio for the company is Capitali ntensityr atio = Fixed assets/Full-capacity sales = $1,800/$1,111 =1.62 This means that Rosengarten needs $1.62 in fixed assets for every dollar in sales when it reaches full capacity. At the projected sales level of $1,250, it needs $1,250 × 1.62 = $2,025

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JARROW CORPORATION 2009 and 2010 Balance Sheets

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Overview

in fixed assets, which is $225 lower than our projection of $2,250 in fixed assets. So, EFN is only $565 – 225 =$340. 19. Full-Capacity Sales Thorpe Mfg., Inc., is currently operating at only 85 percent of fixed asset capacity. Current sales are $630,000. How much can sales increase before any new fixed assets are needed? 20. Fixed Assets and Capacity Usage For the company in the previous problem, suppose fixed assets are $580,000 and sales are projected to grow to $790,000. How much in new fixed assets are required to support this growth in sales? 21. Calculating EFN The most recent financial statements for Moose Tours, Inc., appear below. Sales for 2010 are projected to grow by 20 percent. Interest expense will remain constant; the tax rate and the dividend payout rate will also remain constant. Costs, other expenses, current assets, fixed assets, and accounts payable increase spontaneously with sales. If the firm is operating at full capacity and no new debt or equity is issued, what external financing is needed to support the 20 percent growth rate in sales? 22. Capacity Usage and Growth In the previous problem, suppose the firm was operating at only 80 percent capacity in 2009. What is EFN now?

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MOOSE TOURS, INC. 2009 Income Statement

Sales

$929,000

Costs

723,000

Other expenses

19,000

Earnings before interest and taxes

$187,000

Interest expense

14,000

Taxable income

$173,000

Taxes

60,550

Net income

$112,450

Dividends

$33,735

Addition to retained earnings

78,715

MOOSE TOURS, INC. Balance Sheet as of December 31, 2009

Assets

Liabilities and Owners’ Equity Current liabilities

Current assets Cash

$ 25,300

Accounts receivable

40,700

Inventory

86,900

Total

$152,900

Accounts payable Notes payable Total Long-term debt

$ 68,000 17,000 $ 85,000 $158,000

Owners’ equity Common stock and paid-in surplus

Fixed assets Net plant and equipment

$413,000

Retained earnings Total

Total assets

$565,900

Total liabilities and owners’ equity

$140,000 182,900 $322,900 $565,900

Chapter 3

23. CHALLENGE (Questions 24–30)

24.

25.

26.

27.

Financial Statements Analysis and Financial Models

83

EFN = – PM(S)b + [A – PM(S)b] × g

28.

29.

Hint: Asset needs will equal A × g. The addition to retained earnings will equal PM(S)b × (1 + g). Sustainable Growth Rate Based on the results in Problem 27, show that the internal and sustainable growth rates can be calculated as shown in Equations 3.23 and 3.24. Hint: For the internal growth rate, set EFN equal to zero and solve for g. Sustainable Growth Rate In the chapter, we discussed one calculation of the sustainable growth rate as: ROE × b Sustainablegr owthr ate = ____________ 1 – ROE × b

30.

In practice, probably the most commonly used calculation of the sustainable growth rate is ROE × b. This equation is identical to the sustainable growth rate equation presented in the chapter if the ROE is calculated using the beginning of period equity. Derive this equation from the equation presented in the chapter. Sustainable Growth Rate Use the sustainable growth rate equations from the previous problem to answer the following questions. No Return, Inc., had total assets of $310,000 and equity of $183,000 at the beginning of the year. At the end of the year, the company had total assets of $355,000. During the year the company sold no new equity. Net income for the year was $95,000 and dividends were $68,000. What is the sustainable growth rate for the company? What is the sustainable growth rate if you calculate ROE based on the beginning of period equity?

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Calculating EFN In Problem 21, suppose the firm wishes to keep its debt–equity ratioc onstant.W hatis E FNn ow? EFN and Internal Growth Redo Problem 21 using sales growth rates of 15 and 25 percent in addition to 20 percent. Illustrate graphically the relationship between EFN and the growth rate, and use this graph to determine the relationship between them. EFN and Sustainable Growth Redo Problem 23 using sales growth rates of 30 and 35 percent in addition to 20 percent. Illustrate graphically the relationship between EFN and the growth rate, and use this graph to determine the relationship between them. Constraints on Growth Bulla Recording, Inc., wishes to maintain a growth rate of 12 percent per year and a debt–equity ratio of .30. Profit margin is 5.9 percent, and the ratio of total assets to sales is constant at .85. Is this growth rate possible? To answer, determine what the dividend payout ratio must be. How do you interpret the result? EFN Define the following: S = Previous year’s sales A = Total assets D = Total debt E = Total equity g = Projected growth in sales PM = Profit margin b =R etention( plowback)r atio Show that EFN can be written as:

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Mini Case

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S&P Problems

Part I

Overview

www.mhhe.com/edumarketinsight 1. Calculating the Du Pont Identity Find the annual income statements and balance sheets for Dow Chemical (DOW) and AutoZone (AZO). Calculate the Du Pont identity for each company for the most recent three years. Comment on the changes in each component of the Du Pont identity for each company over this period and compare the components between the two companies. Are the results what you expected? Why or why not? 2. Ratio Analysis Find and download the “Profitability” spreadsheet for Southwest Airlines (LUV) and Continental Airlines (CAL). Find the ROA (Net ROA), ROE (Net ROE), PE ratio (P/E—high and P/E—low), and the market-to-book ratio (Price/Book—high and Price/Book—low) for each company. Because stock prices change daily, PE and market-to-book ratios are often reported as the highest and lowest values over the year, as is done in this instance. Look at these ratios for both companies over the past five years. Do you notice any trends in these ratios? Which company appears to be operating at a more efficient level based on these four ratios? If you were going to invest in an airline, which one (if either) of these companies would you choose based on this information? Why? 3. Sustainable Growth Rate Use the annual income statements and balance sheets under the “Excel Analytics” link to calculate the sustainable growth rate for CocaCola (KO) each year for the past four years. Is the sustainable growth rate the same for every year? What are possible reasons the sustainable growth rate may vary from year to year? 4. External Funds Needed Look up Black & Decker (BDK). Under the “Financial Highlights”link you can find a five-year growth rate for sales. Using this growth rate and the most recent income statement and balance sheet, compute the external funds needed for BDK next year.

RATIOS AND FINANCIAL PLANNING AT EAST COAST YACHTS Dan Ervin was recently hired by East Coast Yachts to assist the company with its shortterm financial planning and also to evaluate the company’s financial performance. Dan graduated from college five years ago with a finance degree, and he has been employed in the treasury department of a Fortune 500 company since then. East Coast Yachts was founded 10 years ago by Larissa Warren. The company’s operations are located near Hilton Head Island, South Carolina, and the company is structured as an LLC. The company has manufactured custom midsize, high-performance yachts for clients over this period, and its products have received high reviews for safety and reliability. The company’s yachts have also recently received the highest award for customer satisfaction. The yachts are primarily purchased by wealthy individuals for pleasure use. Occasionally, a yacht is manufactured for purchase by a company for business purposes. The custom yacht industry is fragmented, with a number of manufacturers. As with any industry, there are market leaders, but the diverse nature of the industry ensures that no manufacturer dominates the market. The competition in the market, as well as the product cost, ensures that attention to detail is a necessity. For instance, East Coast Yachts will spend 80 to 100 hours on hand-buffing the stainless steel stem-iron, which is the metal cap on the yacht’s bow that conceivably could collide with a dock or another boat. To get Dan started with his analyses, Larissa has provided the following financial statements. Dan has gathered the industry ratios for the yacht manufacturing industry.

Chapter 3

Financial Statements Analysis and Financial Models

85

EAST CO AST YACHTS 2009 Income Statement

Sales Cost of goods sold Other expenses Depreciation Earnings before interest and taxes (EBIT) Interest Taxable income Taxes (40%) Net income Dividends Addition to RE

$167,310,000 117,910,000 19,994,000 5,460,000 $ 23,946,000 3,009,000 $ 20,937,000 8,374,800 $ 12,562,200 $7,537,320 5,024,880

EAST COAST YACHTS Balance Sheet as of December 31, 2009

Assets Current assets Cash Accounts receivable Inventory Total Fixed assets Net plant and equipment

Liabilities & Equity $

3,042,000 5,473,000 6,136,000 $ 14,651,000

Current liabilities Accounts payable Notes payable

$

Total Long-term debt

$ 19,539,000 $ 33,735,000

$ 93,964,000 Shareholders’ equity Common stock Retained earnings Total equity

Total assets

6,461,000 13,078,000

$108,615,000

Total liabilities and equity

$

5,200,000 50,141,000 $ 55,341,000 $108,615,000

Yacht Industry Ratios

Current ratio Quick ratio Total asset turnover Inventory turnover Receivables turnover Debt ratio Debt–equity ratio Equity multiplier Interest coverage Profit margin Return on assets Return on equity

Lower Quartile

Median

0.50 0.21 0.68 4.89 6.27 0.44 0.79 1.79 5.18 4.05% 6.05% 9.93%

1.43 0.38 0.85 6.15 9.82 0.52 1.08 2.08 8.06 6.98% 10.53% 16.54%

Upper Quartile 1.89 0.62 1.38 10.89 14.11 0.61 1.56 2.56 9.83 9.87% 13.21% 26.15%

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1. Calculate all of the ratios listed in the industry table for East Coast Yachts. 2. Compare the performance of East Coast Yachts to the industry as a whole. For each ratio, comment on why it might be viewed as positive or negative relative to the industry. Suppose you create an inventory ratio calculated as inventory divided by current liabilities. How do you interpret this ratio? How does East Coast Yachts compare to the industry average? 3. Calculate the sustainable growth rate of East Coast Yachts. Calculate external funds needed (EFN) and prepare pro forma income statements and balance sheets assuming growth at precisely this rate. Recalculate the ratios in the previous question. What do youo bserve? 4. As a practical matter, East Coast Yachts is unlikely to be willing to raise external equity capital, in part because the owners don’t want to dilute their existing ownership and control positions. However, East Coast Yachts is planning for a growth rate of 20 percent next year. What are your conclusions and recommendations about the feasibility of East Coast’s expansion plans? 5. Most assets can be increased as a percentage of sales. For instance, cash can be increased by any amount. However, fixed assets often must be increased in specific amounts because it is impossible, as a practical matter, to buy part of a new plant or machine. In this case a company has a “staircase” or “lumpy” fixed cost structure. Assume that East Coast Yachts is currently producing at 100 percent of capacity. As a result, to expand production, the company must set up an entirely new line at a cost of $30 million. Calculate the new EFN with this assumption. What does this imply about capacity utilization for East Coast Yachts next year?

PART II

CHAPTER 4

DiscountedCashFl ow Valuation What do baseball players Jason Varitek, Mark Teixeira, and C. C. Sabathia have in common? All three athletes signed big contracts in late 2008 or early 2009. The contract values were reported as $10 million, $180 million, and $161.5 million, respectively. But reported figures like these are often misleading. For example, in February 2009, Jason Varitek signed with the Boston Red Sox. His contract called for salaries of $5 million, and a club option of $5 million for 2010, for a total of $10 million. Not bad, especially for someone who makes a living using the “tools of ignorance” (jock jargon for a catcher’s equipment). A closer look at the numbers shows that Jason, Mark, and C. C. did pretty well, but nothing like the quoted figures. Using Mark’s contract as an example, although the value was reported to be $180 million, it was actually payable over several years. It consisted of a $5 million signing bonus plus $175 million in future salary and bonuses. The $175 million was to be distributed as $20 million per year in 2009 and 2010 and $22.5 million per year for years 2011 through 2016. Because the payments were spread out over time, we must consider the time value of money, which means his contract was worth less than reported. How much did he really get? This chapter gives you the “tools of knowledge” to answer this question.

4.1 Valuation: The One-Period Case Keith Vaughn is trying to sell a piece of raw land in Alaska. Yesterday he was offered $10,000 for the property. He was about ready to accept the offer when another individual offered him $11,424. However, the second offer was to be paid a year from now. Keith has satisfied himself that both buyers are honest and financially solvent, so he has no fear that the offer he selects will fall through. These two offers are pictured as cash flows in Figure 4.1. Which offer should Keith choose? Mike Tuttle, Keith’s financial adviser, points out that if Keith takes the first offer, he could invest the $10,000 in the bank at an insured rate of 12 percent. At the end of one year, he would have: $10,000 + (.12 × $10,000) = $10,000 × 1.12 = $11,200 Return of Interest principal

87

88

Figure 4.1 Cash Flow for Keith Vaughn’s Sale

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Valuation and Capital Budgeting

Alternative sale prices

$10,000

$11,424

0

1

Year:

Because this is less than the $11,424 Keith could receive from the second offer, Mike recommends that he take the latter. This analysis uses the concept of future value (FV) or compound value, which is the value of a sum after investing over one or more periods. The compound or future value of $10,000 at 12 percent is $11,200. An alternative method employs the concept of present value (PV). One can determine present value by asking the following question: How much money must Keith put in the bank today so that he will have $11,424 next year? We can write this algebraically as: PV × 1.12 =$11,424 We want to solve for PV, the amount of money that yields $11,424 if invested at 12 percent today. Solving for PV, we have: $11,424 PV = _______ =$10,200 1.12 The formula for PV can be written as follows: Present Value of Investment: C1 PV = _____ 1+r

(4.1)

where C1 is cash flow at date 1 and r is the rate of return that Keith Vaughn requires on his land sale. It is sometimes referred to as the discount rate. Present value analysis tells us that a payment of $11,424 to be received next year has a present value of $10,200 today. In other words, at a 12 percent interest rate, Keith is indifferent between $10,200 today or $11,424 next year. If you gave him $10,200 today, he could put it in the bank and receive $11,424 next year. Because the second offer has a present value of $10,200, whereas the first offer is for only $10,000, present value analysis also indicates that Keith should take the second offer. In other words, both future value analysis and present value analysis lead to the same decision. As it turns out, present value analysis and future value analysis must always lead to the same decision. As simple as this example is, it contains the basic principles that we will be working with over the next few chapters. We now use another example to develop the concept of net present value.

EXAMPLE 4.1

Present Value Lida Jennings, a financial analyst at Kaufman & Broad, a leading real estate firm, is thinking about recommending that Kaufman & Broad invest in a piece of land that costs $85,000. She is certain that next year the land will be worth $91,000, a sure $6,000 gain. Given that the guaranteed interest rate in the bank is 10 percent, should Kaufman & Broad undertake the investment in land? Ms. Jennings’s choice is described in Figure 4.2 with the cash flow time chart. A moment’s thought should be all it takes to convince her that this is not an attractive business deal. By investing $85,000 in the land, she will have $91,000 available next year. Suppose, instead,

Chapter 4

Discounted Cash Flow Valuation

Figure 4.2

89

Cash Flows for Land Investment

Cash inflow

$91,000

Time Cash outflow

0

1

$85,000

that Kaufman & Broad puts the same $85,000 into the bank. At the interest rate of 10 percent, this $85,000 would grow to: (1 + .10) × $85,000 = $93,500 next year. It would be foolish to buy the land when investing the same $85,000 in the financial market would produce an extra $2,500 (that is, $93,500 from the bank minus $91,000 from the land investment). This is a future value calculation. Alternatively, she could calculate the present value of the sale price next year as: $91,000 Present value = _______ 1.10 = $82,727.27 Because the present value of next year’s sales price is less than this year’s purchase price of $85,000, present value analysis also indicates that she should not recommend purchasing the property.

Frequently, financial analysts want to determine the exact cost or benefit of a decision. In Example 4.1, the decision to buy this year and sell next year can be evaluated as: −$2,273 =

−$85,000

+

Cost of land today

$91,000 _______ 1.10 Present value of next year’s sales price

The formula for NPV can be written as follows: Net Present Value of Investment: NPV = −Cost + PV

(4.2)

Equation 4.2 says that the value of the investment is −$2,273, after stating all the benefits and all the costs as of date 0. We say that −$2,273 is the net present value (NPV) of the investment. That is, NPV is the present value of future cash flows minus the present value of the cost of the investment. Because the net present value is negative, Lida Jennings should not recommend purchasing the land. Both the Vaughn and the Jennings examples deal with perfect certainty. That is, Keith Vaughn knows with perfect certainty that he could sell his land for $11,424 next year. Similarly, Lida Jennings knows with perfect certainty that Kaufman & Broad could receive $91,000 for selling its land. Unfortunately, businesspeople frequently do not know future cash flows. This uncertainty is treated in the next example.

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EXAMPLE 4.2

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Valuation and Capital Budgeting

Uncertainty and Valuation Professional Artworks, Inc., is a firm that speculates in modern paintings. The manager is thinking of buying an original Picasso for $400,000 with the intention of selling it at the end of one year. The manager expects that the painting will be worth $480,000 in one year. The relevant cash flows are depicted in Figure 4.3.

Figure 4.3

Cash Flows for Investment in Painting

Expected cash inflow

$480,000

Time Cash outflow

0

1

ⴚ$400,000

Of course, this is only an expectation—the painting could be worth more or less than $480,000. Suppose the guaranteed interest rate granted by banks is 10 percent. Should the firm purchase the piece of art? Our first thought might be to discount at the interest rate, yielding: $480,000 ________ 1.10

= $436,364

Because $436,364 is greater than $400,000, it looks at first glance as if the painting should be purchased. However, 10 percent is the return one can earn on a riskless investment. Because the painting is quite risky, a higher discount rate is called for. The manager chooses a rate of 25 percent to reflect this risk. In other words, he argues that a 25 percent expected return is fair compensation for an investment as risky as this painting. The present value of the painting becomes: $480,000 ________ 1.25

= $384,000

Thus, the manager believes that the painting is currently overpriced at $400,000 and does not make thepur chase.

The preceding analysis is typical of decision making in today’s corporations, though real-world examples are, of course, much more complex. Unfortunately, any example with risk poses a problem not faced in a riskless example. In an example with riskless cash flows, the appropriate interest rate can be determined by simply checking with a few banks. The selection of the discount rate for a risky investment is quite a difficult task. We simply don’t know at this point whether the discount rate on the painting in Example 4.2 should be 11 percent, 25 percent, 52 percent, or some other percentage. Because the choice of a discount rate is so difficult, we merely wanted to broach the subject here. We must wait until the specific material on risk and return is covered in later chapters before a risk-adjusted analysis can be presented.

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Discounted Cash Flow Valuation

91

4.2 TheMul tiperiodCase The previous section presented the calculation of future value and present value for one period only. We will now perform the calculations for the multiperiod case.

Future Value and Compounding Suppose an individual were to make a loan of $1. At the end of the first year, the borrower would owe the lender the principal amount of $1 plus the interest on the loan at the interest rate of r. For the specific case where the interest rate is, say, 9 percent, the borrower owes the lender: $1 × (1 + r) = $1 × 1.09 =$1.09 At the end of the year, though, the lender has two choices. She can either take the $1.09—or, more generally, (1 + r)—out of the financial market, or she can leave it in and lend it again for a second year. The process of leaving the money in the financial market and lending it for another year is called compounding. Suppose the lender decides to compound her loan for another year. She does this by taking the proceeds from her first one-year loan, $1.09, and lending this amount for the next year. At the end of next year, then, the borrower will owe her: $1 × (1 + r) × (1 + r) = $1 × (1 + r)2 = 1 + 2r + r2 $1 × (1.09) × (1.09) = $1 × (1.09)2 = $1 + $.18 + $.0081 =$1.1881 This is the total she will receive two years from now by compounding the loan. In other words, the capital market enables the investor, by providing a ready opportunity for lending, to transform $1 today into $1.1881 at the end of two years. At the end of three years, the cash will be $1 × (1.09)3 = $1.2950. The most important point to notice is that the total amount the lender receives is not just the $1 that she lent plus two years’ worth of interest on $1: 2 × r = 2 × $.09 =$.18 The lender also gets back an amount r2, which is the interest in the second year on the interest that was earned in the first year. The term 2 × r represents simple interest over the two years, and the term r2 is referred to as the interest on interest. In our example, this latter amount is exactly: r2 = ($.09)2 =$.0081 When cash is invested at compound interest, each interest payment is reinvested. With simple interest, the interest is not reinvested. Benjamin Franklin’s statement, “Money makes money and the money that money makes makes more money,” is a colorful way of explaining compound interest. The difference between compound interest and simple interest is illustrated in Figure 4.4. In this example, the difference does not amount to much because the loan is for $1. If the loan were for $1 million, the lender would receive $1,188,100 in two years’ time. Of this amount, $8,100 is interest on interest. The lesson is that those small numbers beyond the decimal point can add up to big dollar amounts when the transactions are for big amounts. In addition, the longer-lasting the loan, the more important interest on interest becomes.

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Figure 4.4

$1.295 $1.270

Simple and Compound Interest

$1.188 $1.180

$1.09

$1

1 year 2 years 3 years The dark-shaded area indicates the difference between compound and simple interest. The difference is substantial over a period of many years or decades.

The general formula for an investment over many periods can be written as follows: Future Value of an Investment: FV = C0 × (1 + r)T

(4.3)

where C0 is the cash to be invested at date 0 (i.e., today), r is the interest rate per period, and T is the number of periods over which the cash is invested.

I Interest on Interest Suh-Pyng Ku has put $500 in a savings account at the First National Bank of Kent. The account earns 7 percent, compounded annually. How much will Ms. Ku have at the end o of three years? The answer is: $500 × 1.07 × 1.07 × 1.07 = $500 × (1.07)3 = $612.52 Figure 4.5 illustrates the growth of Ms. Ku’s account.

Figure 4.5

Suh-Pyng Ku’s Savings Account

$612.52 Dollars

EXAMPLE 4.3

$500

$612.52 0

1

2 Time

3

0 $500

1

2 Time

3

Chapter 4

EXAMPLE4.4

Discounted Cash Flow Valuation

93

Compound Growth Jay Ritter invested $1,000 in the stock of the SDH Company. The company pays a current dividend of $2, which is expected to grow by 20 percent per year for the next two years. What will the dividend of the SDH Company be after two years? A simple calculation gives: $2 × (1.20)2 = $2.88 Figure 4.6 illustrates the increasing value of SDH’s dividends.

Figure 4.6

The Growth of the SDH Dividends

$2.88

Dollars

$2.88 Cash inflows $2.40

$2.40

$2.00

$2.00

0

1 Time

2

0

1 Time

2

The two previous examples can be calculated in any one of several ways. The computations could be done by hand, by calculator, by spreadsheet, or with the help of a table. We will introduce spreadsheets in a few pages, and we show how to use a calculator in Appendix 4B on the Web site. The appropriate table is Table A.3, which appears in the back of the text. This table presents future value of $1 at the end of T periods. The table is used by locating the appropriate interest rate on the horizontal and the appropriate number of periods on the vertical. For example, Suh-Pyng Ku would look at the following portion of Table A.3: Interest Rate Period

6%

7%

8%

1 2 3 4

1.0600 1.1236 1.1910 1.2625

1.0700 1.1449 1.2250 1.3108

1.0800 1.1664 1.2597 1.3605

She could calculate the future value of her $500 as: × = $612.50 $500 1.2250 Initial Future value investment of $1 In the example concerning Suh-Pyng Ku, we gave you both the initial investment and the interest rate and then asked you to calculate the future value. Alternatively, the interest rate could have been unknown, as shown in the following example.

EXAMPLE 4.5

F Finding the Rate Carl Voigt, who recently won $10,000 in the lottery, wants to buy a car in five years. Carl estimates that the car will cost $16,105 at that time. His cash flows are displayed in Figure 4.7. C What interest rate must he earn to be able to afford the car? (continued )

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Figure 4.7

Cash Flows for Purchase of Carl Voigt’s Car

$10,000

Cash inflow

5 0 Cash outflow

Time

$16,105

The ratio of purchase price to initial cash is: $16,105 _______

$10,000 = 1.6105

Thus, he must earn an interest rate that allows $1 to become $1.6105 in five years. Table A.3 tells us that an interest rate of 10 percent will allow him to purchase the car. We can express the problem algebraically as: $10,000 × (1 + r)5 = $16,105 where r is the interest rate needed to purchase the car. Because $16,105 $10,000 = 1.6105, we have: (1 + r)5 = 1.6105 r = 10% Either the table, a spreadsheet, or a hand calculator lets us solve for r.

The Power of Compounding: A Digression Most people who have had any experience with compounding are impressed with its power over long periods. Take the stock market, for example. Ibbotson and Sinquefield have calculated what the stock market returned as a whole from 1926 through 2008.1 They find that one dollar placed in these stocks at the beginning of 1926 would have been worth $2,049.45 at the end of 2008. This is 9.62 percent compounded annually for 83 years—that is, (1.0962)83 = $2,049.45, ignoring a small rounding error. The example illustrates the great difference between compound and simple interest. At 9.62 percent, simple interest on $1 is 9.62 cents a year. Simple interest over 83 years is $7.98 (=83 × $.0962). That is, an individual withdrawing 9.62 cents every year would have withdrawn $7.98 (=83 × $.0962) over 83 years. This is quite a bit below the $2,049.45 that was obtained by reinvestment of all principal and interest. The results are more impressive over even longer periods. A person with no experience in compounding might think that the value of $1 at the end of 166 years would be twice the value of $1 at the end of 83 years, if the yearly rate of return stayed the same. Actually the value of $1 at the end of 166 years would be the square of the value of $1 at the end of 83 years. That is, if the annual rate of return remained the same, a $1 investment in common stocks should be worth $4,200,245.30 [=$1 × (2,049.45 × 2,049.45)]. A few years ago, an archaeologist unearthed a relic stating that Julius Caesar lent the Roman equivalent of one penny to someone. Because there was no record of the penny ever being repaid, the archaeologist wondered what the interest and principal 1

Stocks, Bonds, Bills, and Inflation [SBBI]. 2009 Yearbook. Morningstar, Chicago, 2009.

Chapter 4

Discounted Cash Flow Valuation

95

would be if a descendant of Caesar tried to collect from a descendant of the borrower in the 20th century. The archaeologist felt that a rate of 6 percent might be appropriate. To his surprise, the principal and interest due after more than 2,000 years was vastly greater than the entire wealth on earth. The power of compounding can explain why the parents of well-to-do families frequently bequeath wealth to their grandchildren rather than to their children. That is, they skip a generation. The parents would rather make the grandchildren very rich than make the children moderately rich. We have found that in these families the grandchildren have a more positive view of the power of compounding than do the children.

EXAMPLE 4.6

How Much for That Island? Some people have said that it was the best real estate deal in history. Peter Minuit, director general of New Netherlands, the Dutch West India Company’s colony in North America, in 1626 allegedly bought Manhattan Island for 60 guilders’ worth of trinkets from native Americans. By 1667, the Dutch were forced by the British to exchange it for Suriname (perhaps the worst real estate deal ever). This sounds cheap; but did the Dutch really get the better end of the deal? It is reported that 60 guilders was worth about $24 at the prevailing exchange rate. If the native Americans had sold the trinkets at a fair market value and invested the $24 at 5 percent (tax free), it would now, about 383 years later, be worth more than $3.1 billion. Today, Manhattan is undoubtedly worth more than $3.1 billion, so at a 5 percent rate of return the native Americans got the worst of the deal. However, if invested at 10 percent, the amount of money they received would be worth about: $24(1 + r)T = 24 × 1.1383 ≅ $171 quadrillion This is a lot of money. In fact, $171 quadrillion is more than all the real estate in the world is worth today. Note that no one in the history of the world has ever been able to find an investment yielding 10 percent every year for 383 years.

PresentV aluea ndDi scounting We now know that an annual interest rate of 9 percent enables the investor to transform $1 today into $1.1881 two years from now. In addition, we would like to know the following: How much would an investor need to lend today so that she could receive $1 two years from today?

Algebraically, we can write this as: PV × (1.09)2 =$1 In the preceding equation, PV stands for present value, the amount of money we must lend today to receive $1 in two years’ time. Solving for PV in this equation, we have: $1 PV = ______ =$.84 1.1881 This process of calculating the present value of a future cash flow is called discounting. It is the opposite of compounding. The difference between compounding and discounting is illustrated in Figure 4.8. To be certain that $.84 is in fact the present value of $1 to be received in two years, we must check whether or not, if we lent $.84 today and rolled over the loan for two years,

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Figure 4.8

$2,367.36 Compound interest

Compounding and Discounting

Dollars

Compounding at 9%

$1,900 Simple interest $1,000

$1,000

$422.41

Discounting at 9% 1

2

3

4 5 6 7 8 9 10 Future years The top line shows the growth of $1,000 at compound interest with the funds invested at 9 percent: $1,000 × (1.09)10 = $2,367.36. Simple interest is shown on the next line. It is $1,000 + [10 × ($1,000 × .09)] = $1,900. The bottom line shows the discounted value of $1,000 if the interest rate is 9 percent.

we would get exactly $1 back. If this were the case, the capital markets would be saying that $1 received in two years’ time is equivalent to having $.84 today. Checking the exact numbers, we get: $.84168 × 1.09 × 1.09 =$1 In other words, when we have capital markets with a sure interest rate of 9 percent, we are indifferent between receiving $.84 today or $1 in two years. We have no reason to treat these two choices differently from each other because if we had $.84 today and lent it out for two years, it would return $1 to us at the end of that time. The value .84 [=1 (1.09)2] is called the present value factor. It is the factor used to calculate the present value of a future cash flow. In the multiperiod case, the formula for PV can be written as follows: Present Value of Investment: CT PV = ________ (1 + r)T

(4.4)

Here, CT is the cash flow at date T and r is the appropriate discount rate.

EXAMPLE 4.7

Multiperiod Discounting Bernard Dumas will receive $10,000 three years from now. Bernard can earn 8 percent on his investments, so the appropriate discount rate is 8 percent. What is the present value of his future cash flow? The answer is:

( )

1 PV = $10,000 × ____ 1.08

3

= $10,000 × .7938 = $7,938 Figure 4.9 illustrates the application of the present value factor to Bernard’s investment. When his investments grow at an 8 percent rate of interest, Bernard Dumas is equally inclined toward receiving $7,938 now and receiving $10,000 in three years’ time. After all, he could convert the $7,938 he receives today into $10,000 in three years by lending it at an interest rate of 8 percent.

Chapter 4

Discounted Cash Flow Valuation

Figure 4.9

97

Discounting Bernard Dumas’s Opportunity

Dollars

$10,000

Cash inflows

$7,938

0 0

1

2

$10,000 1

2 Time

3

3

Time Bernard d Dumas D could ld have h reached h d his h present value l calculation l l in one off severall ways. The Th computation could have been done by hand, by calculator, with a spreadsheet, or with the help of Table A.1, which appears in the back of the text. This table presents the present value of $1 to be received after T periods. We use the table by locating the appropriate interest rate on the horizontal and the appropriate number of periods on the vertical. For example, Bernard Dumas would look at the following portion of Table A.1: Interest Rate Period

7%

8%

9%

1 2 3 4

.9346 .8734 .8163 .7629

.9259 .8573 .7938 .7350

.9174 .8417 .7722 .7084

The appropriate present value factor is .7938.

In the preceding example we gave both the interest rate and the future cash flow. Alternatively, the interest rate could have been unknown.

EXAMPLE 4.8

Finding the Rate A customer of the Chaffkin Corp. wants to buy a tugboat today. Rather than paying immediately, he will pay $50,000 in three years. It will cost the Chaffkin Corp. $38,610 to build the tugboat immediately. The relevant cash flows to Chaffkin Corp. are displayed in Figure 4.10. What interest rate would the Chaffkin Corp. charge to neither gain nor lose on the sale?

Figure 4.10

Cash Flows for Tugboat

Cash inflows

$50,000

Time 0 Cash outflows

3

$38,610 (continued )

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The ratio of construction cost (present value) to sale price (future value) is: $38,610 _______

$50,000 = .7722

We must determine the interest rate that allows $1 to be received in three years to have a present value of $.7722. Table A.1 tells us that 9 percent is that interest rate.

Finding the Number of Periods Suppose we are interested in purchasing an asset that costs $50,000. We currently have $25,000. If we can earn 12 percent on this $25,000, how long until we have the $50,000? Finding the answer involves solving for the last variable in the basic present value equation, the number of periods. You already know how to get an approximate answer to this particular problem. Notice that we need to double our money. From the Rule of 72 (see Problem 75 at the end of the chapter), this will take about 72 12 = 6 years at 12 percent. To come up with the exact answer, we can again manipulate the basic present value equation. The present value is $25,000, and the future value is $50,000. With a 12 percent discount rate, the basic equation takes one of the following forms: $25,000 = $50,000 1.12t $50,000 25,000 = 1.12t = 2 We thus have a future value factor of 2 for a 12 percent rate. We now need to solve for t. If you look down the column in Table A.1 that corresponds to 12 percent, you will see that a future value factor of 1.9738 occurs at six periods. It will thus take about six years, as we calculated. To get the exact answer, we have to explicitly solve for t (by using a financial calculator or the spreadsheet on the next page). If you do this, you will see that the answer is 6.1163 years, so our approximation was quite close in this case.

EXAMPLE 4.9

Waiting for Godot You’ve been saving up to buy the Godot Company. The total cost will be $10 million. You currently have about $2.3 million. If you can earn 5 percent on your money, how long will you have to wait? At 16 percent, how long must you wait? At 5 percent, you’ll have to wait a long time. From the basic present value equation: $2.3 million = $10 million 1.05t 1.05t = 4.35 t = 30 years At 16 percent, things are a little better.Verify for yourself that it will take about 10 years.

Learn more about using Excel for time value and other calculations at www.studyfinance .com.

Frequently, an investor or a business will receive more than one cash flow. The present value of a set of cash flows is simply the sum of the present values of the individual cash flows. This is illustrated in the following two examples.

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99

SPREADSHEET APPLICATIONS

Using a Spreadsheet for Time Value of Money Calculations More and more, businesspeople from many different areas (not just finance and accounting) rely on spreadsheets to do all the different types of calculations that come up in the real world. As a result, in this section, we will show you how to use a spreadsheet to handle the various time value of money problems we present in this chapter. We will use Microsoft Excel™, but the commands are similar for other types of software. We assume you are already familiar with basic spreadsheet operations. As we have seen, you can solve for any one of the following four potential unknowns: future value, present value, the discount rate, or the number of periods. With a spreadsheet, there is a separate formula for each. In Excel, these are shown in a nearby box. In these formulas, pv and fv are present and To Find Enter This Formula future value, nper is the number of periods, and rate is the discount, or interest, rate. Future value = FV (rate,nper,pmt,pv) Two things are a little tricky here. First, unlike Present value = PV (rate,nper,pmt,fv) a financial calculator, the spreadsheet requires Discount rate = RATE (nper,pmt,pv,fv) that the rate be entered as a decimal. Second, Number of periods as with most financial calculators, you have to = NPER (rate,pmt,pv,fv) put a negative sign on either the present value or the future value to solve for the rate or the number of periods. For the same reason, if you solve for a present value, the a negative l h answer will ill have h i sign i unless you input a negative future value. The same is true when you compute a future value. To illustrate how you might use these formulas, we will go back to an example in the chapter. If you invest $25,000 at 12 percent per year, how long until you have $50,000? You might set up a spreadsheet like this: A 1 2 3 4 5 6 7 8 9 10 11 12 13 14

EXAMPLE4.1 0

B

C

D

E

F

G

H

Using a spreadsheet for time value of money calculations If we invest $25,000 at 12 percent, how long until we have $50,000? We need to solve for the unknown number of periods, so we use the formula NPER(rate, pmt, pv, fv). Present value (pv): Future value (fv): Rate (rate):

$25,000 $50,000 .12

Periods: 6.1162554 The formula entered in cell B11 is =NPER(B9,0,-B7,B8); notice that pmt is zero and that pv has a negative sign on it. Also notice that rate is entered as a decimal, not a percentage.

C Cash Flow Valuation Kyle Mayer has won the Kentucky State Lottery and will receive the following set of cash flows over the next two years: lo Year

Cash Flow

1 2

$20,000 50,000 (continued )

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Mr. Mayer can currently earn 6 percent in his money market account, so the appropriate discount rate is 6 percent. The present value of the cash flows is: Year

Cash Flow × Present Value Factor = Present Value 1 1 ____ $20,000 × ____ 1.06 = $20,000 × 1.06 = $18,867.9

1

1 2 1 ______ $50,000 × ____ 1.06 = $50,000 × (1.06)2 = $44,499.8 Total $63,367.7

(

2

)

In other words, Mr. Mayer is equally inclined toward receiving $63,367.7 today and receiving $20,000 and $50,000 over the next two years.

EXAMPLE 4.11

NPV Finance.com has an opportunity to invest in a new high-speed computer that costs $50,000. The computer will generate cash flows (from cost savings) of $25,000 one year from now, $20,000 two years from now, and $15,000 three years from now. The computer will be worthless after three years, and no additional cash flows will occur. Finance.com has determined that the appropriate discount rate is 7 percent for this investment. Should Finance.com make this investment in a new high-speed computer? What is the net present value of the investment? The cash flows and present value factors of the proposed computer are as follows: Cash Flows

Present Value Factor

Year 0

−$50,000

1

$25,000

2

$20,000

3

$15,000

1=1 1 ____ 1.07 = .9346 1 2 ____ 1.07 = .8734 1 3 = .8163 ____ 1.07

( (

) )

The present value of the cash flows is: Cash Flows × Present value factor = Present value Year 0 1 2 3

−$50,000 × 1 $25,000 × .9346 $20,000 × .8734 $15,000 × .8163

= = = = Total:

−$50,000 $23,365 $17,468 $12,244.5 $ 3,077.5

Finance.com should invest in the new high-speed computer because the present value of its future cash flows is greater than its cost. The NPV is $3,077.5.

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TheAl gebraicF ormula To derive an algebraic formula for the net present value of a cash flow, recall that the PV of receiving a cash flow one year from now is: PV = C1 (1 + r) and the PV of receiving a cash flow two years from now is: PV = C2 (1 + r)2 We can write the NPV of a T-period project as: CT C1 C2 NPV = −C0 + _____ + _______2 + . . . + ________ = −C0 + 1 + r (1 + r) (1 + r)T

T

Ci

∑_______ (1 + r) i

(4.5)

i=1

The initial flow, –C0, is assumed to be negative because it represents an investment. The ∑ is shorthand for the sum of the series. We will close out this section by answering the question we posed at the beginning of the chapter concerning baseball player Mark Teixeira’s contract. Remember that the contract reportedly called for a signing bonus of $5 million to be paid immediately, plus a salary of $175 million to be distributed as $20 million per year in 2009 and 2010 and $22.5 million per year for 2011 through 2016. If 12 percent is the appropriate discount rate, what kind of deal did the New York Yankees’ first baseman snag? To answer, we can calculate the present value by discounting each year’s salary back to the present as follows (notice we assumed the future salaries will be paid at the end of the year): Year 0: $5,000,000 Year 1: $20,000,000 × 1 Year 2: $20,000,000 × 1 Year 3: $22,500,000 × 1 . . . . . . Year 8: $22,500,000 × 1

1.12 1.122 1.123

1.128

= $ 5,000,000 = $17,857,142.86 = $15,943,877.55 = $16,015,055.58 . . . = $ 9,087,372.63

If you fill in the missing rows and then add (do it for practice), you will see that Teixeira’s contract had a present value of about $112.55 million, or only about 63 percent of the $180 million reported value, but still pretty good.

4.3 Compounding Periods So far, we have assumed that compounding and discounting occur yearly. Sometimes, compounding may occur more frequently than just once a year. For example, imagine that a bank pays a 10 percent interest rate “compounded semiannually.” This means that a $1,000 deposit in the bank would be worth $1,000 × 1.05 = $1,050 after six months, and $1,050 × 1.05 = $1,102.50 at the end of the year. The end-of-the-year wealth can be written as:

(

)

.10 2 $1,000 1 + _ = $1,000 × (1.05)2 =$1,102.50 2 Of course, a $1,000 deposit would be worth $1,100 (=$1,000 × 1.10) with yearly compounding. Note that the future value at the end of one year is greater with semiannual

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compounding than with yearly compounding. With yearly compounding, the original $1,000 remains the investment base for the full year. The original $1,000 is the investment base only for the first six months with semiannual compounding. The base over the second six months is $1,050. Hence one gets interest on interest with semiannual compounding. Because $1,000 × 1.1025 = $1,102.50, 10 percent compounded semiannually is the same as 10.25 percent compounded annually. In other words, a rational investor could not care less whether she is quoted a rate of 10 percent compounded semiannually or a rate of 10.25 percent compounded annually. Quarterly compounding at 10 percent yields wealth at the end of one year of:

(

)

.10 4 $1,000 1 + _ =$1,103.81 4 More generally, compounding an investment m times a year provides end-of-year wealth of: r m (4.6) C0( 1 + _ ) m where C0 is the initial investment and r is the stated annual interest rate. The stated annual interest rate is the annual interest rate without consideration of compounding. Banks and other financial institutions may use other names for the stated annual interest rate. Annual percentage rate (APR) is perhaps the most common synonym.

EXAMPLE 4.12

EARs What is the end-of-year wealth if Jane Christine receives a stated annual interest rate of 24 percent compounded monthly on a $1 investment? Using Equation 4.6, her wealth is:

(

.24 $1 1 + _ 12

)

12

= $1 × (1.02)12 = $1.2682

The annual rate of return is 26.82 percent. This annual rate of return is called either the effective annual rate (EAR) or the effective annual yield (EAY). Due to compounding, the effective annual interest rate is greater than the stated annual interest rate of 24 percent. Algebraically, we can rewrite the effective annual interest rate as follows: Effective Annual Rate: r )m (1 + _ −1 (4.7) m Students are often bothered by the subtraction of 1 in Equation 4.7. Note that end-of-year wealth is composed of both the interest earned over the year and the original principal. We remove the original principal by subtracting 1 in Equation 4.7.

EXAMPLE4.1 3

Compounding Frequencies If the stated annual rate of interest, 8 percent, is compounded quarterly, what is the effective annual rate? Using Equation 4.7, we have: r ) (1 + _ m

m

(

.08 −1= 1+_ 4

)

4

− 1 = .0824 = 8.24%

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103

Referring back to our original example where C0 = $1,000 and r = 10%, we can generate the following table:

C0

Compounding Frequency (m)

C1

Effective Annual Rate m= r) ( 1 + __ −1 m

$1,000 1,000 1,000 1,000

Yearly (m = 1) Semiannually (m = 2) Quarterly (m = 4) Daily (m = 365)

$1,100.00 1,102.50 1,103.81 1,105.16

.10 .1025 .10381 .10516

Distinction between Stated Annual Interest Rate and Effective Annual Rate The distinction between the stated annual interest rate (SAIR), or APR, and the effective annual rate (EAR) is frequently troubling to students. We can reduce the confusion by noting that the SAIR becomes meaningful only if the compounding interval is given. For example, for an SAIR of 10 percent, the future value at the end of one year with semiannual compounding is [1 + (.10 2)]2 = 1.1025. The future value with quarterly compounding is [1 + (.10 4)]4 = 1.1038. If the SAIR is 10 percent but no compounding interval is given, we cannot calculate future value. In other words, we do not know whether to compound semiannually, quarterly, or over some other interval. By contrast, the EAR is meaningful without a compounding interval. For example, an EAR of 10.25 percent means that a $1 investment will be worth $1.1025 in one year. We can think of this as an SAIR of 10 percent with semiannual compounding or an SAIR of 10.25 percent with annual compounding, or some other possibility. There can be a big difference between an SAIR and an EAR when interest rates are large. For example, consider “payday loans.” Payday loans are short-term loans made to consumers, often for less than two weeks, and are offered by companies such as AmeriCash Advance and National Payday. The loans work like this: You write a check today that is postdated. When the check date arrives, you go to the store and pay the cash for the check, or the company cashes the check. For example, AmeriCash Advance allows you to write a postdated check for $125 for 15 days later. In this case, they would give you $100 today. So, what are the APR and EAR of this arrangement? First, we need to find the interest rate, which we can find by the FV equation as follows: FV = PV (1 + r )T $125 = $100 × (1 + r )1 1.25 = (1 + r ) r = .25 or 25% That doesn’t seem too bad until you remember this is the interest rate for 15 days! The APR of the loan is: APR = .25 × 365 15 APR =6.0833o r608.33%

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And the EAR for this loan is: EAR = (1 + r m)m − 1 EAR = (1 + .25)365 15 − 1 EAR = 227.1096 or 22,710.96% Now that’s an interest rate! Just to see what a difference a day (or three) makes, let’s look at National Payday’s terms. This company will allow you to write a postdated check for the same amount, but will allow you 18 days to repay. Check for yourself that the APR of this arrangement is 506.94 percent and the EAR is 9,128.26 percent. This is lower, but still not a loan we usually recommend.

Compoundingo verMa nyY ears Equation 4.6 applies for an investment over one year. For an investment over one or more (T) years, the formula becomes this: Future Value with Compounding: r mT FV = C0( 1 + _ ) m

EXAMPLE4.1 4

(4.8)

Multiyear Compounding Harry DeAngelo is investing $5,000 at a stated annual interest rate of 12 percent per year, compounded quarterly, for five years. What is his wealth at the end of five years? Using Equation 4.8, his wealth is: .12 4×5 $5,000 × 1 + _ = $5,000 × (1.03)20 = $5,000 × 1.8061 = $9,030.50 4

(

)

ContinuousCo mpounding The previous discussion shows that we can compound much more frequently than once a year. We could compound semiannually, quarterly, monthly, daily, hourly, each minute, or even more often. The limiting case would be to compound every infinitesimal instant, which is commonly called continuous compounding. Surprisingly, banks and other financial institutions sometimes quote continuously compounded rates, which is why we study them. Though the idea of compounding this rapidly may boggle the mind, a simple formula is involved. With continuous compounding, the value at the end of T years is expressed as: C0 × e r T

(4.9)

where C0 is the initial investment, r is the stated annual interest rate, and T is the number of years over which the investment runs. The number e is a constant and is approximately equal to 2.718. It is not an unknown like C0, r,an d T.

EXAMPLE4.1 5

Continuous Compounding Linda DeFond invested $1,000 at a continuously compounded rate of 10 percent for one year. What is the value of her wealth at the end of one year? From Equation 4.9 we have: $1,000 × e .10 = $1,000 × 1.1052 = $1,105.20

Chapter 4

Discounted Cash Flow Valuation

105

This number can easily be read from Table A.5. We merely set r, the value on the horizontal dimension, to 10 percent and T, the value on the vertical dimension, to 1. For this problem the relevant portion of the table is shown here: Period (T ) 1 2 3

Continuously Compounded Rate (r) 9%

10%

11%

1.0942 1.1972 1.3100

1.1052 1.2214 1.3499

1.1163 1.2461 1.3910

Note that a continuously compounded rate of 10 percent is equivalent to an annually compounded rate of 10.52 percent. In other words, Linda DeFond would not care whether her bank quoted a continuously compounded rate of 10 percent or a 10.52 percent rate, compounded annually.

EXAMPLE4.1 6

Continuous Compounding, Continued Linda DeFond’s brother, Mark, invested $1,000 at a continuously compounded rate of 10 percent for two years. The appropriate formula here is: $1,000 × e .10×2 = $1,000 × e .20 = $1,221.40 Using the portion of the table of continuously compounded rates shown in the previous example, we find the value to be 1.2214.

Figure Fi 4.11 4 11 illustrates ill the h relationship l i hi among annual, l semiannual, i l and d continuous i compounding. Semiannual compounding gives rise to both a smoother curve and a higher ending value than does annual compounding. Continuous compounding has both the smoothest curve and the highest ending value of all.

EXAMPLE4.1 7

Present Value with Continuous Compounding The Michigan State Lottery is going to pay you $100,000 at the end of four years. If the annual continuously compounded rate of interest is 8 percent, what is the present value of this payment? 1 1 $100,000 × _ = $100,000 × __ 1.3771 = $72,616.37 e .08×4

Figure 4.11 4

4

3 2

4 Interest earned

3

Dollars

Interest earned

Dollars

Dollars

Annual, Semiannual, and Continuous Compounding

2

0

1

2 3 Years

4

Annual compounding

5

Interest earned

2 1

1

1

3

0

1

2 3 Years

4

5

Semiannual compounding

0

1

2 3 Years

4

5

Continuous compounding

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4.4 Simplifications The first part of this chapter has examined the concepts of future value and present value. Although these concepts allow us to answer a host of problems concerning the time value of money, the human effort involved can be excessive. For example, consider a bank calculating the present value of a 20-year monthly mortgage. This mortgage has 240 (=20 × 12) payments, so a lot of time is needed to perform a conceptually simple task. Because many basic finance problems are potentially time-consuming, we search for simplifications in this section. We provide simplifying formulas for four classes of cash flow streams: • • • •

Perpetuity. Growingp erpetuity. Annuity. Growingan nuity.

Perpetuity A perpetuity is a constant stream of cash flows without end. If you are thinking that perpetuities have no relevance to reality, it will surprise you that there is a well-known case of an unending cash flow stream: The British bonds called consols. An investor purchasing a consol is entitled to receive yearly interest from the British government forever. How can the price of a consol be determined? Consider a consol that pays a coupon of C dollars each year and will do so forever. Simply applying the PV formula gives us: C C C PV = _ + __2 + __3 + . . . 1 + r (1 + r ) (1 + r ) where the dots at the end of the formula stand for the infinite string of terms that continues the formula. Series like the preceding one are called geometric series. It is well known that even though they have an infinite number of terms, the whole series has a finite sum because each term is only a fraction of the preceding term. Before turning to our calculus books, though, it is worth going back to our original principles to see if a bit of financial intuition can help us find the PV. The present value of the consol is the present value of all of its future coupons. In other words, it is an amount of money that, if an investor had it today, would enable him to achieve the same pattern of expenditures that the consol and its coupons would. Suppose an investor wanted to spend exactly C dollars each year. If he had the consol, he could do this. How much money must he have today to spend the same amount? Clearly, he would need exactly enough so that the interest on the money would be C dollars per year. If he had any more, he could spend more than C dollars each year. If he had any less, he would eventually run out of money spending C dollars per year. The amount that will give the investor C dollars each year, and therefore the present value of the consol, is simply: C (4.10) PV = __ r To confirm that this is the right answer, notice that if we lend the amount C r, the interest it earns each year will be: C Interest = __ × r = C r

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107

which is exactly the consol payment. We have arrived at this formula for a consol: Formula for Present Value of Perpetuity: C C C PV = _ + __2 + __3 + . . . 1 + r (1 + r ) (1 + r ) C = __ r

(4.11)

It is comforting to know how easily we can use a bit of financial intuition to solve this mathematical problem.

EXAMPLE4.1 8

Perpetuities Consider a perpetuity paying $100 a year. If the relevant interest rate is 8 percent, what is the value of the consol? Using Equation 4.10 we have: $100 PV = _ .08 = $1,250 Now suppose that interest rates fall to 6 percent. Using Equation 4.10 the value of the perpetuity is: $100 PV = _ .06 = $1,666.67 Note that the value of the perpetuity rises with a drop in the interest rate. Conversely, the value of the perpetuity falls with a rise in the interest rate.

GrowingP erpetuity Imagine an apartment building where cash flows to the landlord after expenses will be $100,000 next year. These cash flows are expected to rise at 5 percent per year. If one assumes that this rise will continue indefinitely, the cash flow stream is termed a growing perpetuity. The relevant interest rate is 11 percent. Therefore, the appropriate discount rate is 11 percent, and the present value of the cash flows can be represented as: $100,000(1.05)2 $100,000 $100,000(1.05) ___ PV = __ + ___ + +... 1.11 (1.11)2 (1.11)3 $100,000(1.05)N−1 + ____ + ... (1.11)N Algebraically, we can write the formula as: N−1

C × (1 + g ) ___ C × (1 + g ) C × (1 + g ) C PV = _ + ___ + + . . . + ___ +... 1+r (1 + r )2 (1 + r )3 (1 + r )N 2

where C is the cash flow to be received one period hence, g is the rate of growth per period, expressed as a percentage, and r is the appropriate discount rate. Fortunately, this formula reduces to the following simplification: Formula for Present Value of Growing Perpetuity: C (4.12) PV = _ r−g From Equation 4.12 the present value of the cash flows from the apartment building is: $100,000 __ =$1,666,667 .11 − .05

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There are three important points concerning the growing perpetuity formula: 1. The numerator: The numerator in Equation 4.12 is the cash flow one period hence, not at date 0. Consider the following example.

EXAMPLE4.1 9

Paying Dividends Popovich Corporation is just about to pay a dividend of $3.00 per share. Investors anticipate that the annual dividend will rise by 6 percent a year forever. The applicable discount rate is 11 percent. What is the price of the stock today? The numerator in Equation 4.12 is the cash flow to be received next period. Since the growth rate is 6 percent, the dividend next year is $3.18 (=$3.00 × 1.06). The price of the stock today is: $66.60

=

$3.00 Imminent dividend

+

$3.18 __ .11 − .06 Present value of all dividends beginning a year from now

The price of $66.60 includes both the dividend to be received immediately and the present value of all dividends beginning a year from now. Equation 4.12 makes it possible to calculate only the present value of all dividends beginning a year from now. Be sure you understand this example; test questions on this subject always seem to trip up a few of our students.

2. The discount rate and the growth rate: The discount rate r must be greater than the growth rate g for the growing perpetuity formula to work. Consider the case in which the growth rate approaches the interest rate in magnitude. Then, the denominator in the growing perpetuity formula gets infinitesimally small and the present value grows infinitely large. The present value is in fact undefined when r is less than g. 3. The timing assumption: Cash generally flows into and out of real-world firms both randomly and nearly continuously. However, Equation 4.12 assumes that cash flows are received and disbursed at regular and discrete points in time. In the example of the apartment, we assumed that the net cash flows of $100,000 occurred only once a year. In reality, rent checks are commonly received every month. Payments for maintenance and other expenses may occur anytime within the year. We can apply the growing perpetuity formula of Equation 4.12 only by assuming a regular and discrete pattern of cash flow. Although this assumption is sensible because the formula saves so much time, the user should never forget that it is an assumption. This point will be mentioned again in the chapters ahead. A few words should be said about terminology. Authors of financial textbooks generally use one of two conventions to refer to time. A minority of financial writers treat cash flows as being received on exact dates—for example date 0, date 1, and so forth. Under this convention, date 0 represents the present time. However, because a year is an interval, not a specific moment in time, the great majority of authors refer to cash flows that occur at the end of a year (or alternatively, the end of a period). Under this end-of-the-year convention, the end of year 0 is the present, the end of year 1 occurs one period hence, and so on. (The beginning of year 0 has already passed and is not generally referred to.)2 2

Sometimes, financial writers merely speak of a cash flow in year x. Although this terminology is ambiguous, such writers generally mean the end of year x.

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109

The interchangeability of the two conventions can be seen from the following chart:

Date 0 = Now End of year 0 = Now

Date 1

Date 2

Date 3

...

End of year 1

End of year 2

End of year 3

...

We strongly believe that the dates convention reduces ambiguity. However, we use both conventions because you are likely to see the end-of-year convention in later courses. In fact, both conventions may appear in the same example for the sake of practice.

Annuity An annuity is a level stream of regular payments that lasts for a fixed number of periods. Not surprisingly, annuities are among the most common kinds of financial instruments. The pensions that people receive when they retire are often in the form of an annuity. Leases and mortgages are also often annuities. To figure out the present value of an annuity we need to evaluate the following equation: C C C C _ + __ + __ + . . . + __ 1 + r (1 + r)2 (1 + r)3 (1 + r)T The present value of receiving the coupons for only T periods must be less than the present value of a consol, but how much less? To answer this, we have to look at consols a bit more closely. Consider the following time chart: Now

Date (or end of year) Consol 1 Consol 2 Annuity

0

1 C

2 C

3 C ...

T C

C

C

C ...

C

(T + 1) (T + 2) C C ... C C ...

Consol 1 is a normal consol with its first payment at date 1. The first payment of consol 2 occurs at date T + 1. The present value of having a cash flow of C at each of T dates is equal to the present value of consol 1 minus the present value of consol 2. The present value of consol 1 is given by: C PV = _ (4.13) r Consol 2 is just a consol with its first payment at date T + 1. From the perpetuity formula, this consol will be worth C r at date T.3 However, we do not want the value Students frequently think that C/r is the present value at date T + 1 because the consol’s first payment is at date T + 1. However, the formula values the consol as of one period prior to the first payment.

3

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at date T. We want the value now, in other words, the present value at date 0. We must discount C r back by T periods. Therefore, the present value of consol 2 is:

[

C 1 PV = _ __ r (1 + r)T

]

(4.14)

The present value of having cash flows for T years is the present value of a consol with its first payment at date 1 minus the present value of a consol with its first payment at date T + 1. Thus the present value of an annuity is Equation 4.13 minus Equation 4.14. This can be written as:

[

C __ C _ 1 _ − r r (1 + r)T

]

This simplifies to the following: Formula for Present Value of Annuity: 1 1 PV = C _ − __T r r(1 + r)

[

]

This can also be written as:

[

1 1 − __T (1 + r) PV = C ___ r

EXAMPLE 4.20

]

(4.15)

Lottery Valuation Mark Young has just won the state lottery, paying $50,000 a year for 20 years. He is to receive his first payment a year from now. The state advertises this as the Million Dollar Lottery because $1,000,000 = $50,000 × 20. If the interest rate is 8 percent, what is the present value of the lottery? Equation 4.15 yields:

Present value of Million Dollar Lottery

[

1 1 − __ (1.08)20 ___ = $50,000 × .08

]

Periodic payment Annuity factor = $50,000 × 9.8181 = $490,905 Rather than being overjoyed at winning, Mr. Young sues the state for misrepresentation and fraud. His legal brief states that he was promised $1 million but received only $490,905.

The term we use to compute the present value of the stream of level payments, C, for T years is called an annuity factor. The annuity factor in the current example is 9.8181. Because the annuity factor is used so often in PV calculations, we have included it in Table A.2 in the back of this book. The table gives the values of these factors for a range of interest rates, r, and maturity dates, T. The annuity factor as expressed in the brackets of Equation 4.15 is a complex formula. For simplification, we may from time to time refer to the annuity factor as: A Tr

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111

This expression stands for the present value of $1 a year for T years at an interest rate of r. We can also provide a formula for the future value of an annuity:

[

] [

(1 + r)T 1 (1 + r)T − 1 FV = C __ − _ = C ___ r r r

]

(4.16)

As with present value factors for annuities, we have compiled future value factors in Table A.4 in the back of this book.

EXAMPLE 4.21

Retirement Investing Suppose you put $3,000 per year into a Roth IRA. The account pays 6 percent interest per year. How much will you have when you retire in 30 years? This question asks for the future value of an annuity of $3,000 per year for 30 years at 6 percent, which we can calculate as follows:

[

]

(1 + r)T − 1 1.0630 − 1 FV = C ___ = $3,000 × __ r .06 = $3,000 × 79.0582 = $237,174.56

[

]

So, you’ll have close to a quarter million dollars in the account.

Our experience is that annuity formulas are not hard, but tricky, for the beginning student. We present four tricks next.

SPREADSHEET APPLICATIONS

Annuity Present Values Using a spreadsheet to find annuity present values goes like this: A

B

C

D

E

F

G

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Using a spreadsheet to find annuity present values What is the present value of $500 per year for 3 years if the discount rate is 10 percent? We need to solve for the unknown present value, so we use the formula PV(rate, nper, pmt, fv). Payment amount per period: Number of payments: Discount rate:

$500 3 0.1

Annuity present value:

$1,243.43

The formula entered in cell B11 is =PV(B9,B8,-B7,0); notice that fv is zero and that pmt has a negative sign on it. Also notice that rate is entered as a decimal, not a percentage.

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Trick 1: A Delayed Annuity One of the tricks in working with annuities or perpetuities is getting the timing exactly right. This is particularly true when an annuity or perpetuity begins at a date many periods in the future. We have found that even the brightest beginning student can make errors here. Consider the following example.

EXAMPLE 4.22

Delayed Annuities Danielle Caravello will receive a four-year annuity of $500 per year, beginning at date 6. If the interest rate is 10 percent, what is the present value of her annuity? This situation can be graphed as follows:

0

1

2

3

4

5

6 $500

7 $500

8 $500

9 $500

10

The analysis involves two steps: 1. Calculate the present value of the annuity using Equation 4.15: Present Value of Annuity at Date 5:

[

]

1 1 − __ (1.10)4 $500 __ = $500 × A 4.10 .10 = $500 × 3.1699 = $1,584.95 Note that $1,584.95 represents the present value at date 5. Students frequently think that $1,584.95 is the present value at date 6 because the annuity begins at date 6. However, our formula values the annuity as of one period prior to the first payment. This can be seen in the most typical case where the first payment occurs at date 1. The formula values the annuity as of date 0 in that case. 2. Discount the present value of the annuity back to date 0: Present Value at Date 0: $1,584.95 __ (1.10)5 = $984.13 Again, it is worthwhile mentioning that because the annuity formula brings Danielle’s annuity back to date 5, the second calculation must discount over the remaining five periods. The two-step procedure is graphed in Figure 4.12.

Figure 4.12 Date 0 Cash flow $984.13

Discounting Danielle Caravello’s Annuity

1

2

3

4

5

6 $500

7 $500

8 $500

$1,584.95

Step one: Discount the four payments back to date 5 by using the annuity formula. Step two: Discount the present value at date 5 ($1,584.95) back to present value at date 0.

9 $500

10

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113

Trick 2: Annuity Due The annuity formula of Equation 4.15 assumes that the first annuity payment begins a full period hence. This type of annuity is sometimes called an annuity in arrears or an ordinary annuity. What happens if the annuity begins today—in other words, at date 0?

EXAMPLE 4.23

Annuity Due In a previous example, Mark Young received $50,000 a year for 20 years from the state lottery. In that example, he was to receive the first payment a year from the winning date. Let us now assume that the first payment occurs immediately. The total number of payments remains 20. Under this new assumption, we have a 19-date annuity with the first payment occurring at date 1—plus an extra payment at date 0. The present value is: 19 $50,000 × A .08

$50,000

+

Payment at date 0

19-year annuity = $50,000 + ($50,000 × 9.6036) = $530,180

$530,180, the present value in this example, is greater than $490,905, the present value in the earlier lottery example. This is to be expected because the annuity of the current example begins earlier. An annuity with an immediate initial payment is called an annuity in advance or, more commonly, an annuity due. Always remember that Equation 4.15 and Table A.2 in this book refer to an ordinary annuity.

Trick 3: The Infrequent Annuity The following example treats an annuity with payments occurring less frequently than once a year.

EXAMPLE 4.24

Infrequent Annuities Ann Chen receives an annuity of $450, payable once every two years. The annuity stretches out over 20 years. The first payment occurs at date 2—that is, two years from today. The annual interest rate is 6 percent. The trick is to determine the interest rate over a two-year period. The interest rate over two years is: (1.06 × 1.06) − 1 = 12.36% That is, $100 invested over two years will yield $112.36. What we want is the present value of a $450 annuity over 10 periods, with an interest rate of 12.36 percent per period:

[

]

1 1 − ___ (1 + .1236)10 ___ $450 = $450 × A 10 .1236 = $2,505.57 .1236

Trick 4: Equating Present Value of Two Annuities The following example equates the present value of inflows with the present value of outflows.

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EXAMPLE 4.25

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Working with Annuities Harold and Helen Nash are saving for the college education of their newborn daughter, Susan. The Nashes estimate that college expenses will run $30,000 per year when their daughter reaches college in 18 years. The annual interest rate over the next few decades will be 14 percent. How much money must they deposit in the bank each year so that their daughter will be completely supported through four years of college? To simplify the calculations, we assume that Susan is born today. Her parents will make the first of her four annual tuition payments on her 18th birthday. They will make equal bank deposits on each of her first 17 birthdays, but no deposit at date 0. This is illustrated as follows:

Date 0

1

Susan’s Parents’ birth 1st deposit

2

...

Parents’ . . . 2nd deposit

17 Parents’ 17th and last deposit

18

19

Tuition Tuition payment payment 1 2

20

21

Tuition Tuition payment payment 3 4

Mr. and Ms. Nash will be making deposits to the bank over the next 17 years. They will be withdrawing $30,000 per year over the following four years. We can be sure they will be able to withdraw fully $30,000 per year if the present value of the deposits is equal to the present value of the four $30,000 withdrawals. This calculation requires three steps.The first two determine the present value of the withdrawals. The final step determines yearly deposits that will have a present value equal to that of the withdrawals. 1. We calculate the present value of the four years at college using the annuity formula:

[

]

1 1 − __4 (1.14) __ $30,000 × = $30,000 × A 4.14 .14 = $30,000 × 2.9137 = $87,411 We assume that Susan enters college on her 18th birthday. Given our discussion in Trick 1, $87,411 represents the present value at date 17. 2. We calculate the present value of the college education at date 0 as: $87,411 __ = $9,422.91 (1.14)17 3. Assuming that Harold and Helen Nash make deposits to the bank at the end of each of the 17 years, we calculate the annual deposit that will yield a present value of all deposits of $9,422.91. This is calculated as: C × A 17 .14 = $9,422.91 Because A 17 .14 = 6.3729, $9,422.91 C = __ 6.3729 = $1,478.59 Thus deposits of $1,478.59 made at the end of each of the first 17 years and invested at 14 percent will provide enough money to make tuition payments of $30,000 over the following four years.

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115

An alternative method in Example 4.25 would be to (1) calculate the present value of the tuition payments at Susan’s 18th birthday and (2) calculate annual deposits so that the future value of the deposits at her 18th birthday equals the present value of the tuition payments at that date. Although this technique can also provide the right answer, we have found that it is more likely to lead to errors. Therefore, we equate only present values in our presentation.

GrowingAnnui ty Cash flows in business are likely to grow over time, due either to real growth or to inflation. The growing perpetuity, which assumes an infinite number of cash flows, provides one formula to handle this growth. We now consider a growing annuity, which is a finite number of growing cash flows. Because perpetuities of any kind are rare, a formula for a growing annuity would be useful indeed. Here is the formula: Formula for Present Value of Growing Annuity: 1+g T 1 − __ T 1 1 1 + g 1+r PV = C _ − _ × _ = C ___ r−g r−g 1+r r−g

[

(

[

)]

(

)

]

(4.17)

As before, C is the payment to occur at the end of the first period, r is the interest rate, g is the rate of growth per period, expressed as a percentage, and T is the number of periodsf orth ean nuity.

EXAMPLE 4.26

Growing Annuities Stuart Gabriel, a second-year MBA student, has just been offered a job at $80,000 a year. He anticipates his salary increasing by 9 percent a year until his retirement in 40 years. Given an interest rate of 20 percent, what is the present value of his lifetime salary? We simplify by assuming he will be paid his $80,000 salary exactly one year from now, and that his salary will continue to be paid in annual installments. The appropriate discount rate is 20 percent. From Equation 4.17, the calculation is: 1.09 40 1− _ 1.20 Present value of Stuart’s lifetime salary = $80,000 × ___ .20 − .09 = $711,730.71

[

(

)

]

Though the growing annuity formula is quite useful, it is more tedious than the other simplifying formulas. Whereas most sophisticated calculators have special programs for perpetuity, growing perpetuity, and annuity, there is no special program for a growing annuity. Hence, we must calculate all the terms in Equation 4.17 directly.

EXAMPLE 4.27

More Growing Annuities In a previous example, Helen and Harold Nash planned to make 17 identical payments to fund the college education of their daughter, Susan. Alternatively, imagine that they planned to increase their payments at 4 percent per year. What would their first payment be? The first two steps of the previous Nash family example showed that the present value of the college costs was $9,422.91.These two steps would be the same here. However, the third step must be altered. Now we must ask, How much should their first payment be so that, if payments increase by 4 percent per year, the present value of all payments will be $9,422.91? (continued )

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We set the growing annuity formula equal to $9,422.91 and solve for C:

[

] [

1+g T 1.04 17 1− _ 1− _ 1.14 1 + r = C ___ C ___ r−g .14 − .04 = $9,422.91

(

)

(

)

]

Here, C = $1,192.78. Thus, the deposit on their daughter’s first birthday is $1,192.78, the deposit on the second birthday is $1,240.49 (=1.04 × $1,192.78), and so on.

4.5 Loan Amortization Whenever a lender extends a loan, some provision will be made for repayment of the principal (the original loan amount). A loan might be repaid in equal installments, for example, or it might be repaid in a single lump sum. Because the way that the principal and interest are paid is up to the parties involved, there are actually an unlimited number of possibilities. In this section, we describe amortized loans. Working with these loans is a very straightforward application of the present value principles that we have already developed. An amortized loan may require the borrower to repay parts of the loan amount over time. The process of providing for a loan to be paid off by making regular principal reductions is called amortizing the loan. A simple way of amortizing a loan is to have the borrower pay the interest each period plus some fixed amount. This approach is common with medium-term business loans. For example, suppose a business takes out a $5,000, five-year loan at 9 percent. The loan agreement calls for the borrower to pay the interest on the loan balance each year and to reduce the loan balance each year by $1,000. Because the loan amount declines by $1,000 each year, it is fully paid in five years. In the case we are considering, notice that the total payment will decline each year. The reason is that the loan balance goes down, resulting in a lower interest charge each year, whereas the $1,000 principal reduction is constant. For example, the interest in the first year will be $5,000 × .09 = $450. The total payment will be $1,000 + 450 = $1,450. In the second year, the loan balance is $4,000, so the interest is $4,000 × .09 = $360, and the total payment is $1,360. We can calculate the total payment in each of the remaining years by preparing a simple amortization schedule as follows:

Year 1 2 3 4 5 Totals

Beginning Balance

Total Payment

Interest Paid

Principal Paid

Ending Balance

$5,000 4,000 3,000 2,000 1,000

$1,450 1,360 1,270 1,180 1,090 $6,350

$ 450 360 270 180 90 $1,350

$1,000 1,000 1,000 1,000 1,000 $5,000

$4,000 3,000 2,000 1,000 0

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Discounted Cash Flow Valuation

117

Notice that in each year, the interest paid is given by the beginning balance multiplied by the interest rate. Also notice that the beginning balance is given by the ending balance from the previous year. Probably the most common way of amortizing a loan is to have the borrower make a single, fixed payment every period. Almost all consumer loans (such as car loans) and mortgages work this way. For example, suppose our five-year, 9 percent, $5,000 loan was amortized this way. How would the amortization schedule look? We first need to determine the payment. From our discussion earlier in the chapter, we know that this loan’s cash flows are in the form of an ordinary annuity. In this case, we can solve for the payment as follows: $5,000 = C × { [1 − (1 1.095)] .09} = C × [(1 − .6499) .09] This gives us: C = $5,000 3.8897 =$1,285.46 The borrower will therefore make five equal payments of $1,285.46. Will this pay off the loan? We will check by filling in an amortization schedule. In our previous example, we knew the principal reduction each year. We then calculated the interest owed to get the total payment. In this example, we know the total payment. We will thus calculate the interest and then subtract it from the total payment to calculate the principal portion in each payment. In the first year, the interest is $450, as we calculated before. Because the total payment is $1,285.46, the principal paid in the first year must be: Principal paid = $1,285.46 − 450 =$835.46 The ending loan balance is thus: Ending balance = $5,000 − 835.46 =$4,164.54 The interest in the second year is $4,164.54 × .09 = $374.81, and the loan balance declines by $1,285.46 − 374.81 = $910.65. We can summarize all of the relevant calculations in the following schedule:

Year 1 2 3 4 5 Totals

Beginning Balance

Total Payment

Interest Paid

Principal Paid

Ending Balance

$5,000.00 4,164.54 3,253.88 2,261.27 1,179.32

$1,285.46 1,285.46 1,285.46 1,285.46 1,285.46 $6,427.30

$ 450.00 374.81 292.85 203.51 106.14 $1,427.31

$ 835.46 910.65 992.61 1,081.95 1,179.32 $5,000.00

$4,164.54 3,253.88 2,261.27 1,179.32 0.00

Because the loan balance declines to zero, the five equal payments do pay off the loan. Notice that the interest paid declines each period. This isn’t surprising because the loan balance is going down. Given that the total payment is fixed, the principal paid must be rising each period.

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If you compare the two loan amortizations in this section, you will see that the total interest is greater for the equal total payment case: $1,427.31 versus $1,350. The reason for this is that the loan is repaid more slowly early on, so the interest is somewhat higher. This doesn’t mean that one loan is better than the other; it simply means that one is effectively paid off faster than the other. For example, the principal reduction in the first year is $835.46 in the equal total payment case as compared to $1,000 in the first case.

EXAMPLE 4.28

Partial Amortization, or “Bite the Bullet” A common arrangement in real estate lending might call for a 5-year loan with, say, a 15-year amortization. What this means is that the borrower makes a payment every month of a fixed amount based on a 15-year amortization. However, after 60 months, the borrower makes a single, much larger payment called a “balloon” or “bullet” to pay off the loan. Because the monthly payments don’t fully pay off the loan, the loan is said to be partially amortized. Suppose we have a $100,000 commercial mortgage with a 12 percent APR and a 20-year (240-month) amortization. Further suppose the mortgage has a five-year balloon. What will the monthly payment be? How big will the balloon payment be? The monthly payment can be calculated based on an ordinary annuity with a present value of $100,000. There are 240 payments, and the interest rate is 1 percent per month. The payment is: $100,000 = C × [1 − (1 1.01240) .01] = C × 90.8194 C = $1,101.09 Now, there is an easy way and a hard way to determine the balloon payment. The hard way is to actually amortize the loan for 60 months to see what the balance is at that time. The easy way is to recognize that after 60 months, we have a 240 − 60 = 180-month loan. The payment is still $1,101.09 per month, and the interest rate is still 1 percent per month. The loan balance is thus the present value of the remaining payments: Loan balance = $1,101.09 × [1 − (1 1.01180) .01] = $1,101.09 × 83.3217 = $91,744.69 The balloon payment is a substantial $91,744. Why is it so large? To get an idea, consider the first payment on the mortgage. The interest in the first month is $100,000 × .01 = $1,000. Your payment is $1,101.09, so the loan balance declines by only $101.09. Because the loan balance declines so slowly, the cumulative “pay down” over five years is not great.

We will close this section with an example that may be of particular relevance. Federal Stafford loans are an important source of financing for many college students, helping to cover the cost of tuition, books, new cars, condominiums, and many other things. Sometimes students do not seem to fully realize that Stafford loans have a serious drawback: They must be repaid in monthly installments, usually beginning six months after the student leaves school. Some Stafford loans are subsidized, meaning that the interest does not begin to accrue until repayment begins (this is a good thing). If you are a dependent undergraduate student under this particular option, the total debt you can run up is,

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119

at most, $23,000. The maximum interest rate is 8.25 percent, or 8.25 12 = .6875 percent per month. Under the “standard repayment plan,” the loans are amortized over 10 years (subject to a minimum payment of $50). Suppose you max out borrowing under this program and also get stuck paying the maximum interest rate. Beginning six months after you graduate (or otherwise depart the ivory tower), what will your monthly payment be? How much will you owe after making payments for four years? Given our earlier discussions, see if you don’t agree that your monthly payment assuming a $23,000 total loan is $282.10 per month. Also, as explained in Example 4.28, after making payments for four years, you still owe the present value of the remaining payments. There are 120 payments in all. After you make 48 of them (the first four years), you have 72 to go. By now, it should be easy for you to verify that the present

SPREADSHEET APPLICATIONS

Loan Amortization Using a Spreadsheet Loan amortization is a common spreadsheet application. To illustrate, we will set up the problem that we examined earlier: a five-year, $5,000, 9 percent loan with constant payments. Our spreadsheet looks like this: A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

B

C

D

E

F

G

Using a spreadsheet to amortize a loan Loan amount: Interest rate: Loan term: Loan payment:

$5,000 0.09 5 $1,285.46 Note: Payment is calculated using PMT(rate, nper, -pv, fv).

Amortization table: Year 1 2 3 4 5 Totals

Beginning Balance $5,000.00 4,164.54 3,253.88 2,261.27 1,179.32

Total Payment $1,285.46 1,285.46 1,285.46 1,285.46 1,285.46 6,427.31

Interest Paid $450.00 374.81 292.85 203.51 106.14 1,427.31

Principal Paid $835.46 910.65 992.61 1,081.95 1,179.32 5,000.00

Ending Balance $4,164.54 3,253.88 2,261.27 1,179.32 0.00

Formulas in the amortization table: Year 1 2 3 4 5

Beginning Balance =+D4 =+G13 =+G14 =+G15 =+G16

Total Payment =$D$7 =$D$7 =$D$7 =$D$7 =$D$7

Interest Paid =+$D$5*C13 =+$D$5*C14 =+$D$5*C15 =+$D$5*C16 =+$D$5*C17

Principal Paid =+D13-E13 =+D14-E14 =+D15-E15 =+D16-E16 =+D17-E17

Ending Balance =+C13-F13 =+C14-F14 =+C15-F15 =+C16-F16 =+C17-F17

Note: Totals in the amortization table are calculated using the SUM formula.

H

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value of $282.10 per month for 72 months at .6875 percent per month is just under $16,000, so you still have a long way to go. Of course, it is possible to rack up much larger debts. According to the Association of American Medical Colleges, medical students who borrowed to attend medical school and graduated in 2005 had an average student loan balance of $120,280. Ouch! How long will it take the average student to pay off her medical school loans?

4.6 What Is a Firm Worth? Suppose you are a business appraiser trying to determine the value of small companies. How can you determine what a firm is worth? One way to think about the question of how much a firm is worth is to calculate the present value of its future cash flows. Let us consider the example of a firm that is expected to generate net cash flows (cash inflows minus cash outflows) of $5,000 in the first year and $2,000 for each of the next five years. The firm can be sold for $10,000 seven years from now. The owners of the firm would like to be able to make 10 percent on their investment in the firm. The value of the firm is found by multiplying the net cash flows by the appropriate present value factor. The value of the firm is simply the sum of the present values of the individual net cash flows. The present value of the net cash flows is given next. The Present Value of the Firm End of Year

Net Cash Flow of the Firm

Present Value Factor (10%)

Present Value of Net Cash Flows

1 2 3 4 5 6 7

$ 5,000 2,000 2,000 2,000 2,000 2,000 10,000

.90909 .82645 .75131 .68301 .62092 .56447 .51316 Present value of firm

$ 4,545.45 1,652.90 1,502.62 1,366.02 1,241.84 1,128.94 5,131.58 $16,569.35

We can also use the simplifying formula for an annuity: (2,000 × A 5.10) __ 10,000 $5,000 ___ __ + + =$16,569.35 1.1 1.1 (1.1)7 Suppose you have the opportunity to acquire the firm for $12,000. Should you acquire the firm? The answer is yes because the NPV is positive: NPV = PV − Cost $4,569.35 = $16,569.35 −$12,000 The incremental value (NPV) of acquiring the firm is $4,569.35.

Chapter 4

EXAMPLE 4.29

Discounted Cash Flow Valuation

121

Firm Valuation The Trojan Pizza Company is contemplating investing $1 million in four new outlets in Los Angeles. Andrew Lo, the firm’s chief financial officer (CFO), has estimated that the investments will pay out cash flows of $200,000 per year for nine years and nothing thereafter. (The cash flows will occur at the end of each year and there will be no cash flow after year 9.) Mr. Lo has determined that the relevant discount rate for this investment is 15 percent. This is the rate of return that the firm can earn at comparable projects. Should the Trojan Pizza Company make the investments in the new outlets? The decision can be evaluated as follows: $200,000 __ $200,000 . . . __ $200,000 NPV = −$1,000,000 + __ + 1.15 + (1.15)2 + (1.15)9 9 = −$1,000,000 + $200,000 × A .15 = −$1,000,000 + $954,316.78 = −$45,683.22 The present value of the four new outlets is only $954,316.78. The outlets are worth less than they cost. The Trojan Pizza Company should not make the investment because the NPV is −$45,683.22. If the Trojan Pizza Company requires a 15 percent rate of return, the new outlets are nota g ood investment.

SPREADSHEET APPLICATIONS

How to Calculate Present Values with Multiple Future Cash Flows Using a Spreadsheet We can set up a basic spreadsheet to calculate the present values of the individual cash flows as follows. Notice that we have simply calculated the present values one at a time and added them up: A

B

C

D

E

1

Using a spreadsheet to value multiple future cash flows

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

What is the present value of $200 in one year, $400 the next year, $600 the next year, and $800 the last year if the discount rate is 12 percent? Rate:

0.12

Year

Cash flows

1 2 3 4

$200 $400 $600 $800 Total PV:

Present values $178.57 $318.88 $427.07 $508.41 $1,432.93

Formula used =PV($B$7,A10,0,⫺B10) =PV($B$7,A11,0,⫺B11) =PV($B$7,A12,0,⫺B12) =PV($B$7,A13,0,⫺B13) =SUM(C10:C13)

Notice the negative signs inserted in the PV formulas. These just make the present values have positive signs. Also, the discount rate in cell B7 is entered as $B$7 (an "absolute" reference) because it is used over and over. We could have just entered ".12" instead, but our approach is more flexible.

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Valuation and Capital Budgeting

1. Two basic concepts, future value and present value, were introduced in the beginning of this chapter. With a 10 percent interest rate, an investor with $1 today can generate a future value of $1.10 in a year, $1.21 [=$1 × (1.10)2] in two years, and so on. Conversely, present value analysis places a current value on a future cash flow. With the same 10 percent interest rate, a dollar to be received in one year has a present value of $.909 (=$1 1.10) in year 0. A dollar to be received in two years has a present value of $.826 [=$1 (1.10)2]. 2. We commonly express an interest rate as, say, 12 percent per year. However, we can speak of the interest rate as 3 percent per quarter. Although the stated annual interest rate remains 12 percent (=3 percent × 4), the effective annual interest rate is 12.55 percent [=(1.03)4 − 1]. In other words, the compounding process increases the future value of an investment. The limiting case is continuous compounding, where funds are assumed to be reinvested every infinitesimal instant. 3. A basic quantitative technique for financial decision making is net present value analysis. The net present value formula for an investment that generates cash flows (Ci ) in future periods is:

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C1 C2 CT NPV = −C0 + __ + __2 + . . . + __T = −C0 + (1 + r ) (1 + r ) (1 + r)

T

Ci

∑__ (1 + r) i

i=1

The formula assumes that the cash flow at date 0 is the initial investment (a cash outflow). 4. Frequently, the actual calculation of present value is long and tedious. The computation of the present value of a long-term mortgage with monthly payments is a good example of this. We presented four simplifying formulas: C Perpetuity: PV = _ r C Growing perpetuity: PV = _ r−g

[

1 1 − __T (1 + r) ___ Annuity: PV = C r

[

]

1+g T 1 − __ 1+r Growing annuity: PV = C ___ r−g

(

)

]

5. We stressed a few practical considerations in the application of these formulas: a. The numerator in each of the formulas, C, is the cash flow to be received one full period hence. b. Cash flows are generally irregular in practice. To avoid unwieldy problems, assumptions to create more regular cash flows are made both in this textbook and in the real world. c. A number of present value problems involve annuities (or perpetuities) beginning a few periods hence. Students should practice combining the annuity (or perpetuity) formula with the discounting formula to solve these problems. d. Annuities and perpetuities may have periods of every two or every n years, rather than once a year. The annuity and perpetuity formulas can easily handle such circumstances. e. We frequently encounter problems where the present value of one annuity must be equated with the present value of another annuity.

Chapter 4

Concept Questions

1. 2. 3.

4. 5.

Discounted Cash Flow Valuation

123

Compounding and Period As you increase the length of time involved, what happens to future values? What happens to present values? Interest Rates What happens to the future value of an annuity if you increase the rate r? What happens to the present value? Present Value Suppose two athletes sign 10-year contracts for $80 million. In one case, we’re told that the $80 million will be paid in 10 equal installments. In the other case, we’re told that the $80 million will be paid in 10 installments, but the installments will increase by 5 percent per year. Who got the better deal? APR and EAR Should lending laws be changed to require lenders to report EARs instead of APRs? Why or why not? Time Value On subsidized Stafford loans, a common source of financial aid for college students, interest does not begin to accrue until repayment begins. Who receives a bigger subsidy, a freshman or a senior? Explain.

Questions and Problems

1.

2. BASIC (Questions 1–20)

Simple Interest versus Compound Interest First City Bank pays 9 percent simple interest on its savings account balances, whereas Second City Bank pays 9 percent interest compounded annually. If you made a $5,000 deposit in each bank, how much more money would you earn from your Second City Bank account at the end of 10y ears? Calculating Future Values Compute the future value of $1,000 compounded annually for a. 10y earsa t6p ercent. b. 10 years at 9 percent. c. 20 years at 6 percent. d. Why is the interest earned in part (c) not twice the amount earned in part (a)?

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Use the following information to answer the next five questions: Toyota Motor Credit Corporation (TMCC), a subsidiary of Toyota Motor Corporation, offered some securities for sale to the public on March 28, 2008. Under the terms of the deal, TMCC promised to repay the owner of one of these securities $100,000 on March 28, 2038, but investors would receive nothing until then. Investors paid TMCC $24,099 for each of these securities; so they gave up $24,099 on March 28, 2008, for the promise of a $100,000 payment 30 years later. 6. Time Value of Money Why would TMCC be willing to accept such a small amount today ($24,099) in exchange for a promise to repay about four times that amount ($100,000) in the future? 7. Call Provisions TMCC has the right to buy back the securities on the anniversary date at a price established when the securities were issued (this feature is a term of this particular deal). What impact does this feature have on the desirability of this security as an investment? 8. Time Value of Money Would you be willing to pay $24,099 today in exchange for $100,000 in 30 years? What would be the key considerations in answering yes or no? Would your answer depend on who is making the promise to repay? 9. Investment Comparison Suppose that when TMCC offered the security for $24,099 the U.S. Treasury had offered an essentially identical security. Do you think it would have had a higher or lower price? Why? 10. Length of Investment The TMCC security is bought and sold on the New York Stock Exchange. If you looked at the price today, do you think the price would exceed the $24,099 original price? Why? If you looked in the year 2019, do you think the price would be higher or lower than today’s price? Why?

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3.

Valuation and Capital Budgeting

CalculatingP resentV alues Present Value

4.

$

242 410 51,700 18,750

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$

625 810 18,400 21,500

7.

8.

9.

10.

Interest Rate

Future Value

6 9 18 23

7% 15 11 18

$ 15,451 51,557 886,073 550,164

Solve for the unknown interest rate in each of the

Years

Interest Rate

2 9 15 30

Future Value $

307 896 162,181 483,500

Calculating the Number of Periods Solve for the unknown number of years in each of the following: Present Value

6.

Years

Calculating Interest Rates following: Present Value

5.

For each of the following, compute the present value:

Years

Interest Rate

Future Value

6% 13 32 16

$ 1,284 4,341 402,662 173,439

Calculating the Number of Periods At 9 percent interest, how long does it take to double your money? To quadruple it? Calculating Present Values Imprudential, Inc., has an unfunded pension liability of $750 million that must be paid in 20 years. To assess the value of the firm’s stock, financial analysts want to discount this liability back to the present. If the relevant discount rate is 8.2 percent, what is the present value of this liability? Calculating Rates of Return Although appealing to more refined tastes, art as a collectible has not always performed so profitably. During 2003, Sotheby’s sold the Edgar Degas bronze sculpture Petite Danseuse de Quartorze Ans at auction for a price of $10,311,500. Unfortunately for the previous owner, he had purchased it in 1999 at a price of $12,377,500. What was his annual rate of return on this sculpture? Perpetuities An investor purchasing a British consol is entitled to receive annual payments from the British government forever. What is the price of a consol that pays $120 annually if the next payment occurs one year from today? The market interest rate is 5.7 percent. Continuous Compounding Compute the future value of $1,900 continuously compounded for a. 5 years at a stated annual interest rate of 12 percent. b. 3 years at a stated annual interest rate of 10 percent. c. 10 years at a stated annual interest rate of 5 percent. d. 8 years at a stated annual interest rate of 7 percent.

Chapter 4

11.

12.

13.

14.

Present Value and Multiple Cash Flows Conoly Co. has identified an investment project with the following cash flows. If the discount rate is 10 percent, what is the present value of these cash flows? What is the present value at 18 percent? At 24 percent? Year

Cash Flow

1 2 3 4

$1,200 730 965 1,590

Present Value and Multiple Cash Flows Investment X offers to pay you $5,500 per year for nine years, whereas Investment Y offers to pay you $8,000 per year for five years. Which of these cash flow streams has the higher present value if the discount rate is 5 percent? If the discount rate is 22 percent? Calculating Annuity Present Value An investment offers $4,300 per year for 15 years, with the first payment occurring one year from now. If the required return is 9 percent, what is the value of the investment? What would the value be if the payments occurred for 40 years? For 75 years? Forever? Calculating Perpetuity Values The Perpetual Life Insurance Co. is trying to sell you an investment policy that will pay you and your heirs $20,000 per year forever. If the required return on this investment is 6.5 percent, how much will you pay for the policy? Suppose the Perpetual Life Insurance Co. told you the policy costs $340,000. At what interest rate would this be a fair deal? CalculatingE AR Find the EAR in each of the following cases: Stated Rate (APR) 8% 18 12 14

16.

125

Calculating APR Stated Rate (APR)

Number of Times Compounded Quarterly Monthly Daily Infinite

Find the APR, or stated rate, in each of the following cases: Number of Times Compounded Semiannually Monthly Weekly Infinite

17.

18.

Effective Rate (EAR)

Effective Rate (EAR) 10.3% 9.4 7.2 15.9

Calculating EAR First National Bank charges 10.1 percent compounded monthly on its business loans. First United Bank charges 10.4 percent compounded semiannually. As a potential borrower, to which bank would you go for a new loan? Interest Rates Well-known financial writer Andrew Tobias argues that he can earn 177 percent per year buying wine by the case. Specifically, he assumes that he will consume one $10 bottle of fine Bordeaux per week for the next 12 weeks. He can either pay $10 per week or buy a case of 12 bottles today. If he buys the case, he

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15.

Discounted Cash Flow Valuation

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19.

20.

INTERMEDIATE (Questions 21–50)

21.

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22.

23.

24.

25.

26.

27.

28.

29.

Valuation and Capital Budgeting

receives a 10 percent discount and, by doing so, earns the 177 percent. Assume he buys the wine and consumes the first bottle today. Do you agree with his analysis? Do you see a problem with his numbers? Calculating Number of Periods One of your customers is delinquent on his accounts payable balance. You’ve mutually agreed to a repayment schedule of $600 per month. You will charge .9 percent per month interest on the overdue balance. If the current balance is $18,400, how long will it take for the account to be paid off ? Calculating EAR Friendly’s Quick Loans, Inc., offers you “three for four or I knock on your door.” This means you get $3 today and repay $4 when you get your paycheck in one week (or else). What’s the effective annual return Friendly’s earns on this lending business? If you were brave enough to ask, what APR would Friendly’s sayy ouw erep aying? Future Value What is the future value in seven years of $1,000 invested in an account with a stated annual interest rate of 8 percent, a. Compoundedan nually? b. Compoundeds emiannually? c. Compoundedmo nthly? d. Compoundedc ontinuously? e. Why does the future value increase as the compounding period shortens? Simple Interest versus Compound Interest First Simple Bank pays 6 percent simple interest on its investment accounts. If First Complex Bank pays interest on its accounts compounded annually, what rate should the bank set if it wants to match First Simple Bank over an investment horizon of 10 years? Calculating Annuities You are planning to save for retirement over the next 30 years. To do this, you will invest $700 a month in a stock account and $300 a month in a bond account. The return of the stock account is expected to be 10 percent, and the bond account will pay 6 percent. When you retire, you will combine your money into an account with an 8 percent return. How much can you withdraw each month from your account assuming a 25-year withdrawal period? Calculating Rates of Return Suppose an investment offers to quadruple your money in 12 months (don’t believe it). What rate of return per quarter are you being offered? Calculating Rates of Return You’re trying to choose between two different investments, both of which have up-front costs of $75,000. Investment G returns $135,000 in six years. Investment H returns $195,000 in 10 years. Which of these investments has the higher return? Growing Perpetuities Mark Weinstein has been working on an advanced technology in laser eye surgery. His technology will be available in the near term. He anticipates his first annual cash flow from the technology to be $215,000, received two years from today. Subsequent annual cash flows will grow at 4 percent in perpetuity. What is the present value of the technology if the discount rate is 10 percent? Perpetuities A prestigious investment bank designed a new security that pays a quarterly dividend of $5 in perpetuity. The first dividend occurs one quarter from today. What is the price of the security if the stated annual interest rate is 7 percent, compoundedq uarterly? Annuity Present Values What is the present value of an annuity of $5,000 per year, with the first cash flow received three years from today and the last one received 25 years from today? Use a discount rate of 8 percent. Annuity Present Values What is the value today of a 15-year annuity that pays $750 a year? The annuity’s first payment occurs six years from today. The annual interest rate is 12 percent for years 1 through 5, and 15 percent thereafter.

Chapter 4

30.

31.

32.

33.

35.

36.

37.

38.

127

Balloon Payments Audrey Sanborn has just arranged to purchase a $450,000 vacation home in the Bahamas with a 20 percent down payment. The mortgage has a 7.5 percent stated annual interest rate, compounded monthly, and calls for equal monthly payments over the next 30 years. Her first payment will be due one month from now. However, the mortgage has an eight-year balloon payment, meaning that the balance of the loan must be paid off at the end of year 8. There were no other transaction costs or finance charges. How much will Audrey’s balloon payment be in eighty ears? Calculating Interest Expense You receive a credit card application from Shady Banks Savings and Loan offering an introductory rate of 2.40 percent per year, compounded monthly for the first six months, increasing thereafter to 18 percent compounded monthly. Assuming you transfer the $6,000 balance from your existing credit card and make no subsequent payments, how much interest will you owe at the end of the first year? Perpetuities Barrett Pharmaceuticals is considering a drug project that costs $150,000 today and is expected to generate end-of-year annual cash flows of $13,000, forever. At what discount rate would Barrett be indifferent between accepting or rejecting the project? Growing Annuity Southern California Publishing Company is trying to decide whether to revise its popular textbook, Financial Psychoanalysis Made Simple. The company has estimated that the revision will cost $65,000. Cash flows from increased sales will be $18,000 the first year. These cash flows will increase by 4 percent per year. The book will go out of print five years from now. Assume that the initial cost is paid now and revenues are received at the end of each year. If the company requires an 11 percent return for such an investment, should it undertake the revision? Growing Annuity Your job pays you only once a year for all the work you did over the previous 12 months. Today, December 31, you just received your salary of $60,000, and you plan to spend all of it. However, you want to start saving for retirement beginning next year. You have decided that one year from today you will begin depositing 5 percent of your annual salary in an account that will earn 9 percent per year. Your salary will increase at 4 percent per year throughout your career. How much money will you have on the date of your retirement 40 years from today? Present Value and Interest Rates What is the relationship between the value of an annuity and the level of interest rates? Suppose you just bought a 12-year annuity of $7,500 per year at the current interest rate of 10 percent per year. What happens to the value of your investment if interest rates suddenly drop to 5 percent? What if interest rates suddenly rise to 15 percent? Calculating the Number of Payments You’re prepared to make monthly payments of $250, beginning at the end of this month, into an account that pays 10 percent interest compounded monthly. How many payments will you have made when your account balance reaches $30,000? Calculating Annuity Present Values You want to borrow $80,000 from your local bank to buy a new sailboat. You can afford to make monthly payments of $1,650, but no more. Assuming monthly compounding, what is the highest APR you can afford on a 60-month loan? Calculating Loan Payments You need a 30-year, fixed-rate mortgage to buy a new home for $250,000. Your mortgage bank will lend you the money at a 6.8 percent APR for this 360-month loan. However, you can only afford monthly payments of $1,200, so you offer to pay off any remaining loan balance at the end of the loan in the form of a single balloon payment. How large will this balloon payment have to be for you to keep your monthly payments at $1,200?

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34.

Discounted Cash Flow Valuation

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39.

40.

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41.

42.

43.

44.

45.

46.

47.

48.

Valuation and Capital Budgeting

Present and Future Values The present value of the following cash flow stream is $6,453 when discounted at 10 percent annually. What is the value of the missing cash flow? Year

Cash Flow

1 2 3 4

$1,200 ? 2,400 2,600

Calculating Present Values You just won the TVM Lottery. You will receive $1 million today plus another 10 annual payments that increase by $350,000 per year. Thus, in one year you receive $1.35 million. In two years, you get $1.7 million, and so on. If the appropriate interest rate is 9 percent, what is the present value of your winnings? EAR versus APR You have just purchased a new warehouse. To finance the purchase, you’ve arranged for a 30-year mortgage for 80 percent of the $2,600,000 purchase price. The monthly payment on this loan will be $14,000. What is the APR on this loan? The EAR? Present Value and Break-Even Interest Consider a firm with a contract to sell an asset for $135,000 three years from now. The asset costs $96,000 to produce today. Given a relevant discount rate on this asset of 13 percent per year, will the firm make a profit on this asset? At what rate does the firm just break even? Present Value and Multiple Cash Flows What is the present value of $4,000 per year, at a discount rate of 7 percent, if the first payment is received 9 years from now and the last payment is received 25 years from now? Variable Interest Rates A 15-year annuity pays $1,500 per month, and payments are made at the end of each month. If the interest rate is 13 percent compounded monthly for the first seven years, and 9 percent compounded monthly thereafter, what is the present value of the annuity? Comparing Cash Flow Streams You have your choice of two investment accounts. Investment A is a 15-year annuity that features end-of-month $1,200 payments and has an interest rate of 9.8 percent compounded monthly. Investment B is a 9 percent continuously compounded lump-sum investment, also good for 15 years. How much money would you need to invest in B today for it to be worth as much as Investment A 15 years from now? Calculating Present Value of a Perpetuity Given an interest rate of 7.3 percent per year, what is the value at date t = 7 of a perpetual stream of $2,100 annual payments that begins at date t =15? Calculating EAR A local finance company quotes a 15 percent interest rate on oneyear loans. So, if you borrow $26,000, the interest for the year will be $3,900. Because you must repay a total of $29,900 in one year, the finance company requires you to pay $29,900 12, or $2,491.67, per month over the next 12 months. Is this a 15 percent loan? What rate would legally have to be quoted? What is the effective annual rate? Calculating Present Values A 5-year annuity of ten $4,500 semiannual payments will begin 9 years from now, with the first payment coming 9.5 years from now. If the discount rate is 12 percent compounded monthly, what is the value of this annuity five years from now? What is the value three years from now? What is the current value of the annuity?

Chapter 4

CHALLENGE (Questions 51–76)

Discounted Cash Flow Valuation

129

Calculating Annuities Due Suppose you are going to receive $10,000 per year for five years. The appropriate interest rate is 11 percent. a. What is the present value of the payments if they are in the form of an ordinary annuity? What is the present value if the payments are an annuity due? b. Suppose you plan to invest the payments for five years. What is the future value if the payments are an ordinary annuity? What if the payments are an annuity due? c. Which has the highest present value, the ordinary annuity or annuity due? Which has the highest future value? Will this always be true?

50.

Calculating Annuities Due You want to buy a new sports car from Muscle Motors for $65,000. The contract is in the form of a 48-month annuity due at a 6.45 percent APR. What will your monthly payment be?

51.

Calculating Annuities Due You want to lease a set of golf clubs from Pings Ltd. The lease contract is in the form of 24 equal monthly payments at a 10.4 percent stated annual interest rate, compounded monthly. Because the clubs cost $3,500 retail, Pings wants the PV of the lease payments to equal $3,500. Suppose that your first payment is due immediately. What will your monthly lease payments be?

52.

Annuities You are saving for the college education of your two children. They are two years apart in age; one will begin college 15 years from today and the other will begin 17 years from today. You estimate your children’s college expenses to be $35,000 per year per child, payable at the beginning of each school year. The annual interest rate is 8.5 percent. How much money must you deposit in an account each year to fund your children’s education? Your deposits begin one year from today. You will make your last deposit when your oldest child enters college. Assume four years of college.

53.

Growing Annuities Tom Adams has received a job offer from a large investment bank as a clerk to an associate banker. His base salary will be $45,000. He will receive his first annual salary payment one year from the day he begins to work. In addition, he will get an immediate $10,000 bonus for joining the company. His salary will grow at 3.5 percent each year. Each year he will receive a bonus equal to 10 percent of his salary. Mr. Adams is expected to work for 25 years. What is the present value of the offer if the discount rate is 12 percent?

54.

Calculating Annuities You have recently won the super jackpot in the Washington State Lottery. On reading the fine print, you discover that you have the following two options: a. You will receive 31 annual payments of $175,000, with the first payment being delivered today. The income will be taxed at a rate of 28 percent. Taxes will be withheld when the checks are issued. b. You will receive $530,000 now, and you will not have to pay taxes on this amount. In addition, beginning one year from today, you will receive $125,000 each year for 30 years. The cash flows from this annuity will be taxed at 28 percent. Using a discount rate of 10 percent, which option should you select?

55.

Calculating Growing Annuities You have 30 years left until retirement and want to retire with $1.5 million. Your salary is paid annually, and you will receive $70,000 at the end of the current year. Your salary will increase at 3 percent per year, and you can earn a 10 percent return on the money you invest. If you save a constant percentage of your salary, what percentage of your salary must you save each year?

56.

Balloon Payments On September 1, 2007, Susan Chao bought a motorcycle for $25,000. She paid $1,000 down and financed the balance with a five-year loan at a stated annual interest rate of 8.4 percent, compounded monthly. She started the monthly payments exactly one month after the purchase (i.e., October 1, 2007). Two years later, at the end of October 2009, Susan got a new job and decided to pay off the loan. If the bank charges her a 1 percent prepayment penalty based on the loan balance, how much must she pay the bank on November 1, 2009?

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49.

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57.

58.

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59.

60.

61.

Valuation and Capital Budgeting

Calculating Annuity Values Bilbo Baggins wants to save money to meet three objectives. First, he would like to be able to retire 30 years from now with a retirement income of $20,000 per month for 20 years, with the first payment received 30 years and 1 month from now. Second, he would like to purchase a cabin in Rivendell in 10 years at an estimated cost of $320,000. Third, after he passes on at the end of the 20 years of withdrawals, he would like to leave an inheritance of $1,000,000 to his nephew Frodo. He can afford to save $1,900 per month for the next 10 years. If he can earn an 11 percent EAR before he retires and an 8 percent EAR after he retires, how much will he have to save each month in years 11 through 30? Calculating Annuity Values After deciding to buy a new car, you can either lease the car or purchase it with a three-year loan. The car you wish to buy costs $38,000. The dealer has a special leasing arrangement where you pay $1 today and $520 per month for the next three years. If you purchase the car, you will pay it off in monthly payments over the next three years at an 8 percent APR. You believe that you will be able to sell the car for $26,000 in three years. Should you buy or lease the car? What break-even resale price in three years would make you indifferent between buying andle asing? Calculating Annuity Values An All-Pro defensive lineman is in contract negotiations. The team has offered the following salary structure: Time

Salary

0 1 2 3 4 5 6

$7,500,000 4,200,000 5,100,000 5,900,000 6,800,000 7,400,000 8,100,000

All salaries are to be paid in a lump sum. The player has asked you as his agent to renegotiate the terms. He wants a $9 million signing bonus payable today and a contract value increase of $750,000. He also wants an equal salary paid every three months, with the first paycheck three months from now. If the interest rate is 5 percent compounded daily, what is the amount of his quarterly check? Assume 365 days in a year. Discount Interest Loans This question illustrates what is known as discount interest. Imagine you are discussing a loan with a somewhat unscrupulous lender. You want to borrow $20,000 for one year. The interest rate is 14 percent. You and the lender agree that the interest on the loan will be .14 × $20,000 = $2,800. So, the lender deducts this interest amount from the loan up front and gives you $17,200. In this case, we say that the discount is $2,800. What’s wrong here? Calculating Annuity Values You are serving on a jury. A plaintiff is suing the city for injuries sustained after a freak street sweeper accident. In the trial, doctors testified that it will be five years before the plaintiff is able to return to work. The jury has already decided in favor of the plaintiff. You are the foreperson of the jury and propose that the jury give the plaintiff an award to cover the following: (1) The present value of two years’ back pay. The plaintiff’s annual salary for the last two years would have been $42,000 and $45,000, respectively. (2) The present value of five years’ future salary. You assume the salary will be $49,000 per year. (3) $150,000 for pain and suffering. (4) $25,000 for court costs. Assume that the salary payments are

Chapter 4

62.

63.

64.

Discounted Cash Flow Valuation

131

$1,000 × 1.16 3 = $1,000 × 1.56090 =$1,560.90

65.

Judy recognizes that coming up with $1,560.90 all at once might be a strain, so she lets you make “low, low monthly payments” of $1,560.90 36 = $43.36 per month, even though this is extra bookkeeping work for her. Is this a 16 percent loan? Why or why not? What is the APR on this loan? What is the EAR? Why do you think this is called add-on interest? Calculating Annuity Payments Your friend is celebrating her 35th birthday today and wants to start saving for her anticipated retirement at age 65. She wants to be able to withdraw $110,000 from her savings account on each birthday for 25 years following her retirement; the first withdrawal will be on her 66th birthday. Your friend intends to invest her money in the local credit union, which offers 9 percent interest per year. She wants to make equal annual payments on each birthday into the account established at the credit union for her retirement fund. a. If she starts making these deposits on her 36th birthday and continues to make deposits until she is 65 (the last deposit will be on her 65th birthday), what amount must she deposit annually to be able to make the desired withdrawals at retirement? b. Suppose your friend has just inherited a large sum of money. Rather than making equal annual payments, she has decided to make one lump-sum payment on her 35th birthday to cover her retirement needs. What amount does she have to deposit? c. Suppose your friend’s employer will contribute $1,500 to the account every year as part of the company’s profit-sharing plan. In addition, your friend expects a $50,000 distribution from a family trust fund on her 55th birthday, which she will also put into the retirement account. What amount must she deposit annually now to be able to make the desired withdrawals at retirement?

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equal amounts paid at the end of each month. If the interest rate you choose is a 9 percent EAR, what is the size of the settlement? If you were the plaintiff, would you like to see a higher or lower interest rate? Calculating EAR with Points You are looking at a one-year loan of $10,000. The interest rate is quoted as 9 percent plus three points. A point on a loan is simply 1 percent (one percentage point) of the loan amount. Quotes similar to this one are very common with home mortgages. The interest rate quotation in this example requires the borrower to pay three points to the lender up front and repay the loan later with 9 percent interest. What rate would you actually be paying here? What is the EAR for a one-year loan with a quoted interest rate of 12 percent plus two points? Is your answer affected by the loan amount? EAR versus APR Two banks in the area offer 30-year, $200,000 mortgages at 6.8 percent and charge a $2,100 loan application fee. However, the application fee charged by Insecurity Bank and Trust is refundable if the loan application is denied, whereas that charged by I. M. Greedy and Sons Mortgage Bank is not. The current disclosure law requires that any fees that will be refunded if the applicant is rejected be included in calculating the APR, but this is not required with nonrefundable fees (presumably because refundable fees are part of the loan rather than a fee). What are the EARs on these two loans? What are the APRs? Calculating EAR with Add-On Interest This problem illustrates a deceptive way of quoting interest rates called add-on interest. Imagine that you see an advertisement for Crazy Judy’s Stereo City that reads something like this: “$1,000 Instant Credit! 16% Simple Interest! Three Years to Pay! Low, Low Monthly Payments!” You’re not exactly sure what all this means and somebody has spilled ink over the APR on the loan contract, so you ask the manager for clarification. Judy explains that if you borrow $1,000 for three years at 16 percent interest, in three years you will owe:

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68.

69.

70.

71.

72.

Valuation and Capital Budgeting

Calculating the Number of Periods Your Christmas ski vacation was great, but it unfortunately ran a bit over budget. All is not lost: You just received an offer in the mail to transfer your $9,000 balance from your current credit card, which charges an annual rate of 18.6 percent, to a new credit card charging a rate of 8.2 percent. How much faster could you pay the loan off by making your planned monthly payments of $200 with the new card? What if there was a 2 percent fee charged on any balances transferred? Future Value and Multiple Cash Flows An insurance company is offering a new policy to its customers. Typically the policy is bought by a parent or grandparent for a child at the child’s birth. The details of the policy are as follows: The purchaser (say, the parent) makes the following six payments to the insurance company: Firstb irthday: $ 800 Secondb irthday: $ 800 Thirdb irthday: $ 900 Fourthb irthday: $ 900 Fifthb irthday: $1,000 Sixthb irthday: $1,000 After the child’s sixth birthday, no more payments are made. When the child reaches age 65, he or she receives $350,000. If the relevant interest rate is 11 percent for the first six years and 7 percent for all subsequent years, is the policy worth buying? Annuity Present Values and Effective Rates You have just won the lottery. You will receive $2,000,000 today, and then receive 40 payments of $750,000. These payments will start one year from now and will be paid every six months. A representative from Greenleaf Investments has offered to purchase all the payments from you for $15 million. If the appropriate interest rate is a 9 percent APR compounded daily, should you take the offer? Assume there are 12 months in a year, each with 30 days. Calculating Interest Rates A financial planning service offers a college savings program. The plan calls for you to make six annual payments of $8,000 each, with the first payment occurring today, your child’s 12th birthday. Beginning on your child’s 18th birthday, the plan will provide $20,000 per year for four years. What return is this investment offering? Break-Even Investment Returns Your financial planner offers you two different investment plans. Plan X is a $20,000 annual perpetuity. Plan Y is a 10-year, $35,000 annual annuity. Both plans will make their first payment one year from today. At what discount rate would you be indifferent between these two plans? Perpetual Cash Flows What is the value of an investment that pays $8,500 every other year forever, if the first payment occurs one year from today and the discount rate is 13 percent compounded daily? What is the value today if the first payment occurs four years from today? Assume 365 days in a year. Ordinary Annuities and Annuities Due As discussed in the text, an annuity due is identical to an ordinary annuity except that the periodic payments occur at the beginning of each period and not at the end of the period. Show that the relationship between the value of an ordinary annuity and the value of an otherwise equivalent annuity due is: Annuity due value = Ordinary annuity value × (1 + r ) Show this for both present and future values.

Chapter 4

73.

75.

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133

Calculating EAR A check-cashing store is in the business of making personal loans to walk-up customers. The store makes only one-week loans at 9 percent interest per week. a. What APR must the store report to its customers? What is the EAR that the customers are actually paying? b. Now suppose the store makes one-week loans at 9 percent discount interest per week (see Question 60). What’s the APR now? The EAR? c. The check-cashing store also makes one-month add-on interest loans at 9 percent discount interest per week. Thus, if you borrow $100 for one month (four weeks), the interest will be ($100 × 1.094) − 100 = $41.16. Because this is discount interest, your net loan proceeds today will be $58.84. You must then repay the store $100 at the end of the month. To help you out, though, the store lets you pay off this $100 in installments of $25 per week. What is the APR of this loan? What is the EAR? Present Value of a Growing Perpetuity What is the equation for the present value of a growing perpetuity with a payment of C one period from today if the payments grow by Ce achp eriod? Rule of 72 A useful rule of thumb for the time it takes an investment to double with discrete compounding is the “Rule of 72.” To use the Rule of 72, you simply divide 72 by the interest rate to determine the number of periods it takes for a value today to double. For example, if the interest rate is 6 percent, the Rule of 72 says it will take 72 6 = 12 years to double. This is approximately equal to the actual answer of 11.90 years. The Rule of 72 can also be applied to determine what interest rate is needed to double money in a specified period. This is a useful approximation for many interest rates and periods. At what rate is the Rule of 72 exact? Rule of 69.3 A corollary to the Rule of 72 is the Rule of 69.3. The Rule of 69.3 is exactly correct except for rounding when interest rates are compounded continuously. Prove the Rule of 69.3 for continuously compounded interest.

www.mhhe.com/edumarketinsight 1. Under the “Excel Analytics” link find the “Mthly. Adj. Price” for Elizabeth Arden (RDEN) stock. What was your annual return over the last four years assuming you purchased the stock at the close price four years ago? (Assume no dividends were paid.) Using this same return, what price will Elizabeth Arden stock sell for five years from now? Ten years from now? What if the stock price increases at 11 percent per year? 2. Calculating the Number of Periods Find the monthly adjusted stock prices for Southwest Airlines (LUV). You find an analyst who projects the stock price will increase 12 percent per year for the foreseeable future. Based on the most recent monthly stock price, if the projection holds true, when will the stock price reach $150? When will it reach $200?

Appendix 4A Net Present Value: First Principles

of Finance To access the appendix for this chapter, please go to www.mhhe.com/rwj.

Appendix 4B Using Financial Calculators To access the appendix for this chapter, please go to www.mhhe.com/rwj.

www.mhhe.com/rwj

74.

Discounted Cash Flow Valuation

Mini Case

THEMB A DECISION Ben Bates graduated from college six years ago with a finance undergraduate degree. Although he is satisfied with his current job, his goal is to become an investment banker. He feels that an MBA degree would allow him to achieve this goal. After examining schools, he has narrowed his choice to either Wilton University or Mount Perry College. Although internships are encouraged by both schools, to get class credit for the internship, no salary can be paid. Other than internships, neither school will allow its students to work while enrolled in its MBA program. Ben currently works at the money management firm of Dewey and Louis. His annual salary at the firm is $60,000 per year, and his salary is expected to increase at 3 percent per year until retirement. He is currently 28 years old and expects to work for 40 more years. His current job includes a fully paid health insurance plan, and his current average tax rate is 26 percent. Ben has a savings account with enough money to cover the entire cost of his MBA program. The Ritter College of Business at Wilton University is one of the top MBA programs in the country. The MBA degree requires two years of full-time enrollment at the university. The annual tuition is $65,000, payable at the beginning of each school year. Books and other supplies are estimated to cost $3,000 per year. Ben expects that after graduation from Wilton, he will receive a job offer for about $110,000 per year, with a $20,000 signing bonus. The salary at this job will increase at 4 percent per year. Because of the higher salary, his average income tax rate will increase to 31 percent. The Bradley School of Business at Mount Perry College began its MBA program 16 years ago. The Bradley School is smaller and less well known than the Ritter College. Bradley offers an accelerated, one-year program, with a tuition cost of $80,000 to be paid upon matriculation. Books and other supplies for the program are expected to cost $4,500. Ben thinks that he will receive an offer of $92,000 per year upon graduation, with an $18,000 signing bonus. The salary at this job will increase at 3.5 percent per year. His average tax rate at this level of income will be 29 percent. Both schools offer a health insurance plan that will cost $3,000 per year, payable at the beginning of the year. Ben also estimates that room and board expenses will cost $2,000 more per year at both schools than his current expenses, payable at the beginning of each year. The appropriate discount rate is 6.5 percent. 1. How does Ben’s age affect his decision to get an MBA? 2. What other, perhaps nonquantifiable factors affect Ben’s decision to get an MBA? 3. Assuming all salaries are paid at the end of each year, what is the best option for Ben—from a strictly financial standpoint? 4. Ben believes that the appropriate analysis is to calculate the future value of each option. How would you evaluate this statement? 5. What initial salary would Ben need to receive to make him indifferent between attending Wilton University and staying in his current position? 6. Suppose, instead of being able to pay cash for his MBA, Ben must borrow the money. The current borrowing rate is 5.4 percent. How would this affect his decision?

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Net Present Value and Other InvestmentR ules In 2008, with gasoline prices reaching record levels, companies began developing alternative energy sources, and Finnish company Neste Oil was no exception. In June 2008, n the Neste announced plans to spend $1 billion building an 800,000-ton biodiesel plant in Netherlands. The plant, which will be one of the largest biodiesel projects in the world, s the will produce Neste’s proprietary NExBTL biodiesel. The only comparable project is 800+ billion ton plant in Singapore that Neste announced in January 2008. Decisions such as these, with price tags of up to $1 billion, are obviously major undertakings, and the risks ed in and rewards must be carefully weighed. In this chapter, we discuss the basic tools used making such decisions. In Chapter 1, we show that increasing the value of a company’s stock is the goal of finanfinanment cial management. Thus, what we need to know is how to tell whether a particular investment ancial will achieve that purpose or not. This chapter considers a variety of techniques financial an be analysts routinely use. More importantly, it shows how many of these techniques can misleading, and it explains why the net present value approach is the right one.

5.1 Why Use Net Present Value?

Find out more about capital budgeting for small businesses at www.missouribusiness .net.

This chapter, as well as the next two, focuses on capital budgeting, the decision-making process for accepting or rejecting projects. This chapter develops the basic capital budgeting methods, leaving much of the practical application to subsequent chapters. But we don’t have to develop these methods from scratch. In Chapter 4, we pointed out that a dollar received in the future is worth less than a dollar received today. The reason, of course, is that today’s dollar can be reinvested, yielding a greater amount in the future. And we showed in Chapter 4 that the exact worth of a dollar to be received in the future is its present value. Furthermore, Section 4.1 suggested calculating the net present value of any project. That is, the section suggested calculating the difference between the sum of the present values of the project’s future cash flows and the initial cost of the project. The net present value (NPV) method is the first one to be considered in this chapter. We begin by reviewing the approach with a simple example. Then, we ask why the method leads to good decisions.

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Net Present Value The Alpha Corporation is considering investing in a riskless project costing $100. The project receives $107 in one year and has no other cash flows. The discount rate is 6 percent. The NPV of the project can easily be calculated as: $107 $.94 = −$100 + _____ 1.06

(5.1)

From Chapter 4, we know that the project should be accepted because its NPV is positive. Had the NPV of the project been negative, as would have been the case with an interest rate greater than 7 percent, the project should be rejected.

The basic investment rule can be generalized to: Accept a project if the NPV is greater than zero. Reject a project if NPV is less than zero. We refer to this as the NPVrule . Why does the NPV rule lead to good decisions? Consider the following two strategies available to the managers of Alpha Corporation: 1. Use $100 of corporate cash to invest in the project. The $107 will be paid as a dividend in one year. 2. Forgo the project and pay the $100 of corporate cash as a dividend today. If strategy 2 is employed, the stockholder might deposit the dividend in a bank for one year. With an interest rate of 6 percent, strategy 2 would produce cash of $106 (=$100 × 1.06) at the end of the year. The stockholder would prefer strategy 1 because strategy 2 produces less than $107 at the end of the year. Our basic point is: Accepting positive NPV projects benefits the stockholders.

How do we interpret the exact NPV of $.94? This is the increase in the value of the firm from the project. For example, imagine that the firm today has productive assets worth $V and has $100 of cash. If the firm forgoes the project, the value of the firm today would simply be: $V +$100 If the firm accepts the project, the firm will receive $107 in one year but will have no cash today. Thus, the firm’s value today would be: $107 $V + _____ 1.06 The difference between these equations is just $.94, the net present value of Equation 5.1. Thus: The value of the firm rises by the NPV of the project.

Note that the value of the firm is merely the sum of the values of the different projects, divisions, or other entities within the firm. This property, called value additivity, is quite important. It implies that the contribution of any project to a firm’s value is

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simply the NPV of the project. As we will see later, alternative methods discussed in this chapter do not generally have this nice property. One detail remains. We assumed that the project was riskless, a rather implausible assumption. Future cash flows of real-world projects are invariably risky. In other words, cash flows can only be estimated, rather than known. Imagine that the managers of Alpha expect the cash flow of the project to be $107 next year. That is, the cash flow could be higher, say $117, or lower, say $97. With this slight change, the project is risky. Suppose the project is about as risky as the stock market as a whole, where the expected return this year is perhaps 10 percent. Then 10 percent becomes the discount rate, implying that the NPV of the project would be: $107 −$2.73 = −$100 + _____ 1.10 Because the NPV is negative, the project should be rejected. This makes sense: A stockholder of Alpha receiving a $100 dividend today could invest it in the stock market, expecting a 10 percent return. Why accept a project with the same risk as the market but with an expected return of only 7 percent?

SPREADSHEET APPLICATIONS

Calculating NPVs with a Spreadsheet Spreadsheets are commonly used to calculate NPVs. Examining the use of spreadsheets in this context also allows us to issue an important warning. Consider the following: A

B

C

D

E

F

G

H

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Using a spreadsheet to calculate net present values A project’s cost is $10,000. The cash flows are $2,000 per year for the first two years, $4,000 per year for the next two, and $5,000 in the last year. The discount rate is 10 percent; what’s the NPV? Year 0 1 2 3 4 5

Cash flow -$10,000 2,000 2,000 4,000 4,000 5,000

Discount rate = NPV = NPV =

10% $2,102.72 (wrong answer) $2,312.99 (right answer)

The formula entered in cell F11 is =NPV(F9, C9:C14). However, this gives the wrong answer because the NPV function actually calculates present values, not net present values. The formula entered in cell F12 is =NPV(F9, C10:C14) + C9. This gives the right answer because the NPV function is used to calculate the present value of the cash flows and then the initial cost is subtracted to calculate the answer. Notice that we added cell C9 because it is already negative.

In our spreadsheet example, notice that we have provided two answers. The first answer is wrong even though we used the spreadsheet’s NPV formula. What happened is that the “NPV” function in our spreadsheet is actually a PV function; unfortunately, one of the original spreadsheet programs many years ago got the definition wrong, and subsequent spreadsheets have copied it! Our second answer shows how to use the formula properly. The example here illustrates the danger of blindly using calculators or computers without understanding what is going on; we shudder to think of how many capital budgeting decisions in the real world are based on incorrect use of this particular function.

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Conceptually, the discount rate on a risky project is the return that one can expect to earn on a financial asset of comparable risk. This discount rate is often referred to as an opportunity cost because corporate investment in the project takes away the stockholder’s opportunity to invest the dividend in a financial asset. If the actual calculation of the discount rate strikes you as extremely difficult in the real world, you are probably right. Although you can call a bank to find out the current interest rate, whom do you call to find the expected return on the market this year? And, if the risk of the project differs from that of the market, how do you make the adjustment? However, the calculation is by no means impossible. We forgo the calculation in this chapter but present it in later chapters of the text. Having shown that NPV is a sensible approach, how can we tell whether alternative methods are as good as NPV? The key to NPV is its three attributes: 1. NPV uses cash flows. Cash flows from a project can be used for other corporate purposes (such as dividend payments, other capital budgeting projects, or payments of corporate interest). By contrast, earnings are an artificial construct. Although earnings are useful to accountants, they should not be used in capital budgeting because they do not represent cash. 2. NPV uses all the cash flows of the project. Other approaches ignore cash flows beyond a particular date; beware of these approaches. 3. NPV discounts the cash flows properly. Other approaches may ignore the time value of money when handling cash flows. Beware of these approaches as well. Calculating NPVs by hand can be tedious. A nearby Spreadsheet Applications box shows how to do it the easy way and also illustrates an important caveat calculator.

5.2 The Payback Period Method Definingthe R ule One of the most popular alternatives to NPV is payback. Here is how payback works: Consider a project with an initial investment of −$50,000. Cash flows are $30,000, $20,000, and $10,000 in the first three years, respectively. These flows are illustrated in Figure 5.1. A useful way of writing down investments like the preceding is with the notation: (−$50,000, $30,000, $20,000, $10,000) The minus sign in front of the $50,000 reminds us that this is a cash outflow for the investor, and the commas between the different numbers indicate that they are

Figure 5.1 Cash Flows of an Investment Project

$30,000

$20,000

$10,000

1

2

3

Cash inflow

Time

Cash outflow

0

ⴚ$50,000

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received—or if they are cash outflows, that they are paid out—at different times. In this example we are assuming that the cash flows occur one year apart, with the first one occurring the moment we decide to take on the investment. The firm receives cash flows of $30,000 and $20,000 in the first two years, which add up to the $50,000 original investment. This means that the firm has recovered its investment within two years. In this case two years is the payback period of the investment. The payback period rule for making investment decisions is simple. A particular cutoff date, say two years, is selected. All investment projects that have payback periods of two years or less are accepted, and all of those that pay off in more than two years—if at all—are rejected.

Problems with the Payback Method There are at least three problems with payback. To illustrate the first two problems, we consider the three projects in Table 5.1. All three projects have the same three-year payback period, so they should all be equally attractive—right? Actually, they are not equally attractive, as can be seen by a comparison of different pairs of projects. Problem 1: Timing of Cash Flows within the Payback Period Let us compare project A with project B. In years 1 through 3, the cash flows of project A rise from $20 to $50, while the cash flows of project B fall from $50 to $20. Because the large cash flow of $50 comes earlier with project B, its net present value must be higher. Nevertheless, we just saw that the payback periods of the two projects are identical. Thus, a problem with the payback method is that it does not consider the timing of the cash flows within the payback period. This example shows that the payback method is inferior to NPV because, as we pointed out earlier, the NPV method discounts the cash flows properly. Problem 2: Payments after the Payback Period Now consider projects B and C, which have identical cash flows within the payback period. However, project C is clearly preferred because it has a cash flow of $60,000 in the fourth year. Thus, another problem with the payback method is that it ignores all cash flows occurring after the payback period. Because of the short-term orientation of the payback method, some valuable long-term projects are likely to be rejected. The NPV method does not have this flaw because, as we pointed out earlier, this method uses all the cash flows of the project.

Table 5.1 Expected Cash Flows for Projects A through C ($)

Year

A

B

C

0 1 2 3 4 Payback period (years)

−$100 20 30 50 60 3

−$100 50 30 20 60 3

−$100 50 30 20 60,000 3

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Problem 3: Arbitrary Standard for Payback Period We do not need to refer to Table 5.1 when considering a third problem with the payback method. Capital markets help us estimate the discount rate used in the NPV method. The riskless rate, perhaps proxied by the yield on a Treasury instrument, would be the appropriate rate for a riskless investment. Later chapters of this textbook show how to use historical returns in the capital markets to estimate the discount rate for a risky project. However, there is no comparable guide for choosing the payback cutoff date, so the choice is somewhat arbitrary.

ManagerialP erspective The payback method is often used by large, sophisticated companies when making relatively small decisions. The decision to build a small warehouse, for example, or to pay for a tune-up for a truck is the sort of decision that is often made by lower-level management. Typically, a manager might reason that a tune-up would cost, say, $200, and if it saved $120 each year in reduced fuel costs, it would pay for itself in less than two years. On such a basis the decision would be made. Although the treasurer of the company might not have made the decision in the same way, the company endorses such decision making. Why would upper management condone or even encourage such retrograde activity in its employees? One answer would be that it is easy to make decisions using payback. Multiply the tune-up decision into 50 such decisions a month, and the appeal of this simple method becomes clearer. The payback method also has some desirable features for managerial control. Just as important as the investment decision itself is the company’s ability to evaluate the manager’s decision-making ability. Under the NPV method, a long time may pass before one decides whether a decision was correct. With the payback method we know in two years whether the manager’s assessment of the cash flows was correct. It has also been suggested that firms with good investment opportunities but no available cash may justifiably use payback. For example, the payback method could be used by small, privately held firms with good growth prospects but limited access to the capital markets. Quick cash recovery increases the reinvestment possibilities for such firms. Finally, practitioners often argue that standard academic criticisms of the payback method overstate any real-world problems with the method. For example, textbooks typically make fun of payback by positing a project with low cash inflows in the early years but a huge cash inflow right after the payback cutoff date. This project is likely to be rejected under the payback method, though its acceptance would, in truth, benefit the firm. Project C in our Table 5.1 is an example of such a project. Practitioners point out that the pattern of cash flows in these textbook examples is much too stylized to mirror the real world. In fact, a number of executives have told us that for the overwhelming majority of real-world projects, both payback and NPV lead to the same decision. In addition, these executives indicate that if an investment like project C were encountered in the real world, decision makers would almost certainly make ad hoc adjustments to the payback rule so that the project would be accepted. Notwithstanding all of the preceding rationale, it is not surprising to discover that as the decisions grow in importance, which is to say when firms look at bigger projects, NPV becomes the order of the day. When questions of controlling and evaluating the manager become less important than making the right investment decision, payback is used less frequently. For big-ticket decisions, such as whether or not to buy a machine, build a factory, or acquire a company, the payback method is seldom used.

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Summaryo fP ayback The payback method differs from NPV and is therefore conceptually wrong. With its arbitrary cutoff date and its blindness to cash flows after that date, it can lead to some flagrantly foolish decisions if used too literally. Nevertheless, because of its simplicity, as well as its other mentioned advantages, companies often use it as a screen for making the myriad of minor investment decisions they continually face. Although this means that you should be wary of trying to change approaches such as the payback method when you encounter them in companies, you should probably be careful not to accept the sloppy financial thinking they represent. After this course, you would do your company a disservice if you used payback instead of NPV when youh adac hoice.

5.3 The Discounted Payback Period Method Aware of the pitfalls of payback, some decision makers use a variant called the discounted payback period method. Under this approach, we first discount the cash flows. Then we ask how long it takes for the discounted cash flows to equal the initial investment. For example, suppose that the discount rate is 10 percent and the cash flows on a project are given by: (−$100, $50, $50, $20) This investment has a payback period of two years because the investment is paid back in that time. To compute the project’s discounted payback period, we first discount each of the cash flows at the 10 percent rate. These discounted cash flows are: [−$100, $50/1.1, $50/(1.1)2, $20/(1.1)3] = (−$100, $45.45, $41.32, $15.03) The discounted payback period of the original investment is simply the payback period for these discounted cash flows. The payback period for the discounted cash flows is slightly less than three years because the discounted cash flows over the three years are $101.80 (=$45.45 + 41.32 + 15.03). As long as the cash flows and discount rate are positive, the discounted payback period will never be smaller than the payback period because discounting reduces the value of the cash flows. At first glance discounted payback may seem like an attractive alternative, but on closer inspection we see that it has some of the same major flaws as payback. Like payback, discounted payback first requires us to choose an arbitrary cutoff period, and then it ignores all cash flows after that date. If we have already gone to the trouble of discounting the cash flows, we might just as well add up all the discounted cash flows and use NPV to make the decision. Although discounted payback looks a bit like NPV, it is just a poor compromise between the payback method and NPV.

5.4 The Internal Rate of Return Now we come to the most important alternative to the NPV method: The internal rate of return, universally known as the IRR. The IRR is about as close as you can get to the NPV without actually being the NPV. The basic rationale behind the IRR method

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Figure 5.2

$110

Cash inflow

Cash Flows for a SimpleP roject

Time

0

Cash outflow

1

ⴚ$100

is that it provides a single number summarizing the merits of a project. That number does not depend on the interest rate prevailing in the capital market. That is why it is called the internal rate of return; the number is internal or intrinsic to the project and does not depend on anything except the cash flows of the project. For example, consider the simple project (−$100, $110) in Figure 5.2. For a given rate, the net present value of this project can be described as: $110 NPV = −$100 + ______ 1+R where R is the discount rate. What must the discount rate be to make the NPV of the project equal to zero? We begin by using an arbitrary discount rate of .08, which yields: $110 $1.85 = −$100 + _____ 1.08 Because the NPV in this equation is positive, we now try a higher discount rate, such as .12. This yields: $110 −$1.79 = −$100 + _____ 1.12 Because the NPV in this equation is negative, we try lowering the discount rate to .10. This yields: $110 0 = −$100 + _____ 1.10 This trial-and-error procedure tells us that the NPV of the project is zero when R equals 10 percent.1 Thus, we say that 10 percent is the project’s internal rate of return (IRR). In general, the IRR is the rate that causes the NPV of the project to be zero. The implication of this exercise is very simple. The firm should be equally willing to accept or reject the project if the discount rate is 10 percent. The firm should accept the project if the discount rate is below 10 percent. The firm should reject the project if the discount rate is above 10 percent. The general investment rule is clear: Accept the project if the IRR is greater than the discount rate. Reject the project if the IRR is less than the discount rate.

1

Of course, we could have directly solved for R in this example after setting NPV equal to zero. However, with a long series of cash flows, one cannot generally solve for R directly. Instead, one is forced to use trial and error (or let a machine use trial and error).

Chapter 5

Figure 5.3

Net Present Value and Other Investment Rules

Cash inflow

Cash Flows for a MoreC omplexP roject

Time

Cash outflow

0

143

$100

$100

$100

1

2

3

ⴚ$200

We refer to this as the basic IRR rule. Now we can try the more complicated example (−$200, $100, $100, $100) in Figure 5.3. As we did previously, let’s use trial and error to calculate the internal rate of return. We try 20 percent and 30 percent, yielding the following: Discount Rate

NPV

20% 30

$10.65 −18.39

After much more trial and error, we find that the NPV of the project is zero when the discount rate is 23.37 percent. Thus, the IRR is 23.37 percent. With a 20 percent discount rate, the NPV is positive and we would accept it. However, if the discount rate were 30 percent, we would reject it. Algebraically, IRR is the unknown in the following equation:2 $100 $100 $100 0 = −$200 + ________ + __________2 + __________3 1 + IRR (1 + IRR) (1 + IRR) Figure 5.4 illustrates what the IRR of a project means. The figure plots the NPV as a function of the discount rate. The curve crosses the horizontal axis at the IRR of 23.37 percent because this is where the NPV equals zero. It should also be clear that the NPV is positive for discount rates below the IRR and negative for discount rates above the IRR. If we accept projects like this one when the discount rate is less than the IRR, we will be accepting positive NPV projects. Thus, the IRR rule coincides exactly with the NPV rule. If this were all there were to it, the IRR rule would always coincide with the NPV rule. But the world of finance is not so kind. Unfortunately, the IRR rule and the NPV rule are consistent with each other only for examples like the one just discussed. Several problems with the IRR approach occur in more complicated situations, a topic to be examined in the next section. The IRR in the previous example was computed through trial and error. This laborious process can be averted through spreadsheets. A nearby Spreadsheet Applications boxsh owsh ow. 2

One can derive the IRR directly for a problem with an initial cash outflow and up to four subsequent inflows. In the case of two subsequent inflows, for example, the quadratic formula is needed. In general, however, only trial and error will work for an outflow and five or more subsequent inflows.

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Figure 5.4 NetP resent Value (NPV) and Discount Rates for a More ComplexP roject

NPV

$100

$10.65

23.37

$0

10

20

ⴚ$18.39

30

40

IRR Discount rate (%)

The NPV is positive for discount rates below the IRR and negative for discount rates above the IRR.

SPREADSHEET APPLICATIONS

Calculating IRRs with a Spreadsheet Because IRRs are so tedious to calculate by hand, financial calculators and, especially, spreadsheets are generally used. The procedures used by various financial calculators are too different for us to illustrate here, so we will focus on using a spreadsheet. As the following example illustrates, using a spreadsheet is very easy. A

B

C

D

E

F

G

H

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Using a spreadsheet to calculate internal rates of return Suppose we have a four-year project that costs $500. The cash flows over the four-year life will be $100, $200, $300, and $400. What is the IRR? Year 0 1 2 3 4

Cash flow -$500 100 200 300 400

IRR =

27.3%

The formula entered in cell F9 is =IRR(C8:C12). Notice that the Year 0 cash flow has a negative sign representing the initial cost of the project.

5.5 Problems with the IRR Approach Definition of Independent and Mutually Exclusive Projects An independent project is one whose acceptance or rejection is independent of the acceptance or rejection of other projects. For example, imagine that McDonald’s is considering putting a hamburger outlet on a remote island. Acceptance or rejection of

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this unit is likely to be unrelated to the acceptance or rejection of any other restaurant in its system. The remoteness of the outlet in question ensures that it will not pull sales away from other outlets. Now consider the other extreme, mutually exclusive investments. What does it mean for two projects, A and B, to be mutually exclusive? You can accept A or you can accept B or you can reject both of them, but you cannot accept both of them. For example, A might be a decision to build an apartment house on a corner lot that you own, and B might be a decision to build a movie theater on the same lot. We now present two general problems with the IRR approach that affect both independent and mutually exclusive projects. Then we deal with two problems affecting mutually exclusive projects only.

Two General Problems Affecting Both Independent and Mutually Exclusive Projects We begin our discussion with project A, which has the following cash flows: (−$100,$130) The IRR for project A is 30 percent. Table 5.2 provides other relevant information about the project. The relationship between NPV and the discount rate is shown for this project in Figure 5.5. As you can see, the NPV declines as the discount rate rises.

Table 5.2

The Internal Rate of Return and Net Present Value

Project A Dates: Cash flows IRR NPV @10% Accept if market rate Financing or investing

Figure 5.5

0

1

–$100 30% $18.2 30% Financing

–$130

Project C 2

0

1

2

–$100 10% and 20% 0 >10% but R. Reject if IRR < R.

Accept if NPV > 0. Reject if NPV < 0.

1

Accept if IRR < R. Reject if IRR > R.

Accept if NPV > 0. Reject if NPV < 0.

No valid IRR.

Accept if NPV > 0. Reject if NPV < 0.

May be more than 1.

Note that the NPV criterion is the same for each of the three cases. In other words, NPV analysis is always appropriate. Conversely, the IRR can be used only in certain cases. When it comes to NPV, the preacher’s words, “You just can’t lose with the stuff I use,” clearly apply.

Problems Specific to Mutually Exclusive Projects As mentioned earlier, two or more projects are mutually exclusive if the firm can accept only one of them. We now present two problems dealing with the application of the IRR approach to mutually exclusive projects. These two problems are quite similar, though logically distinct. The Scale Problem A professor we know motivates class discussions of this topic with this statement: “Students, I am prepared to let one of you choose between two mutually exclusive ‘business’ propositions. Opportunity 1—You give me $1 now and I’ll give you $1.50 back at the end of the class period. Opportunity 2—You give me $10 and I’ll give you $11 back at the end of the class period. You can choose only one of the two opportunities. And you cannot choose either opportunity more than once. I’ll pick the first volunteer.”

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Which would you choose? The correct answer is opportunity 2.6 To see this, look at the following chart: Cash Flow at Beginning of Class

Cash Flow at End of Class (90 Minutes Later)

NPV 7

IRR

−$ 1 −10

+$ 1.50 +11.00

$ .50 1.00

50% 10

Opportunity 1 Opportunity 2

As we have stressed earlier in the text, one should choose the opportunity with the highest NPV. This is opportunity 2 in the example. Or, as one of the professor’s students explained it, “I’m bigger than the professor, so I know I’ll get my money back. And I have $10 in my pocket right now so I can choose either opportunity. At the end of the class, I’ll be able to buy one song on itunes with opportunity 2 and still have my original investment, safe and sound. The profit on opportunity 1 pays for only one half of a song.” This business proposition illustrates a defect with the internal rate of return criterion. The basic IRR rule indicates the selection of opportunity 1 because the IRR is 50 percent. The IRR is only 10 percent for opportunity 2. Where does IRR go wrong? The problem with IRR is that it ignores issues of scale. Although opportunity 1 has a greater IRR, the investment is much smaller. In other words, the high percentage return on opportunity 1 is more than offset by the ability to earn at least a decent return8 on a much bigger investment under opportunity 2. Because IRR seems to be misguided here, can we adjust or correct it? We illustrate how in the next example.

EXAMPLE 5.2

NPV versus IRR Stanley Jaffe and Sherry Lansing have just purchased the rights to Corporate Finance: The Motion Picture. They will produce this major motion picture on either a small budget or a big budget. Here are the estimated cash flows:

Small budget Large budget

Cash Flow at Date 0

Cash Flow at Date 1

– $10 million – 25 million

$40 million 65 million

NPV @25%

IRR

$22 million 27 million

300% 160

Because of high risk, a 25 percent discount rate is considered appropriate. Sherry wants to adopt the large budget because the NPV is higher. Stanley wants to adopt the small budget because the IRR is higher. Who is right?

6

The professor uses real money here. Though many students have done poorly on the professor’s exams over the years, no student ever chose opportunity 1. The professor claims that his students are “money players.” 7 We assume a zero rate of interest because his class lasted only 90 minutes. It just seemed like a lot longer. 8

A 10 percent return is more than decent over a 90-minute interval!

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For the reasons espoused in the classroom example, NPV is correct. Hence Sherry is right. However, Stanley is very stubborn where IRR is concerned. How can Sherry justify the large budget to Stanley using the IRR approach? This is where incremental IRR comes in. Sherry calculates the incremental cash flows from choosing the large budget instead of the small budget as follows: Cash Flow at Date 0 (in $ millions) Incremental cash flows from choosing large budget instead of small budget

−$25 – (–10) = −$15

Cash Flow at Date 1 (in $ millions) $65 – 40 = $25

This chart shows that the incremental cash flows are −$15 million at date 0 and $25 million at date 1. Sherry calculates incremental IRR as follows: Formula for Calculating the Incremental IRR: $25 million 0 = –$15 million + __________ 1 + IRR IRR equals 66.67 percent in this equation, implying that the incremental IRR is 66.67 percent. Incremental IRR is the IRR on the incremental investment from choosing the large project instead of the small project. In addition, we can calculate the NPV of the incremental cash flows: NPV of Incremental Cash Flows: $25 million –$15 million + __________ = $5 million 1.25 We know the small-budget picture would be acceptable as an independent project because its NPV is positive. We want to know whether it is beneficial to invest an additional $15 million to make the large-budget picture instead of the small-budget picture. In other words, is it beneficial to invest an additional $15 million to receive an additional $25 million next year? First, our calculations show the NPV on the incremental investment to be positive. Second, the incremental IRR of 66.67 percent is higher than the discount rate of 25 percent. For both reasons, the incremental investment can be justified, so the large-budget movie should be made. The second reason is what Stanley needed to hear to be convinced.

In review, we can handle this example (or any mutually exclusive example) in one of three ways: 1. Compare the NPVs of the two choices. The NPV of the large-budget picture is greater than the NPV of the small-budget picture. That is, $27 million is greater than $22 million. 2. Calculate the incremental NPV from making the large-budget picture instead of the small-budget picture. Because the incremental NPV equals $5 million, we choose the large-budget picture. 3. Compare the incremental IRR to the discount rate. Because the incremental IRR is 66.67 percent and the discount rate is 25 percent, we take the large-budget picture.

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All three approaches always give the same decision. However, we must not compare the IRRs of the two pictures. If we did, we would make the wrong choice. That is, we would accept the small-budget picture. Although students frequently think that problems of scale are relatively unimportant, the truth is just the opposite. No real-world project comes in one clear-cut size. Rather, the firm has to determine the best size for the project. The movie budget of $25 million is not fixed in stone. Perhaps an extra $1 million to hire a bigger star or to film at a better location will increase the movie’s gross. Similarly, an industrial firm must decide whether it wants a warehouse of, say, 500,000 square feet or 600,000 square feet. And, earlier in the chapter, we imagined McDonald’s opening an outlet on a remote island. If it does this, it must decide how big the outlet should be. For almost any project, someone in the firm has to decide on its size, implying that problems of scale abound in the real world. One final note here. Students often ask which project should be subtracted from the other in calculating incremental flows. Notice that we are subtracting the smaller project’s cash flows from the bigger project’s cash flows. This leaves an outflow at date 0. We then use the basic IRR rule on the incremental flows.9 The Timing Problem Next we illustrate another, somewhat similar problem with the IRR approach to evaluating mutually exclusive projects.

EXAMPLE 5.3

Mutually Exclusive Investments Suppose that the Kaufold Corporation has two alternative uses for a warehouse. It can store toxic waste containers (investment A) or electronic equipment (investment B). The cash flows are as follows: Cash Flow at Year Year: Investment A Investment B

0

1

2

NPV 3

−$10,000 $10,000 $1,000 $ 1,000 –10,000 1,000 1,000 12,000

@ 0 % @10 % @15 % $2,000 4,000

$669 751

$109 −484

IRR 16.04% 12.94

We find that the NPV of investment B is higher with low discount rates, and the NPV of investment A is higher with high discount rates. This is not surprising if you look closely at the cash flow patterns. The cash flows of A occur early, whereas the cash flows of B occur later. If we assume a high discount rate, we favor investment A because we are implicitly assuming that the early cash flow (for example, $10,000 in year 1) can be reinvested at that rate. Because most of investment B’s cash flows occur in year 3, B’s value is relatively high with low discount rates.

The patterns of cash flow for both projects appear in Figure 5.6. Project A has an NPV of $2,000 at a discount rate of zero. This is calculated by simply adding up the cash flows without discounting them. Project B has an NPV of $4,000 at the zero rate. However, the NPV of project B declines more rapidly as the discount rate increases 9 Alternatively, we could have subtracted the larger project’s cash flows from the smaller project’s cash flows. This would have left an inflow at date 0, making it necessary to use the IRR rule for financing situations. This would work, but we find it more confusing.

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Figure 5.6 $4,000

Net present value ($)

NetP resent Valueand the Internal Rate of Return for Mutually ExclusiveP rojects

NPVB ⬎ NPVA 2,000

NPVA ⬎ NPVB 0

10.55 12.94

16.04

ⴚ484

Project A Project B Discount rate (%)

than does the NPV of project A. As we mentioned, this occurs because the cash flows of B occur later. Both projects have the same NPV at a discount rate of 10.55 percent. The IRR for a project is the rate at which the NPV equals zero. Because the NPV of B declines more rapidly, B actually has a lower IRR. As with the movie example, we can select the better project with one of three different methods: 1. Compare NPVs of the two projects. Figure 5.6 aids our decision. If the discount rate is below 10.55 percent, we should choose project B because B has a higher NPV. If the rate is above 10.55 percent, we should choose project A because A has a higher NPV. 2. Compare incremental IRR to discount rate. Method 1 employed NPV. Another way of determining that B is a better project is to subtract the cash flows of Af rom the cash flows of B and then to calculate the IRR. This is the incremental IRR approach we spoke of earlier. Here are the incremental cash flows: NPV of Incremental Cash Flows

Year:

0

1

2

3

Incremental IRR

@0%

@10 %

@15 %

B–A

0

−$9,000

0

$11,000

10.55%

$2,000

$83

−$593

This chart shows that the incremental IRR is 10.55 percent. In other words, the NPV on the incremental investment is zero when the discount rate is 10.55 percent. Thus, if the relevant discount rate is below 10.55 percent, project B is preferred to project A. If the relevant discount rate is above 10.55 percent, project A is preferred to project B. Figure 5.6 shows that the NPVs of the two projects are equal when the discount rate is 10.55 percent. In other words, the crossover rate in the figure is 10.55. The incremental cash flows chart shows that the incremental IRR is also 10.55 percent. It is not a coincidence that the crossover rate and the incremental IRR are the same; this equality must always hold. The incremental IRR is the rate that causes the incremental cash flows to have zero NPV. The incremental cash flows have zero NPV when the two projects have the same NPV.

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3. Calculate NPV on incremental cash flows. Finally, we could calculate the NPV on the incremental cash flows. The chart that appears with the previous method displays these NPVs. We find that the incremental NPV is positive when the discount rate is either 0 percent or 10 percent. The incremental NPV is negative if the discount rate is 15 percent. If the NPV is positive on the incremental flows, we should choose B. If the NPV is negative, we should choose A. In summary, the same decision is reached whether we (1) compare the NPVs of the two projects, (2) compare the incremental IRR to the relevant discount rate, or (3) examine the NPV of the incremental cash flows. However, as mentioned earlier, we should not compare the IRR of project A with the IRR of project B. We suggested earlier that we should subtract the cash flows of the smaller project from the cash flows of the bigger project. What do we do here when the two projects have the same initial investment? Our suggestion in this case is to perform the subtraction so that the first nonzero cash flow is negative. In the Kaufold Corp. example we achieved this by subtracting A from B. In this way, we can still use the basic IRR rule for evaluating cash flows. The preceding examples illustrate problems with the IRR approach in evaluating mutually exclusive projects. Both the professor–student example and the motion picture example illustrate the problem that arises when mutually exclusive projects have different initial investments. The Kaufold Corp. example illustrates the problem that arises when mutually exclusive projects have different cash flow timing. When working with mutually exclusive projects, it is not necessary to determine whether it is the scale problem or the timing problem that exists. Very likely both occur in any real-world situation. Instead, the practitioner should simply use either an incremental IRR or an NPV approach.

Redeeming Qualities of IRR IRR probably survives because it fills a need that NPV does not. People seem to want a rule that summarizes the information about a project in a single rate of return. This single rate gives people a simple way of discussing projects. For example, one manager in a firm might say to another, “Remodeling the north wing has a 20 percent IRR.” To their credit, however, companies that employ the IRR approach seem to understand its deficiencies. For example, companies frequently restrict managerial projections of cash flows to be negative at the beginning and strictly positive later. Perhaps, then, both the ability of the IRR approach to capture a complex investment project in a single number, and the ease of communicating that number explain the survival of the IRR.

AT est To test your knowledge, consider the following two statements: 1. You must know the discount rate to compute the NPV of a project, but you compute the IRR without referring to the discount rate. 2. Hence, the IRR rule is easier to apply than the NPV rule because you don’t use the discount rate when applying IRR. The first statement is true. The discount rate is needed to compute NPV. The IRR is computed by solving for the rate where the NPV is zero. No mention is made of the discount rate in the mere computation. However, the second statement is false. To apply IRR, you must compare the internal rate of return with the discount rate. Thus the discount rate is needed for making a decision under either the NPV or IRR approach.

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5.6 ThePro fitability Index Another method used to evaluate projects is called the profitability index. It is the ratio of the present value of the future expected cash flows after initial investment divided by the amount of the initial investment. The profitability index can be represented as: PV of cash flows subsequent to initial investment Profitability index (PI) = __________________________________________ Initial investment

EXAMPLE 5.4

Profitability Index ment opportunities.

Hiram Finnegan Inc. (HFI) applies a 12 percent discount rate to two invest-

Cash Flows ($000,000) Project 1 2

C0

C1

C2

PV @ 12 % of Cash Flows Subsequent to Initial Investment ($000,000)

– $20 –10

$70 15

$10 40

$70.5 45.3

Profitability Index

NPV @12% ($000,000)

3.53 4.53

$50.5 35.3

Calculation of Profitability Index The profitability index is calculated for project 1 as follows. The present value of the cash flows after the initial investment is: $70 $10 $70.5 = ____ + ______2 1.12 (1.12) The profitability index is obtained by dividing this result by the initial investment of $20. This yields: $70.5 3.53 = _____ $20 Application of the Profitability Index How do we use the profitability index? We consider threesitu ations: 1. Independent projects: Assume that HFI’s two projects are independent. According to the NPV rule, both projects should be accepted because NPV is positive in each case. The profitability index (PI) is greater than 1 whenever the NPV is positive. Thus, the PI decision ruleis: • Accept an independent project if PI >1. • Reject it if PI RB, RS increases with leverage, a result that we also found in the notax case. As stated earlier in this chapter, R0 should exceed RB. That is, because equity (even unlevered equity) is risky, it should have an expected return greater than that on the less risky debt. Let’s check our calculations by determining the value of the levered equity in another way. The algebraic formula for the value of levered equity is: (EBIT − RBB) × (1 − tC ) S = ______________________ RS 16

This relationship can be shown as follows: Given MM Proposition I under taxes, a levered firm’s market value balance sheet can be written as: tC B = Tax shie ld

S = Equity

VU = Value of unlevered firm

B = Debt

The value of the unlevered firm is simply the value of the assets without benefit of leverage. The balance sheet indicates that the firm’s value increases by tCB when debt of B is added. The expected cash flow from the left side of the balance sheet can be written as: VU R0 + tC BRB

(a)

Because assets are risky, their expected rate of return is R0. The tax shield has the same risk as the debt, so its expected rate of return is RB. The expected cash to bondholders and stockholders together is: S RS + BRB

(b)

Expression (b) reflects the fact that stock earns an expected return of RS and debt earns the interest rate RB. Because all cash flows are paid out as dividends in our no-growth perpetuity model, the cash flows going into the firm equal those going to stockholders. Hence (a) and (b) are equal: S RS + BRB = VU R0 + tC BRB

(c)

Dividing both sides of (c) by S, subtracting BRB from both sides, and rearranging yields: RS =

V B × R0 − (1 − tC) × __ S RB S

U _____

(d)

Because the value of the levered firm, VL, equals VU + tCB = B + S, it follows that VU = S + (1 − tC) × B. Thus (d) can be rewritten as: S + (1 − tC ) × B B RS = _______________ × R0 − (1 − tC ) × __ S S RB Bringing the terms involving (1 − tC) × (B/S) together produces Equation 16.6.

(e)

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The Effect of Financial Leverage on the Cost of Debt and Equity Capital

Cost of capital: R

Figure 16.6 RS

.2351 .20 ⴝ R 0

R WACC RB

.10 0

200 ——

370 Debt – equity ratio (B/S)

200 = .2351 RS = R0 + (1 − tC)(R0 − RB)B S = .20 + .65 × .10 × ___ 370

(

)

Financial leverage adds risk to the firm’s equity. As compensation, the cost of equity rises with the firm’s risk. Note that R0 is a single point whereas RS, RB, and RWACC are all entire lines.

The numerator is the expected cash flow to levered equity after interest and taxes. The denominator is the rate at which the cash flow to equity is discounted. For Divided Airlines we get: ($153.85 − .10 ×$200) (1 − .35) ____________________________ .2351

= $370

the same result we obtained earlier (ignoring a small rounding error).

The Weighted Average Cost of Capital, RWACC , and Corporate Taxes In Chapter 13, we defined the weighted average cost of capital (with corporate taxes) as follows (note that VL = S + B): S B ___ RWACC = ___ VL RS + VL RB(1 − tC) Note that the cost of debt capital, RB, is multiplied by (1 − tC) because interest is tax deductible at the corporate level. However, the cost of equity, RS, is not multiplied by this factor because dividends are not deductible. In the no-tax case, RWACC is not affected by leverage. This result is reflected in Figure 16.3, which we discussed earlier. However, because debt is tax advantaged relative to equity, it can be shown that RWACC declines with leverage in a world with corporate taxes. This result can be seen in Figure 16.6. For Divided Airlines, RWACC is equal to:

(

) (

)

370 200 RWACC = ____ × .2351 + ____ × .10 × .65 =.1754 570 570 Divided Airlines has reduced its RWACC from .20 (with no debt) to .1754 with reliance on debt. This result is intuitively pleasing because it suggests that when a firm lowers its RWACC, the firm’s value will increase. Using the RWACC approach, we can confirm that the value of Divided Airlines is $570: EBIT × (1 − tC ) _____ $100 VL = _______________ = = $570 RWACC .1754

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511

Stock Price and Leverage under Corporate Taxes At this point students often believe the numbers—or at least are too intimidated to dispute them. However, they sometimes think we have asked the wrong question. “Why are we choosing to maximize the value of the firm?” they will say. “If managers are looking out for the stockholders’ interest, why aren’t they trying to maximize stock price?” If this question occurred to you, you have come to the right section. Our response is twofold: First, we showed in the first section of this chapter that the capital structure that maximizes firm value is also the one that most benefits the interests of the stockholders. However, that general explanation is not always convincing to students. As a second procedure, we calculate the stock price of Divided Airlines both before and after the exchange of debt for stock. We do this by presenting a set of market value balance sheets. The market value balance sheet for the company in its all-equity form can be represented as follows: DIVIDED AIRLINES Balance Sheet (All-Equity Firm) Physical assets

Equity

$153.85 _______ .20 × (1 − .35) = $500

$500 (100 shares)

Assuming that there are 100 shares outstanding, each share is worth $5 = $500/100. Next, imagine the company announces that in the near future it will issue $200 of debt to buy back $200 of stock. We know from our previous discussion that the value of the firm will rise to reflect the tax shield of debt. If we assume that capital markets efficiently price securities, the increase occurs immediately. That is, the rise occurs on the day of the announcement, not on the date of the debt-for-equity exchange. The market value balance sheet now becomes this: DIVIDED AIRLINES Balance Sheet (upon Announcement of Debt Issue) Physical assets

$500

Present value of tax shield: tC B = 35% × $200 = Total assets

70 $570

Equity

$570 (100 shares)

Note that the debt has not yet been issued. Therefore, only equity appears on the right side of the balance sheet. Each share is now worth $570/100 = $5.70, implying that the stockholders have benefited by $70. The equityholders gain because they are the owners of a firm that has improved its financial policy. The introduction of the tax shield to the balance sheet is perplexing to many students. Although physical assets are tangible, the ethereal nature of the tax shield bothers these students. However, remember that an asset is any item with value. The tax shield has value because it reduces the stream of future taxes. The fact that one cannot

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touch the shield in the way that one can touch a physical asset is a philosophical, not financial, consideration. At some point the exchange of debt for equity occurs. Debt of $200 is issued, and the proceeds are used to buy back shares. How many shares of stock are repurchased? Because shares are now selling at $5.70 each, the number of shares that the firm acquires is $200/$5.70 = 35.09. This leaves 64.91 (=100 − 35.09) shares of stock outstanding. The market value balance sheet is now this: DIVIDED AIRLINES Balance Sheet (after Exchange Has Taken Place) Physical assets

$500

Present value of tax shield Total assets

70 $570

Equity $370 (100 − 35.09 = 64.91 shares) Debt 200 Debt plus equity $570

Each share of stock is worth $370/64.91 = $5.70 after the exchange. Notice that the stock price does not change on the exchange date. As we mentioned, the stock price moves on the date of the announcement only. Because the shareholders participating in the exchange receive a price equal to the market price per share after the exchange, they do not care whether they exchange their stock. This example was provided for two reasons. First, it shows that an increase in the value of the firm from debt financing leads to an increase in the price of the stock. In fact, the stockholders capture the entire $70 tax shield. Second, we wanted to provide more work with market value balance sheets. A summary of the main results of Modigliani–Miller with corporate taxes is presented in the following boxed section:

Summary of Modigliani–Miller Propositions with Corporate Taxes Assumptions • Corporations are taxed at the rate tC, on earnings after interest. • Not ransactionc osts. • Individuals and corporations borrow at same rate. Results VL = VU + tCB (for a firm with perpetual debt) B PropositionI I: RS = R0 + __ S (1 − tC)(R0 − RB) Proposition I:

Intuition Proposition I: Because corporations can deduct interest payments but not dividend payments, corporate leverage lowers tax payments. Proposition II: The cost of equity rises with leverage because the risk to equity riseswit hle verage.

Chapter 16 Capital Structure

Summary and Conclusions

513

1. We began our discussion of the capital structure decision by arguing that the particular capital structure that maximizes the value of the firm is also the one that provides the most benefit to the stockholders. 2. In a world of no taxes, the famous Proposition I of Modigliani and Miller proves that the value of the firm is unaffected by the debt–equity ratio. In other words, a firm’s capital structure is a matter of indifference in that world. The authors obtain their results by showing that either a high or a low corporate ratio of debt to equity can be offset by homemade leverage. The result hinges on the assumption that individuals can borrow at the same rate as corporations, an assumption we believe to be quite plausible. 3. MM’s Proposition II in a world without taxes states that: B RS = R0 + __ S (R0 − RB)

VL = VU + tC B Expected return on levered equity can be expressed as: B RS = R0 + (1 − tC ) × (R0 − RB ) × __ S Here, value is positively related to leverage. This result implies that firms should have a capital structure almost entirely composed of debt. Because real-world firms select more moderate levels of debt, the next chapter considers modifications to the results of thisc hapter.

Concept Questions

1.

2.

3.

4. 5.

MM Assumptions List the three assumptions that lie behind the Modigliani–Miller theory in a world without taxes. Are these assumptions reasonable in the real world? Explain. MM Propositions In a world with no taxes, no transaction costs, and no costs of financial distress, is the following statement true, false, or uncertain? If a firm issues equity to repurchase some of its debt, the price per share of the firm’s stock will rise because the shares are less risky. Explain. MM Propositions In a world with no taxes, no transaction costs, and no costs of financial distress, is the following statement true, false, or uncertain? Moderate borrowing will not increase the required return on a firm’s equity. Explain. MM Propositions What is the quirk in the tax code that makes a levered firm more valuable than an otherwise identical unlevered firm? Business Risk versus Financial Risk Explain what is meant by business and financial risk. Suppose firm A has greater business risk than firm B. Is it true that firm A also has a higher cost of equity capital? Explain.

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This implies that the expected rate of return on equity (also called the cost of equity or the required return on equity) is positively related to the firm’s leverage. This makes intuitive sense because the risk of equity rises with leverage, a point illustrated by Figure 16.2. 4. Although the above work of MM is quite elegant, it does not explain the empirical findings on capital structure very well. MM imply that the capital structure decision is a matter of indifference, whereas the decision appears to be a weighty one in the real world. To achieve real-world applicability, we next considered corporate taxes. 5. In a world with corporate taxes but no bankruptcy costs, firm value is an increasing function of leverage. The formula for the value of the firm is:

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6.

7.

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8. 9. 10.

Questions and Problems

1.

BASIC (Questions 1–16)

2. 3.

4.

Capital Structure and Dividend Policy

MM Propositions How would you answer in the following debate? Q: Isn’t it true that the riskiness of a firm’s equity will rise if the firm increases its use of debt financing? A: Yes, that’s the essence of MM Proposition II. Q: And isn’t it true that, as a firm increases its use of borrowing, the likelihood of default increases, thereby increasing the risk of the firm’s debt? A:Y es. Q: In other words, increased borrowing increases the risk of the equity and the debt? A:T hat’sr ight. Q: Well, given that the firm uses only debt and equity financing, and given that the risks of both are increased by increased borrowing, does it not follow that increasing debt increases the overall risk of the firm and therefore decreases the value of thef irm? A:? ? Optimal Capital Structure Is there an easily identifiable debt–equity ratio that will maximize the value of a firm? Why or why not? Financial Leverage Why is the use of debt financing referred to as financial “leverage”? Homemade Leverage What is homemade leverage? Capital Structure Goal What is the basic goal of financial management with regard toc apitals tructure?

EBIT and Leverage Money, Inc., has no debt outstanding and a total market value of $225,000. Earnings before interest and taxes, EBIT, are projected to be $19,000 if economic conditions are normal. If there is strong expansion in the economy, then EBIT will be 30 percent higher. If there is a recession, then EBIT will be 60 percent lower. Money is considering a $90,000 debt issue with an 8 percent interest rate. The proceeds will be used to repurchase shares of stock. There are currently 5,000 shares outstanding. Ignore taxes for this problem. a. Calculate earnings per share, EPS, under each of the three economic scenarios before any debt is issued. Also calculate the percentage changes in EPS when the economy expands or enters a recession. b. Repeat part (a) assuming that Money goes through with recapitalization. What doy ouo bserve? EBIT, Taxes, and Leverage Repeat parts (a) and (b) in Problem 1 assuming Money has a tax rate of 35 percent. ROE and Leverage Suppose the company in Problem 1 has a market-to-book ratio of 1.0. a. Calculate return on equity, ROE, under each of the three economic scenarios before any debt is issued. Also calculate the percentage changes in ROE for economic expansion and recession, assuming no taxes. b. Repeat part (a) assuming the firm goes through with the proposed recapitalization. c. Repeat parts (a) and (b) of this problem assuming the firm has a tax rate of 35p ercent. Break-Even EBIT Rolston Corporation is comparing two different capital structures, an all-equity plan (Plan I) and a levered plan (Plan II). Under Plan I, Rolston would have 240,000 shares of stock outstanding. Under Plan II, there would be 160,000 shares of stock outstanding and $3.1 million in debt outstanding. The interest rate on the debt is 10 percent and there are no taxes.

Chapter 16 Capital Structure

5. 6.

7. 8.

10. 11. 12.

a. If EBIT is $750,000, which plan will result in the higher EPS? b. If EBIT is $1,500,000, which plan will result in the higher EPS? c. Whatis t heb reak-evenE BIT? MM and Stock Value In Problem 4, use MM Proposition I to find the price per share of equity under each of the two proposed plans. What is the value of the firm? Break-Even EBIT and Leverage Kolby Corp. is comparing two different capital structures. Plan I would result in 1,500 shares of stock and $20,000 in debt. Plan II would result in 1,100 shares of stock and $30,000 in debt. The interest rate on the debt is 10 percent. a. Ignoring taxes, compare both of these plans to an all-equity plan assuming that EBIT will be $12,000. The all-equity plan would result in 2,300 shares of stock outstanding. Which of the three plans has the highest EPS? The lowest? b. In part (a) what are the break-even levels of EBIT for each plan as compared to that for an all-equity plan? Is one higher than the other? Why? c. Ignoring taxes, when will EPS be identical for Plans I and II? d. Repeat parts (a), (b), and (c) assuming that the corporate tax rate is 40 percent. Are the break-even levels of EBIT different from before? Why or why not? Leverage and Stock Value Ignoring taxes in Problem 6, what is the price per share of equity under Plan I? Plan II? What principle is illustrated by your answers? Homemade Leverage Star, Inc., a prominent consumer products firm, is debating whether or not to convert its all-equity capital structure to one that is 40 percent debt. Currently there are 5,000 shares outstanding and the price per share is $65. EBIT is expected to remain at $37,500 per year forever. The interest rate on new debt is 8 percent, and there are no taxes. a. Ms. Brown, a shareholder of the firm, owns 100 shares of stock. What is her cash flow under the current capital structure, assuming the firm has a dividend payout rate of 100 percent? b. What will Ms. Brown’s cash flow be under the proposed capital structure of the firm? Assume that she keeps all 100 of her shares. c. Suppose Star does convert, but Ms. Brown prefers the current all-equity capital structure. Show how she could unlever her shares of stock to recreate the original capitals tructure. d. Using your answer to part (c), explain why Star’s choice of capital structure is irrelevant. Homemade Leverage and WACC ABC Co. and XYZ Co. are identical firms in all respects except for their capital structure. ABC is all equity financed with $800,000 in stock. XYZ uses both stock and perpetual debt; its stock is worth $400,000 and the interest rate on its debt is 10 percent. Both firms expect EBIT to be $95,000. Ignore taxes. a. Richard owns $30,000 worth of XYZ’s stock. What rate of return is he expecting? b. Show how Richard could generate exactly the same cash flows and rate of return by investing in ABC and using homemade leverage. c. What is the cost of equity for ABC? What is it for XYZ? d. What is the WACC for ABC? For XYZ? What principle have you illustrated? MM Nina Corp. uses no debt. The weighted average cost of capital is 11 percent. If the current market value of the equity is $43 million and there are no taxes, what is EBIT? MM and Taxes In the previous question, suppose the corporate tax rate is 35 percent. What is EBIT in this case? What is the WACC? Explain. Calculating WACC Weston Industries has a debt–equity ratio of 1.5. Its WACC is 12 percent, and its cost of debt is 9 percent. The corporate tax rate is 35 percent. a. What is Weston’s cost of equity capital? b. What is Weston’s unlevered cost of equity capital? c. What would the cost of equity be if the debt–equity ratio were 2? What if it were 1.0? What if it were zero?

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13.

14.

15.

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INTERMEDIATE (Questions 17–25)

17.

18.

19.

20.

Capital Structure and Dividend Policy

Calculating WACC Shadow Corp. has no debt but can borrow at 7 percent. The firm’s WACC is currently 11 percent, and the tax rate is 35 percent. a. What is Shadow’s cost of equity? b. If the firm converts to 25 percent debt, what will its cost of equity be? c. If the firm converts to 50 percent debt, what will its cost of equity be? d. What is Shadow’s WACC in part (b)? In part (c)? MM and Taxes Bruce & Co. expects its EBIT to be $140,000 every year forever. The firm can borrow at 9 percent. Bruce currently has no debt, and its cost of equity is 17 percent. If the tax rate is 35 percent, what is the value of the firm? What will the value be if Bruce borrows $135,000 and uses the proceeds to repurchase shares? MM and Taxes In Problem 14, what is the cost of equity after recapitalization? What is the WACC? What are the implications for the firm’s capital structure decision? MM Proposition I Levered, Inc., and Unlevered, Inc., are identical in every way except their capital structures. Each company expects to earn $65 million before interest per year in perpetuity, with each company distributing all its earnings as dividends. Levered’s perpetual debt has a market value of $185 million and costs 8 percent per year. Levered has 3.4 million shares outstanding, currently worth $100 per share. Unlevered has no debt and 7 million shares outstanding, currently worth $80 per share. Neither firm pays taxes. Is Levered’s stock a better buy than Unlevered’s stock? MM Tool Manufacturing has an expected EBIT of $42,000 in perpetuity and a tax rate of 35 percent. The firm has $70,000 in outstanding debt at an interest rate of 8 percent, and its unlevered cost of capital is 15 percent. What is the value of the firm according to MM Proposition I with taxes? Should Tool change its debt–equity ratio if the goal is to maximize the value of the firm? Explain. Firm Value Old School Corporation expects an EBIT of $15,000 every year forever. Old School currently has no debt, and its cost of equity is 17 percent. The firm can borrow at 10 percent. If the corporate tax rate is 35 percent, what is the value of the firm? What will the value be if Old School converts to 50 percent debt? To 100 percent debt? MM Proposition I with Taxes The Maxwell Company is financed entirely with equity. The company is considering a loan of $1.4 million. The loan will be repaid in equal installments over the next two years, and it has an 8 percent interest rate. The company’s tax rate is 35 percent. According to MM Proposition I with taxes, what would be the increase in the value of the company after the loan? MM Proposition I without Taxes Alpha Corporation and Beta Corporation are identical in every way except their capital structures. Alpha Corporation, an allequity firm, has 10,000 shares of stock outstanding, currently worth $20 per share. Beta Corporation uses leverage in its capital structure. The market value of Beta’s debt is $50,000, and its cost of debt is 12 percent. Each firm is expected to have earnings before interest of $55,000 in perpetuity. Neither firm pays taxes. Assume that every investor can borrow at 12 percent per year. a. What is the value of Alpha Corporation? b. What is the value of Beta Corporation? c. What is the market value of Beta Corporation’s equity? d. How much will it cost to purchase 20 percent of each firm’s equity? e. Assuming each firm meets its earnings estimates, what will be the dollar return to each position in part (d) over the next year? f. Construct an investment strategy in which an investor purchases 20 percent of Alpha’s equity and replicates both the cost and dollar return of purchasing 20 percent of Beta’s equity. g. Is Alpha’s equity more or less risky than Beta’s equity? Explain.

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21.

22.

Capital Structure

Cost of Capital Acetate, Inc., has equity with a market value of $35 million and debt with a market value of $14 million. Treasury bills that mature in one year yield 6 percent per year, and the expected return on the market portfolio is 13 percent. The beta of Acetate’s equity is 1.15. The firm pays no taxes. a. What is Acetate’s debt–equity ratio? b. What is the firm’s weighted average cost of capital? c. What is the cost of capital for an otherwise identical all-equity firm? Homemade Leverage The Veblen Company and the Knight Company are identical in every respect except that Veblen is not levered. The market value of Knight Company’s 6 percent bonds is $1.2 million. Financial information for the two firms appears here. All earnings streams are perpetuities. Neither firm pays taxes. Both firms distribute all earnings available to common stockholders immediately.

Projected operating income Year-end interest on debt Market value of stock Market value of debt

24.

Veblen

Knight

$ 400,000 — 3,600,000 —

$ 400,000 72,000 2,532,000 1,200,000

a. An investor who can borrow at 6 percent per year wishes to purchase 5 percent of Knight’s equity. Can he increase his dollar return by purchasing 5 percent of Veblen’s equity if he borrows so that the initial net costs of the two strategies are thes ame? b. Given the two investment strategies in (a), which will investors choose? When will thisp rocessc ease? MM Propositions Locomotive Corporation is planning to repurchase part of its common stock by issuing corporate debt. As a result, the firm’s debt–equity ratio is expected to rise from 40 percent to 50 percent. The firm currently has $4.3 million worth of debt outstanding. The cost of this debt is 10 percent per year. Locomotive expects to have an EBIT of $1.68 million per year in perpetuity. Locomotive pays no taxes. a. What is the market value of Locomotive Corporation before and after the repurchasean nouncement? b. What is the expected return on the firm’s equity before the announcement of the stock repurchase plan? c. What is the expected return on the equity of an otherwise identical all-equity firm? d. What is the expected return on the firm’s equity after the announcement of the stockr epurchasep lan? Stock Value and Leverage Green Manufacturing, Inc., plans to announce that it will issue $3 million of perpetual debt and use the proceeds to repurchase common stock. The bonds will sell at par with a 6 percent annual coupon rate. Green is currently an all-equity firm worth $9.5 million with 600,000 shares of common stock outstanding. After the sale of the bonds, Green will maintain the new capital structure indefinitely. Green currently generates annual pretax earnings of $1.8 million. This level of earnings is expected to remain constant in perpetuity. Green is subject to a corporate tax rate of 40 percent. a. What is the expected return on Green’s equity before the announcement of the debtis sue? b. Construct Green’s market value balance sheet before the announcement of the debt issue. What is the price per share of the firm’s equity? c. Construct Green’s market value balance sheet immediately after the announcement of the debt issue.

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25.

CHALLENGE (Questions 26–30)

26. 27.

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29.

30.

Capital Structure and Dividend Policy

d. What is Green’s stock price per share immediately after the repurchase announcement? e. How many shares will Green repurchase as a result of the debt issue? How many shares of common stock will remain after the repurchase? f. Construct the market value balance sheet after the restructuring. g. What is the required return on Green’s equity after the restructuring? MM with Taxes Williamson, Inc., has a debt–equity ratio of 2.5. The firm’s weighted average cost of capital is 15 percent, and its pretax cost of debt is 10 percent. Williamson is subject to a corporate tax rate of 35 percent. a. What is Williamson’s cost of equity capital? b. What is Williamson’s unlevered cost of equity capital? c. What would Williamson’s weighted average cost of capital be if the firm’s debt– equity ratio were .75? What if it were 1.5? Weighted Average Cost of Capital In a world of corporate taxes only, show that the RWACC can be written as RWACC = R0 × [1 − tC(B V) ]. Cost of Equity and Leverage Assuming a world of corporate taxes only, show that the cost of equity, RS, is as given in the chapter by MM Proposition II with corporate taxes. Business and Financial Risk Assume a firm’s debt is risk-free, so that the cost of debt equals the risk-free rate, Rf. Define βA as the firm’s asset beta—that is, the systematic risk of the firm’s assets. Define βS to be the beta of the firm’s equity. Use the capital asset pricing model, CAPM, along with MM Proposition II to show that βS = βA × (1 + B S), where B S is the debt–equity ratio. Assume the tax rate is zero. Stockholder Risk Suppose a firm’s business operations mirror movements in the economy as a whole very closely—that is, the firm’s asset beta is 1.0. Use the result of previous problem to find the equity beta for this firm for debt–equity ratios of 0, 1, 5, and 20. What does this tell you about the relationship between capital structure and shareholder risk? How is the shareholders’ required return on equity affected? Explain. Unlevered Cost of Equity Beginning with the cost of capital equation—that is: S B ______ RWACC = ______ B + S RS + B + S RB show that the cost of equity capital for a levered firm can be written as follows: B RS = R0 + __ S (R0 − RB)

S&P Problems

www.mhhe.com/edumarketinsight 1. Locate the annual balance sheets for General Motors (GM), Merck (MRK), and Kellogg (K). For each company calculate the long-term debt–equity ratio for the prior two years. Why would these companies use such different capital structures? 2. Look up a company and download the annual income statements. For the most recent year, calculate the average tax rate and EBIT, and find the total interest expense. From the annual balance sheets calculate the total long-term debt (including the portion due within one year). Using the interest expense and total long-term debt, calculate the average cost of debt. Next, find the estimated beta for the company on the S&P Stock Report. Use this reported beta, a current T-bill rate, and the historical average market risk premium found in a previous chapter to calculate the levered cost of equity. Now calculate the unlevered cost of equity, then the unlevered EBIT. What is the unlevered value of the company? What is the value of the interest tax shield and the value of the levered company?

Mini Case

STEPHENSON REAL ESTATE RECAPITALIZATION Stephenson Real Estate Company was founded 25 years ago by the current CEO, Robert Stephenson. The company purchases real estate, including land and buildings, and rents the property to tenants. The company has shown a profit every year for the past 18 years, and the shareholders are satisfied with the company’s management. Prior to founding Stephenson Real Estate, Robert was the founder and CEO of a failed alpaca farming operation. The resulting bankruptcy made him extremely averse to debt financing. As a result, the company is entirely equity financed, with 20 million shares of common stock outstanding. The stock currently trades at $35.50 per share. Stephenson is evaluating a plan to purchase a huge tract of land in the southeastern United States for $60 million. The land will subsequently be leased to tenant farmers. This purchase is expected to increase Stephenson’s annual pretax earnings by $14 million in perpetuity. Kim Weyand, the company’s new CFO, has been put in charge of the project. Kim has determined that the company’s current cost of capital is 12.5 percent. She feels that the company would be more valuable if it included debt in its capital structure, so she is evaluating whether the company should issue debt to entirely finance the project. Based on some conversations with investment banks, she thinks that the company can issue bonds at par value with an 8 percent coupon rate. Based on her analysis, she also believes that a capital structure in the range of 70 percent equity∕30 percent debt would be optimal. If the company goes beyond 30 percent debt, its bonds would carry a lower rating and a much higher coupon because the possibility of financial distress and the associated costs would rise sharply. Stephenson has a 40 percent corporate tax rate (state and federal). 1. If Stephenson wishes to maximize its total market value, would you recommend that it issue debt or equity to finance the land purchase? Explain. 2. Construct Stephenson’s market value balance sheet before it announces the purchase. 3. Suppose Stephenson decides to issue equity to finance the purchase. a. What is the net present value of the project? b. Construct Stephenson’s market value balance sheet after it announces that the firm will finance the purchase using equity. What would be the new price per share of the firm’s stock? How many shares will Stephenson need to issue to finance the purchase? c. Construct Stephenson’s market value balance sheet after the equity issue but before the purchase has been made. How many shares of common stock does Stephenson have outstanding? What is the price per share of the firm’s stock? d. Construct Stephenson’s market value balance sheet after the purchase has been made. 4. Suppose Stephenson decides to issue debt to finance the purchase. a. What will the market value of the Stephenson company be if the purchase is financed withd ebt? b. Construct Stephenson’s market value balance sheet after both the debt issue and the land purchase. What is the price per share of the firm’s stock? 5. Which method of financing maximizes the per-share stock price of Stephenson’s equity?

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CHAPTER 17

CapitalSt ructure Limits to the Use of Debt One of the consequences of the recession that began in late 2008 was an increase in the number of bankruptcy filings. For example, Waterford Wedgewood PLC’s crystal ball must have been cracked because the company filed for bankruptcy protection in early 2009. The company, whose Wedgewood brand dates to 1759, filed for bankruptcy hoping to recapitalize or find a buyer. Another major bankruptcy filing in January 2009 was that of Nortel Networks, North America’s biggest telephone equipment maker. Nortel’s bankruptcy was especially notable since the company was the largest company in Canada as recently as 2000, when its stock was about 35 percent of the total net equity on the Toronto Stock Exchange. In the United States, the bankruptcy of Circuit City made headlines. The company announced it was filing for bankruptcy protection to reorganize in November 2008. The company said it would close 156 stores; some of these would be sold, which would inject cash into the business, while the bankruptcy would allow the company to get out of leases on the remaining closed stores. Unfortunately, things didn’t go as planned, and two months later in January 2009, the company announced it would close its remaining stores and liquidate all of its assets. As these situations point out, there is a limit to the financial leverage a company can use, and the risk of too much leverage is bankruptcy. In this chapter, we discuss the costs associated with bankruptcies and how companies attempt to avoid this process.

17.1 Costs of Financial Distress Bankruptcy Risk or Bankruptcy Cost? As mentioned throughout the previous chapter, debt provides tax benefits to the firm. However, debt puts pressure on the firm because interest and principal payments are obligations. If these obligations are not met, the firm may risk some sort of financial distress. The ultimate distress is bankruptcy, where ownership of the firm’s assets is legally transferred from the stockholders to the bondholders. These debt obligations are fundamentally different from stock obligations. Although stockholders like and expect dividends, they are not legally entitled to dividends in the way bondholders are legally entitled to interest and principal payments. We show next that bankruptcy costs, or more generally financial distress costs, tend to offset the advantages to debt. We begin by positing a simple example of bankruptcy. All taxes are ignored to focus only on the costs of debt. 520

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EXAMPLE1 7.1

Capital Structure

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Bankruptcy Costs The Knight Corporation plans to be in business for one more year. It forecasts a cash flow of either $100 or $50 in the coming year, each occurring with 50 percent probability. The firm has no other assets. Previously issued debt requires payments of $49 of interest and principal. The Day Corporation has identical cash flow prospects but has $60 of interest and principal obligations. The cash flows of these two firms can be represented as follows: Knight Corporation

Cash flow Payment of interest and principal on debt Distribution to stockholders

Day Corporation

Boom Times (prob. 50%)

Recession (prob. 50%)

Boom Times (prob. 50%)

Recession (prob. 50%)

$100

$50

$100

$50

49 $ 51

49 $ 1

60 $ 40

50 $ 0

For Knight Corporation in both boom times and recession and for Day Corporation in boom times, cash flow exceeds interest and principal payments. In these situations the bondholders are paid in full, and the stockholders receive any residual. However, the most interesting of the four columns involves Day Corporation in a recession. Here the bondholders are owed $60, but the firm has only $50 in cash. Because we assume that the firm has no other assets, the bondholders cannot be satisfied in full. If bankruptcy occurs, the bondholders will receive all of the firm’s cash, and the stockholders will receive nothing. Importantly, the stockholders do not have to come up with the additional $10 (=$60 − $50). Corporations have limited liability in America and most other countries, implying that bondholders cannot sue the stockholders for the extra $10.1 We assume that (1) both bondholders and stockholders are risk-neutral and (2) the interest rate is 10 percent. Due to this risk neutrality, cash flows to both stockholders and bondholders are to be discounted at the 10 percent rate.2 We can evaluate the debt, the equity, and the entire firm for both Knight and Day as follows: $51 × _2 + $1 × _2 SKNIGHT = $23.64 = ________________ 1.10 1

$40 × _2 + 0 × _2 SDAY = $18.18 = _______________ 1.10

1

1

1

$49 × _2 + $49 × _2 BKNIGHT = $44.54 = _________________ 1.10

$60 × _2 + $50 × _2 BDAY = $50 = _________________ 1.10

VKNIGHT = $68.18

VDAY = $68.18

1

1

1

1

(continued ) 1

There are situations where the limited liability of corporations can be “pierced.” Typically, fraud or misrepresentation must be present. 2 Normally, we assume that investors are averse to risk. In that case, the cost of debt capital, RB, is less than the cost of equity capital, RS, which rises with leverage as shown in the previous chapter. In addition, RB may rise when the increase in leverage allows the possibility of default. For simplicity, we assume risk neutrality in this example. This means that investors are indifferent to the level of risk. Here, RS = RB because risk-neutral investors do not demand compensation for bearing risk. In addition, neither RS nor RB rises with leverage. Because the interest rate is 10 percent, our assumption of risk neutrality implies that RS = 10% as well. Though financial economists believe that investors are risk-averse, they frequently develop examples based on risk neutrality to isolate a point unrelated to risk. This is our approach because we want to focus on bankruptcy costs—not bankruptcy risk. The same qualitative conclusions from this example can be drawn in a world of risk aversion, albeit with much more difficulty for the reader.

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Note that the two firms have the same value, even though Day runs the risk of bankruptcy. Furthermore, notice that Day’s bondholders are valuing the bonds with “their eyes open.” Though the promised payment of principal and interest is $60, the bondholders are willing to pay only $50. Hence their promised return or yield is: $60 ____ $50 − 1 = 20% Day’s debt can be viewed as a junk bond because the probability of default is so high. As with all junk bonds, Day’s bondholders demand a high promised yield. Day’s example is not realistic because it ignores an important cash flow to be discussed next. A more realistic set of numbers might be these: Day Corporation Boom Times Recession (prob. 50%) (prob. 50%) $40 × _2 + 0 × _2 SDAY = $18.18 = _______________ 1.10 1

Earnings

$100

$50

60

35

$ 40

$ 0

$60 × _2 + $35 × _2 BDAY = $43.18 = _________________ 1.10 1

Debt repayment Distribution to stockholders

1

1

VDAY = $61.36

Why do the bondholders receive only $35 in a recession? If cash flow is only $50, bondholders will be informed that they will not be paid in full. These bondholders are likely to hire lawyers to negotiate or even to sue the company. Similarly, the firm is likely to hire lawyers to defend itself. Further costs will be incurred if the case gets to a bankruptcy court. These fees are always paid before the bondholders get paid. In this example, we are assuming that bankruptcy costs total $15 (=$50 − $35). The value of the firm is now $61.36, an amount below the $68.18 figure calculated earlier. By comparing Day’s value in a world with no bankruptcy costs to Day’s value in a world with these costs, we conclude the following: The possibility of bankruptcy has a negative effect on the value of the firm. However, it is not the risk of bankruptcy itself that lowers value. Rather it is the costs associated with bankruptcy that lower value. The explanation follows from our pie example. In a world without bankruptcy costs, the bondholders and the stockholders share the entire pie. However, bankruptcy costs eat up some of the pie in the real world, leaving less for the stockholders and bondholders. Because the bondholders are aware that they will receive little in a recession, they pay the low price of $43.18. In this case, their promised return is: $60 ______ $43.18 − 1 = 39.0% The bondholders are paying a fair price if they are realistic about both the probability and the cost of bankruptcy. It is the stockholders who bear these future bankruptcy costs. To see this, imagine that Day Corporation was originally all equity. The stockholders want the firm to issue debt with a promised payment of $60 and use the proceeds to pay a dividend. If there had been no bankruptcy costs, our results show that bondholders would pay $50 to purchase debt with a promised payment of $60. Hence, a dividend of $50 could be paid to the stockholders. However, if bankruptcy costs exist, bondholders would only pay $43.18 for the debt. In that case, only a dividend of $43.18 could be paid to the stockholders. Because the dividend is smaller with bankruptcy costs, the stockholders are hurt by these costs.

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17.2 Description of Financial Distress Costs The preceding example showed that bankruptcy costs can lower the value of the firm. In fact, the same general result holds even if a legal bankruptcy is prevented. Thus financial distress costs may be a better phrase than bankruptcy costs. It is worthwhile to describe these costs in more detail.

Direct Costs of Financial Distress: Legal and Administrative Costs of Liquidation or Reorganization As mentioned earlier, lawyers are involved throughout all the stages before and during bankruptcy. With fees often in the hundreds of dollars an hour, these costs can add up quickly. A wag once remarked that bankruptcies are to lawyers what blood is to sharks. In addition, administrative and accounting fees can substantially add to the total bill. And if a trial takes place, we must not forget expert witnesses. Each side may hire a number of these witnesses to testify about the fairness of a proposed settlement. Their fees can easily rival those of lawyers or accountants. (However, we personally look upon these witnesses kindly because they are frequently drawn from the ranks of finance professors.) One of the most well-publicized bankruptcies in recent years concerned a municipality, Orange County, California, not a corporation. This bankruptcy followed large bond trading losses in the county’s financial portfolio. The Los Angeles Times stated: Orange County taxpayers lost $1.69 billion, and their government, one year ago today, sank into bankruptcy. Now they are spending millions more to get out of it. Accountants pore over fiscal ledgers at $325 an hour. Lawyers toil into the night—at $385 an hour. Financial advisers from one of the nation’s most prominent investment houses labor for the taxpayers at $150,000 a month. Clerks stand by the photocopy machines, running up bills that sometimes exceed $3,000. Total so far: $29 million. And it’s nowhere near over. The multipronged effort to lift Orange County out of the nation’s worst municipal bankruptcy has become a money-eating machine, gobbling up taxpayer funds at a rate of $2.4 million a month. That’s $115,000 a day. County administrators are not alarmed. They say Orange County’s bankruptcy was an epic disaster that will require equally dramatic expenditures of taxpayer cash to help it survive. While they have refused to pay several thousand dollars worth of claimed expenses—lavish dinners, big hotel bills—they have rarely questioned the sky-high hourly fees. They predict the costs could climb much higher. Indeed, participants in the county’s investment pool have agreed to create a separate $50 million fund to pay the costs of doing legal battle with Wall Street.3

Bankruptcy costs in the private sector are often far larger than those in Orange County. For example, as of 2005, the direct costs of Enron’s and WorldCom’s bankruptcies were commonly estimated to exceed $1 billion and $600 million, respectively. A number of academic studies have measured the direct costs of financial distress. Although large in absolute amount, these costs are actually small as a percentage of firm value. White, Altman, and Weiss estimate the direct costs of financial distress

3

“The High Cost of Going Bankrupt,” Los Angeles Times Orange County Edition, December 6, 1995. Taken from Lexis∕Nexis.

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to be about 3 percent of the market value of the firm.4 In a study of direct financial distress costs of 20 railroad bankruptcies, Warner finds that net financial distress costs were, on average, 1 percent of the market value of the firm seven years before bankruptcy and were somewhat larger percentages as bankruptcy approached (for example, 2.5 percent of the market value of the firm three years before bankruptcy).5 Lubben estimates the average cost of legal fees alone to be about 1.5 percent of total assets for bankrupt firms.6 Bris, Welch, and Zhu find bankruptcy expenses as measured against asset values to be in the 2 to 10 percent range.7

Indirect Costs of Financial Distress Impaired Ability to Conduct Business Bankruptcy hampers conduct with customers and suppliers. Sales are frequently lost because of both fear of impaired service and loss of trust. For example, many loyal Chrysler customers switched to other manufacturers when Chrysler skirted insolvency in the 1970s. These buyers questioned whether parts and servicing would be available were Chrysler to fail. Sometimes the taint of impending bankruptcy is enough to drive customers away. For example, gamblers avoided Atlantis casino in Atlantic City after it became technically insolvent. Gamblers are a superstitious bunch. Many wondered, “If the casino itself cannot make money, how can I expect to make money there?” A particularly outrageous story concerned two unrelated stores both named Mitchells in New York City. When one Mitchells declared bankruptcy, customers stayed away from both stores. In time, the second store was forced to declare bankruptcy as well. Though these costs clearly exist, it is quite difficult to measure them. Altman estimates that both direct and indirect costs of financial distress are frequently greater than 20 percent of firm value.8 Andrade and Kaplan estimate total distress costs to be between 10 percent and 20 percent of firm value.9 Bar-Or estimates expected future distress costs for firms that are currently healthy to be 8 to 10 percent of operating value, a number below the estimates of either Altman or Andrade and Kaplan.10 However, unlike Bar-Or, these authors consider distress costs for firms already in distress, not expected distress costs for currently healthy firms. Cutler and Summers examine the costs of the well-publicized Texaco bankruptcy.11 In January 1984, Pennzoil reached what it believed to be a binding agreement to acquire three-sevenths of Getty Oil. However, less than a week later, Texaco acquired all of Getty at a higher per-share price. Pennzoil then sued Getty for breach of contract. 4

M. J. White, “Bankruptcy Costs and the New Bankruptcy Code,” Journal of Finance (May 1983); E. I. Altman, “A Further Empirical Investigation of the Bankruptcy Cost Question,” Journal of Finance (September 1984); and Lawrence A. Weiss, “Bankruptcy Resolution: Direct Costs and Violation of Priority of Claims,” Journal of Financial Economics 27 (1990). 5 J. B. Warner, “Bankruptcy Costs: Some Evidence,” Journal of Finance (May 1977). 6 Stephen J. Lubben, “The Direct Costs of Corporate Reorganization: An Empirical Examination of Professional Fees in Large Chapter 11 Cases,” American Bankruptcy Law Journal (2000). 7 Arturo Bris, Ivo Welch, and Ning Zhu, “The Cost of Bankruptcy: Chapter 7 Liquidation versus Chapter 11 Reorganization,” Journal of Finance (June 2006). 8 E. I. Altman, op. cit. 9 Gregor Andrade and Steven N. Kaplan, “How Costly Is Financial (Not Economic) Distress? Evidence from Highly Leveraged Transactions That Became Distressed,” Journal of Finance (October 1998). 10 Yuval Bar-Or, “An Investigation of Expected Financial Distress Costs,” unpublished paper, Wharton School, University of Pennsylvania (March 2000). 11 David M. Cutler and Lawrence H. Summers, “The Costs of Conflict Resolution and Financial Distress: Evidence from the Texaco–Pennzoil Litigation,” Rand Journal of Economics (Summer 1988).

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Because Texaco had previously indemnified Getty against litigation, Texaco became liable for damages. In November 1985, the Texas State Court awarded damages of $12 billion to Pennzoil, although this amount was later reduced. As a result, Texaco filed for bankruptcy. Cutler and Summers identify nine important events over the course of the litigation. They find that Texaco’s market value (stock price times number of shares outstanding) fell a cumulative $4.1 billion over these events, whereas Pennzoil rose only $682 million. Thus, Pennzoil gained about one-sixth of what Texaco lost, resulting in a net loss to the two firms of almost $3.5 billion. What could explain this net loss? Cutler and Summers suggest that it is likely due to costs that Texaco and Pennzoil incurred from the litigation and subsequent bankruptcy. The authors argue that direct bankruptcy fees represent only a small part of these costs, estimating Texaco’s aftertax legal expenses to be about $165 million. Legal costs to Pennzoil were more difficult to assess because Pennzoil’s lead lawyer, Joe Jamail, stated publicly that he had no set fee. However, using a clever statistical analysis, the authors estimate his fee to be about $200 million. Thus we must search elsewhere for the bulk of the costs. Indirect costs of financial distress may be the culprit. An affidavit by Texaco stated that, following the lawsuit, some of its suppliers were demanding cash payment. Other suppliers halted or canceled shipments of crude oil. Certain banks restricted Texaco’s use of futures contracts on foreign exchange. The affidavit stressed that these constraints were reducing Texaco’s ability to run its business, leading to deterioration of its financial condition. Could these sorts of indirect costs explain the $3.5 billion disparity between Texaco’s drop and Pennzoil’s rise in market value? Unfortunately, although it is quite likely that indirect costs play a role here, there is simply no way to obtain a decent quantitative estimate for them.

AgencyCo sts When a firm has debt, conflicts of interest arise between stockholders and bondholders. Because of this, stockholders are tempted to pursue selfish strategies. These conflicts of interest, which are magnified when financial distress is incurred, impose agency costs on the firm. We describe three kinds of selfish strategies that stockholders use to hurt the bondholders and help themselves. These strategies are costly because they will lower the market value of the whole firm. Selfish Investment Strategy 1: Incentive to Take Large Risks Firms near bankruptcy often take great chances because they believe that they are playing with someone else’s money. To see this, imagine a levered firm considering two mutually exclusive projects, a low-risk one and a high-risk one. There are two equally likely outcomes, recession and boom. The firm is in such dire straits that should a recession hit, it will come near to bankruptcy with one project and actually fall into bankruptcy with the other. The cash flows for the entire firm if the low-risk project is taken can be described as follows: Value of Entire Firm if Low-Risk Project Is Chosen

Recession Boom

Probability

Value of Firm

=

Stock

+

Bonds

.5 .5

$100 200

= =

$ 0 100

+ +

$100 100

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If recession occurs, the value of the firm will be $100; if boom occurs, the value of the firm will be $200. The expected value of the firm is $150 (=.5 × $100 + .5 × $200). The firm has promised to pay bondholders $100. Shareholders will obtain the difference between the total payoff and the amount paid to the bondholders. In other words, the bondholders have the prior claim on the payoffs, and the shareholders have the residual claim. Now suppose that the riskier project can be substituted for the low-risk project. The payoffs and probabilities are as follows: Value of Entire Firm if High-Risk Project Is Chosen

Recession Boom

Probability

Value of Firm

=

Stock

+

Bonds

.5 .5

$ 50 240

= =

$ 0 140

+ +

$ 50 100

The expected value of the firm is $145 (=.5 × $50 + .5 × $240), which is lower than the expected value of the firm with the low-risk project. Thus the low-risk project would be accepted if the firm were all equity. However, note that the expected value of the stock is $70 (=.5 × 0 + .5 × $140) with the high-risk project, but only $50 (=.5 × 0 + .5 × $100) with the low-risk project. Given the firm’s present levered state, stockholders will select the high-risk project, even though the high-risk project has a lower NPV. The key is that relative to the low-risk project, the high-risk project increases firm value in a boom and decreases firm value in a recession. The increase in value in a boom is captured by the stockholders because the bondholders are paid in full (they receive $100) regardless of which project is accepted. Conversely, the drop in value in a recession is lost by the bondholders because they are paid in full with the low-risk project but receive only $50 with the high-risk one. The stockholders will receive nothing in a recession anyway, whether the high-risk or low-risk project is selected. Thus, financial economists argue that stockholders expropriate value from the bondholders by selecting high-risk projects. A story, perhaps apocryphal, illustrates this idea. It seems that Federal Express was near financial collapse within a few years of its inception. The founder, Frederick Smith, took $20,000 of corporate funds to Las Vegas in despair. He won at the gaming tables, providing enough capital to allow the firm to survive. Had he lost, the banks would simply have received $20,000 less when the firm reached bankruptcy. Selfish Investment Strategy 2: Incentive toward Underinvestment Stockholders of a firm with a significant probability of bankruptcy often find that new investment helps the bondholders at the stockholders’ expense. The simplest case might be a real estate owner facing imminent bankruptcy. If he took $100,000 out of his own pocket to refurbish the building, he could increase the building’s value by, say, $150,000. Though this investment has a positive net present value, he will turn it down if the increase in value cannot prevent bankruptcy. “Why,” he asks, “should I use my own funds to improve the value of a building that the bank will soon repossess?” This idea is formalized by the following simple example. Consider the firm in Table 17.1, which must decide whether to accept or reject a new project. The first two columns in the table show cash flows without the project. The firm receives cash

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527

Table 17.1 Example Illustrating Incentive to Underinvest

Firm without Project

Firm cash flows Bondholders’ claim Stockholders’ claim

Firm with Project Costing $1,000

Boom

Recession

Boom

Recession

$5,000 4,000 $1,000

$2,400 2,400 $ 0

$6,700 4,000 $2,700

$4,100 4,000 $ 100

The project has positive NPV. However, much of its value is captured by bondholders. Rational managers, acting in the stockholders’ interest, will reject the project.

inflows of $5,000 and $2,400 under a boom and a recession, respectively. Because the firm must pay principal and interest of $4,000, the firm will default in a recession. Alternatively, as indicated in the next two columns of the table, the firm could raise equity to invest in a new project. The project brings in $1,700 in either state, which is enough to prevent bankruptcy even in a recession. Because $1,700 is much greater than the project’s cost of $1,000, the project has a positive NPV at any plausible interest rate. Clearly, an all-equity firm would accept the project. However, the project hurts the stockholders of the levered firm. To see this, imagine the old stockholders contribute the $1,000 themselves.12 Assuming that a boom and a recession are equally likely, the expected value of the stockholders’ interest without the project is $500 (=.5 × $1,000 + .5 × 0). The expected value with the project is $1,400 (=.5 × $2,700 + .5 × $100). The stockholders’ interest rises by only $900 (= $1,400 − $500) while costing $1,000. Why does a project with a positive NPV hurt the stockholders? The key is that the stockholders contribute the full $1,000 investment, but the stockholders and bondholders share the benefits. The stockholders take the entire gain if boom times occur. Conversely, the bondholders reap most of the cash flow from the project in a recession. The discussion of selfish strategy 1 is quite similar to the discussion of selfish strategy 2. In both cases, an investment strategy for the levered firm is different from the one for the unlevered firm. Thus, leverage results in distorted investment policy. Whereas the unlevered corporation always chooses projects with positive net present value, the levered firm may deviate from this policy. Selfish Investment Strategy 3: Milking the Property Another strategy is to pay out extra dividends or other distributions in times of financial distress, leaving less in the firm for the bondholders. This is known as milking the property, a phrase taken from real estate. Strategies 2 and 3 are very similar. In strategy 2, the firm chooses not to raise new equity. Strategy 3 goes one step further because equity is actually withdrawn through the dividend. Summary of Selfish Strategies The distortions just discussed occur only when there is a probability of bankruptcy or financial distress. Thus, these distortions should not affect, say, General Electric because bankruptcy is not a realistic possibility for a diversified blue-chip firm such as this. In other words, General Electric’s debt will be virtually risk-free, regardless of the projects it accepts. The same argument could be 12

The same qualitative results will be obtained if the $1,000 is raised from new stockholders. However, the arithmetic becomes much more difficult because we must determine how many new shares are issued.

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made for regulated companies that are protected by state utility commissions. By contrast, small firms in risky industries, such as computers, are more likely to experience financial distress and, in turn, to be affected by such distortions. Who pays for the cost of selfish investment strategies? We argue that it is ultimately the stockholders. Rational bondholders know that when financial distress is imminent, they cannot expect help from stockholders. Rather, stockholders are likely to choose investment strategies that reduce the value of the bonds. Bondholders protect themselves accordingly by raising the interest rate that they require on the bonds. Because the stockholders must pay these high rates, they ultimately bear the costs of selfish strategies. For firms that face these distortions, debt will be difficult and costly to obtain. These firms will have low leverage ratios. The relationship between stockholders and bondholders is very similar to the relationship between Erroll Flynn and David Niven, good friends and movie stars in the 1930s. Niven reportedly said that the good thing about Flynn was that you knew exactly where you stood with him. When you needed his help, you could always count on him to let you down.

17.3 Can Costs of Debt Be Reduced? As U.S. senators are prone to say, “A billion here, a billion there. Pretty soon it all adds up.” Each of the costs of financial distress we have mentioned is substantial in its own right. The sum of them may well affect debt financing severely. Thus, managers have an incentive to reduce these costs. We now turn to some of their methods. However, it should be mentioned at the outset that the methods here can, at most, reduce the costs of debt. They cannot eliminate them entirely.

ProtectiveCo venants Because the stockholders must pay higher interest rates as insurance against their own selfish strategies, they frequently make agreements with bondholders in hopes of lower rates. These agreements, called protective covenants, are incorporated as part of the loan document (or indenture) between stockholders and bondholders. The covenants must be taken seriously because a broken covenant can lead to default. Protective covenants can be classified into two types: negative covenants and positive covenants. A negative covenant limits or prohibits actions that the company may take. Here are some typical negative covenants: 1. 2. 3. 4. 5.

Limitations are placed on the amount of dividends a company may pay. The firm may not pledge any of its assets to other lenders. The firm may not merge with another firm. The firm may not sell or lease its major assets without approval by the lender. The firm may not issue additional long-term debt.

A positive covenant specifies an action that the company agrees to take or a condition the company must abide by. Here are some examples: 1. The company agrees to maintain its working capital at a minimum level. 2. The company must furnish periodic financial statements to the lender. These lists of covenants are not exhaustive. The authors have seen loan agreements with more than 30 covenants.

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Table 17.2

Capital Structure

529

Loan Covenants

Shareholder Action or Firm Circumstances

Covenant Type

Reason for Covenant

As firm approaches financial distress, shareholders may want firm to make high-risk investments.

Financial statement restrictions 1. Minimum working capital 2. Minimum interest coverage 3. Minimum net worth

Shareholders may attempt to transfer corporate assets to themselves.

Restrictions on asset disposition 1. Limit on dividends 2. Limit on sale of assets 3. Collateral and mortgages Restrictions on switching assets

High-risk investments transfer value from bondholders to stockholders when financial distress is a realistic possibility. Covenants reduce probability of financial distress. Covenants limit the ability of shareholders to transfer assets to themselves and to underinvest.

Shareholders may attempt to increase risk of firm. Shareholders may attempt to issue new debt of equal or greater priority.

Dilution restrictions 1. Limit on leasing 2. Limit on further borrowing

Increased firm risk helps shareholders and hurts bondholders. Covenants restrict dilution of the claim of existing bondholders.

Smith and Warner examined public issues of debt and found that 91 percent of the bond indentures included covenants that restricted the issuance of additional debt, 23 percent restricted dividends, 39 percent restricted mergers, and 36 percent limited the sale of assets.13 Protective covenants should reduce the costs of bankruptcy, ultimately increasing the value of the firm. Thus, stockholders are likely to favor all reasonable covenants. To see this, consider three choices by stockholders to reduce bankruptcy costs: 1. Issue no debt. Because of the tax advantages to debt, this is a very costly way of avoidingc onflicts. 2. Issue debt with no restrictive and protective covenants. In this case, bondholders will demand high interest rates to compensate for the unprotected status of their debt. 3. Write protective and restrictive covenants into the loan contracts. If the covenants are clearly written, the creditors may receive protection without large costs being imposed on the shareholders. The creditors will gladly accept a lower interest rate. Thus, bond covenants, even if they reduce flexibility, can increase the value of the firm. They can be the lowest-cost solution to the stockholder–bondholder conflict. A list of typical bond covenants and their uses appears in Table 17.2.

Consolidationo fDe bt One reason bankruptcy costs are so high is that different creditors (and their lawyers) contend with each other. This problem can be alleviated by proper arrangement of bondholders and stockholders. For example, perhaps one, or at most a few, lenders can shoulder the entire debt. Should financial distress occur, negotiating costs are minimized under this arrangement. In addition, bondholders can purchase stock as well. In this way, stockholders and debtholders are not pitted against each other because they are not separate entities. This appears to be the approach in Japan, where 13

C. W. Smith and J. B. Warner, “On Financial Contracting: An Analysis of Bond Covenants,” Journal of Financial Economics 7 (1979).

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Figure 17.1

Capital Structure and Dividend Policy

Value of firm (V)

The Optimal Amount of Debt and the Value of the Firm

Present value of tax shield on debt Maximum firm value

VL = VU + tC B = Value of firm under MM with corporate taxes and debt Present value of financial distress costs V = Actual value of firm VU = Value of firm with no debt

B* Optimal amount of debt

Debt (B)

The tax shield increases the value of the levered firm. Financial distress costs lower the value of the levered firm. The two offsetting factors produce an optimal amount of debt at B*. Cost of capital (%)

Ro

Ro

RWACC

B*

Debt (B)

According to the static theory, the RWACC falls initially because of the tax advantage of debt. Beyond point B*, it begins to rise because of financial distress costs.

large banks generally take significant stock positions in the firms to which they lend money.14 Debt–equity ratios in Japan are far higher than those in the United States.

17.4 Integration of Tax Effects and Financial Distress Costs Modigliani and Miller argue that the firm’s value rises with leverage in the presence of corporate taxes. Because this relationship implies that all firms should choose maximum debt, the theory does not predict the behavior of firms in the real world. Other authors have suggested that bankruptcy and related costs reduce the value of the levered firm. The integration of tax effects and distress costs appears in Figure 17.1. In the top graph of the figure, the diagonal straight line represents the value of the firm in a 14

Legal limitations may prevent this practice in the United States.

Chapter 17 Capital Structure

531

world without bankruptcy costs. The ∩-shaped curve represents the value of the firm with these costs. This curve rises as the firm moves from all equity to a small amount of debt. Here, the present value of the distress costs is minimal because the probability of distress is so small. However, as more and more debt is added, the present value of these costs rises at an increasing rate. At some point, the increase in the present value of these costs from an additional dollar of debt equals the increase in the present value of the tax shield. This is the debt level maximizing the value of the firm and is represented by B* in Figure 17.1. In other words, B* is the optimal amount of debt. Bankruptcy costs increase faster than the tax shield beyond this point, implying a reduction in firm value from further leverage. In the bottom graph of Figure 17.1, the weighted average cost of capital (RWACC) falls as debt is added to the capital structure. After reaching B*, the weighted average cost of capital rises. The optimal amount of debt produces the lowest weighted average cost of capital. Our discussion implies that a firm’s capital structure decision involves a trade-off between the tax benefits of debt and the costs of financial distress. In fact, this approach is frequently called the trade-off or the static trade-off theory of capital structure. The implication is that there is an optimal amount of debt for any individual firm. This amount of debt becomes the firm’s target debt level. Because financial distress costs cannot be expressed in a precise way, no formula has yet been developed to determine a firm’s optimal debt level exactly. However, the last section of this chapter offers some rules of thumb for selecting a debt–equity ratio in the real world. Our situation reminds us of a quote from John Maynard Keynes. He reputedly said that although most historians would agree that Queen Elizabeth I was both a better monarch and an unhappier woman than Queen Victoria, no one has yet been able to express the statement in a precise and rigorous formula.

PieAga in Now that we have considered bankruptcy costs, let’s return to the pie approach of the previous chapter. The cash flows of the firm go to four different claimants: Stockholders, bondholders, the government (in the form of taxes), and, during the bankruptcy process, lawyers (and others). Algebraically, we must have: CF = Payments to stockholders + Payments to bondholders + Payments to the government + Payments to lawyers (and others) It follows that the total value of the firm, VT, equals the sum of the following four components: VT = S + B + G + L where S is the value of the equity, B is the value of the bonds, G is the value of the government claims from taxes, and L stands for the value that lawyers and others receive when the firm is under financial distress. This relationship is illustrated in Figure 17.2. Nor have we even begun to exhaust the list of financial claims to the firm’s cash flows. To give an unusual example, everyone reading this book has an economic claim to the cash flows of General Motors. After all, if you are injured in an accident, you

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Figure 17.2

Value of firm

The Pie Model with Real-World Factors

Bondholder claims

Shareholder claims

Bankruptcy claims

Tax claims

Paid out to

Value of firm

Shareholders Bondholders Bankruptcy claims Taxes (government)

might sue GM. Win or lose, GM will expend resources dealing with the matter. If you think this is far-fetched and unimportant, ask yourself what GM might be willing to pay every man, woman, and child in the country to have them promise that they would never sue GM, no matter what happened. The law does not permit such payments, but that does not mean that a value to all of those potential claims does not exist. We guess that it would run into the billions of dollars, and, for GM or any other company, there should be a slice of the pie labeled LS for “potential lawsuits.” Figure 17.2 illustrates the essence of MM’s intuition. While VT is determined by the firm’s cash flows, the firm’s capital structure merely cuts VT into slices. Capital structure does not affect the total value, VT . There is, however, a difference between claims such as those of stockholders and bondholders on the one hand and those of government and potential litigants in lawsuits on the other. The first set of claims are marketable claims, and the second set are nonmarketable claims. Marketable claims can be bought and sold in financial markets, and the nonmarketable claims cannot. This distinction between marketable and nonmarketable claims is important. When stock is issued, stockholders pay cash to the firm for the privilege of later receiving dividends. Similarly, bondholders pay cash to the firm for the privilege of receiving interest in the future. However, the IRS pays nothing to the firm for the privilege of receiving taxes in the future. Similarly, lawyers pay nothing to the firm for the privilege of receiving fees from the firm in the future. When we speak of the value of the firm, we are referring just to the value of the marketable claims, VM, and not the value of nonmarketable claims, VN . What we have shown is that capital structure does not affect the total value: VT = S + B + G + L = VM + VN But as we saw, the value of the marketable claims, VM, can change with changes in the capital structure. By the pie theory, any increase in VM must imply an identical decrease in VN . Rational financial managers will choose a capital structure to maximize the value of the marketable claims, VM. Equivalently, rational managers will work to minimize the value of the nonmarketable claims, VN. These are taxes and bankruptcy costs in the previous example, but they also include all the other nonmarketable claims such as the LS claim.

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533

17.5 Signaling The previous section pointed out that the corporate leverage decision involves a tradeoff between a tax subsidy and financial distress costs. This idea was graphed in Figure 17.1, where the marginal tax subsidy of debt exceeds the distress costs of debt for low levels of debt. The reverse holds for high levels of debt. The firm’s capital structure is optimized where the marginal subsidy to debt equals the marginal cost. Let’s explore this idea a little more. What is the relationship between a company’s profitability and its debt level? A firm with low anticipated profits will likely take on a low level of debt. A small interest deduction is all that is needed to offset all of this firm’s pretax profits. And too much debt would raise the firm’s expected distress costs. A more successful firm would probably take on more debt. This firm could use the extra interest to reduce the taxes from its greater earnings. Being more financially secure, this firm would find its extra debt increasing the risk of bankruptcy only slightly. In other words, rational firms raise debt levels (and the concomitant interest payments) when profits are expected to increase. How do investors react to an increase in debt? Rational investors are likely to infer a higher firm value from a higher debt level. Thus, these investors are likely to bid up a firm’s stock price after the firm has, say, issued debt in order to buy back equity. We say that investors view debt as a signal of firm value. Now we get to the incentives of managers to fool the public. Consider a firm whose level of debt is optimal. That is, the marginal tax benefit of debt exactly equals the marginal distress costs of debt. However, imagine that the firm’s manager desires to increase the firm’s current stock price, perhaps because he knows that many of his stockholders want to sell their stock soon. This manager might want to increase the level of debt just to make investors think that the firm is more valuable than it really is. If the strategy works, investors will push up the price of the stock. This implies that firms can fool investors by taking on some additional leverage. Now let’s ask the big question. Are there benefits to extra debt but no costs, implying that all firms will take on as much debt as possible? The answer, fortunately, is that there are costs as well. Imagine that a firm has issued extra debt just to fool the public. At some point, the market will learn that the company is not that valuable after all. At this time the stock price should actually fall below what it would have been had the debt never been increased. Why? Because the firm’s debt level is now above the optimal level. That is, the marginal tax benefit of debt is below the marginal cost of debt. Thus if the current stockholders plan to sell, say, half of their shares now and retain the other half, an increase in debt will help them on immediate sales but likely hurt them on later ones. Now here is the important point: We said that in a world where managers do not attempt to fool investors, valuable firms issue more debt than less valuable ones. It turns out that even when managers attempt to fool investors, the more valuable firms will still want to issue more debt than the less valuable firms. That is, while all firms will increase debt levels somewhat to fool investors, the costs of extra debt prevent the less valuable firms from issuing more debt than the more valuable firms issue. Thus, investors can still treat debt level as a signal of firm value. In other words, investors can still view an announcement of debt as a positive sign for the firm. The foregoing is a simplified example of debt signaling, and you might argue that it is too simplified. For example, perhaps the stockholders of some firms want to sell most of their stock immediately, whereas the stockholders of other firms want to sell only a little of theirs now. It is impossible to tell here whether the firms with the most debt are the most valuable or merely the ones with the most impatient stockholders. Because

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Figure 17.3

Capital Structure and Dividend Policy

5

Stock Returns at the Time of Announcements of Exchange Offers

0 – 100 –5

– 50

0

50

Days relative to announcement date

% return

– 10 Leverage-increasing offers

– 15 – 20 – 25

Leverage-decreasing offers

– 30 – 35 – 40

Exchange offers change the debt–equity ratios of firms. The graph shows that stock prices increase for firms whose exchange offers increase leverage. Conversely, stock prices decrease for firms whose offers decrease leverage. SOURCE: K. Shah, “The Nature of Information Conveyed by Pure Capital Structure Changes,” Journal of Financial Economics 36 (August 1994).

other objections can be brought up as well, signaling theory is best validated by empirical evidence. And fortunately, the empirical evidence tends to support the theory. For example, consider the evidence concerning exchange offers. Firms often change their debt levels through exchange offers, of which there are two types. The first type of offer allows stockholders to exchange some of their stock for debt, thereby increasing leverage. The second type allows bondholders to exchange some of their debt for stock, decreasing leverage. Figure 17.3 shows the stock price behavior of firms that change their proportions of debt and equity via exchange offers. The solid line in the figure indicates that stock prices rise substantially on the date when an exchange offering increasing leverage is announced. (This date is referred to as date 0 in the figure.) Conversely, the dotted line in the figure indicates that stock price falls substantially when an offer decreasing leverage is announced. The market infers from an increase in debt that the firm is better off, leading to a stock price rise. Conversely, the market infers the reverse from a decrease in debt, implying a stock price fall. Thus, we say that managers signal information when they change leverage.

17.6 Shirking, Perquisites, and Bad Investments: A Note on Agency Cost of Equity A previous section introduced the static trade-off model, where a rise in debt increases both the tax shield and the costs of distress. We now extend the trade-off model by considering an important agency cost of equity. A discussion of this cost of equity is contained in a well-known quote from Adam Smith:15 The directors of such [joint-stock] companies, however, being the managers of other people’s money than of their own, it cannot well be expected that they should watch over it with the same anxious vigilance with which the partners in a private copartnery frequently watch 15 Adam Smith, The Wealth of Nations [1776], Cannon edition (New York: Modern Library, 1937), p. 700, as quoted in M. C. Jensen and W. Meckling, “Theory of the Firm: Managerial Behavior, Agency Costs, and Ownership Structure,” Journal of Financial Economics 3 (1978).

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535

over their own. Like the stewards of a rich man, they are apt to consider attention to small matters as not for their master’s honor, and very easily give themselves a dispensation from having it. Negligence and profusion, therefore, must always prevail, more or less, in the management of the affairs of such a company.

This elegant prose can be restated in modern vocabulary. An individual will work harder for a firm if she is one of its owners than if she is just an employee. In addition, the individual will work harder if she owns a large percentage of the company than if she owns a small percentage. This idea has an important implication for capital structure, which we illustrate with the following example.

EXAMPLE1 7.2

Agency Costs Ms. Pagell is an owner–entrepreneur running a computer services firm worth $1 million. She currently owns 100 percent of the firm. Because of the need to expand, she must raise another $2 million. She can either issue $2 million of debt at 12 percent interest or issue $2 million in stock. The cash flows under the two alternatives are presented here: Debt Issue

Work Intensity

Cash Flow

6-hour days 10-hour days

$300,000 400,000

Stock Issue

Interest

Cash Flow to Equity

Cash Flow to Ms. Pagell (100% of equity)

$240,000 240,000

$ 60,000 160,000

$ 60,000 160,000

Cash Flow $300,000 400,000

Interest

Cash Flow to Equity

Cash Flow to Ms. Pagell 1 (33 _3 % of equity)

0 0

$300,000 400,000

$100,000 133,333

Like any entrepreneur, Ms. Pagell can choose the degree of intensity with which she works. In our example, she can work either a 6- or a 10-hour day. With the debt issue, the extra work brings her $100,000 (=$160,000 − $60,000) more income. However, let’s assume that with a stock issue she retains only a one-third interest in the equity. Here, the extra work brings her merely $33,333 (=$133,333 – $100,000). Being human, she is likely to work harder if she issues debt. In other words, she has more incentive to shirk if she issues equity. In addition, she is likely to obtain more perquisites (a big office, a company car, more expense account meals) if she issues stock. If she is a one-third stockholder, two-thirds of these costs are paid for by the other stockholders. If she is the sole owner, any additional perquisites reduce her equity stake alone. Finally, she is more likely to take on capital budgeting projects with negative net present values. It might seem surprising that a manager with any equity interest at all would take on negative NPV projects: Stock price would clearly fall here. However, managerial salaries generally rise with firm size, providing managers with an incentive to accept some unprofitable projects after all the profitable ones have been taken on. That is, when an unprofitable project is accepted, the loss in stock value to a manager with only a small equity interest may be less than the increase in salary. In fact, it is our opinion that losses from accepting bad projects are far greater than losses from either shirking or excessive perquisites. Hugely unprofitable projects have bankrupted whole firms, something that even the largest expense account is unlikely to do. Thus, as the firm issues more equity, our entrepreneur will likely increase leisure time, workrelated perquisites, and unprofitable investments. These three items are called agency costs because managers of the firm are agents of the stockholders.16

16

As previously discussed, agency costs are generally defined as the costs from the conflicts of interest among stockholders, bondholders, and managers.

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This example is quite applicable to a small company considering a large stock offering. Because a manager–owner will greatly dilute his or her share of the total equity in this case, a significant drop in work intensity or a significant increase in fringe benefits is possible. However, the example may be less applicable for a large corporation with many stockholders. For example, consider a large company such as General Motors issuing stock for the umpteenth time. The typical manager there already has such a small percentage stake in the firm that any temptation for negligence has probably been experienced before. An additional offering cannot be expected to increase this temptation. Who bears the burden of these agency costs? Stockholders do not bear these costs as long as they invest with their eyes open. Knowing that Ms. Pagell may work shorter hours, they will pay only a low price for the stock. Thus, it is the owner who is hurt by agency costs. However, Ms. Pagell can protect herself to some extent. Just as stockholders reduce bankruptcy costs through protective covenants, an owner may allow monitoring by new stockholders. However, though proper reporting and surveillance may reduce the agency costs of equity, these techniques are unlikely to eliminate them. It is commonly suggested that leveraged buyouts (LBOs) significantly reduce these costs of equity. In an LBO, a purchaser (usually a team of existing management) buys out the stockholders at a price above the current market. In other words, the company goes private: The stock is placed in the hands of only a few people. Because the managers now own a substantial chunk of the business, they are likely to work harder than when they were simply hired hands.17

Effect of Agency Costs of Equity on Debt–Equity Financing The preceding discussion of the agency costs of equity should be viewed as an extension of the static trade-off model. That is, we stated in Section 17.4 that the change in the value of the firm when debt is substituted for equity is the difference between (1) the tax shield on debt, and (2) the increase in the costs of financial distress (including the agency costs of debt). Now the change in the value of the firm is (1) the tax shield on debt, plus (2) the reduction in the agency costs of equity, minus (3) the increase in the costs of financial distress (including the agency costs of debt). The optimal debt– equity ratio would be higher in a world with agency costs of equity than in a world without these costs. However, because costs of financial distress are so significant, the costs of equity do not imply 100 percent debt financing.

FreeCa shF low Any reader of murder mysteries knows that a criminal must have both motive and opportunity. The discussion thus far has been about motive. Managers with only a small ownership interest have an incentive for wasteful behavior. For example, they bear only a small portion of the costs of, say, excessive expense accounts, and they reap all of the benefits. Now let’s talk about opportunity. A manager can pad his expense account only if the firm has the cash flow to cover it. Thus, we might expect to see more wasteful activity in a firm with a capacity to generate large cash flows than in one with a capacity 17

One professor we know introduces his classes to LBOs by asking the students three questions: 1. How many of you have ever owned a car? 2. How many of you have ever rented a car? 3. How many of you took better care of the car you owned than the car you rented?

Just as it is human nature to take better care of your own car, it is human nature to work harder when you own more of the company.

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to generate only small cash flows. This simple idea, which is formally called the free cash flow hypothesis,18 is backed by a fair amount of empirical research. For example, a frequently cited paper found that firms with high free cash flow are more likely to make bad acquisitions than firms with low free cash flow.19 The hypothesis has important implications for capital structure. Since dividends leave the firm, they reduce free cash flow. Thus, according to the free cash flow hypothesis, an increase in dividends should benefit the stockholders by reducing the ability of managers to pursue wasteful activities. Furthermore, since interest and principal also leave the firm, debt reduces free cash flow as well. In fact, interest and principal should have a greater effect than dividends have on the free-spending ways of managers, because bankruptcy will occur if the firm is unable to make future debt payments. By contrast, a future dividend reduction will cause fewer problems to the managers, since the firm has no legal obligation to pay dividends. Because of this, the free cash flow hypothesis argues that a shift from equity to debt will boost firm value. In summary, the free cash flow hypothesis provides still another reason for firms to issue debt. We previously discussed the cost of equity; new equity dilutes the holdings of managers with equity interests, increasing their motive to waste corporate resources. We now state that debt reduces free cash flow, because the firm must make interest and principal payments. The free cash flow hypothesis implies that debt reduces the opportunity for managers to waste resources.

17.7 The Pecking-Order Theory Although the trade-off theory has dominated corporate finance circles for a long time, attention is also being paid to the pecking-order theory.20 To understand this view of the world, let’s put ourselves in the position of a corporate financial manager whose firm needs new capital. The manager faces a choice between issuing debt and issuing equity. Previously, we evaluated the choice in terms of tax benefits, distress costs, and agency costs. However, there is one consideration that we have so far neglected: timing. Imagine the manager saying: I want to issue stock in one situation only—when it is overvalued. If the stock of my firm is selling at $50 per share, but I think that it is actually worth $60, I will not issue stock. I would actually be giving new stockholders a gift because they would receive stock worth $60 but would only have to pay $50 for it. More important, my current stockholders would be upset because the firm would be receiving $50 in cash but giving away something worth $60. So if I believe that my stock is undervalued, I would issue bonds. Bonds, particularly those with little or no risk of default, are likely to be priced correctly. Their value is determined primarily by the marketwide interest rate, a variable that is publicly known. But suppose our stock is selling at $70. Now I’d like to issue stock. If I can get some fool to buy our stock for $70 while the stock is really worth only $60, I will be making $10 for our currentsh areholders.

Although this may strike you as a cynical view, it seems to square well with reality. Before the United States adopted insider trading and disclosure laws, many managers 18

The seminal theoretical article is Michael C. Jensen, “The Agency Costs of Free Cash Flow: Corporate Finance and Takeovers,” American Economic Review (May 1986), pp. 323–39. 19

L. Lang, R. Stulz, and R. Walkling, “Managerial Performance, Tobin’s Q and the Gains in Tender Offers,” Journal of Financial Economics (1989). 20

The pecking-order theory is generally attributed to S. C. Myers, “The Capital Structure Puzzle,” Journal of Finance 39 (July 1984).

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were alleged to have unfairly trumpeted their firm’s prospects prior to equity issuance. And even today, managers seem more willing to issue equity after the price of their stock has risen than after their stock has fallen in price. Thus, timing might be an important motive in equity issuance, perhaps even more important than the motives in the trade-off model. After all, the firm in the preceding example immediately makes $10 by properly timing the issuance of equity. Ten dollars’ worth of agency costs and bankruptcy cost reduction might take many years to realize. The key that makes the example work is asymmetric information: The manager must know more about his firm’s prospects than does the typical investor. If the manager’s estimate of the true worth of the company is no better than the estimate of a typical investor, any attempts by the manager to time will fail. This assumption of asymmetry is quite plausible. Managers should know more about their company than do outsiders because managers work at the company every day. (One caveat is that some managers are perpetually optimistic about their firm, blurring good judgment.) But we are not done with this example yet; we must consider the investor. Imagine an investor saying: I make investments carefully because they involve my hard-earned money. However, even with all the time I put into studying stocks, I can’t possibly know what the managers themselves know. After all, I’ve got a day job to be concerned with. So I watch what the managers do. If a firm issues stock, the firm was likely overvalued beforehand. If a firm issues debt, it was likely undervalued.

When we look at both issuers and investors, we see a kind of poker game, with each side trying to outwit the other. What should the issuing firm do in this poker game? Clearly, the firm should issue debt if the equity is undervalued. But what if the equity is overvalued? Here it gets tricky because a first thought is that the firm should issue equity. However, if a firm issues equity, investors will infer that the stock is overvalued. They will not buy it until the stock has fallen enough to eliminate any advantage from equity issuance. In fact, it can be shown that only the most overvalued firms have any incentive to issue equity. Should even a moderately overpriced firm issue equity, investors will infer that this firm is among the most overpriced, causing the stock to fall more than is deserved. Thus, the end result is that virtually no one will issue equity.21 This result that essentially all firms should issue debt is clearly an extreme one. It is as extreme as (1) the Modigliani–Miller (MM) result that in a world without taxes, firms are indifferent to capital structure and (2) the MM result that in a world of corporate taxes but no financial distress costs, all firms should be 100 percent debtfinanced. Perhaps we in finance have a penchant for extreme models! But just as we can temper MM’s conclusions by combining financial distress costs with corporate taxes, we can temper those of the pure pecking-order theory. This pure version assumes that timing is the financial manager’s only consideration. In reality, a manager must consider taxes, financial distress costs, and agency costs as well. Thus, a firm may issue debt only up to a point. If financial distress becomes a real possibility beyond that point, the firm may issue equity instead.

Rules of the Pecking Order The previous discussion presented the basic ideas behind the pecking-order theory. What are the practical implications of the theory for financial managers? The theory provides the following two rules for the real world. 21 In the interest of simplicity, we have not presented our results in the form of a rigorous model. To the extent that a reader wants a deeper explanation, we refer him or her to S. C. Myers, “The Capital StructureP uzzle,” Journal of Finance (July 1984).

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Rule #1: Use Internal Financing For expository purposes, we have oversimplified by comparing equity to riskless debt. Managers cannot use special knowledge of their firm to determine if this type of debt is mispriced because the price of riskless debt is determined solely by the marketwide interest rate. However, in reality, corporate debt has the possibility of default. Thus, just as managers tend to issue equity when they think it is overvalued, managers also tend to issue debt when they think it is overvalued. When would managers view their debt as overvalued? Probably in the same situations when they think their equity is overvalued. For example, if the public thinks that the firm’s prospects are rosy but the managers see trouble ahead, these managers would view their debt—as well as their equity—as being overvalued. That is, the public might see the debt as nearly risk-free, whereas the managers see a strong possibility of default. Thus, investors are likely to price a debt issue with the same skepticism that they have when pricing an equity issue. The way managers get out of this box is to finance projects out of retained earnings. You don’t have to worry about investor skepticism if you can avoid going to investors in the first place. So the first rule of the pecking order is this: Useinte rnalfinanc ing. Rule #2: Issue Safe Securities First Although investors fear mispricing of both debt and equity, the fear is much greater for equity. Corporate debt still has relatively little risk compared to equity because if financial distress is avoided, investors receive a fixed return. Thus, the pecking-order theory implies that if outside financing is required, debt should be issued before equity. Only when the firm’s debt capacity is reached should the firm consider equity. Of course, there are many types of debt. For example, because convertible debt is more risky than straight debt, the pecking-order theory implies that managers should issue straight debt before issuing convertibles. So, the second rule of pecking-order theory is this: Issuethe safe stse curitiesfirst.

Implications A number of implications associated with the pecking-order theory are at odds with those of the trade-off theory. 1. There is no target amount of leverage. According to the trade-off model, each firm balances the benefits of debt, such as the tax shield, with the costs of debt, such as distress costs. The optimal amount of leverage occurs where the marginal benefit of debt equals the marginal cost of debt. By contrast, the pecking-order theory does not imply a target amount of leverage. Rather, each firm chooses its leverage ratio based on financing needs. Firms first fund projects out of retained earnings. This should lower the percentage of debt in the capital structure, because profitable, internally funded projects raise both the book value and the market value of equity. Additional projects are funded with debt, clearly raising the debt level. However, at some point the debt capacity of the firm may be exhausted, giving way to equity issuance. Thus, the amount of leverage is determined by the happenstance of available projects. Firms do not pursue a target ratio of debt to equity. 2. Profitable firms use less debt. Profitable firms generate cash internally, implying less need for outside financing. Because firms desiring outside capital turn to debt first, profitable firms end up relying on less debt. The trade-off model does not have this implication. Here the greater cash flow of more profitable firms creates

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greater debt capacity. These firms will use that debt capacity to capture the tax shield and the other benefits of leverage. 3. Companies like financial slack. The pecking-order theory is based on the difficulties of obtaining financing at a reasonable cost. A skeptical investing public thinks a stock is overvalued if the managers try to issue more of it, thereby leading to a stock price decline. Because this happens with bonds only to a lesser extent, managers rely first on bond financing. However, firms can only issue so much debt before encountering the potential costs of financial distress. Wouldn’t it be easier to have the cash ahead of time? This is the idea behind financial slack. Because firms know that they will have to fund profitable projects at various times in the future, they accumulate cash today. They are then not forced to go to the capital markets when a project comes up. However, there is a limit to the amount of cash a firm will want to accumulate. As mentioned earlier in this chapter, too much free cash may tempt managers to pursue wasteful activities.

17.8 Growth and the Debt–Equity Ratio Although the trade-off between the tax shield and bankruptcy costs (as illustrated in Figure 17.1) is often viewed as the “standard model” of capital structure, it has its critics. For example, some point out that bankruptcy costs in the real world appear to be much smaller than the tax subsidy. Thus, the model implies that the optimal debt∕value ratio should be near 100 percent, an implication at odds with reality.22 Perhaps the pecking-order theory is more consistent with the real world here. That is, firms are likely to have more equity in their capital structure than implied by the static trade-off theory because internal financing is preferred to external financing. There is another approach that implies significant equity financing, even in a world with low bankruptcy costs. This idea, developed by Berens and Cuny,23 argues that equity financing follows from growth. To explain the idea, we first consider an example of a no-growth firm. Next, we examine the effect of growth on firm leverage.

NoG rowth Imagine a world of perfect certainty24 where a firm has annual earnings before interest and taxes (EBIT) of $100. In addition, the firm has issued $1,000 of debt at an interest rate of 10 percent, implying interest payments of $100 per year. Here are the cash flows to the firm: Date

Earnings before interest and taxes (EBIT) Interest Taxable income

1

2

3

4 ...

$100

$100

$100

$100 . . .

−100 $ 0

−100 $ 0

−100 $ 0

−100 . . . $ 0

22 See Merton Miller’s Presidential Address to the American Finance Association, reprinted as “Debt and Taxes,” Journal of Finance (May 1977). 23 J. L. Berens and C. L. Cuny, “Inflation, Growth and Capital Structure,” Review of Financial Studies 8 (Winter 1995). 24

The same qualitative results occur under uncertainty, though the mathematics is more troublesome.

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The firm has issued just enough debt so that all EBIT is paid out as interest. Because interest is tax deductible, the firm pays no taxes. In this example, the equity is worthless because stockholders receive no cash flows. Since debt is worth $1,000, the firm is also valued at $1,000. Therefore the debt-to-value ratio is 100 percent (= $1,000/$1,000). Had the firm issued less than $1,000 of debt, the corporation would have positive taxable income and, consequently, would have ended up paying some taxes. Had the firm issued more than $1,000 of debt, interest would have exceeded EBIT, causing default. Consequently, the optimal debt-to-value ratio is 100 percent.

Growth Now imagine another firm where EBIT is also $100 at date 1 but is growing at 5 percent per year.25 To eliminate taxes, this firm also wants to issue enough debt so that interest equals EBIT. Because EBIT is growing at 5 percent per year, interest must also grow at this rate. This is achieved by increasing debt by 5 percent per year.26 The debt, EBIT, interest, and taxable income levels are these: Date

Debt New debt issued EBIT Interest Taxable income

0

1

2

3

4 ...

$1,000

$1,050 50 $ 100

$1,102.50 52.50 $ 105

$1,157.63 … 55.13 … $ 110.25

$115.76 . . .

−100 $ 0

−105 $ 0

−110.25 $ 0

−115.76 . . . $ 0

Note that interest on a particular date is always 10 percent of the debt on the previous date. Debt is set so that interest is exactly equal to EBIT. As in the no-growth case, the levered firm has the maximum amount of debt at each date. Default would occur if interest payments were increased. Because growth is 5 percent per year, the value of the firm is:27 $100 VFirm = ________ = $2,000 .10 − .05 The equity at date 0 is the difference between the value of the firm at that time, $2,000, and the debt of $1,000. Hence, equity must be equal to $1,000,28 implying a debt-tovalue ratio of 50 percent (= $1,000/$2,000). Note the important difference between the 25

For simplicity, assume that growth is achieved without earnings retention. The same conclusions would be reached with retained earnings, though the arithmetic would become more involved. Of course, growth without earnings retention is less realistic than growth with retention. 26 Because the firm makes no real investment, the new debt is used to buy back shares of stock. 27

The firm can also be valued by a variant of Equation 16.5: VL = VU + PVTS $100(1 − tC) tC × $100 = ___________ + _________ = $2,000 .10 − .05 .10 − .05

Because of firm growth, both VU and PVTS are growing perpetuities. Students are often surprised that equity has value when taxable income is zero. Actually, the equityholders are receiving cash flow each period. The proceeds from the new debt can be used either to pay dividends or to buy back stock. 28

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no-growth and the growth example. The no-growth example has no equity; the value of the firm is simply the value of the debt. With growth, there is equity as well as debt. We can also value the equity in another way. It may appear at first glance that the stockholders receive nothing because the EBIT is paid out as interest each year. However, the new debt issued each year can be paid as a dividend to the stockholders. Because the new debt is $50 at date 1 and grows at 5 percent per year, the value of the stockholders’ interest is: $50 ________ .10 − .05

= $1,000

the same number that we obtained in the previous paragraph. As we mentioned earlier, any further increase in debt above $1,000 at date 0 would lower the value of the firm in a world with bankruptcy costs. Thus, with growth, the optimal amount of debt is less than 100 percent. Note, however, that bankruptcy costs need not be as large as the tax subsidy. In fact, even with infinitesimally small bankruptcy costs, firm value would decline if promised interest rose above $100 in the first year. The key to this example is that today’s interest is set equal to today’s income. Although the introduction of future growth opportunities increases firm value, it does not increase the current level of debt needed to shield today’s income from today’s taxes. Because equity is the difference between firm value and debt, growth increases the value of equity. The preceding example captures an essential feature of the real world: Growth. The same conclusion is reached in a world of inflation but with no growth opportunities. Thus, the result of this section, that 100 percent debt financing is suboptimal, holds whether inflation or growth opportunities are present. Furthermore, high-growth firms should have lower debt ratios than low-growth firms. Most firms have growth opportunities, and inflation has been with us for most of this and the previous centuries, so this section’s example is based on realistic assumptions.29

17.9 Personal Taxes So far in this chapter, we have considered corporate taxes only. Because interest on debt is tax deductible whereas dividends on stock are not deductible, we argued that the tax code gives firms an incentive to issue debt. But corporations are not the only ones paying taxes; individuals must pay taxes on both the dividends and the interest that they receive. We cannot fully understand the effect of taxes on capital structure until all taxes, both corporate and personal, are considered.

The Basics of Personal Taxes Let’s begin by examining an all-equity firm that receives $1 of pretax earnings. If the corporate tax rate is tC, the firm pays taxes tC, leaving itself with earnings after taxes of 1 − tC. Let’s assume that this entire amount is distributed to the stockholders as 29

Our example assumes a single perpetual bond with level coupon payments. Berens and Cuny (BC) point out (p. 1201) that, with a number of different bonds, a firm might be able to construct an equally optimal capital structure with a greater debt-to-value ratio. Because both capital structures are equally optimal, a firm might choose either one. Although the analysis with many financing instruments is more complex, a firm can still choose a low debt-to-value ratio with no ill effect. Thus, BC’s conclusion that firms can employ a significant amount of equity in a world with a low level of bankruptcy costs still holds.

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dividends. If the personal tax rate on stock dividends is tS, the stockholders pay taxes of (1 − tC) × tS, leaving them with (1 − tC) × (1 − tS) after taxes. Alternatively, imagine that the firm is financed with debt. Here, the entire $1 of earnings will be paid out as interest because interest is deductible at the corporate level. If the personal tax rate on interest is tB, the bondholders pay taxes of tB,le aving them with 1 − tBafte rtax es.

The Effect of Personal Taxes on Capital Structure To explore the effect of personal taxes on capital structure, let’s consider three questions: 1. Ignoring costs of financial distress, what is the firm’s optimal capital structure if dividends and interest are taxed at the same personal rate—that is, tS = tB? The firm should select the capital structure that gets the most cash into the hands of its investors. This is tantamount to selecting a capital structure that minimizes the total amount of taxes at both the corporate and personal levels. As we have said, beginning with $1 of pretax corporate earnings, stockholders receive (1 − tC) × (1 − tS), and bondholders receive 1 − tB. We can see that if tS = tB, bondholders receive more than stockholders. Thus, the firm should issue debt, not equity, in this situation. Intuitively, income is taxed twice—once at the corporate level and once at the personal level—if it is paid to stockholders. Conversely, income is taxed only at the personal level if it is paid to bondholders. Note that the assumption of no personal taxes, which we used in the previous chapter, is a special case of the assumption that both interest and dividends are taxed at the same rate. Without personal taxes, the stockholders receive 1 − tC while the bondholders receive $1. Thus, as we stated in a previous chapter, firms should issue debt in a world without personal taxes. 2. Under what conditions will the firm be indifferent between issuing equity or debt? The firm will be indifferent if the cash flow to stockholders equals the cash flow to bondholders. That is, the firm is indifferent when: (1 − tC ) × (1 − tS ) = 1 − tB

(17.1)

3. What should companies do in the real world? Although this is clearly an important question, it is, unfortunately, a hard one— perhaps too hard to answer definitely. Nevertheless, let’s begin by working with the highest tax rates. As of 2005, the corporate tax rate was 35 percent. For investors in the highest marginal tax bracket, interest income was also taxed at 35 percent. Investors in this highest bracket faced a 15 percent tax rate on dividends. At these rates, the left side of Equation 17.1 becomes (1 − .35) × (1 − .15), which equals .55. The right side of the equation becomes 1 − .35, which equals .65. Because any rational firm would rather put $.65 instead of $.55 into its investors’ hands, it appears at first glance that firms should prefer debt over equity, just as we argued in the previous chapter. Does anything else in the real world alter this conclusion? Perhaps: Our discussion on equity income is not yet complete. Firms can repurchase shares with excess cash instead of paying a dividend. Although capital gains are also taxed at a maximum of 15 percent, the shareholder pays a capital gains tax only on the gain from sale, not on the entire proceeds from the repurchase. Thus, the effective tax rate on capital gains is actually lower than 15 percent. Because firms both pay dividends and repurchase shares, the effective personal tax rate on stock distributions must be below 15 percent.

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This lower effective tax rate makes equity issuance less burdensome, but the lower rate will not induce any firm to choose stocks over bonds. For example, suppose that the effective tax rate on stock distributions is 10 percent. From every dollar of pretax corporate income, stockholders receive (1 − .35) × (1 − .10), which equals $.59. This amount is less than the $.65 that bondholders receive. In fact, as long as the effective tax rate on stock income is positive, bondholders will still receive more than stockholders from a dollar of pretax corporate income. And we have assumed that all bondholders face a tax rate of .35 on interest income. In reality, plenty of bondholders are in lower tax brackets, further tipping the scales toward bond financing. Was there ever a time when stocks had a tax advantage over bonds? Very likely, yes. Consider the 1970s, when the marginal tax rate on interest income was as high as 70 percent. While dividends were taxed at the same rate as interest, capital gains were taxed at a much lower rate. Corporate income was taxed at 46 percent. Thus, both the effective tax rate on equity income and the corporate tax rate were well below the maximum rate on interest. Under reasonable assumptions we can make a case that stocks had the tax advantage at that time.30 However, given that bonds appear to have the tax advantage today, is there anything that might cause firms to issue stock rather than bonds? Yes—the same costs of financial distress we discussed earlier in the chapter. We previously said that these costs are an offset to debt’s tax advantage, causing firms to employ less than 100 percent leverage. The same point applies in the presence of personal taxes. And as long as the personal tax rate on equity income is below the personal tax rate on interest, the tax advantage to debt is smaller in a world with personal taxes than in a world without personal taxes. Thus, the optimal amount of debt will be lower in a world with personal taxes than in a world without them.

17.10 How Firms Establish Capital Structure The theories of capital structure are among the most elegant and sophisticated in the field of finance. Financial economists should (and do!) pat themselves on the back for contributions in this area. However, the practical applications of the theories are less than fully satisfying. Consider that our work on net present value produced an exact formula for evaluating projects. Prescriptions for capital structure under either the trade-off model or the pecking-order theory are vague by comparison. No exact formula is available for evaluating the optimal debt–equity ratio. Because of this, we turn to evidence from the real world. The following empirical regularities are worthwhile to consider when formulating capital structure policy. 1. Most corporations have low debt–asset ratios. How much debt is used in the real world? As we saw in Chapter 16, the average debt-to-equity ratio for U.S. firms usually has been less than 100% (the average debt-to-value ratio usually has been below 50%). Figure 17.4 shows the debt-to-total-value ratios of firms in different countries in recent years. Differences in accounting procedures make the figures somewhat difficult to interpret. However, the debt ratios of U.S. and Canadian firms are the lowest. 30 Actually, a well-known model of capital structure argues that an equilibrium would have occurred with firms issuing both debt and equity. Investors in low-tax brackets would buy the debt and investors in hightax brackets would buy the equity. See Merton Miller, “Debt and Taxes,” Journal of Finance (May 1977).

Chapter 17

Figure 17.4

Capital Structure

545

Estimated Ratios of Debt to Total Value (Accounting Value) of Nonfinancial Firms, Various Countries

Percent 80 72 70

60

50

58

59

49

48

45 40

30

20

10

0 United States

Japan

Germany

Canada

France

Italy

Country

Definition: Debt is short-term debt plus long-term debt. Total value is debt plus equity (in book value terms). SOURCE: OECD financial statistics.

Should we view these ratios as being high or low? Because academics generally see corporate tax reduction as a chief motivation for debt, we might wonder if real-world companies issue enough debt to greatly reduce, if not downright eliminate, corporate taxes. The empirical evidence suggests that this is not the case. For example, corporate taxes in the United States for 2007 were over $460 billion. Thus, it is clear that corporations do not issue debt up to the point where tax sheltersar ec ompletelyu sedu p.31 There are clearly limits to the amount of debt corporations can issue, perhaps because of the financial distress costs discussed earlier in this chapter. 2. A number of firms use no debt. In a fascinating study, Agrawal and Nagarajan examined approximately 100 firms on the New York Stock Exchange without long-term debt.32 They found that these firms are averse to leverage of any kind, with little short-term debt as well. In addition, they have levels of cash and marketable securities well above their levered counterparts. Typically, the managers of these firms have high equity ownership. Furthermore, there is significantly greater family involvement in all-equity firms than in levered firms. 31

For further insight, see John Graham, “How Big Are the Tax Benefits of Debt?” Journal of Finance (2000). Anup Agrawal and Nandu Nagarajan, “Corporate Capital Structure, Agency Costs, and Ownership Control: The Case of All-Equity Firms,” Journal of Finance 45 (September 1990). 32

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Table 17.3

Debt as a Percentage of the Market Value of Equity and Debt (Industry Medians)

Capital Structure Ratios for Selected U.S. Nonfinancial Firms (Medians), Five-Year Average

High Leverage Air transport Television broadcasting stations Hotels and lodging Natural gas distribution Building construction Low Leverage Educational services Drugs Biological products Electronics Computers

57.9 54.0 44.2 41.8 40.4 7.8 6.8 5.9 3.3 1.6

DEFINITION: Debt is the total of short-term debt and long-term debt. SOURCE: Ibbotson 2008 Cost of Capital Yearbook (Chicago: Morningstar, 2008).

Thus, a story emerges. Managers of all-equity firms are less diversified than the managers of similar, but levered, firms. Because of this, significant leverage represents an added risk that the managers of all-equity firms are loath to accept. 3. There are differences in the capital structures of different industries. There are significant interindustry differences in debt ratios that persist over time. As can be seen in Table 17.3, debt ratios tend to be quite low in high-growth industries with ample future investment opportunities, such as the drug and electronics industries. This is true even when the need for external financing is great. Industries with large investments in tangible assets, such as building construction, tend to have high leverage. 4. Most corporations employ target debt–equity ratios. Graham and Harvey asked 392 chief financial officers (CFOs) whether their firms use target debt–equity ratios, with the results being presented in Figure 17.5.33 As can be seen, the great majority of the firms use targets, though the strictness of the targets varies across companies. Only 19 percent of the firms avoid target ratios. Results elsewhere in the paper indicate that large firms are more likely than small firms to employ these targets. The CFOs did not specify what they meant by either flexible or strictt argets. However, elsewhere in the study, the respondents indicated that, by and large, they did not rebalance in response to changes in their firm’s stock price, suggesting some flexibility in target ratios. How should companies establish target debt–equity ratios? While there is no mathematical formula for establishing a target ratio, we present three important factors affecting the ratio:

33

John Graham and Campbell Harvey, “The Theory and Practice of Corporate Finance,” Journal of Financial Economics (May∕June 2001).

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Figure 17.5 Survey Results on the Use of Target Debt–Equity Ratios Flexible target 37%

No target ratio or range 19%

Somewhat tight target/range 34% Very strict target 10% This figure shows the survey responses of 392 CFOs concerning their use of target debt–equity ratios. SOURCE: Figure 6 of John Graham and Campbell Harvey, “The Theory and Practice of Corporate Finance,” Journal of Financial Economics (May/June 2001).

• Taxes: As we pointed out earlier, firms can deduct interest for tax purposes only to the extent of their profits before interest. Thus, highly profitable firms are more likely to have larger target ratios than less profitable firms.34 • Types of assets: Financial distress is costly with or without formal bankruptcy proceedings. The costs of financial distress depend on the types of assets that the firm has. For example, if a firm has a large investment in land, buildings, and other tangible assets, it will have smaller costs of financial distress than a firm with a large investment in research and development. Research and development typically has less resale value than land; thus, most of its value disappears in financial distress. Therefore, firms with large investments in tangible assets are likely to have higher target debt–equity ratios than firms with large investments in research and development. • Uncertainty of operating income: Firms with uncertain operating income have a high probability of experiencing financial distress, even without debt. Thus, these firms must finance mostly with equity. For example, pharmaceutical firms have uncertain operating income because no one can predict whether today’s research will generate new, profitable drugs. Consequently, these firms issue little debt. By contrast, the operating income of firms in regulated industries, such as utilities, generally has low volatility. Relative to other industries, utilities use a great deal of debt. One final note is in order. Because no formula supports them, the preceding points may seem too nebulous to assist financial decision making. Instead, many real-world firms simply base their capital structure decisions on industry averages. This may strike some as a cowardly approach, but it at least keeps firms from deviating far from accepted practice. After all, the existing firms in any industry are the survivors. Therefore we should pay at least some attention to their decisions. 34

By contrast, the pecking-order theory argues that profitable firms will employ less debt because they can invest out of retained earnings. However, the pecking-order theory argues against the use of target ratios in the first place.

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1. We mentioned in the last chapter that according to theory, firms should create all-debt capital structures under corporate taxation. Because firms generally employ moderate amounts of debt in the real world, the theory must have been missing something at that point. We stated in this chapter that costs of financial distress cause firms to restrain their issuance of debt. These costs are of two types: direct and indirect. Lawyers’ and accountants’ fees during the bankruptcy process are examples of direct costs. We mentioned four examples of indirect costs: Impaireda bilityt o conductb usiness. Incentive to take on risky projects. Incentivet owardu nderinvestment. Distribution of funds to stockholders prior to bankruptcy.

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2. Because financial distress costs are substantial and the stockholders ultimately bear them, firms have an incentive to reduce costs. Protective covenants and debt consolidation are two common cost reduction techniques. 3. Because costs of financial distress can be reduced but not eliminated, firms will not finance entirely with debt. Figure 17.1 illustrates the relationship between firm value and debt. In the figure, firms select the debt–equity ratio at which firm value is maximized. 4. Signaling theory argues that profitable firms are likely to increase their leverage because the extra interest payments will offset some of the pretax profits. Rational stockholders will infer higher firm value from a higher debt level. Thus investors view debt as a signal of firm value. 5. Managers owning a small proportion of a firm’s equity can be expected to work less, maintain more lavish expense accounts, and accept more pet projects with negative NPVs than managers owning a large proportion of equity. Because new issues of equity dilute a manager’s percentage interest in the firm, such agency costs are likely to increase when a firm’s growth is financed through new equity rather than through new debt. 6. The pecking-order theory implies that managers prefer internal to external financing. If external financing is required, managers tend to choose the safest securities, such as debt. Firms may accumulate slack to avoid external equity. 7. Berens and Cuny argue that significant equity financing can be explained by real growth and inflation, even in a world of low bankruptcy costs. 8. The results so far have ignored personal taxes. If distributions to equityholders are taxed at a lower effective personal tax rate than are interest payments, the tax advantage to debt at the corporate level is partially offset. 9. Debt–equity ratios vary across industries. We present three factors determining the target debt–equity ratio: a. Taxes: Firms with high taxable income should rely more on debt than firms with low taxablein come. b. Types of assets: Firms with a high percentage of intangible assets such as research and development should have low debt. Firms with primarily tangible assets should have higher debt. c. Uncertainty of operating income: Firms with high uncertainty of operating income shouldr elymo stlyo ne quity.

Concept Questions

1. 2.

3.

Bankruptcy Costs What are the direct and indirect costs of bankruptcy? Briefly explaine ach. Stockholder Incentives Do you agree or disagree with the following statement? A firm’s stockholders will never want the firm to invest in projects with negative net present values. Why? Capital Structure Decisions Due to large losses incurred in the past several years, a firm has $2 billion in tax loss carryforwards. This means that the next $2 billion of the firm’s income will be free from corporate income taxes. Security analysts estimate

Chapter 17 Capital Structure

4. 5.

6. 7.

8.

9.

Questions and Problems BASIC (Questions 1–5)

1.

2.

3.

4.

that it will take many years for the firm to generate $2 billion in earnings. The firm has a moderate amount of debt in its capital structure. The firm’s CEO is deciding whether to issue debt or equity to raise the funds needed to finance an upcoming project. Which method of financing would you recommend? Why? Cost of Debt What steps can stockholders take to reduce the costs of debt? M&M and Bankruptcy Costs How does the existence of financial distress costs and agency costs affect Modigliani and Miller’s theory in a world where corporations pay taxes? AgencyCos tsof E quity What are the sources of agency costs of equity? Observed Capital Structures Refer to the observed capital structures given in Table 17.3 of the text. What do you notice about the types of industries with respect to their average debt–equity ratios? Are certain types of industries more likely to be highly leveraged than others? What are some possible reasons for this observed segmentation? Do the operating results and tax history of the firms play a role? How about their future earnings prospects? Explain. Bankruptcy and Corporate Ethics As mentioned in the text, some firms have filed for bankruptcy because of actual or likely litigation-related losses. Is this a proper use of the bankruptcy process? Bankruptcy and Corporate Ethics Firms sometimes use the threat of a bankruptcy filing to force creditors to renegotiate terms. Critics argue that in such cases the firm is using bankruptcy laws “as a sword rather than a shield.” Is this an ethical tactic? Bankruptcy and Corporate Ethics Continental Airlines once filed for bankruptcy, at least in part, as a means of reducing labor costs. Whether this move was ethical or proper was hotly debated. Give both sides of the argument. Firm Value Janetta Corp. has an EBIT rate of $850,000 per year that is expected to continue in perpetuity. The unlevered cost of equity for the company is 14 percent, and the corporate tax rate is 35 percent. The company also has a perpetual bond issue outstanding with a market value of $1.9 million. a. What is the value of the company? b. The CFO of the company informs the company president that the value of the company is $4.3 million. Is the CFO correct? Agency Costs Tom Scott is the owner, president, and primary salesperson for Scott Manufacturing. Because of this, the company’s profits are driven by the amount of work Tom does. If he works 40 hours each week, the company’s EBIT will be $400,000 per year; if he works a 50-hour week, the company’s EBIT will be $500,000 per year. The company is currently worth $2.5 million. The company needs a cash infusion of $1.2 million, and it can issue equity or issue debt with an interest rate of 8 percent. Assume there are no corporate taxes. a. What are the cash flows to Tom under each scenario? b. Under which form of financing is Tom likely to work harder? c. What specific new costs will occur with each form of financing? Capital Structure and Growth Edwards Construction currently has debt outstanding with a market value of $70,000 and a cost of 8 percent. The company has EBIT of $5,600 that is expected to continue in perpetuity. Assume there are no taxes. a. What is the value of the company’s equity? What is the debt-to-value ratio? b. What are the equity value and debt-to-value ratio if the company’s growth rate is 3p ercent? c. What are the equity value and debt-to-value ratio if the company’s growth rate is 7p ercent? Nonmarketed Claims Dream, Inc., has debt outstanding with a face value of $5 million. The value of the firm if it were entirely financed by equity would be

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5.

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INTERMEDIATE (Questions 6–8)

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$14.5 million. The company also has 300,000 shares of stock outstanding that sell at a price of $35 per share. The corporate tax rate is 35 percent. What is the decrease in the value of the company due to expected bankruptcy costs? Capital Structure and Nonmarketed Claims Suppose the president of the company in the previous problem stated that the company should increase the amount of debt in its capital structure because of the tax-advantaged status of its interest payments. His argument is that this action would increase the value of the company. How would your espond? Costs of Financial Distress Steinberg Corporation and Dietrich Corporation are identical firms except that Dietrich is more levered. Both companies will remain in business for one more year. The companies’ economists agree that the probability of the continuation of the current expansion is 80 percent for the next year, and the probability of a recession is 20 percent. If the expansion continues, each firm will generate earnings before interest and taxes (EBIT) of $2.4 million. If a recession occurs, each firm will generate earnings before interest and taxes (EBIT) of $900,000. Steinberg’s debt obligation requires the firm to pay $800,000 at the end of the year. Dietrich’s debt obligation requires the firm to pay $1.1 million at the end of the year. Neither firm pays taxes. Assume a discount rate of 15 percent. a. What is the value today of Steinberg’s debt and equity? What about that for Dietrich’s? b. Steinberg’s CEO recently stated that Steinberg’s value should be higher than Dietrich’s because the firm has less debt and therefore less bankruptcy risk. Do you agree or disagree with this statement? Agency Costs Fountain Corporation’s economists estimate that a good business environment and a bad business environment are equally likely for the coming year. The managers of Fountain must choose between two mutually exclusive projects. Assume that the project Fountain chooses will be the firm’s only activity and that the firm will close one year from today. Fountain is obligated to make a $2,500 payment to bondholders at the end of the year. The projects have the same systematic risk but different volatilities. Consider the following information pertaining to the two projects:

Economy Bad Good

8.

Probability .50 .50

Low-Volatility Project Payoff $2,500 2,700

High-Volatility Project Payoff $2,100 2,800

a. What is the expected value of the firm if the low-volatility project is undertaken? What if the high-volatility project is undertaken? Which of the two strategies maximizes the expected value of the firm? b. What is the expected value of the firm’s equity if the low-volatility project is undertaken? What is it if the high-volatility project is undertaken? c. Which project would Fountain’s stockholders prefer? Explain. d. Suppose bondholders are fully aware that stockholders might choose to maximize equity value rather than total firm value and opt for the high-volatility project. To minimize this agency cost, the firm’s bondholders decide to use a bond covenant to stipulate that the bondholders can demand a higher payment if Fountain chooses to take on the high-volatility project. What payment to bondholders would make stockholders indifferent between the two projects? Financial Distress Good Time Company is a regional chain department store. It will remain in business for one more year. The probability of a boom year is 60 percent and the probability of a recession is 40 percent. It is projected that the company will generate a total cash flow of $210 million in a boom year and

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CHALLENGE (Questions 9–10)

9.

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$85 million in a recession. The company’s required debt payment at the end of the year is $120 million. The market value of the company’s outstanding debt is $94 million. The company pays no taxes. a. What payoff do bondholders expect to receive in the event of a recession? b. What is the promised return on the company’s debt? c. What is the expected return on the company’s debt? Personal Taxes, Bankruptcy Costs, and Firm Value When personal taxes on interest income and bankruptcy costs are considered, the general expression for the value of a levered firm in a world in which the tax rate on equity distributions equals zero is: VL = VU + {1 − [(1 − tC ) (1 − tB)]} × B − C(B) where: VL = The value of a levered firm. VU = The value of an unlevered firm. B = The value of the firm’s debt. tC = The tax rate on corporate income. tB = The personal tax rate on interest income. C(B) = The present value of the costs of financial distress.

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10.

a. In their no-tax model, what do Modigliani and Miller assume about tC, tB, and C(B)? What do these assumptions imply about a firm’s optimal debt–equity ratio? b. In their model with corporate taxes, what do Modigliani and Miller assume about tC, tB, and C(B)? What do these assumptions imply about a firm’s optimal debt– equityr atio? c. Consider an all-equity firm that is certain to be able to use interest deductions to reduce its corporate tax bill. If the corporate tax rate is 34 percent, the personal tax rate on interest income is 20 percent, and there are no costs of financial distress, by how much will the value of the firm change if it issues $1 million in debt and uses the proceeds to repurchase equity? d. Consider another all-equity firm that does not pay taxes due to large tax loss carryforwards from previous years. The personal tax rate on interest income is 20 percent, and there are no costs of financial distress. What would be the change in the value of this firm from adding $1 of perpetual debt rather than $1 of equity? Personal Taxes, Bankruptcy Costs, and Firm Value Overnight Publishing Company (OPC) has $2.5 million in excess cash. The firm plans to use this cash either to retire all of its outstanding debt or to repurchase equity. The firm’s debt is held by one institution that is willing to sell it back to OPC for $2.5 million. The institution will not charge OPC any transaction costs. Once OPC becomes an all-equity firm, it will remain unlevered forever. If OPC does not retire the debt, the company will use the $2.5 million in cash to buy back some of its stock on the open market. Repurchasing stock also has no transaction costs. The company will generate $1,300,000 of annual earnings before interest and taxes in perpetuity regardless of its capital structure. The firm immediately pays out all earnings as dividends at the end of each year. OPC is subject to a corporate tax rate of 35 percent, and the required rate of return on the firm’s unlevered equity is 20 percent. The personal tax rate on interest income is 25 percent, and there are no taxes on equity distribution. Assume there are no bankruptcy costs. a. What is the value of OPC if it chooses to retire all of its debt and become an unleveredf irm? b. What is the value of OPC if is decides to repurchase stock instead of retiring its debt? (Hint: Use the equation for the value of a levered firm with personal tax on interest income from the previous problem.) c. Assume that expected bankruptcy costs have a present value of $400,000. How doest hisin fluenceOP C’sd ecision?

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Appendix 17A Some Useful Formulas of Financial Structure Appendix 17B The Miller Model and the Graduated

Income Tax

Mini Case

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McKENZIE CORPORATION’S CAPITAL BUDGETING Sam McKenzie is the founder and CEO of McKenzie Restaurants, Inc., a regional company. Sam is considering opening several new restaurants. Sally Thornton, the company’s CFO, has been put in charge of the capital budgeting analysis. She has examined the potential for the company’s expansion and determined that the success of the new restaurants will depend critically on the state of the economy over the next few years. McKenzie currently has a bond issue outstanding with a face value of $34 million that is due in one year. Covenants associated with this bond issue prohibit the issuance of any additional debt. This restriction means that the expansion will be entirely financed with equity at a cost of $8.4 million. Sally has summarized her analysis in the following table, which shows the value of the company in each state of the economy next year, both with and without expansion: Economic Growth Low Normal High

Probability

Without Expansion

With Expansion

.30 .50 .20

$30,000,000 35,000,000 51,000,000

$33,000,000 46,000,000 64,000,000

1. What is the expected value of the company in one year, with and without expansion? Would the company’s stockholders be better off with or without expansion? Why? 2. What is the expected value of the company’s debt in one year, with and without the expansion? 3. One year from now, how much value creation is expected from the expansion? How much value is expected for stockholders? Bondholders? 4. If the company announces that it is not expanding, what do you think will happen to the price of its bonds? What will happen to the price of the bonds if the company does expand? 5. If the company opts not to expand, what are the implications for the company’s future borrowing needs? What are the implications if the company does expand? 6. Because of the bond covenant, the expansion would have to be financed with equity. How would it affect your answer if the expansion were financed with cash on hand insteado f n ewe quity?

PART III

CHAPTER 18

Valuation and Capital Budgeting for the Levered Firm In December 2008, the state of New Mexico announced that Signet Solar would build the first solar panel production facility in North America near Albuquerque. The first phase called for about a 100,000 square foot facility, with long-term plans for growth to 600,000 square feet. So why did Signet Solar pick New Mexico? One of the reasons was a package granted to the firm consisting of $185 million in state and local tax credits, including a manufacturing tax credit, a high-wage jobs tax credit, a job training incentive program credit, a rural jobs tax credit, and a renewable energy jobs tax credit. When a corporation opens a major plant or considers relocation, municipalities often create packages loaded with subsidies such as these. Other common subsidies include subsidized debt, educational training, and road and infrastructure creation. With subsidized debt, a state or municipality guarantees the debt, which allows the company to borrow at a much lower interest rate. If the interest rate on the debt is lower than the company’s normal cost of debt, how does the firm evaluate the financial benefits of this and other such subsidies? In this chapter, we illustrate how to evaluate projects using the adjusted present value and flows to equity approaches to capital budgeting to answer this and related questions.

18.1 Adjusted Present Value Approach The adjusted present value (APV) method is best described by the following formula: APV = NPV +NP VF In words, the value of a project to a levered firm (APV) is equal to the value of the project to an unlevered firm (NPV) plus the net present value of the financing side effects (NPVF). We can generally think of four side effects: 1. The tax subsidy to debt: This was discussed in Chapter 16, where we pointed out that for perpetual debt the value of the tax subsidy is tC B.( tC is the corporate tax rate, and B is the value of the debt.) The material about valuation under corporate taxes in Chapter 16 is actually an application of the APV approach. 2. The costs of issuing new securities: As we will discuss in detail in Chapter 20, investment bankers participate in the public issuance of corporate debt. These bankers must be compensated for their time and effort, a cost that lowers the value of the project. 3. The costs of financial distress: The possibility of financial distress, and bankruptcy in particular, arises with debt financing. As stated in the previous chapter, financial distress imposes costs, thereby lowering value. 4. Subsidies to debt financing: The interest on debt issued by state and local governments is not taxable to the investor. Because of this, the yield on tax-exempt debt 553

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is generally substantially below the yield on taxable debt. Frequently corporations can obtain financing from a municipality at the tax-exempt rate because the municipality can borrow at that rate as well. As with any subsidy, this subsidy adds value. Although each of the preceding four side effects is important, the tax deduction to debt almost certainly has the highest dollar value in most actual situations. For this reason, the following example considers the tax subsidy but not the other three side effects.1 Consider a project of the P. B. Singer Co. with the following characteristics: Cash inflows: $500,000 per year for the indefinite future. Cash costs: 72% of sales. Initial investment: $475,000. tC = 34% R0 = 20%, where R0 is the cost of capital for a project of an all-equity firm. If both the project and the firm are financed with only equity, the project’s cash flow is as follows: Cash inflows Cash costs Operating income Corporate tax (34% tax rate) Unlevered cash flow (UCF)

$500,000 −360,000 140,000 −47,600 $ 92,400

The distinction between present value and net present value is important for this example. The present value of a project is determined before the initial investment at date 0 is subtracted. The initial investment is subtracted for the calculation of net present value. Given a discount rate of 20 percent, the present value of the project is: $92,400 _______

= $462,000 .20 The net present value (NPV) of the project—that is, the value of the project to an allequity firm—is: $462,000 − $475,000 = −$13,000 Because the NPV is negative, the project would be rejected by an all-equity firm. Now imagine that the firm finances the project with exactly $126,229.50 in debt, so that the remaining investment of $348,770.50 (= $475,000 − $126,229.50) is financed with equity. The net present value of the project under leverage, which we call the adjusted present value, or the APV, is: APV = NPV + tC × B $29,918 = −$13,000 + .34 × $126,229.50 That is, the value of the project when financed with some leverage is equal to the value of the project when financed with all equity plus the tax shield from the debt. Because this number is positive, the project should be accepted.2 1

The Bicksler Enterprises example in Section 18.6 handles both flotation costs and interest subsidies. This example is meant to dramatize the potential importance of the tax benefits of debt. In practice, the firm will likely find the value of a project to an all-equity firm to have at least an NPV of zero.

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You may be wondering why we chose such a precise amount of debt. Actually, we chose it so that the ratio of debt to the present value of the project under leverage is .25.3 In this example, debt is a fixed proportion of the present value of the project, not a fixed proportion of the initial investment of $475,000. This is consistent with the goal of a target debt-to-market-value ratio, which we find in the real world. For example, commercial banks typically lend to real estate developers a fixed percentage of the appraised market value of a project, not a fixed percentage of the initial investment.

18.2 Flow to Equity Approach The flow to equity (FTE) approach is an alternative capital budgeting approach. The formula simply calls for discounting the cash flow from the project to the equityholders of the levered firm at the cost of equity capital, RS. For a perpetuity this becomes: Cash flow from project to equityholders of the levered firm ___________________________________________________ RS There are three steps to the FTE approach.

Step1:Ca lculatingL everedCa shF low( LCF)4 Assuming an interest rate of 10 percent, the perpetual cash flow to equityholders in our P. B. Singer Co. example is: Cash inflows Cash costs Interest (10% × $126,229.50) Income after interest Corporate tax (34% tax rate) Levered cash flow (LCF)

$500,000.00 −360,000.00 −12,622.95 127,377.05 −43,308.20 $ 84,068.85

Alternatively, we can calculate levered cash flow (LCF) directly from unlevered cash flow (UCF). The key here is that the difference between the cash flow that equityholders receive in an unlevered firm and the cash flow that equityholders receive in a levered firm is the aftertax interest payment. (Repayment of principal does not appear in this example because the debt is perpetual.) We write this algebraically as: UCF − LCF = (1 − tC )RBB 3

That is, the present value of the project after the initial investment has been made is $504,918 (= $29,918 + $475,000). Thus, the debt-to-value ratio of the project is .25 (= $126,229.50/$504,918). This level of debt can be calculated directly. Note that: Present value of levered project = Present value of unlevered project + tC × B VWith debt = $462,000 + .34 × .25 × VWith debt Rearranging the last line, we have: VWith debt × (1 − .34 × .25) = $462,000 VWith debt = $504,918 Debt is .25 of value: $126,229.50 = .25 × $504,918. 4

We use the term levered cash flow (LCF) for simplicity. A more complete term would be cash flow from the project to the equityholders of a levered firm. Similarly, a more complete term for unlevered cash flow (UCF) would be cash flow from the project to the equityholders of an unlevered firm.

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The term on the right side of this expression is the aftertax interest payment. Thus, because cash flow to the unlevered equityholders (UCF) is $92,400 and the aftertax interest payment is $8,331.15 (=.66 × .10 × $126,229.50), cash flow to the levered equityholders (LCF) is: $92,400 − $8,331.15 =$84,068.85 which is exactly the number we calculated earlier.

Step 2: Calculating RS

The next step is to calculate the discount rate, RS. Note that we assumed that the discount rate on unlevered equity, R0, is .20. As we saw in an earlier chapter, the formula for RSis: B RS = R0 + __ S (1 − tC )(R0 − RB) Note that our target debt-to-value ratio of 1/4 implies a target debt-to-equity ratio of 1/3. Applying the preceding formula to this example, we have: 1 RS = .222 = .20 + __(.66)(.20 −.10) 3

Step3:V aluation The present value of the project’s LCF is: $84,068.85 __________ =$378,688.50 RS = .222

LCF _____

Because the initial investment is $475,000 and $126,299.50 is borrowed, the firm must advance the project $348,770.50 (=$475,000 − $126,229.50) out of its own cash reserves. The net present value of the project is simply the difference between the present value of the project’s LCF and the investment not borrowed. Thus, the NPV is: $378,688.50 − $348,770.50 =$29,918 which is identical to the result found with the APV approach.

18.3 Weighted Average Cost of Capital Method Finally, we can value a project using the weighted average cost of capital (WACC) method. Although this method was discussed in earlier chapters, it is worthwhile to review it here. The WACC approach begins with the insight that projects of levered firms are simultaneously financed with both debt and equity. The cost of capital is a weighted average of the cost of debt and the cost of equity. The cost of equity is RS. Ignoring taxes, the cost of debt is simply the borrowing rate, RB. However, with corporate taxes, the appropriate cost of debt is (1 − tC)RB, the aftertax cost of debt. The formula for determining the weighted average cost of capital, R WACC,is: S B ______ RWACC = ______ S + B RS + S + B RB(1 − tC) The weight for equity, S/(S + B), and the weight for debt, B/(S + B), are target ratios. Target ratios are generally expressed in terms of market values, not accounting values. (Recall that another phrase for accounting value is book value.)

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The formula calls for discounting the unlevered cash flow of the project (UCF) at the weighted average cost of capital, R WACC. The net present value of the project can be written algebraically as: ∞ UCFt ___________ −In itialin vestment ∑ (1 + RWACC)t t=1 If the project is a perpetuity, the net present value is: UCF ______

RWACC −In itialin vestment

We previously stated that the target debt-to-value ratio of our project is 1/4 and the corporate tax rate is .34, implying that the weighted average cost of capital is: 3 1 RWACC = __ × .222 + __ × .10 × .66 =.183 4 4 Note that RWACC, .183, is lower than the cost of equity capital for an all-equity firm, .20. This must always be the case because debt financing provides a tax subsidy that lowers the average cost of capital. We previously determined the UCF of the project to be $92,400, implying that the present value of the project is: $92,400 _______ =$504,918 .183 This initial investment is $475,000, so the NPV of the project is: $504,918 − $475,000 =$29,918 Note that all three approaches yield the same value.

18.4 A Comparison of the APV, FTE, and WACC Approaches Capital budgeting techniques in the early chapters of this text applied to all-equity firms. Capital budgeting for the levered firm could not be handled early in the book because the effects of debt on firm value were deferred until the previous two chapters. We learned there that debt increases firm value through tax benefits but decreases value through bankruptcy and related costs. In this chapter, we provide three approaches to capital budgeting for the levered firm. The adjusted present value (APV) approach first values the project on an allequity basis. That is, the project’s aftertax cash flows under all-equity financing (called unlevered cash flows, or UCF) are placed in the numerator of the capital budgeting equation. The discount rate, assuming all-equity financing, appears in the denominator. At this point, the calculation is identical to that performed in the early chapters of this book. We then add the net present value of the debt. We point out that the net present value of the debt is likely to be the sum of four parameters: Tax effects, flotation costs, bankruptcy costs, and interest subsidies. The flow to equity (FTE) approach discounts the aftertax cash flow from a project going to the equityholders of a levered firm (LCF). LCF, which stands for levered cash flow, is the residual to equityholders after interest has been deducted. The discount rate is RS, the cost of capital to the equityholders of a levered firm. For a firm with leverage, RS must be greater than R0, the cost of capital for an unlevered firm. This follows from our material in Chapter 16 showing that leverage raises the risk to the equityholders.

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The last approach is the weighted average cost of capital (WACC) method. This technique calculates the project’s aftertax cash flows assuming all-equity financing (UCF). The UCF is placed in the numerator of the capital budgeting equation. The denominator, R WACC, is a weighted average of the cost of equity capital and the cost of debt capital. The tax advantage of debt is reflected in the denominator because the cost of debt capital is determined net of corporate tax. The numerator does not reflect debt at all. All three approaches perform the same task: Valuation in the presence of debt financing. And as illustrated by the previous example, all three provide the same valuation estimate. However, as we saw before, the approaches are markedly different in technique. Because of this, students often ask questions of the following sort: “How can this be? How can the three approaches look so different and yet give the same answer?” We believe that the best way to handle questions like these is through the following two points: 1. APV versus WACC: Of the three approaches, APV and WACC display the greatest similarity. After all, both approaches put the unlevered cash flow (UCF) in the numerator. However, the APV approach discounts these flows at R0, yielding the value of the unlevered project. Adding the present value of the tax shield gives the value of the project under leverage. The WACC approach discounts UCF at R WACC, which is lower than R0. Thus, both approaches adjust the basic NPV formula for unlevered firms to reflect the tax benefit of leverage. The APV approach makes this adjustment directly. It simply adds in the present value of the tax shield as a separate term. The WACC approach makes the adjustment in a more subtle way. Here, the discount rate is lowered below R0. Although we do not provide a proof in this book, it can be shown that these two adjustments always have the same quantitative effect. 2. Entity being valued: The FTE approach appears at first glance to be far different from the other two. For both the APV and the WACC approaches, the initial investment is subtracted out in the final step ($475,000 in our example). However, for the FTE approach, only the firm’s contribution to the initial investment ($348,770.50 = $475,000 − $126,229.50) is subtracted out. This occurs because under the FTE approach only the future cash flows to the levered equityholders (LCF) are valued. By contrast, future cash flows to the unlevered equityholders (UCF) are valued in both the APV and WACC approaches. Thus, because LCFs are net of interest payments, whereas UCFs are not, the initial investment under the FTE approach is correspondingly reduced by debt financing. In this way, the FTE approach produces the same answer that the other two approaches do.

ASugge stedG uideline The net present value of our project is exactly the same under each of the three methods. In theory, this should always be the case.5 However, one method usually provides an easier computation than another, and, in many cases, one or more of the methods are virtually impossible computationally. We first consider when it is best to use the WACC and FTE approaches.

5 See I. Inselbag and H. Kaufold, “Two DCF Approaches for Valuing Companies under Alternative Financial Strategies (and How to Choose between Them),” Journal of Applied Corporate Finance (Spring 1997).

Chapter 18 Valuation and Capital Budgeting for the Levered Firm

559

If the risk of a project stays constant throughout its life, it is plausible to assume that R0 remains constant throughout the project’s life. This assumption of constant risk appears to be reasonable for most real-world projects. In addition, if the debt-tovalue ratio remains constant over the life of the project, both RS and R WACC will remain constant as well. Under this latter assumption, either the FTE or the WACC approach is easy to apply. However, if the debt-to-value ratio varies from year to year, both RS and R WACC vary from year to year as well. Using the FTE or the WACC approach when the denominator changes every year is computationally quite complex, and when computations become complex, the error rate rises. Thus, both the FTE and WACC approaches present difficulties when the debt-to-value ratio changes over time. The APV approach is based on the level of debt in each future period. Consequently, when the debt level can be specified precisely for future periods, the APV approach is quite easy to use. However, when the debt level is uncertain, the APV approach becomes more problematic. For example, when the debt-to-value ratio is constant, the debt level varies with the value of the project. Because the value of the project in a future year cannot be easily forecast, the level of debt cannot be easily forecast either. Thus, we suggest the following guideline: Use WACC or FTE if the firm’s target debt-to-value ratio applies to the project over its life. Use APV if the project’s level of debt is known over the life of the project.

There are a number of situations where the APV approach is preferred. For example, in a leveraged buyout (LBO) the firm begins with a large amount of debt but rapidly pays down the debt over a number of years. Because the schedule of debt reduction in the future is known when the LBO is arranged, tax shields in every future year can be easily forecast. Thus, the APV approach is easy to use here. (An illustration of the APV approach applied to LBOs is provided in the appendix to this chapter.) By contrast, the WACC and FTE approaches are virtually impossible to apply here because the debt-to-equity value cannot be expected to be constant over time. In addition, situations involving interest subsidies and flotation costs are much easier to handle with the APV approach. (The Bicksler Enterprises example in Section 18.6 applies the APV approach to subsidies and flotation costs.) Finally, the APV approach handles the lease-versus-buy decision much more easily than does either the FTE or the WACC approach. (A full treatment of the lease-versus-buy decision appears in a later chapter.) The preceding examples are special cases. Typical capital budgeting situations are more amenable to either the WACC or the FTE approach than to the APV approach. Financial managers generally think in terms of target debt-to-value ratios. If a project does better than expected, both its value and its debt capacity will likely rise. The manager will increase debt correspondingly here. Conversely, the manager would be likely to reduce debt if the value of the project were to decline unexpectedly. Of course, because financing is a time-consuming task, the ratio cannot be adjusted daily or monthly. Rather, the adjustment can be expected to occur over the long run. As mentioned before, the WACC and FTE approaches are more appropriate than is the APV approach when a firm focuses on a target debt-to-value ratio. Because of this, we recommend that the WACC and the FTE approaches, rather than the APV approach, be used in most real-world situations. In addition, frequent discussions with business executives have convinced us that the WACC is by far the most widely used method in the real world. Thus, practitioners seem to agree with us that, outside of the special situations mentioned, the APV approach is a less important method of capital budgeting.

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The Three Methods of Capital Budgeting with Leverage 1. Adjusted present value (APV) method: ∞

UCFt

+ Additional effects of debt −In itialin vestment ∑ ________ (1 + R ) t

t=1

0

UCFt = The project’s cash flow at date t to the equityholders of an unlevered firm. R0 = Cost of capital for project in an unlevered firm. 2. Flow to equity (FTE) method: ∞

LCFt

− (Initial investment −Amo untb orrowed) ∑________ (1 + R ) t

t=1

S

LCFt = The project’s cash flow at date t to the equityholders of a levered firm. RS = Cost of equity capital with leverage. 3. Weighted average cost of capital (WACC) method: ∞

UCFt

−In itialin vestment ∑ ___________ (1 + R ) t=1

t

WACC

RWACC = Weighted average cost of capital. Notes 1. The middle term in the APV formula implies that the value of a project with leverage is greater than the value of the project without leverage. Because R WACC < R0, the WACC formula implies that the value of a project with leverage is greater than the value of the project without leverage. 2. In the FTE method, cash flow after interest (LCF) is used. Initial investment is reduced by amount borrowedas w ell. Guidelines 1. Use WACC or FTE if the firm’s target debt-to-value ratio applies to the project over its life. 2. Use APV if the project’s level of debt is known over the life of the project.

18.5 Capital Budgeting When the Discount Rate Must Be Estimated The previous sections of this chapter introduced APV, FTE, and WACC—the three basic approaches to valuing a levered firm. However, one important detail remains. The example in Sections 18.1 through 18.3 assumed a discount rate. We now want to show how this rate is determined for real-world firms with leverage, with an application to the three preceding approaches. The example in this section brings together the work in Chapters 10–13 on the discount rate for unlevered firms with that in Chapter 16 on the effect of leverage on the cost of capital.

Valuation and Capital Budgeting for the Levered Firm

Chapter 18

EXAMPLE 18.1

561

Cost of Capital World-Wide Enterprises (WWE) is a large conglomerate thinking of entering the widget business, where it plans to finance projects with a debt-to-value ratio of 25 percent (or a debt-to-equity ratio of 1/3). There is currently one firm in the widget industry, American Widgets (AW). This firm is financed with 40 percent debt and 60 percent equity. The beta of AW’s equity is 1.5. AW has a borrowing rate of 12 percent, and WWE expects to borrow for its widget venture at 10 percent. The corporate tax rate for both firms is .40, the market risk premium is 8.5 percent, and the riskless interest rate is 8 percent. What is the appropriate discount rate for WWE to use for its widget venture? As shown in Sections 18.1–18.3, a corporation may use one of three capital budgeting approaches: APV, FTE, or WACC. The appropriate discount rates for these three approaches are R0, RS, and R WACC, respectively. Because AW is WWE’s only competitor in widgets, we look at AW’s cost of capital to calculate R0, RS, and RWACC for WWE’s widget venture. The following four-step procedure will allow us to calculate all three discount rates: 1. Determining AW’s cost of equity capital: First, we determine AW’s cost of equity capital using the security market line (SML): AW’s Cost of Equity Capital __

RS = RF + β × (RM − RF ) 20.75% = 8% + 1.5 × 8.5% __

where RM is the expected return on the market portfolio and RF is the risk-free rate. 2. Determining AW’s hypothetical all-equity cost of capital: We must standardize the preceding number in some way because AW’s and WWE’s widget ventures have different target debt-to-value ratios. The easiest approach is to calculate the hypothetical cost of equity capital for AW, assuming allequity financing. This can be determined from MM’s Proposition II under taxes: AW’s Cost of Capital if All Equity B RS = R0 + __ S (1 − tC )(R0 − RB ) .4 20.75% = R0 + __ .6 (.60)(R0 − 12%) By solving the equation, we find that R0 = .1825. Of course, R0 is less than RS because the cost of equity capital would be less when the firm employs no leverage. At this point, firms in the real world generally make the assumption that the business risk of their venture is about equal to the business risk of the firms already in the business. Applying this assumption to our problem, we assert that the hypothetical discount rate of WWE’s widget venture if all equity financed is also .1825.6 This discount rate would be employed if WWE uses the APV approach because the APV approach calls for R0, the project’s cost of capital in a firm with no leverage. 3. Determining RS for WWE’s widget venture: Alternatively, WWE might use the FTE approach, where the discount rate for levered equity is determined like this: Cost of Equity Capital for WWE’s Widget Venture B RS = R0 + __ S (1 − tC)(R0 − RB) 1 19.9% = 18.25% + __ 3 (.60)(18.25% − 10%) 6

(continued )

Alternatively, a firm might assume that its venture would be somewhat riskier because it is a new entrant. Thus, the firm might select a discount rate slightly higher than .1825. Of course, no exact formula exists for adjusting the discount rate upward.

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Note that the cost of equity capital for WWE’s widget venture, .199, is less than the cost of equity capital for AW, .2075. This occurs because AW has a higher debt-to-equity ratio. (As mentioned, both firms are assumed to have the same business risk.) 4. Determining RWACC for WWE’s widget venture: Finally, WWE might use the WACC approach. Here is the appropriate calculation: RWACC for WWE’s Widget Venture S B _____ R WACC = _____ S + B RB(1 − tC ) + S + B RS 3 1 __ 16.425% = __ 4 10%(.60) + 4 19.9%

The preceding example shows how the three discount rates, R0, RS, and RWACC, are determined in the real world. These are the appropriate rates for the APV, FTE, and WACC approaches, respectively. Note that RS for American Widgets is determined first because the cost of equity capital can be determined from the beta of the firm’s stock. As discussed in an earlier chapter, beta can easily be estimated for any publicly traded firm such as AW.

18.6 APV Example As mentioned earlier in this chapter, firms generally set a target debt-to-equity ratio, allowing the use of WACC and FTE for capital budgeting. APV does not work as well here. However, as we also mentioned earlier, APV is the preferred approach when there are side benefits and side costs to debt. Because the analysis here can be tricky, we now devote an entire section to an example where, in addition to the tax subsidy to debt, both flotation costs and interest subsidies come into play.

EXAMPLE 18.2

APV Bicksler Enterprises is considering a $10 million project that will last five years, implying straight-line depreciation per year of $2 million. The cash revenues less cash expenses per year are $3,500,000. The corporate tax bracket is 34 percent. The risk-free rate is 10 percent, and the cost of unlevered equity is 20 percent. The cash flow projections each year are these:

C0 Initial outlay Depreciation tax shield Revenue less expenses

C1

C2

C3

C4

C5

.34 × $2,000,000 = $680,000 (1 − .34) × $3,500,000 = $2,310,000

$ 680,000

$ 680,000

$ 680,000

$ 680,000

$2,310,000

$2,310,000

$2,310,000

$2,310,000

−$10,000,000

Chapter 18

Valuation and Capital Budgeting for the Levered Firm

563

We stated before that the APV of a project is the sum of its all-equity value plus the additional effects of debt. We examine each in turn. All-Equity Value

Assuming the project is financed with all equity, the value of the project is:

$680,000 1 −$10,000,000 + ________ × 1 − ____ .10 1.10

[ (

$2,310,000 1 × [ 1 − ( ____ ) ] + __________ .20 1.20 ) ] = −$513,951 5

5

Initial cost + Depreciation tax shield + Present value of (Cash revenues − Cash expenses) This calculation uses the techniques presented in the early chapters of this book. Notice that the depreciation tax shield is discounted at the riskless rate of 10 percent. The revenues and expenses are discounted at the higher rate of 20 percent. An all-equity firm would clearly reject this project because the NPV is −$513,951. And equity flotation costs (not mentioned yet) would only make the NPV more negative. However, debt financing may add enough value to the project to justify acceptance. We consider the effects of debt next. Additional Effects of Debt Bicksler Enterprises can obtain a five-year, nonamortizing loan for $7,500,000 after flotation costs at the risk-free rate of 10 percent. Flotation costs are fees paid when stock or debt is issued.These fees may go to printers, lawyers, and investment bankers, among others. Bicksler Enterprises is informed that flotation costs will be 1 percent of the gross proceeds of its loan. The previous chapter indicates that debt financing alters the NPV of a typical project. We look at the effects of debt next. FlotationCo sts

Given that flotation costs are 1 percent of the gross proceeds, we have:

$7,500,000 = (1 − .01) × Gross proceeds = .99 × Gross proceeds Thus, the gross proceeds are: $7,500,000 __________ 1 − .01

$7,500,000 = __________ = $7,575,758 .99

This implies flotation costs of $75,758 (=1% × $7,575,758). To check the calculation, note that net proceeds are $7,500,000 (=$7,575,758 − $75,758). In other words, Bicksler Enterprises receives only $7,500,000. The flotation costs of $75,758 are received by intermediaries such as investment bankers. Flotation costs are paid immediately but are deducted from taxes by amortizing on a straight-line basis over the life of the loan. The cash flows from flotation costs are as follows: Date 0 Flotation costs Deduction

Date 1

Date 2

Date 3

Date 4

Date 5

= $15,152

$15,152

$15,152

$15,152

$15,152

.34 × $15,152 = $ 5,152

$ 5,152

$ 5,152

$ 5,152

$ 5,152

−$75,758 $75,758 _______ 5

Tax shield from flotation costs

The relevant cash flows from flotation costs are in boldface. When we discount at 10 percent, the tax shield has a net present value of: $5,152 × A5.10 = $19,530 This implies a net cost of flotation of: −$75,758 + $19,530 = −$56,228 (continued )

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The net present value of the project after the flotation costs of debt but before the benefits of debt is: −$513,951 − $56,228 = −$570,179 Tax Subsidy Interest must be paid on the gross proceeds of the loan, even though intermediaries receive the flotation costs. Because the gross proceeds of the loan are $7,575,758, annual interest is $757,576 (= $7,575,758 × .10). The interest cost after taxes is $500,000 [= $757,576 × (1 − .34)]. Because the loan is nonamortizing, the entire debt of $7,575,758 is repaid at date 5. These terms are indicated here: Date 0 Loan (gross proceeds) Interest paid

Date 1

Date 2

Date 3

Date 4

Date 5

$757,576

$757,576

$757,576

$500,000

$500,000

$500,000

$7,575,758 10% × $7,575,758 = $757,576 (1 − .34) × $757,576 = $500,000

Interest cost after taxes Repayment of debt

$

757,576

$ 500,000 $7,575,758

The relevant cash flows are listed in boldface in the preceding table. They are (1) loan received, (2) annual interest cost after taxes, and (3) repayment of debt. Note that we include the gross proceeds of the loan as an inflow because the flotation costs have previously been subtracted. In Chapter 16 we mentioned that the financing decision can be evaluated in terms of net present value. The net present value of the loan is simply the sum of the net present values of each of the three cash flows. This can be represented as follows: Amount NPV (loan) = + − borrowed

Present value Present value of loan of aftertax − repayments interest payments

(18.1)

The calculations for this example are: $500,000 1 $976,415 = +$7,575,758 − ________ × 1 − ____ .10 1.10

[ (

$7,575,758 ) ] − __________ (1.10) 5

5

(18.1′)

APV = All-equity value − Flotation costs of debt + NPV (loan)

(18.2)

The NPV (loan) is positive, reflecting the interest tax shield.7 The adjusted present value of the project with this financing is:

$406,236 = −$513,951

−

+ $976,415

$56,228

(18.2′)

Though we previously saw that an all-equity firm would reject the project, a firm would accept the project if a $7,500,000 (net) loan could be obtained. Because the loan just discussed was at the market rate of 10 percent, we have considered only two of the three additional effects of debt (flotation costs and tax subsidy) so far. We now examine another loan where the third effect arises.

7

The NPV (loan) must be zero in a no-tax world because interest provides no tax shield there. To check this intuition, we calculate: $757,576 $7,575,758 1 5 No-tax case: 0 = +$7,575,758 − ________ × 1 − ____ − __________ .10 1.10 (1.10)5

[ (

)]

Chapter 18

Valuation and Capital Budgeting for the Levered Firm

565

Non–Market-Rate Financing A number of companies are fortunate enough to obtain subsidized financing from a governmental authority. Suppose that the project of Bicksler Enterprises is deemed socially beneficial and the state of New Jersey grants the firm a $7,500,000 loan at 8 percent interest. In addition, all flotation costs are absorbed by the state. Clearly, the company will choose this loan over the one we previously calculated. Here are the cash flows from the loan: Date 0 Loan received Interest paid Aftertax interest

Date 1

Date 2

Date 3

Date 4

$600,000

$600,000

$600,000

$396,000

$396,000

$396,000

Date 5

$7,500,000 8% × $7,500,000 = $600,000 (1 − .34) × $600,000 = $396,000

$

600,000

$ 396,000 $7,500,000

Repayment of debt

The relevant cash flows are listed in boldface in the preceding table. Using Equation 18.1, the NPV (loan) is: $396,000 1 $1,341,939 = +$7,500,000 − ________ × 1 − ____ .10 1.10

[ (

$7,500,000 ) ] − __________ (1.10) 5

5

(18.1″)

Why do we discount the cash flows in Equation 18.1″ at 10 percent when the firm is borrowing at 8 percent? We discount at 10 percent because that is the fair or marketwide rate. That is, 10 percent is the rate at which the firm could borrow without benefit of subsidization. The net present value of the subsidized loan is larger than the net present value of the earlier loan because the firm is now borrowing at the below-market rate of 8 percent. Note that the NPV (loan) calculation in Equation 18.1″ captures both the tax effect and the non–market-rate effect. The net present value of the project with subsidized debt financing is: APV = All-equity value − Flotation costs of debt + NPV (loan) +$827,988 = −$513,951

−

0

+ $1,341,939

(18.2) (18.2″)

The preceding example illustrates the adjusted present value (APV) approach. The approach begins with the present value of a project for the all-equity firm. Next, the effects of debt are added in. The approach has much to recommend it. It is intuitively appealing because individual components are calculated separately and added together in a simple way. And, if the debt from the project can be specified precisely, the present value of the debt can be calculated precisely.

18.7 Betaan dL everage A previous chapter provides the formula for the relationship between the beta of the common stock and leverage of the firm in a world without taxes. We reproduce this formula here: The No-Tax Case Debt βEquity = βAsset 1 + ______ Equity

(

)

(18.3)

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As pointed out earlier, this relationship holds under the assumption that the beta of debt is zero. Because firms must pay corporate taxes in practice, it is worthwhile to provide the relationship in a world with corporate taxes. It can be shown that the relationship between the beta of the unlevered firm and the beta of the levered equity is this:8 The Corporate Tax Case (1 − tC)Debt βEquity = 1 + ___________ βUnlevered firm Equity

(

)

(18.4)

when (1) the corporation is taxed at the rate of tC and (2) the debt has a zero beta. Because [1 + (1 − tC) Debt/Equity] must be more than 1 for a levered firm, it follows that βUnlevered firm < βEquity. The corporate tax case of Equation 18.4 is quite similar to the no-tax case of Equation 18.3 because the beta of levered equity must be greater than the beta of the unlevered firm in either case. The intuition that leverage increases the risk of equity applies in both cases. However, notice that the two equations are not equal. It can be shown that leverage increases the equity beta less rapidly under corporate taxes. This occurs because, under taxes, leverage creates a riskless tax shield, thereby lowering the risk of the entire firm. 8

This result holds only if the beta of debt equals zero. To see this, note that:

VU + tCB = VL = B + S where: VU = Value of unlevered firm. VL = Value of levered firm. B = Value of debt in a levered firm. S = Value of equity in a levered firm. As we stated in the text, the beta of the levered firm is a weighted average of the debt beta and the equity beta: S B ______ ______ B + S × βB + B + S × βS

(a)

where βB and βS are the betas of the debt and the equity of the levered firm, respectively. Because VL = B + S, we have: S B ___ ___ (b) VL × βB + VL × βS The beta of the levered firm can also be expressed as a weighted average of the beta of the unlevered firm and the beta of the tax shield: V t CB _________ VU + tCB × βU + VU + tCB × βB

U _________

where βU is the beta of the unlevered firm. This follows from Equation (a). Because VL = VU + tCB, we have: V tCB ____ VL × βU + VL × βB

U ___

(c)

We can equate (b) and (c) because both represent the beta of a levered firm. Equation (a) tells us that VU = S + (1 − tC) × B. Under the assumption that βB = 0, equating (b) and (c) and using Equation (a) yields Equation 18.4. The generalized formula for the levered beta (where βB is not zero) is: B βS = βU + (1 − tC) (βU − βB)__ S and:

B(1 − tC) S βU = ____________ βS + ____________ βB B(1 − tC) + S B(1 − tC) + S

Chapter 18

EXAMPLE 18.3

Valuation and Capital Budgeting for the Levered Firm

567

Unlevered Betas C. F. Lee, Incorporated is considering a scale-enhancing project. The market value of the firm’s debt is $100 million, and the market value of the firm’s equity is $200 million. The debt is considered riskless. The corporate tax rate is 34 percent. Regression analysis indicates that the beta of the firm’s equity is 2. The risk-free rate is 10 percent, and the expected market premium is 8.5 percent. What would the project’s discount rate be in the hypothetical case that C. F. Lee, Inc., is all equity? We can answer this question in two steps. 1. Determining beta of hypothetical all-equity firm: Rearranging Equation 18.4, we have this: Unlevered Beta Equity ______________________

Equity + (1 − tC) × Debt × βEquity = βUnlevered firm

(18.5)

$200 million __________________________________

$200 million + (1 − .34) × $100 million × 2 = 1.50

2. Determining discount rate: We calculate the discount rate from the security market line (SML) as follows: Discount Rate __

RS = RF + β × [RM − RF] 22.75% = 10% + 1.50 × 8.5%

The Project Is Not Scale Enhancing Because the previous example assumed that the project is scale enhancing, we began with the beta of the firm’s equity. If the project is not scale enhancing, we could begin with the equity betas of firms in the industry of the project. For each firm, we could calculate the hypothetical beta of the unlevered equity by Equation 18.5. The SML could then be used to determine the project’s discount rate from the average of these betas.

EXAMPLE 18.4

More Unlevered Betas The J. Lowes Corporation, which currently manufactures staples, is considering a $1 million investment in a project in the aircraft adhesives industry. The corporation estimates unlevered aftertax cash flows (UCF) of $300,000 per year into perpetuity from the project. The firm will finance the project with a debt-to-value ratio of .5 (or, equivalently, a debt-to-equity ratio of 1.0). The three competitors in this new industry are currently unlevered, with betas of 1.2, 1.3, and 1.4. Assuming a risk-free rate of 5 percent, a market risk premium of 9 percent, and a corporate tax rate of 34 percent, what is the net present value of the project? We can answer this question in five steps. 1. Calculating the average unlevered beta in the industry: The average unlevered beta across all three existing competitors in the aircraft adhesives industry is: 1.2 + 1.3 + 1.4 ______________ 3

= 1.3 (continued )

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2. Calculating the levered beta for J. Lowes’s new project : Assuming the same unlevered beta for this new project as for the existing competitors, we have, from Equation 18.4: Levered Beta

(

)

(1 − tC) Debt βUnlevered firm βEquity = 1 + ____________ Equity

(

)

.66 × 1 2.16 = 1 + _______ × 1.3 1 3. Calculating the cost of levered equity for the new project: We calculate the discount rate from the security market line (SML) as follows: Discount Rate __

RS = RF + β × [RM − RF] .244 = .05 + 2.16 × .09 4. Calculating the WACC for the new project: The formula for determining the weighted average cost of capital, RWACC,is : S B __ RWACC = __ V RB(1 − tC) + V RS 1 1 __ .139 = __ 2 × .05 × .66 + 2 × .244 5. Determining the project’s value: Because the cash flows are perpetual, the NPV of the project is: Unlevered cash flows (UCF) _______________________ RWACC $300,000 ________ .139

www.mhhe.com/rwj

Summary and Conclusions

Concept Questions

− Initial investment

− $1 million = $1.16 million

Earlier chapters of this text showed how to calculate net present value for projects of allequity firms. We pointed out in the last two chapters that the introduction of taxes and bankruptcy costs changes a firm’s financing decisions. Rational corporations should employ some debt in a world of this type. Because of the benefits and costs associated with debt, the capital budgeting decision is different for levered firms than for unlevered firms. The present chapter has discussed three methods for capital budgeting by levered firms: the adjusted present value (APV), flows to equity (FTE), and weighted average cost of capital (WACC) approaches.

1. 2. 3. 4.

APV How is the APV of a project calculated? WACC and APV What is the main difference between the WACC and APV methods? FTE What is the main difference between the FTE approach and the other two approaches? Capital Budgeting You are determining whether your company should undertake a new project and have calculated the NPV of the project using the WACC method when the CFO, a former accountant, notices that you did not use the interest payments in

Chapter 18

5.

Questions and Problems

1.

BASIC (Questions 1–9)

2.

4.

5.

569

calculating the cash flows of the project. What should you tell him? If he insists that you include the interest payments in calculating the cash flows, what method can you use? Beta and Leverage What are the two types of risk that are measured by a levered beta?

NPV and APV Zoso is a rental car company that is trying to determine whether to add 25 cars to its fleet. The company fully depreciates all its rental cars over five years using the straight-line method. The new cars are expected to generate $140,000 per year in earnings before taxes and depreciation for five years. The company is entirely financed by equity and has a 35 percent tax rate. The required return on the company’s unlevered equity is 13 percent, and the new fleet will not change the risk of the company. a. What is the maximum price that the company should be willing to pay for the new fleet of cars if it remains an all-equity company? b. Suppose the company can purchase the fleet of cars for $395,000. Additionally, assume the company can issue $260,000 of five-year, 8 percent debt to finance the project. All principal will be repaid in one balloon payment at the end of the fifth year. What is the adjusted present value (APV) of the project? APV Gemini, Inc., an all-equity firm, is considering a $1.9 million investment that will be depreciated according to the straight-line method over its four-year life. The project is expected to generate earnings before taxes and depreciation of $685,000 per year for four years. The investment will not change the risk level of the firm. The company can obtain a four-year, 9.5 percent loan to finance the project from a local bank. All principal will be repaid in one balloon payment at the end of the fourth year. The bank will charge the firm $28,000 in flotation fees, which will be amortized over the four-year life of the loan. If the company financed the project entirely with equity, the firm’s cost of capital would be 13 percent. The corporate tax rate is 30 percent. Using the adjusted present value method, determine whether the company should undertake the project. Flow to Equity Milano Pizza Club owns three identical restaurants popular for their specialty pizzas. Each restaurant has a debt–equity ratio of 40 percent and makes interest payments of $34,000 at the end of each year. The cost of the firm’s levered equity is 19 percent. Each store estimates that annual sales will be $1.2 million; annual cost of goods sold will be $510,000; and annual general and administrative costs will be $340,000. These cash flows are expected to remain the same forever. The corporate tax rate is 40 percent. a. Use the flow to equity approach to determine the value of the company’s equity. b. What is the total value of the company? WACC If Wild Widgets, Inc., were an all-equity company, it would have a beta of 1.1. The company has a target debt–equity ratio of .40. The expected return on the market portfolio is 12 percent, and Treasury bills currently yield 5 percent. The company has one bond issue outstanding that matures in 20 years and has an 8 percent coupon rate. The bond currently sells for $975. The corporate tax rate is 34 percent. a. What is the company’s cost of debt? b. What is the company’s cost of equity? c. What is the company’s weighted average cost of capital? Beta and Leverage North Pole Fishing Equipment Corporation and South Pole Fishing Equipment Corporation would have identical equity betas of 1.25 if both were all equity financed. The market value information for each company is shown here:

Debt Equity

North Pole

South Pole

$2,900,000 $3,800,000

$3,800,000 $2,900,000

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6.

7.

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9.

INTERMEDIATE (Questions 10–13)

10.

Capital Structure and Dividend Policy

The expected return on the market portfolio is 12.40 percent, and the risk-free rate is 5.30 percent. Both companies are subject to a corporate tax rate of 35 percent. Assume the beta of debt is zero. a. What is the equity beta of each of the two companies? b. What is the required rate of return on each of the two companies’ equity? NPV of Loans Daniel Kaffe, CFO of Kendrick Enterprises, is evaluating a 10-year, 8 percent loan with gross proceeds of $5,350,000. The interest payments on the loan will be made annually. Flotation costs are estimated to be 1.25 percent of gross proceeds and will be amortized using a straight-line schedule over the 10-year life of the loan. The company has a tax rate of 40 percent, and the loan will not increase the risk of financial distress for the company. a. Calculate the net present value of the loan excluding flotation costs. b. Calculate the net present value of the loan including flotation costs. NPV for an All-Equity Company Shattered Glass, Inc., is an all-equity firm. The cost of the company’s equity is currently 14 percent, and the risk-free rate is 6 percent. The company is currently considering a project that will cost $11.4 million and last six years. The project will generate revenues minus expenses each year in the amount of $3.8 million. If the company has a tax rate of 40 percent, should it accept thep roject? WACC National Electric Company (NEC) is considering a $40 million project in its power systems division. Tom Edison, the company’s chief financial officer, has evaluated the project and determined that the project’s unlevered cash flows will be $2.6 million per year in perpetuity. Mr. Edison has devised two possibilities for raising the initial investment: Issuing 10-year bonds or issuing common stock. NEC’s pretax cost of debt is 7.2 percent, and its cost of equity is 11.4 percent. The company’s target debt-to-value ratio is 80 percent. The project has the same risk as NEC’s existing businesses, and it will support the same amount of debt. NEC is in the 34 percent tax bracket. Should NEC accept the project? WACC Bolero, Inc., has compiled the following information on its financing costs:

Type of Financing

Book Value

Market Value

Cost

Short-term debt Long-term debt Common stock Total

$10,000,000 3,000,000 6,000,000 $19,000,000

$11,000,000 3,000,000 26,000,000 $40,000,000

6.8 3.5% 14.5

The company is in the 35 percent tax bracket and has a target debt–equity ratio of 60 percent. The target short-term debt/long-term debt ratio is 20 percent. a. What is the company’s weighted average cost of capital using book value weights? b. What is the company’s weighted average cost of capital using market value weights? c. What is the company’s weighted average cost of capital using target capital structurew eights? d. What is the difference between WACCs? Which is the correct WACC to use for projecte valuation? APV Triad Corporation has established a joint venture with Tobacco Road Construction, Inc., to build a toll road in North Carolina. The initial investment in paving equipment is $30 million. The equipment will be fully depreciated using the straight-line method over its economic life of five years. Earnings before interest,

Chapter 18

11.

12.

CHALLENGE (Questions 14–17)

14.

571

taxes, and depreciation collected from the toll road are projected to be $3.8 million per annum for 20 years starting from the end of the first year. The corporate tax rate is 35 percent. The required rate of return for the project under all-equity financing is 13 percent. The pretax cost of debt for the joint partnership is 8.5 percent. To encourage investment in the country’s infrastructure, the U.S. government will subsidize the project with an $18 million, 15-year loan at an interest rate of 5 percent per year. All principal will be repaid in one balloon payment at the end of year 15. What is the adjusted present value of this project? APV For the company in the previous problem, what is the value of being able to issue subsidized debt instead of having to issue debt at the terms it would normally receive? Assume the face amount and maturity of the debt issue are the same. APV MVP, Inc., has produced rodeo supplies for over 20 years. The company currently has a debt–equity ratio of 50 percent and is in the 40 percent tax bracket. The required return on the firm’s levered equity is 16 percent. MVP is planning to expand its production capacity. The equipment to be purchased is expected to generate the following unlevered cash flows: Year

Cash Flow

0 1 2 3

–$21,000,000 6,900,000 11,000,000 9,500,000

The company has arranged a $7 million debt issue to partially finance the expansion. Under the loan, the company would pay interest of 9 percent at the end of each year on the outstanding balance at the beginning of the year. The company would also make year-end principal payments of $2,333,333 per year, completely retiring the issue by the end of the third year. Using the adjusted present value method, should the company proceed with the expansion? WACC Neon Corporation’s stock returns have a covariance with the market portfolio of .036. The standard deviation of the returns on the market portfolio is 20 percent, and the expected market risk premium is 7.5 percent. The company has bonds outstanding with a total market value of $35 million and a yield to maturity of 8 percent. The company also has 6 million shares of common stock outstanding, each selling for $20. The company’s CEO considers the firm’s current debt–equity ratio optimal. The corporate tax rate is 35 percent, and Treasury bills currently yield 6 percent. The company is considering the purchase of additional equipment that would cost $45 million. The expected unlevered cash flows from the equipment are $13.5 million per year for five years. Purchasing the equipment will not change the risk level of the firm. a. Use the weighted average cost of capital approach to determine whether Neon should purchase the equipment. b. Suppose the company decides to fund the purchase of the equipment entirely with debt. What is the cost of capital for the project now? Explain. APV, FTE, and WACC Seger, Inc., is an unlevered firm with expected annual earnings before taxes of $28 million in perpetuity. The current required return on the firm’s equity is 20 percent, and the firm distributes all of its earnings as dividends at the end of each year. The company has 1.5 million shares of common stock outstanding and is subject to a corporate tax rate of 35 percent. The firm is planning a

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16.

17.

S&P Problem

Capital Structure and Dividend Policy

recapitalization under which it will issue $35 million of perpetual 9 percent debt and use the proceeds to buy back shares. a. Calculate the value of the company before the recapitalization plan is announced. What is the value of equity before the announcement? What is the price per share? b. Use the APV method to calculate the company value after the recapitalization plan is announced. What is the value of equity after the announcement? What is the price per share? c. How many shares will be repurchased? What is the value of equity after the repurchase has been completed? What is the price per share? d. Use the flow to equity method to calculate the value of the company’s equity after ther ecapitalization. APV, FTE, and WACC Mojito Mint Company has a debt–equity ratio of .35. The required return on the company’s unlevered equity is 17 percent, and the pretax cost of the firm’s debt is 9 percent. Sales revenue for the company is expected to remain stable indefinitely at last year’s level of $28,900,000. Variable costs amount to 60 percent of sales. The tax rate is 40 percent, and the company distributes all its earnings as dividends at the end of each year. a. If the company were financed entirely by equity, how much would it be worth? b. What is the required return on the firm’s levered equity? c. Use the weighted average cost of capital method to calculate the value of the company. What is the value of the company’s equity? What is the value of the company’sd ebt? d. Use the flow to equity method to calculate the value of the company’s equity. APV, FTE, and WACC Lone Star Industries just issued $195,000 of perpetual 9 percent debt and used the proceeds to repurchase stock. The company expects to generate $83,000 of earnings before interest and taxes in perpetuity. The company distributes all its earnings as dividends at the end of each year. The firm’s unlevered cost of capital is 15 percent, and the corporate tax rate is 40 percent. a. What is the value of the company as an unlevered firm? b. Use the adjusted present value method to calculate the value of the company with leverage. c. What is the required return on the firm’s levered equity? d. Use the flow to equity method to calculate the value of the company’s equity. Projects That Are Not Scale Enhancing Blue Angel, Inc., a private firm in the holiday gift industry, is considering a new project. The company currently has a target debt–equity ratio of .40, but the industry target debt–equity ratio is .35. The industry average beta is 1.2. The market risk premium is 7 percent, and the risk-free rate is 5 percent. Assume all companies in this industry can issue debt at the risk-free rate. The corporate tax rate is 40 percent. The project requires an initial outlay of $475,000 and is expected to result in an $80,000 cash inflow at the end of the first year. The project will be financed at Blue Angel’s target debt–equity ratio. Annual cash flows from the project will grow at an constant rate of 5 percent until the end of the fifth year and remain constant forever thereafter. Should Blue Angel invest in the project?

www.mhhe.com/edumarketinsight 1. Locate the annual income statements for Walt Disney (DIS) and calculate the marginal tax rate for the company for the last year. Next, find the beta for Disney in the S&P stock report. Using the current debt and equity from the most recent annual balance sheet, calculate the unlevered beta for Disney.

Chapter 18

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Appendix 18A The Adjusted Present Value Approach

to Valuing Leveraged Buyouts

Mini Case

To access the appendix for this chapter, please visit www.mhhe.com/rwj.

THE LEVERAGED BUYOUT OF CHEEK PRODUCTS, INC. Cheek Products, Inc. (CPI) was founded 53 years ago by Joe Cheek and originally sold snack foods such as potato chips and pretzels. Through acquisitions, the company has grown into a conglomerate with major divisions in the snack food industry, home security systems, cosmetics, and plastics. Additionally, the company has several smaller divisions. In recent years, the company has been underperforming, but the company’s management doesn’t seem to be aggressively pursuing opportunities to improve operations (and the stock price). Meg Whalen is a financial analyst specializing in identifying potential buyout targets. She believes that two major changes are needed at Cheek. First, she thinks that the company would be better off if it sold several divisions and concentrated on its core competencies in snack foods and home security systems. Second, the company is financed entirely with equity. Because the cash flows of the company are relatively steady, Meg thinks the company’s debt–equity ratio should be at least .25. She believes these changes would significantly enhance shareholder wealth, but she also believes that the existing board and company management are unlikely to take the necessary actions. As a result, Meg thinks the company is a good candidate for a leveraged buyout. A leveraged buyout (LBO) is the acquisition by a small group of equity investors of a public or private company. Generally, an LBO is financed primarily with debt. The new shareholders service the heavy interest and principal payments with cash from operations and/or asset sales. Shareholders generally hope to reverse the LBO within three to seven years by way of a public offering or sale of the company to another firm. A buyout is therefore likely to be successful only if the firm generates enough cash to serve the debt in the early years and if the company is attractive to other buyers a few years down the road. Meg has suggested the potential LBO to her partners, Ben Feller and Brenton Flynn. Ben and Brenton have asked Meg to provide projections of the cash flows for the company. Meg has provided the following estimates (in millions):

2010

2011

2012

2013

2014

Sales Costs Depreciation EBT

$2,115 562 373 $1,180

$2,371 738 397 $1,236

$2,555 776 413 $1,366

$2,616 839 434 $1,343

$2,738 884 442 $1,412

Capital expenditures Change in NWC Asset sales

$ 215 $ (94) $1,092

$ 186 $ (143) $ 791

$ 234 $ 78

$ 237 $ 73

$ 234 $ 83

At the end of five years, Meg estimates that the growth rate in cash flows will be 3.5 percent per year. The capital expenditures are for new projects and the replacement

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of equipment that wears out. Additionally, the company would realize cash flow from the sale of several divisions. Even though the company will sell these divisions, overall sales should increase because of a more concentrated effort on the remaining divisions. After plowing through the company’s financials and various pro forma scenarios, Ben and Brenton feel that in five years they will be able to sell the company to another party or take it public again. They are also aware that they will have to borrow a considerable amount of the purchase price. The interest payments on the debt for each of the next five years if the LBO is undertaken will be these (in millions):

Interest payments

2010

2011

2012

2013

2014

$1,482

$1,430

$1,534

$1,495

$1,547

The company currently has a required return on assets of 14 percent. Because of the high debt level, the debt will carry a yield to maturity of 12.5 percent for the next five years. When the debt is refinanced in five years, they believe the new yield to maturity will be 8 percent. CPI currently has 167 million shares of stock outstanding that sell for $53 per share. The corporate tax rate is 40 percent. If Meg, Ben, and Brenton decide to undertake the LBO, what is the most they should offer per share?

PART III

CHAPTER 19

Dividends and Other Payouts On May 28, 2008, tractor manufacturer John Deere announced a broad plan to reward stockholders for the recent success of the firm’s business. Under the plan, Deere would (1) boost its quarterly dividend by 12 percent from 25 cents per share to 28 cents per share and (2) increase its planned repurchase of Deere’s common stock from $1.9 billion to $6.9 billion, or about oneseventh of the company’s outstanding shares. Investors cheered, bidding up the stock price by 3.4 percent on the day of the announcement. Why were investors so pleased? To find out, this chapter explores these types of actions and their implications for shareholders.

19.1 Different Types of Payouts The term dividend usually refers to a cash distribution of earnings. If a distribution is made from sources other than current or accumulated retained earnings, the term distribution rather than dividend is used. However, it is acceptable to refer to a distribution from earnings as a dividend and a distribution from capital as a liquidating dividend. The most common type of dividend is in the form of cash. When public companies pay dividends, they usually pay regular cash dividends four times a year. Sometimes firms will pay a regular cash dividend and an extra cash dividend. Paying a cash dividend reduces corporate cash and retained earnings—except in the case of a liquidating dividend (where paid-in capital may be reduced). Another type of dividend is paid out in shares of stock. This dividend is referred to as a stock dividend. It is not a true dividend because no cash leaves the firm. Rather, a stock dividend increases the number of shares outstanding, thereby reducing the value of each share. A stock dividend is commonly expressed as a ratio; for example, with a 2 percent stock dividend a shareholder receives 1 new share for every 50 currently owned. When a firm declares a stock split, it increases the number of shares outstanding. Because each share is now entitled to a smaller percentage of the firm’s cash flow, the stock price should fall. For example, if the managers of a firm whose stock is selling at $90 declare a 3:1 stock split, the price of a share of stock should fall to about $30. A stock split strongly resembles a stock dividend except that it is usually much larger. An alternative form of cash payout is a stock repurchase. Just as a firm may use cash to pay dividends, it may use cash to buy back shares of its stock. The shares are held by the corporation and accounted for as treasury stock.

19.2 Standard Method of Cash Dividend Payment The decision to pay a dividend rests in the hands of the board of directors of the corporation. A dividend is distributable to shareholders of record on a specific date. When a dividend has been declared, it becomes a liability of the firm and cannot be easily rescinded by the corporation. The amount of the dividend is expressed as dollars per share (dividend per share), as a percentage of the market price (dividend yield), or as a percentage of earnings per share (dividend payout). 575

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Figure 19.1 Example of Procedure for Dividend Payment

Days Thursday, January 15

Wednesday, January 28

Friday, January 30

Monday, February 16

Declaration date

Ex-dividend date

Record date

Payment date

1. Declaration date: The board of directors declares a payment of dividends. 2. Record date: The declared dividends are distributable to shareholders of record on a specific date. 3. Ex-dividend date : A share of stock becomes ex dividend on the date the seller is entitled to keep the dividend; under NYSE rules, shares are traded ex dividend on and after the second business day before the record date. 4. Payment date: The dividend checks are mailed to shareholders of record.

The mechanics of a dividend payment can be illustrated by the example in Figure 19.1 and the following chronology: For a list of today’s dividends, go to www.earnings.com.

1. Declaration date: On January 15 (the declaration date), the board of directors passes a resolution to pay a dividend of $1 per share on February 16 to all holders of record on January 30. 2. Date of record: The corporation prepares a list on January 30 of all individuals believed to be stockholders as of this date. The word believed is important here: The dividend will not be paid to individuals whose notification of purchase is received by the company after January 30. 3. Ex-dividend date: The procedure for the date of record would be unfair if efficient brokerage houses could notify the corporation by January 30 of a trade occurring on January 29, whereas the same trade might not reach the corporation until February 2 if executed by a less efficient house. To eliminate this problem, all brokerage firms entitle stockholders to receive the dividend if they purchased the stock three business days before the date of record. The second day before the date of record, which is Wednesday, January 28, in our example, is called the ex-dividend date. Before this date the stock is said to trade cum dividend. 4. Date of payment: The dividend checks are mailed to the stockholders on February 16. Obviously, the ex-dividend date is important because an individual purchasing the security before the ex-dividend date will receive the current dividend, whereas another individual purchasing the security on or after this date will not receive the dividend. The stock price will therefore fall on the ex-dividend date (assuming no other events occur). It is worthwhile to note that this drop is an indication of efficiency, not inefficiency, because the market rationally attaches value to a cash dividend. In a world with neither taxes nor transaction costs, the stock price would be expected to fall by the amount of the dividend: Beforee x-dividendd ate On or after ex-dividend date

Price = $(P + 1) Price = $P

This is illustrated in Figure 19.2. The amount of the price drop may depend on tax rates. For example, consider the case with no capital gains taxes. On the day before a stock goes ex dividend, a purchaser must decide either (1) to buy the stock immediately and pay tax on the forthcoming dividend or (2) to buy the stock tomorrow, thereby missing the dividend. If all investors are in the 15 percent tax bracket and the quarterly dividend is $1, the stock price should fall

Chapter 19

Dividends and Other Payouts

Figure 19.2

577

Perfect World Case

PriceB ehavior around the Ex-Dividend Date for a $1 Cash Dividend

Ex-date

Price ⴝ $(P ⴙ 1)

ⴚt

ⴚ2

ⴚ1

0

ⴙ1

ⴙ2

t

$1 is the ex-dividend price drop Price ⴝ $P In a world without taxes, the stock price will fall by the amount of the dividend on the ex-date (time 0). If the dividend is $1 per share, the price will be equal to P on the ex-date. Before ex-date (−1) Price = $(P + 1) Ex-date (0) Price = $P

b $ by $.85 85 on th the ex-dividend di id d d date. t Th Thatt iis, if th the stock t k price i falls f ll by b this thi amountt on the th ex-dividend date, purchasers will receive the same return from either strategy. As an example of the price drop on the ex-dividend date, consider the enormous dividend Microsoft paid in November 2004. The special dividend payment totaled a whopping $32.6 billion, the largest corporate cash disbursement in history. What makes the Microsoft special dividend extraordinary is its sheer size. The total dividends paid in 2004 by all the companies in the S&P 500 for the year totaled $213.6 billion, so Microsoft’s special dividend amounted to about 15 percent of the total paid by S&P 500 companies for the year. To give you another idea of the size of the special dividend, consider that, in December, when the dividend was sent to investors, personal income in the United States rose 3.7 percent. Without the dividend, personal income rose only .3 percent; so, the dividend payment accounted for about 3 percent of all personal income in the United States for the month! The stock went ex dividend on November 15, 2004, with a total dividend of $3.08 per share, consisting of a $3 special dividend and an $.08 regular dividend. The stock price chart here shows the change in Microsoft stock four days prior to the ex-dividend date and on the ex-dividend date.

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The stock closed at $29.97 on November 12 (a Friday) and opened at $27.34 on November 15, a drop of $2.63. With a 15 percent tax rate on dividends, we would have expected a drop of $2.62, and the actual price drop was almost exactly that amount.

19.3 The Benchmark Case: An Illustration of the Irrelevance of Dividend Policy A powerful argument can be made that dividend policy does not matter (or at least this timing of dividends when cash flows do not change). This will be illustrated with the Bristol Corporation. Bristol is an all-equity firm started 10 years ago. The current financial managers know at the present time (date 0) that the firm will dissolve in one year (date 1). At date 0 the managers are able to forecast cash flows with perfect certainty. The managers know that the firm will receive a cash flow of $10,000 immediately and another $10,000 next year. Bristol has no additional positive NPV projects.

Current Policy: Dividends Set Equal to Cash Flow At the present time, dividends (Div) at each date are set equal to the available cash flow of $10,000. The value of the firm can be calculated by discounting these dividends. This value is expressed as: Div1 V0 = Div0 + _______ 1 + RS where Div0 and Div1 are the cash flows paid out in dividends, and RS is the discount rate. The first dividend is not discounted because it will be paid immediately. Assuming RS = 10 percent, the value of the firm is: $10,000 $19,090.91 = $10,000 + _______ 1.1 If 1,000 shares are outstanding, the value of each share is: $10 $19.09 = $10 + ____ 1.1

(19.1)

To simplify the example, we assume that the ex-dividend date is the same as the date of payment. After the imminent dividend is paid, the stock price will immediately fall to $9.09 (= $19.09 − $10). Several members of Bristol’s board have expressed dissatisfaction with the current dividend policy and have asked you to analyze an alternative policy.

Alternative Policy: Initial Dividend Is Greater Than Cash Flow Another policy is for the firm to pay a dividend of $11 per share immediately, which is, of course, a total dividend payout of $11,000. Because the available cash flow is only $10,000, the extra $1,000 must be raised in one of a few ways. Perhaps the simplest would be to issue $1,000 of bonds or stock now (at date 0). Assume that stock is issued and the new stockholders will desire enough cash flow at date 1 to let them earn the required 10 percent return on their date 0 investment. The new stockholders will demand $1,100 of the date 1 cash flow, leaving only $8,900 to the old stockholders. The dividends to the old stockholders will be these:

Aggregate dividends to old stockholders Dividends per share

Date 0

Date 1

$11,000 $ 11.00

$ 8,900 $ 8.90

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The present value of the dividends per share is therefore: $8.90 $19.09 = $11 + _____ 1.1

(19.2)

Students often find it instructive to determine the price at which the new stock is issued. Because the new stockholders are not entitled to the immediate dividend, they would pay $8.09 (= $8.90/1.1) per share. Thus, 123.61 (= $1,000/$8.09) new shares are issued.

TheI ndifferenceP roposition Note that the values in Equations 19.1 and 19.2 are equal. This leads to the initially surprising conclusion that the change in dividend policy did not affect the value of a share of stock. However, on reflection, the result seems sensible. The new stockholders are parting with their money at date 0 and receiving it back with the appropriate return at date 1. In other words, they are taking on a zero NPV investment. As illustrated in Figure 19.3, old stockholders are receiving additional funds at date 0 but must pay the new stockholders their money with the appropriate return at date 1. Because the old stockholders must pay back principal plus the appropriate return, the act of issuing

10,000

0

Alternative policy: Old shareholders receive additional $1,000 at date 0 but receive $1,100 less at date 1

Dividends ($)

Current dividend policy: Old shareholders receive $10,000 at both date 0 and date 1

11,000 8,900

0

Date 0 Date 1 Time

Alternative policy: New shareholders pay in $1,000 at date 0 and receive $1,100 in dividends at date 1

Cash flows ($)

Currentand Alternative Dividend Policies

Dividends ($)

Figure 19.3

1,100 0

Date 0 Date 1

ⴚ1,000

Time

Date 0 Date 1 Time

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new stock at date 0 will not increase or decrease the value of the old stockholders’ holdings. That is, they are giving up a zero NPV investment to the new stockholders. An increase in dividends at date 0 leads to the necessary reduction of dividends at date 1, so the value of the old stockholders’ holdings remains unchanged. This illustration is based on the pioneering work of Miller and Modigliani (MM). Although our presentation is in the form of a numerical example, the MM paper proves that investors are indifferent to dividend policy in a more general setting.

HomemadeDi vidends To illustrate the indifference investors have toward dividend policy in our example, we used present value equations. An alternative and perhaps more intuitively appealing explanation avoids the mathematics of discounted cash flows. Suppose individual investor X prefers dividends per share of $10 at both dates 0 and 1. Would she be disappointed when informed that the firm’s management is adopting the alternative dividend policy (dividends of $11 and $8.90 on the two dates, respectively)? Not necessarily: She could easily reinvest the $1 of unneeded funds received on date 0, yielding an incremental return of $1.10 at date 1. Thus, she would receive her desired net cash flow of $11 − $1 = $10 at date 0 and $8.90 + $1.10 = $10 at date 1. Conversely, imagine investor Z preferring $11 of cash flow at date 0 and $8.90 of cash flow at date 1, who finds that management will pay dividends of $10 at both dates 0 and 1. He can sell off shares of stock at date 0 to receive the desired amount of cash flow. That is, if he sells off shares (or fractions of shares) at date 0 totaling $1, his cash flow at date 0 becomes $10 + $1 = $11. Because a $1 sale of stock at date 0 will reduce his dividends by $1.10 at date 1, his net cash flow at date 1 would be $10 − $1.10 = $8.90. The example illustrates how investors can make homemade dividends. In this instance, corporate dividend policy is being undone by a potentially dissatisfied stockholder. This homemade dividend is illustrated by Figure 19.4. Here the firm’s cash flows of $10 per share at both dates 0 and 1 are represented by point A. This point also represents the initial dividend payout. However, as we just saw, the firm could alternatively pay out $11 per share at date 0 and $8.90 per share at date 1, a strategy represented by point B. Similarly, by either issuing new stock or buying back old stock, the firm could achieve a dividend payout represented by any point on the diagonal line. The previous paragraph describes the choices available to the managers of the firm. The same diagonal line also represents the choices available to the shareholder. For example, if the shareholder receives a per-share dividend distribution of ($11, $8.90), he or she can either reinvest some of the dividends to move down and to the right on the graph or sell off shares of stock and move up and to the left. The implications of the graph can be summarized in two sentences: 1. By varying dividend policy, managers can achieve any payout along the diagonal line in Figure 19.4. 2. Either by reinvesting excess dividends at date 0 or by selling off shares of stock at this date, an individual investor can achieve any net cash payout along the diagonallin e. Thus, because both the corporation and the individual investor can move only along the diagonal line, dividend policy in this model is irrelevant. The changes the managers make in dividend policy can be undone by an individual who, by either reinvesting dividends or selling off stock, can move to a desired point on the diagonal line.

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Figure 19.4 Homemade Dividends: A Trade-off between Dividends per Share at Date 0 and Dividends per Share at Date 1

Date 0

$11

B A

$10

($10, $10)

$9

1 Slope ⴝ ⴚ — 1.1 $8.90

C

$10.00 $11.10 Date 1

The graph illustrates both (1) how managers can vary dividend policy and (2) how individuals can undo the firm’s dividend policy. Managers varying dividend policy : A firm paying out all cash flows immediately is at point A on the graph. The firm could achieve point B by issuing stock to pay extra dividends or achieve point C by buying back old stock with some of its cash. Individuals undoing the firm’s dividend policy : Suppose the firm adopts the dividend policy represented by point B: dividends per share of $11 at date 0 and $8.90 at date 1. An investor can reinvest $1 of the dividends at 10 percent, which will place her at point A. Suppose, alternatively, the firm adopts the dividend policy represented by point A. An investor can sell off $1 of stock at date 0, placing him at point B. No matter what dividend policy the firm establishes, a shareholder can undo it.

ATTestt You can test your knowledge of this material by examining these true statements: 1. Dividendsar er elevant. 2. Dividendp olicyisirr elevant. The first statement follows from common sense. Clearly, investors prefer higher dividends to lower dividends at any single date if the dividend level is held constant at every other date. In other words, if the dividend per share at a given date is raised while the dividend per share for each other date is held constant, the stock price will rise. This act can be accomplished by management decisions that improve productivity, increase tax savings, or strengthen product marketing. In fact, you may recall that in Chapter 9 we argued that the value of a firm’s equity is equal to the discounted present value of all its future dividends. The second statement is understandable once we realize that dividend policy cannot raise the dividend per share at one date while holding the dividend level per share constant at all other dates. Rather, dividend policy merely establishes the trade-off between dividends at one date and dividends at another date. As we saw in Figure 19.4, holding cash flows constant, an increase in date 0 dividends can be accomplished only by a decrease in date 1 dividends. The extent of the decrease is such that the present value of all dividends is not affected. Thus, in this simple world, dividend policy does not matter. That is, managers choosing either to raise or to lower the current dividend do not affect the current value of their firm. This theory is powerful, and the work of MM is generally considered a classic in modern finance. With relatively few assumptions, a rather surprising result is shown to be perfectly true. Nevertheless, because we want to examine many real-world

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factors ignored by MM, their work is only a starting point in this chapter’s discussion of dividends. Later parts of this chapter investigate these real-world considerations.

Dividends and Investment Policy The preceding argument shows that an increase in dividends through issuance of new shares neither helps nor hurts the stockholders. Similarly, a reduction in dividends through share repurchase neither helps nor hurts stockholders. The key to this result is understanding that the overall level of cash flows is assumed to be fixed and that we are not changing the available positive net present value projects. What about reducing capital expenditures to increase dividends? Earlier chapters show that a firm should accept all positive net present value projects. To do otherwise would reduce the value of the firm. Thus, we have an important point: Firms should never give up a positive NPV project to increase a dividend (or to pay a dividend for the first time).

This idea was implicitly considered by Miller and Modigliani. One of the assumptions underlying their dividend irrelevance proposition was this: “The investment policy of the firm is set ahead of time and is not altered by changes in dividend policy.”

19.4 Repurchase of Stock Instead of paying dividends, a firm may use cash to repurchase shares of its own stock. Share repurchases have taken on increased importance in recent years. Consider Figure 19.5, which shows the aggregate dollar amounts of dividends, repurchases, and earnings for U.S. industrial firms in the years from 1984 to 2004. As can be seen, the

$500,000

Earnings Dividends

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Net repurchases 300,000 200,000 100,000 0 ⫺100,000

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Earnings,D ividends, and Net Repurchases for U.S. Industrial Firms

19

Figure 19.5

Year DEFINITIONS: Net repurchases include stock sales, and earnings are net of special items. SOURCE: Douglas Skinner, “The Evolving Relation between Earnings, Dividends, and Stock Repurchases,” Journal of Financial Economics 87 (2008), pp. 582–609. From Appendix 1.

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amount of repurchases was far less than the amount of dividends in the early years. However, the amount of repurchases exceeded the amount of dividends by 1998. This trend reversed after 1999, and then reversed again in 2003. Notice also from Figure 19.5 that there is “stickiness” to repurchases and dividend payouts. In 2001 when aggregate corporate earnings turned negative (including special accounting items), the level of dividends and share repurchases did not change much. More generally, the volatility of aggregate earnings has been greater than that of dividends and share repurchases. Share repurchases are typically accomplished in one of three ways. First, companies may simply purchase their own stock, just as anyone would buy shares of a particular stock. In these open market purchases, the firm does not reveal itself as the buyer. Thus, the seller does not know whether the shares were sold back to the firm or to just another investor. Second, the firm could institute a tender offer. Here, the firm announces to all of its stockholders that it is willing to buy a fixed number of shares at a specific price. For example, suppose Arts and Crafts (A&C), Inc., has 1 million shares of stock outstanding, with a stock price of $50 per share. The firm makes a tender offer to buy back 300,000 shares at $60 per share. A&C chooses a price above $50 to induce shareholders to sell—that is, tender—their shares. In fact, if the tender price is set high enough, shareholders may want to sell more than the 300,000 shares. In the extreme case where all outstanding shares are tendered, A&C will buy back 3 out of every 10 shares that a shareholder has. On the other hand, if shareholders do not tender enough shares, the offer can be cancelled. A method related to a tender offer is the Dutch auction. Here the firm does not set a fixed price for the shares to be sold. Instead, the firm conducts an auction in which it bids for shares. The firm announces the number of shares it is willing to buy back at various prices, and shareholders indicate how many shares they are willing to sell at the various prices. The firm will then pay the lowest price that will achieve its goal. Finally, firms may repurchase shares from specific individual stockholders, a procedure called a targeted repurchase. For example, suppose the International Biotechnology Corporation purchased approximately 10 percent of the outstanding stock of the Prime Robotics Company (P-R Co.) in April at around $38 per share. At that time, International Biotechnology announced to the Securities and Exchange Commission that it might eventually try to take control of P-R Co. In May, P-R Co. repurchased the International Biotechnology holdings at $48 per share, well above the market price at that time. This offer was not extended to other shareholders. Companies engage in targeted repurchases for a variety of reasons. In some rare cases, a single large stockholder can be bought out at a price lower than that in a tender offer. The legal fees in a targeted repurchase may also be lower than those in a more typical buyback. In addition, the shares of large stockholders are often repurchased to avoid a takeover unfavorable to management. We now consider an example of a repurchase presented in the theoretical world of a perfect capital market. We next discuss real-world factors involved in the repurchase decision.

Dividend versus Repurchase: Conceptual Example Imagine that Telephonic Industries has excess cash of $300,000 (or $3 per share) and is considering an immediate payment of this amount as an extra dividend. The firm forecasts that, after the dividend, earnings will be $450,000 per year, or $4.50 for each of the 100,000 shares outstanding. Because the price–earnings ratio is 6 for comparable companies, the shares of the firm should sell for $27 (=$4.50 × 6) after the

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Table 19.1 Dividend versus Repurchase Example for Telephonic Industries

For Entire Firm

Per Share

Extra Dividend Proposed dividend Forecast annual earnings after dividend Market value of stock after dividend

$ 300,000 450,000 2,700,000

(100,000 shares outstanding) $ 3.00 4.50 27.00

Repurchase Forecast annual earnings after repurchase Market value of stock after repurchase

$ 450,000 2,700,000

(90,000 shares outstanding) $ 5.00 30.00

dividend is paid. These figures are presented in the top half of Table 19.1. Because the dividend is $3 per share, the stock would have sold for $30 a share before payment of the dividend. Alternatively, the firm could use the excess cash to repurchase some of its own stock. Imagine that a tender offer of $30 per share is made. Here, 10,000 shares are repurchased so that the total number of shares remaining is 90,000. With fewer shares outstanding, the earnings per share will rise to $5 (=$450,000 90,000). The price– earnings ratio remains at 6 because both the business and financial risks of the firm are the same in the repurchase case as they were in the dividend case. Thus, the price of a share after the repurchase is $30 (=$5 × 6). These results are presented in the bottom half of Table 19.1. If commissions, taxes, and other imperfections are ignored in our example, the stockholders are indifferent between a dividend and a repurchase. With dividends each stockholder owns a share worth $27 and receives $3 in dividends, so that the total value is $30. This figure is the same as both the amount received by the selling stockholders and the value of the stock for the remaining stockholders in the repurchase case. This example illustrates the important point that, in a perfect market, the firm is indifferent between a dividend payment and a share repurchase. This result is quite similar to the indifference propositions established by MM for debt versus equity financing and for dividends versus capital gains. You may often read in the popular financial press that a repurchase agreement is beneficial because earnings per share increase. Earnings per share do rise for Telephonic Industries if a repurchase is substituted for a cash dividend: The EPS is $4.50 after a dividend and $5 after the repurchase. This result holds because the drop in shares after a repurchase implies a reduction in the denominator of the EPS ratio. However, the financial press frequently places undue emphasis on EPS figures in a repurchase agreement. Given the irrelevance propositions we have discussed, the increase in EPS here is not beneficial. Table 19.1 shows that, in a perfect capital market, the total value to the stockholder is the same under the dividend payment strategy as under the repurchase strategy.

Dividends versus Repurchases: Real-World Considerations We previously referred to Figure 19.5, which showed growth in share repurchases relative to dividends. In fact, most firms that pay dividends also repurchase shares of

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stock. This suggests that repurchasing shares of stock is not always a substitute for paying dividends but rather a complement to it. In 2007, the number of U.S. industrial firms that paid dividends only or repurchased only is about the same as the number of firms paying both dividends and repurchasing shares. Why do some firms choose repurchases over dividends? Here are perhaps five of the most common reasons. 1. Flexibility Firms often view dividends as a commitment to their stockholders and are quite hesitant to reduce an existing dividend. Repurchases do not represent a similar commitment. Thus, a firm with a permanent increase in cash flow is likely to increase its dividend. Conversely, a firm whose cash flow increase is only temporary is likely to repurchase shares of stock. 2. Executive Compensation Executives are frequently given stock options as part of their overall compensation. Let’s revisit the Telephonic Industries example of Table 19.1, where the firm’s stock was selling at $30 when the firm was considering either a dividend or a repurchase. Further imagine that Telephonic had granted 1,000 stock options to its CEO, Ralph Taylor, two years earlier. At that time, the stock price was, say, only $20. This means that Mr. Taylor can buy 1,000 shares for $20 a share at any time between the grant of the options and their expiration, a procedure called exercising the options. His gain from exercising is directly proportional to the rise in the stock price above $20. As we saw in the example, the price of the stock would fall to $27 following a dividend but would remain at $30 following a repurchase. The CEO would clearly prefer a repurchase to a dividend because the difference between the stock price and the exercise price of $20 would be $10 (= $30 − $20) following the repurchase but only $7 (= $27 − $20) following the dividend. Existing stock options will always have greater value when the firm repurchases shares instead of paying a dividend because the stock price will be greater after a repurchase than after a dividend. 3. Offset to Dilution In addition, the exercise of stock options increases the number of shares outstanding. In other words, exercise causes dilution of the stock. Firms frequently buy back shares of stock to offset this dilution. However, it is hard to argue that this is a valid reason for repurchase. As we showed in Table 19.1, repurchase is neither better nor worse for the stockholders than a dividend. Our argument holds whether or not stock options have been exercised previously. 4. Undervaluation Many companies buy back stock because they believe that a repurchase is their best investment. This occurs more frequently when managers believe that the stock price is temporarily depressed. The fact that some companies repurchase their stock when they believe it is undervalued does not imply that the management of the company must be correct; only empirical studies can make this determination. The immediate stock market reaction to the announcement of a stock repurchase is usually quite favorable. In addition, some empirical work has shown that the long-term stock price performance of securities after a buyback is better than the stock price performance of comparable companies that do not repurchase. 5. Taxes Because taxes for both dividends and share repurchases are treated in depth in the next section, suffice it to say at this point that repurchases provide a tax advantageo verd ividends.

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19.5 Personal Taxes, Dividends, and Stock Repurchases Section 19.3 asserted that in a world without taxes and other frictions, dividend policy is irrelevant. Similarly, Section 19.4 concluded that the choice between a share repurchase and a dividend is irrelevant in a world of this type. This section examines the effect of taxes on both dividends and repurchases. Our discussion is facilitated by classifying firms into two types: Those without sufficient cash to pay a dividend and those with sufficient cash to do so.

Firms without Sufficient Cash to Pay a Dividend It is simplest to begin with a firm without cash that is owned by a single entrepreneur. If this firm should decide to pay a dividend of $100, it must raise capital. The firm might choose among a number of different stock and bond issues to pay the dividend. However, for simplicity, we assume that the entrepreneur contributes cash to the firm by issuing stock to himself. This transaction, diagrammed in the left side of Figure 19.6, would clearly be a wash in a world of no taxes. $100 cash goes into the firm when stock is issued and is immediately paid out as a dividend. Thus, the entrepreneur neither benefits nor loses when the dividend is paid, a result consistent with Miller–Modigliani. Now assume that dividends are taxed at the owner’s personal tax rate of 15 percent. The firm still receives $100 upon issuance of stock. However, the entrepreneur does not get to keep the full $100 dividend. Instead the dividend payment is taxed, implying that the owner receives only $85 net after tax. Thus, the entrepreneur loses $15. Though the example is clearly contrived and unrealistic, similar results can be reached for more plausible situations. Thus, financial economists generally agree that in a world of personal taxes, firms should not issue stock to pay dividends. The direct costs of issuance will add to this effect. Investment bankers must be paid when new capital is raised. Thus, the net receipts due to the firm from a new issue are

Figure 19.6 Firm Issues Stock to Pay a Dividend

No Taxes

A Personal Tax Rate of 15%

Firm

Firm

Dividend ($100)

Cash from issue of stock ($100)

Dividend ($100) ($15) IRS

Entrepreneur

Cash from issue of stock ($100) ($85) Entrepreneur

In the no-tax case, the entrepreneur receives the $100 in dividends that he gave to the firm when purchasing stock. The entire operation is called a wash; in other words, it has no economic effect. With taxes, the entrepreneur still receives $100 in dividends. However, he must pay $15 in taxes to the IRS. The entrepreneur loses and the IRS wins when a firm issues stock to pay a dividend.

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less than 100 percent of total capital raised. Because the size of new issues can be lowered by a reduction in dividends, we have another argument in favor of a low-dividend policy. Of course, our advice not to finance dividends through new stock issues might need to be modified somewhat in the real world. A company with a large and steady cash flow for many years in the past might be paying a regular dividend. If the cash flow unexpectedly dried up for a single year, should new stock be issued so that dividends could be continued? Although our previous discussion would imply that new stock should not be issued, many managers might issue the stock anyway for practical reasons. In particular, stockholders appear to prefer dividend stability. Thus, managers might be forced to issue stock to achieve this stability, knowing full well the adverse tax consequences.

Firms with Sufficient Cash to Pay a Dividend The previous discussion argued that in a world with personal taxes, a firm should not issue stock to pay a dividend. Does the tax disadvantage of dividends imply the stronger policy, “Never, under any circumstances, pay dividends in a world with personal taxes”? We argue next that this prescription does not necessarily apply to firms with excess cash. To see this, imagine a firm with $1 million in extra cash after selecting all positive NPV projects and determining the level of prudent cash balances. The firm might consider the following alternatives to a dividend: 1. Select additional capital budgeting projects. Because the firm has taken all the available positive NPV projects already, it must invest its excess cash in negative NPV projects. This is clearly a policy at variance with the principles of corporate finance. In spite of our distaste for this policy, researchers have suggested that many managers purposely take on negative NPV projects in lieu of paying dividends.1 The idea here is that managers would rather keep the funds in the firm because their prestige, pay, and perquisites are often tied to the firm’s size. Although managers may help themselves here, they are hurting stockholders. We broached this subject in the section titled “Free Cash Flow” in Chapter 17, and we will have more to say about it later in this chapter. 2. Acquire other companies. To avoid the payment of dividends, a firm might use excess cash to acquire another company. This strategy has the advantage of acquiring profitable assets. However, a firm often incurs heavy costs when it embarks on an acquisition program. In addition, acquisitions are invariably made above the market price. Premiums of 20 to 80 percent are not uncommon. Because of this, a number of researchers have argued that mergers are not generally profitable to the acquiring company, even when firms are merged for a valid business purpose. Therefore, a company making an acquisition merely to avoid a dividend is unlikely to succeed. 3. Purchase financial assets. The strategy of purchasing financial assets in lieu of a dividend payment can be illustrated with the following example.

1

See, for example, M. C. Jensen, “Agency Costs of Free Cash Flows, Corporate Finance, and Takeovers,” American Economic Review (May 1986).

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EXAMPLE 19.1

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Dividends and Taxes The Regional Electric Company has $1,000 of extra cash. It can retain the D ccash and invest it in Treasury bills yielding 10 percent, or it can pay the cash to shareholders as a dividend. Shareholders can also invest in Treasury bills with the same yield. Suppose the corporate tax rate is 34 percent, and the personal tax rate is 28 percent for all individuals. However, the maximum tax rate on dividends is 15 percent. How much cash will investors have after five years under each policy? If dividends are paid now, shareholders will receive: $1,000 × (1 − .15) = $850 today after taxes. Because their return after personal tax on Treasury bills is 7.2 [=10 × (1 − .28)] percent, shareholders will have: $850 × (1.072)5 = $1,203.35

(19.3)

in five years. Note that interest income is taxed at the personal tax rate (28 percent in this example), but dividends are taxed at the lower rate of 15 percent. If Regional Electric Company retains the cash to invest in Treasury bills, its aftertax interest rate will be .066 [=.10 × (1 − .34)]. At the end of five years, the firm will have: $1,000 × (1.066)5 = $1,376.53 If these proceeds are then paid as a dividend, the stockholders will receive: $1,376.53 × (1 − .15) = $1,170.05

(19.4)

after personal taxes at date 5. The value in Equation 19.3 is greater than that in Equation 19.4, implying that cash to stockholders will be greater if the firm pays the dividend now. This example shows that for a firm with extra cash, the dividend payout decision will depend on personal and corporate tax rates. If personal tax rates are higher than corporate tax rates, a firm will have an incentive to reduce dividend payouts. However, if personal tax rates are lower than corporate tax rates, a firm will have an incentive to pay out any excess cash as dividends.

In the United States, both the highest marginal tax rate for individuals and the corporate tax rate were 35 percent in 2006. Because many investors face marginal tax rates well below the maximum, it appears that firms have an incentive not to hoard cash. However, a quirk in the tax code provides an offsetting incentive. In particular, 70 percent of the dividends that one corporation receives from another corporation are excluded from corporate tax.2 Individuals are not granted this exclusion. The quirk increases the likelihood that proceeds will be higher if the firm invests cash in other dividend-paying stocks rather than paying out cash as a dividend. The firm’s decision to invest in financial assets or to pay a dividend is a complex one, depending on the tax rate of the firm, the marginal tax rates of its investors, and the application of the dividend exclusion. While there are likely many real-world situations where the numbers favor investment in financial assets, 2

This exclusion applies if the firm owns less than 20 percent of the stock in the other company. The exclusion rises to 80 percent if the firm owns more than 20 percent of the stock of the other company and is 100 percent if the firm owns more than 80 percent of the stock of the other company. Corporations are not granted an exclusion for interest earned on bonds.

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few companies actually seem to hoard cash in this manner without limit. The reason is that Section 532 of the Internal Revenue Code penalizes firms exhibiting “improper accumulation of surplus.” Thus, in the final analysis, the purchase of financial assets, like selecting negative NPV projects and acquiring other companies, does not obviate the need for companies with excess cash to pay dividends. 4. Repurchase shares. The example we described in the previous section showed that investors are indifferent between share repurchase and dividends in a world without taxes and transaction costs. However, under current tax law, stockholders generally prefer a repurchase to a dividend. As an example, consider an individual receiving a dividend of $1 on each of 100 shares of a stock. With a 15 percent tax rate, that individual would pay taxes of $15 on the dividend. Selling shareholders would pay lower taxes if the firm repurchased $100 of existing shares. This occurs because taxes are paid only on the profit from a sale. The individual’s gain on a sale would be only $40 if the shares sold for $100 were originally purchased for, say, $60. The capital gains tax would be $6 (=.15 × $40), a number below the tax on dividends of $15. Note that the tax from a repurchase is less than the tax on a dividend even though the same 15 percent tax rate applies to both the repurchase and the dividend. Of all the alternatives to dividends mentioned in this section, the strongest case can be made for repurchases. In fact, academics have long wondered why firms ever pay a dividend instead of repurchasing stock. There have been at least two possible reasons for avoiding repurchases. First, Grullon and Michaely point out that in the past the Securities and Exchange Commission (SEC) had accused some firms undergoing share repurchase programs of illegal price manipulation.3 However, these authors indicate that SEC Rule 10b-18, adopted in 1982, provides guidelines for firms to avoid the charge of price manipulation. These guidelines are relatively easy to follow, so firms should not have to worry about this charge today. In fact, Grullon and Michaely believe that the large increase in buyback programs in recent years is at least partially the result of 10b-18. Second, the IRS can penalize firms repurchasing their own stocks if the only reason is to avoid the taxes that would be levied on dividends. However, this threat has not materialized with the growth in corporate repurchases. Thus, these two reasons do not seem to justify the avoidance of repurchases.

Summaryo fP ersonalT axes This section suggests that because of personal taxes, firms have an incentive to reduce dividends. For example, they might increase capital expenditures, acquire other companies, or purchase financial assets. However, due to financial considerations and legal constraints, rational firms with large cash flows will likely exhaust these activities with plenty of cash left over for dividends. It is harder to explain why firms pay dividends instead of repurchasing shares. The tax savings from buybacks are significant, and fear of either the SEC or the IRS seems overblown. Academics are of two minds here. Some argue that corporations were simply slow to grasp the benefits from repurchases. However, since the idea has firmly caught on, the trend toward replacement of dividends with buybacks will continue. We might even conjecture that dividends will be as unimportant in the future as 3

See Gustavo Grullon and Roni Michaely, “Dividends, Share Repurchases, and the Substitution Hypothesis,” Journal of Finance (August 2002), p. 1677.

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repurchases were in the past. Conversely, others argue that companies have paid dividends all along for good reason. Perhaps the legal hassles, particularly from the IRS, are significant after all. Or there may be other, more subtle benefits from dividends. We consider potential benefits of dividends in the next section.

19.6 Real-World Factors Favoring a High-Dividend Policy The previous section pointed out that because individuals pay taxes on dividends, financial managers might seek ways to reduce dividends. While we discussed the problems with taking on more capital budgeting projects, acquiring other firms, and hoarding cash, we stated that share repurchase has many of the benefits of a dividend with less of a tax disadvantage. This section considers reasons why a firm might pay its shareholders high dividends even in the presence of personal taxes on these dividends.

Desire for Current Income It has been argued that many individuals desire current income. The classic example is the group of retired people and others living on a fixed income. The argument further states that these individuals would bid up the stock price should dividends rise and bid down the stock price should dividends fall. This argument does not hold in Miller and Modigliani’s theoretical model. An individual preferring high current cash flow but holding low-dividend securities could easily sell off shares to provide the necessary funds. Thus in a world of no transaction costs, a high–current-dividend policy would be of no value to the stockholder. However, the current income argument is relevant in the real world. Stock sales involve brokerage fees and other transaction costs—direct cash expenses that could be avoided by an investment in high-dividend securities. In addition, stock sales are timeconsuming, further leading investors to buy high-dividend securities. To put this argument in perspective, remember that financial intermediaries such as mutual funds can perform repackaging transactions at low cost. Such intermediaries could buy low-dividend stocks and, by a controlled policy of realizing gains, pay their investors at a higher rate.

BehavioralF inance Suppose it turned out that the transaction costs in selling no-dividend securities could not account for the preference of investors for dividends. Would there still be a reason for high dividends? We introduced the topic of behavioral finance in Chapter 14, pointing out that the ideas of behaviorists represent a strong challenge to the theory of efficient capital markets. It turns out that behavioral finance also has an argument for high dividends. The basic idea here concerns self-control, a concept that, though quite important in psychology, has received virtually no emphasis in finance. Although we cannot review all that psychology has to say about self-control, let’s focus on one example—losing weight. Suppose Al Martin, a college student, just got back from the Christmas break more than a few pounds heavier than he would like. Everyone would probably agree that diet and exercise are the two ways to lose weight. But how should Al put this approach into practice? (We’ll focus on exercise, though the same principle would

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apply to diet as well.) One way—let’s call it the economists’ way—would involve trying to make rational decisions. Each day Al would balance the costs and the benefits of exercising. Perhaps he would choose to exercise on most days because losing the weight is important to him. However, when he is too busy with exams, he might rationally choose not to exercise because he cannot afford the time. And he wants to be socially active as well. So he may rationally choose to avoid exercise on days when parties and other social commitments become too time-consuming. This seems sensible—at first glance. The problem is that he must make a choice every day, and there may simply be too many days when his lack of self-control gets the better of him. He may tell himself that he doesn’t have the time to exercise on a particular day, simply because he is starting to find exercise boring, not because he really doesn’t have the time. Before long, he is avoiding exercise on most days—and overeating in reaction to the guilt from not exercising! Is there an alternative? One way would be to set rigid rules. Perhaps Al decides to exercise five days a week no matter what. This is not necessarily the best approach for everyone, but there is no question that many of us (perhaps most of us) live by a set of rules. For example, Shefrin and Statman4 suggest some typical rules: • Jog at least two miles a day. • Do not consume more than 1,200 calories per day. • Bank the wife’s salary and spend from only the husband’s paycheck. • Save at least 2 percent of every paycheck for children’s college education and never withdraw from this fund. • Neverto uchad ropo f alc ohol. What does this have to do with dividends? Investors must also deal with self-control. Suppose a retiree wants to consume $20,000 a year from savings, in addition to Social Security and her pension. On one hand, she could buy stocks with a dividend yield high enough to generate $20,000 in dividends. On the other hand, she could place her savings in no-dividend stocks, selling off $20,000 each year for consumption. Though these two approaches seem equivalent financially, the second one may allow for too much leeway. If lack of self-control gets the better of her, she might sell off too much, leaving little for her later years. Better, perhaps, to short-circuit this possibility by investing in dividend-paying stocks with a firm personal rule of never “dipping into principal.” Although behaviorists do not claim that this approach is for everyone, they argue that enough people think this way to explain why firms pay dividends—even though, as we said earlier, dividends are tax disadvantaged. Does behavioral finance argue for increased stock repurchases as well as increased dividends? The answer is no, because investors will sell the stock that firms repurchase. As we have said, selling stock involves too much leeway. Investors might sell too many shares of stock, leaving little for later years. Thus, the behaviorist argument may explain why companies pay dividends in a world with personal taxes.

AgencyCo sts Although stockholders, bondholders, and management form firms for mutually beneficial reasons, one party may later gain at the other’s expense. For example, take the potential conflict between bondholders and stockholders. Bondholders would like 4

Hersh M. Shefrin and Meir Statman, “Explaining Investor Preference for Cash Dividends,” Journal of Financial Economics 13 (1984).

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stockholders to leave as much cash as possible in the firm so that this cash would be available to pay the bondholders during times of financial distress. Conversely, stockholders would like to keep this extra cash for themselves. That’s where dividends come in. Managers, acting on behalf of the stockholders, may pay dividends simply to keep the cash away from the bondholders. In other words, a dividend can be viewed as a wealth transfer from bondholders to stockholders. There is empirical evidence for this view of things. For example, DeAngelo and DeAngelo find that firms in financial distress are reluctant to cut dividends.5 Of course, bondholders know about the propensity of stockholders to transfer money out of the firm. To protect themselves, bondholders frequently create loan agreements stating that dividends can be paid only if the firm has earnings, cash flow, and working capital above specified levels. Although managers may be looking out for stockholders in any conflict with bondholders, managers may pursue selfish goals at the expense of stockholders in other situations. For example, as discussed in a previous chapter, managers might pad expense accounts, take on pet projects with negative NPVs, or simply not work hard. Managers find it easier to pursue these selfish goals when the firm has plenty of free cash flow. After all, one cannot squander funds if the funds are not available in the first place. And that is where dividends come in. Several scholars have suggested that the board of directors can use dividends to reduce agency costs.6 By paying dividends equal to the amount of “surplus” cash flow, a firm can reduce management’s ability to squander the firm’s resources. This discussion suggests a reason for increased dividends, but the same argument applies to share repurchases as well. Managers, acting on behalf of stockholders, can just as easily keep cash from bondholders through repurchases as through dividends. And the board of directors, also acting on behalf of stockholders, can reduce the cash available to spendthrift managers just as easily through repurchases as through dividends. Thus, the presence of agency costs is not an argument for dividends over repurchases. Rather, agency costs imply firms may increase either dividends or share repurchases rather than hoard large amounts of cash.

Information Content of Dividends and Dividend Signaling Information Content While there are many things researchers do not know about dividends, we know one thing for sure: The stock price of a firm generally rises when the firm announces a dividend increase and generally falls when a dividend reduction is announced. For example, Asquith and Mullins estimate that stock prices rise about 3 percent following announcements of dividend initiations.7 Michaely, Thaler, and Womack find that stock prices fall about 7 percent following announcements of dividend omissions.8 5

H. DeAngelo and L. DeAngelo, “Dividend Policy and Financial Distress: An Empirical Investigation of Troubled NYSE Firms,” Journal of Finance 45 (1990). 6 Michael Rozeff, “How Companies Set Their Dividend Payout Ratios,” in The Revolution in Corporate Finance, edited by Joel M. Stern and Donald H. Chew (New York: Basil Blackwell, 1986). See also Robert S. Hansen, Raman Kumar, and Dilip K. Shome, “Dividend Policy and Corporate Monitoring: Evidence from the Regulated Electric Utility Industry,” Financial Management (Spring 1994). 7

P. Asquith and D. Mullins, Jr., “The Impact of Initiating Dividend Payments on Shareholder Wealth,” Journal of Business (January 1983).

8

R. Michaely, R. H. Thaler, and K. Womack, “Price Reactions to Dividend Initiations and Omissions: Overreactions or Drift?” Journal of Finance 50 (1995).

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The question is how we should interpret this empirical evidence. Consider the following three positions on dividends: 1. From the homemade dividend argument of MM, dividend policy is irrelevant, given that future earnings (and cash flows) are held constant. 2. Because of tax effects, a firm’s stock price is negatively related to the current dividend when future earnings (or cash flows) are held constant. 3. Because of stockholders’ desire for current income, a firm’s stock price is positively related to its current dividend, even when future earnings (or cash flows) are held constant. At first glance, the empirical evidence that stock prices rise when dividend increases are announced may seem consistent with position 3 and inconsistent with positions 1 and 2. In fact, many writers have said this. However, other authors have countered that the observation itself is consistent with all three positions. They point out that companies do not like to cut a dividend. Thus, firms will raise the dividend only when future earnings, cash flow, and so on are expected to rise enough so that the dividend is not likely to be reduced later to its original level. A dividend increase is management’s signal to the market that the firm is expected to do well. It is the expectation of good times, and not only the stockholders’ affinity for current income, that raises the stock price. The rise in the stock price following the dividend signal is called the information content effect of the dividend. To recapitulate, imagine that the stock price is unaffected or even negatively affected by the level of dividends, given that future earnings (or cash flows) are held constant. Nevertheless, the information content effect implies that the stock price may rise when dividends are raised—if dividends simultaneously cause stockholders to increase their expectations of future earnings and cash flows. Dividend Signaling We just argued that the market infers a rise in earnings and cash flows from a dividend increase, leading to a higher stock price. Conversely, the market infers a decrease in cash flows from a dividend reduction, leading to a fall in stock price. This raises an interesting corporate strategy: Could management increase dividends just to make the market think that cash flows will be higher, even when management knows that cash flows will not rise? While this strategy may seem dishonest, academics take the position that managers frequently attempt the strategy. Academics begin with the following accounting identity for an all-equity firm: Cash flow9 = Capital expenditures + Dividends

(19.5)

Equation 19.5 must hold if a firm is neither issuing nor repurchasing stock. That is, the cash flow from the firm must go somewhere. If it is not paid out in dividends, it must be used in some expenditure. Whether the expenditure involves a capital budgeting project or a purchase of Treasury bills, it is still an expenditure. Imagine that we are in the middle of the year and investors are trying to make some forecast of cash flow over the entire year. These investors may use Equation 19.5 to estimate cash flow. For example, suppose the firm announces that current dividends will be $50 million and the market believes that capital expenditures are $80 million. The market would then determine cash flow to be $130 million (=$50 + $80). 9

The correct representation of Equation 19.5 involves cash flow, not earnings. However, with little loss of understanding, we could discuss dividend signaling in terms of earnings, not cash flow.

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Now, suppose that the firm had, alternatively, announced a dividend of $70 million. The market might assume that cash flow remains at $130 million, implying capital expenditures of $60 million (=$130 − $70). Here, the increase in dividends would hurt stock price because the market anticipates valuable capital expenditures will be crowded out. Alternatively, the market might assume that capital expenditures remain at $80 million, implying the estimate of cash flow to be $150 million (=$70 + $80). Stock price would likely rise here because stock prices usually increase with cash flow. In general, academics believe that models where investors assume capital expenditures remain the same are more realistic. Thus, an increase in dividends raises stock price. Now we come to the incentives of managers to fool the public. Suppose you are a manager who wants to boost stock price, perhaps because you are planning to sell some of your personal holdings of the company’s stock immediately. You might increase dividends so that the market would raise its estimate of the firm’s cash flow, thereby also boosting the current stock price. If this strategy is appealing, would anything prevent you from raising dividends without limit? The answer is yes because there is also a cost to raising dividends. That is, the firm will have to forgo some of its profitable projects. Remember that cash flow in Equation 19.5 is a constant, so an increase in dividends is obtained only by a reduction in capital expenditures. At some point the market will learn that cash flow has not increased, but instead profitable capital expenditures have been cut. Once the market absorbs this information, stock price should fall below what it would have been had dividends never been raised. Thus, if you plan to sell, say, half of your shares and retain the other half, an increase in dividends should help you on the immediate sale but hurt you when you sell your remaining shares years later. So your decision on the level of dividends will be based, among other things, on the timing of your personal stock sales. This is a simplified example of dividend signaling, where the manager sets dividend policy based on maximum benefit for himself.10 Alternatively, a given manager may have no desire to sell his shares immediately but knows that, at any one time, plenty of ordinary shareholders will want to do so. Thus, for the benefit of shareholders in general, a manager will always be aware of the trade-off between current and future stock price. And this, then, is the essence of signaling with dividends. It is not enough for a manager to set dividend policy to maximize the true (or intrinsic) value of the firm. He must also consider the effect of dividend policy on the current stock price, even if the current stock price does not reflect true value. Does a motive to signal imply that managers will increase dividends rather than share repurchases? The answer is likely no: Most academic models imply that dividends and share repurchases are perfect substitutes.11 Rather, these models indicate that managers will consider reducing capital spending (even on projects with positive NPVs) to increase either dividends or share repurchases.

10 Papers examining fully developed models of signaling include S. Bhattacharya, “Imperfect Information, Dividend Policy, and ‘the Bird in the Hand’ Fallacy,” Bell Journal of Economics 10 (1979); S. Bhattacharya, “Non-dissipative Signaling Structure and Dividend Policy,” Quarterly Journal of Economics 95 (1980), p. 1; S. Ross, “The Determination of Financial Structure: The Incentive Signaling Approach,” Bell Journal of Economics 8 (1977), p. 1; M. Miller and K. Rock, “Dividend Policy under Asymmetric Information,” Journal of Finance (1985). 11 Signaling models where dividends and repurchases are not perfect substitutes are contained in Franklin Allen, Antonio Bernardo, and Ivo Welch, “A Theory of Dividends Based on Tax Clienteles,” Journal of Finance (2002) and Kose John and Joseph Williams, “Dividends, Dilution and Taxes: A Signaling Equilibrium,” Journal of Finance(1985).

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19.7 The Clientele Effect: A Resolution of Real-World Factors? In the previous two sections, we pointed out that the existence of personal taxes favors a low-dividend policy, whereas other factors favor high dividends. The financial profession had hoped that it would be easy to determine which of these sets of factors dominates. Unfortunately, after years of research, no one has been able to conclude which of the two is more important. This is surprising: We might be skeptical that the two sets of factors would cancel each other out so perfectly. However, one particular idea, known as the clientele effect, implies that the two sets of factors are likely to cancel each other out after all. To understand this idea, let’s separate investors in high tax brackets from those in low tax brackets. Individuals in high tax brackets likely prefer either no or low dividends. Low tax bracket investors generally fall into three categories. First, there are individual investors in low brackets. They are likely to prefer some dividends if they desire current income. Second, pension funds pay no taxes on either dividends or capital gains. Because they face no tax consequences, pension funds will also prefer dividends if they have a preference for current income. Finally, corporations can exclude at least 70 percent of their dividend income but cannot exclude any of their capital gains. Thus, corporations are likely to prefer high-dividend stocks, even without a preference for current income. Suppose that 40 percent of all investors prefer high dividends and 60 percent prefer low dividends, yet only 20 percent of firms pay high dividends while 80 percent pay low dividends. Here, the high-dividend firms will be in short supply, implying that their stock should be bid up while the stock of low-dividend firms should be bid down. However, the dividend policies of all firms need not be fixed in the long run. In this example, we would expect enough low-dividend firms to increase their payout so that 40 percent of the firms pay high dividends and 60 percent of the firms pay low dividends. After this adjustment, no firm will gain from changing its dividend policy. Once payouts of corporations conform to the desires of stockholders, no single firm can affect its market value by switching from one dividend strategy to another. Clienteles are likely to form in the following way: Group

Stocks

Individuals in high tax brackets Individuals in low tax brackets Tax-free institutions Corporations

Zero- to low-payout stocks Low- to medium-payout stocks Medium-payout stocks High-payout stocks

To see if you understand the clientele effect, consider the following statement: “In a world where many investors like high dividends, a firm can boost its share price by increasing its dividend payout ratio.” True or false? The statement is likely to be false. As long as there are already enough high-dividend firms to satisfy dividend-loving investors, a firm will not be able to boost its share price by paying high dividends. A firm can boost its stock price only if an unsatisfied clientele exists.

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Figure 19.7

35

Preferencesof Investors for Dividend Yield

Low income (inc < 40K) Medium income (40–75K)

30

High income (inc > 75K)

Portfolio weight (in %)

25

20

15

10

5

0

Low

Q2

Q3 Q4 Dividend yield quintile

High

All stocks are ranked on their dividend yields and placed into five quintile portfolios. The figure shows the weight of each quintile in the portfolios of low-, medium-, and high-income investors. Relative to those with lower income, high-income investors place a greater percentage of their assets in low-dividend stocks and a smaller percentage in high-dividend stocks. SOURCE: Adapted from Figure 2 of John Graham and Alok Kumar, “Do Dividend Clienteles Exist? Evidence on Dividend Preferences of Retail Investors,” Journal of Finance 61 (2006), pp. 1305–36.

Our discussion of clienteles followed from the fact that tax brackets vary across investors. If shareholders care about taxes, stocks should attract clienteles based on dividend yield. Is there any evidence that this is the case? Consider Figure 19.7. Here, John Graham and Alok Kumar12 rank common stocks by their dividend yields (the ratio of dividend to stock price) and place them into five portfolios, called quintiles. The bottom quintile contains the 20 percent of stocks with the lowest dividend yields; the next quintile contains the 20 percent of stocks with the next lowest dividend yields; and so on. The figure shows the weight of each quintile in the portfolios of low-, medium-, and high-income investors. As can be seen, relative to low-income investors, high-income investors put a greater percentage of their assets into low-dividend securities. Conversely, again relative to low-income investors, high-income investors put a smaller percentage of their assets into high-dividend securities.

12

John Graham and Alok Kumar, “Do Dividend Clienteles Exist? Evidence on Dividend Preferences of Retail Investors,” Journal of Finance (June 2006).

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19.8 What WeKn owan dD oNo tK now about Dividend Policy CorporateDi videndsAr eSubsta ntial We pointed out earlier in the chapter that dividends are tax disadvantaged relative to capital gains because dividends are taxed upon payment whereas taxes on capital gains are deferred until sale. Nevertheless, dividends in the U.S. economy are substantial. For example, consider Figure 19.8, which shows the ratio of aggregate dividends to aggregate earnings for all U.S. firms from 1959 to 2006. The ratio was approximately 64 percent in 2006, when net income for U.S. firms was about $1.1 trillion and dividends were about $700 billion. We might argue that the taxation on dividends is actually minimal, perhaps because dividends are paid primarily to individuals in low tax brackets or because institutions such as pension funds, which pay no taxes, are the primary recipients. However, Peterson, Peterson, and Ang conducted an in-depth study of dividends for one representative year, 1979.13 They found that about two-thirds of dividends went to individuals and that the average marginal tax bracket for these individuals was about 40 percent. Thus, we must conclude that large amounts of dividends are paid, even in the presence of substantial taxation.

Figure 19.8

Ratio of Aggregate Dividends to Aggregate Earnings for All U.S. Firms: 1959 to 2006

.8

Ratio of dividends to earnings

.7 .6 .5 .4 .3 .2 .1 0 1959 1962 1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 2004 Year SOURCE: The Economic Report of the President. February 2008, Table B-90.

13

P. Peterson, D. Peterson, and J. Ang, “Direct Evidence on the Marginal Rate of Taxation on Dividend Income,” Journal of Financial Economics 14 (1985).

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Figure 19.9 Proportion of Dividend Payers among All U.S. Industrial Firms

.35

.30

.25

.20

.15 2 1984

1 1986

1 1988

1 1990

1 1 1 1992 1994 1996 Quarter/Year

1 1998

1 2000

1 2002

1 2004

This table reports the proportion of U.S. industrial firms that paid dividends over the years from 1984 to 2004. The proportion dropped significantly from 1984 to 2002, with a rebound over the next two years. SOURCE:: Figure 1 of Brandon Julio and David Ikenberry, “Reappearing Dividends,” Journal of Applied Corporate Finance 16 (Fall 2004).

Fewer Companies Pay Dividends Although dividends are substantial, Fama and French (FF) point out that the percentage of companies paying dividends has fallen over the last few decades.14 FF argue that the decline was caused primarily by an explosion of small, currently unprofitable companies that have recently listed on various stock exchanges. For the most part, firms of this type do not pay dividends. Figure 19.9 shows that the proportion of dividend payers among U.S. industrial firms dropped substantially from 1984 to 2002. This figure, presented in a paper by Julio and Ikenberry (JI),15 also shows an increase in the proportion of dividend payers from 2002 to 2004. One obvious explanation is the cut in the maximum tax rate on dividends to 15 percent, signed into law in May 2003. However, JI downplay the effect of the tax cut, suggesting a number of other reasons. Furthermore, the resurgence in dividend payers has been observed only over the two-year period from 2002 to 2004. Perhaps this trend is just a statistical aberration.

14 E. F. Fama and K. R. French, “Disappearing Dividends: Changing Firm Characteristics or Lower Propensity to Pay?” Journal of Financial Economics (April 2001). 15 Brandon Julio and David Ikenberry, “Reappearing Dividends,” Journal of Applied Corporate Finance 16 (Fall 2004).

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Figure 19.9 does not imply that dividends across all firms declined from 1984 to 2002. DeAngelo, DeAngelo, and Skinner16 point out that while small firms have shied away from dividends, the largest firms have substantially increased their dividends over recent decades. This increase has created such concentration in dividends that the 25 top dividend-paying firms accounted for more than 50 percent of aggregate dividends in the United States in 2000. DeAngelo and colleagues conclude (p. 425), “Industrial firms exhibit a two-tier structure in which a small number of firms with very high earnings collectively generates the majority of earnings and dominates the dividend supply, while the vast majority of firms has at best a modest collective impact on aggregate earnings and dividends.”

CorporationsSmo othDi vidends In 1956, John Lintner made two important observations concerning dividend policy that still ring true.17 First, real-world companies typically set long-term target ratios of dividends to earnings. A firm is likely to set a low target ratio if it has many positive NPV projects relative to available cash flow and a high ratio if it has few positive NPV projects. Second, managers know that only part of any change in earnings is likely to be permanent. Because managers need time to assess the permanence of any earnings rise, dividend changes appear to lag earnings changes by a number of periods. Taken together, Lintner’s observations suggest that two parameters describe dividend policy: the target payout ratio (t) and the speed of adjustment of current dividends to the target (s). Dividend changes will tend to conform to the following model: Dividend change ≡ Div1 − Div0 = s ∙ (tEPS1 − Div0)

(19.6)

where Div1 and Div0 are dividends in the next year and dividends in the current year, respectively. EPS1 is earnings per share in the next year.

EXAMPLE 19.2

Dividend Smoothing Calculator Graphics, Inc., (CGI) has a target payout ratio of .30. Last year’s D eearnings per share were $10, and in accordance with the target, CGI paid dividends of $3 per share last year. However, earnings have jumped to $20 this year. Because the managers do not believe that this increase is permanent, they do not plan to raise dividends all the way to $6 (=.30 × $20). Rather, their speed of adjustment coefficient, s, is .5, implying that the increase in dividends from last year to this year will be: .5 × ($6 − $3) = $1.50 That is, the increase in dividends is the product of the speed of adjustment coefficient, .50, times the difference between what dividends would be with full adjustment [$6 (=.30 × $20)] and last year’s dividends. Dividends will increase by $1.50, so dividends this year will be $4.50 (=$3 + $1.50). Now, suppose that earnings stay at $20 next year. The increase in dividends next year will be: .5 × ($6 − $4.50) = $.75

(continued)

16

Harry DeAngelo, Linda DeAngelo, and Douglas Skinner, “Are Dividends Disappearing? Dividend Concentration and the Consolidation of Earnings,” Journal of Financial Economics(2004). 17

J. Lintner, “Distribution and Incomes of Corporations among Dividends, Retained Earnings, and Taxes,” American Economic Review (May 1956).

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In words, the increase in dividends from this year to next year will be the speed of adjustment coefficient (.50) times the difference between what dividends would have been next year with full adjustment ($6) and this year’s dividends ($4.50). Because dividends will increase by $.75, dividends next year will be $5.25 (=$4.50 + $.75). In this way, dividends will slowly rise every year if earnings in all future years remain at $20. However, dividends will reach $6 only at infinity.

The limiting cases in Equation 19.6 occur when s = 1 and s = 0. If s = 1, the actual change in dividends will be equal to the target change in dividends. Here, full adjustment occurs immediately. If s = 0, Div1 = Div0. In other words, there is no change in dividends at all. Real-world companies can be expected to set s between 0 and 1. An implication of Lintner’s model is that the dividends-to-earnings ratio rises when a company begins a period of bad times, and the ratio falls when a company starts a period of good times. Thus, dividends display less variability than do earnings. In other words, firms smoothd ividends.

The Pros and Cons of Paying Dividends Pros

Cons

1. Dividends may appeal to investors who desire stable cash flow but do not want to incur the transaction costs from periodically selling shares of stock.

1. Dividends are taxed as ordinary income.

2. Behavioral finance argues that investors with limited self-control can meet current consumption needs with highdividend stocks while adhering to the policy of never dipping into principal.

2. Dividends can reduce internal sources of financing. Dividends may force the firm to forgo positive NPV projects or to rely on costly external equity financing.

3. Managers, acting on behalf of stockholders, can pay dividends in order to keep cash from bondholders.

3. Once established, dividend cuts are hard to make without adversely affecting a firm’s stock price.

4. The board of directors, acting on behalf of stockholders, can use dividends to reduce the cash available to spendthrift managers. 5. Managers may increase dividends to signal their optimism concerning future cash flow.

Some Survey Evidence about Dividends A recent study surveyed a large number of financial executives regarding dividend policy. One of the questions asked was this: “Do these statements describe factors that affect your company’s dividend decisions?” Table 19.2 shows some of the results. As shown in Table 19.2, financial managers are very disinclined to cut dividends. Moreover, they are very conscious of their previous dividends and desire to maintain

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Table 19.2 Survey Responses on Dividend Decisions*

Percentage Who Agree or Strongly Agree

Policy Statements 1. We try to avoid reducing dividends per share. 2. We try to maintain a smooth dividend from year to year. 3. We consider the level of dividends per share that we have paid in recent quarters. 4. We are reluctant to make dividend changes that might have to be reversed in the future. 5. We consider the change or growth in dividends per share. 6. We consider the cost of raising external capital to be smaller than the cost of cutting dividends. 7. We pay dividends to attract investors subject to “prudent man” investment restrictions.

93.8% 89.6 88.2 77.9 66.7 42.8 41.7

*Survey respondents were asked the question, “Do these statements describe factors that affect your company’s dividend decisions?” SOURCE: Adapted from Table 4 of A. Brav, J. R. Graham, C. R. Harvey, and R. Michaely, “Payout Policy in the 21st Century,” Journal of Financial Economics (2005).

a relatively steady dividend. In contrast, the cost of external capital and the desire to attract “prudent man” investors (those with fiduciary duties) are less important. Table 19.3 is drawn from the same survey, but here the responses are to the question, “How important are the following factors to your company’s dividend decisions?” Not surprisingly given the responses in Table 19.2 and our earlier discussion, the highest priority is maintaining a consistent dividend policy. The next several items are also consistent with our previous analysis. Financial managers are very concerned about earnings stability and future earnings levels in making dividend decisions, and they consider the availability of good investment opportunities. Survey respondents also believed that attracting both institutional and individual (retail) investors was relatively important.

Table 19.3 Survey Responses on Dividend Decisions*

Policy Statements 1. Maintaining consistency with our historic dividend policy. 2. Stability of future earnings. 3. A sustainable change in earnings. 4. Attracting institutional investors to purchase our stock. 5. The availability of good investment opportunities for our firm to pursue. 6. Attracting retail investors to purchase our stock. 7. Personal taxes our stockholders pay when receiving dividends. 8. Flotation costs to issuing new equity.

Percentage Who Think This Is Important or Very Important

84.1% 71.9 67.1 52.5 47.6 44.5 21.1 9.3

*Survey respondents were asked the question, “How important are the following factors to your company’s dividend decisions?” SOURCE: Adapted from Table 5 of A. Brav, J. R. Graham, C. R. Harvey, and R. Michaely, “Payout Policy in the 21st Century,” Journal of Financial Economics (2005).

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In contrast to our discussion in the earlier part of this chapter of taxes and flotation costs, the financial managers in this survey did not think that personal taxes paid on dividends by shareholders are very important. And even fewer think that equity flotationc ostsar er elevant.

19.9 Putting It All Together Much of what we have discussed in this chapter (and much of what we know about dividends from decades of research) can be pulled together and summarized in the followingsixo bservations:18 1. Aggregate dividend and stock repurchases are massive, and they have increased steadily in nominal and real terms over the years. 2. Cash dividends and repurchases are heavily concentrated among a relatively small number of large, mature firms. 3. Managers are very reluctant to cut dividends, normally doing so only due to firmspecificp roblems. 4. Managers smooth dividends, raising them slowly and incrementally as earnings grow. 5. Stock prices react to unanticipated changes in dividends. 6. The magnitude of stock repurchases tends to vary with transitory earnings. The challenge now is to fit these five pieces into a reasonably coherent picture. With regard to payouts in general, meaning the combination of stock repurchases and cash dividends, a simple life cycle theory fits points 1 and 2. The key ideas are straightforward. First, relatively young firms with less available cash generally should not make cash distributions. They need the cash to fund positive NPV projects (and flotation costs discourage the raising of outside cash). However, as a firm survives and matures, it begins to generate free cash flow (which, you will recall, is internally generated cash flow beyond that needed to fund profitable investment activities). Significant free cash flow can lead to agency problems if it is not distributed. Managers may become tempted to pursue empire building or otherwise spend the excess cash in ways not in the shareholders’ best interests. Thus, firms come under shareholder pressure to make distributions rather than hoard cash. And, consistent with what we observe, we expect large firms with a history of profitability to make large distributions. Thus, the life cycle theory says that firms trade off the agency costs of excess cash retention against the potential future costs of external equity financing. A firm should begin making distributions when it generates sufficient internal cash flow to fund its investment needs now and into the foreseeable future. The more complex issue concerns the type of distribution, cash dividends versus repurchase. The tax argument in favor of repurchases is a clear and strong one. Repurchases are a much more flexible option (and managers greatly value financial flexibility), so the question is: Why would firms ever choose a cash dividend? If we are to answer this question, we have to ask a different question. What can a cash dividend accomplish that a share repurchase cannot? One answer is that when 18

This list is distilled in part from a longer list in Harry DeAngelo and Linda DeAngelo, “Payout Policy Pedagogy: What Matters and Why,” European Financial Management 13 (2007).

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a firm makes a commitment to pay a cash dividend now and into the future, it sends a two-part signal to the markets. As we have already discussed, one signal is that the firm anticipates being profitable, with the ability to make the payments on an ongoing basis. Note that a firm cannot benefit by trying to fool the market in this regard because the firm would ultimately be punished when it couldn’t make the dividend payment (or couldn’t make it without relying on external financing). Thus, a cash dividend may let a firm distinguish itself from less profitable rivals. A second, and more subtle, signal takes us back to the agency problem of free cash flow. By committing to pay cash dividends now and in the future, the firm signals that it won’t be hoarding cash (or at least not as much cash), thereby reducing agency costs and enhancing shareholder wealth. This two-part signaling story is consistent with points 3–5 above, but an obvious objection remains. Why don’t firms just commit to a policy of setting aside whatever money would be used to pay dividends and use it instead to buy back shares? After all, either way, a firm is committing to pay out cash to shareholders. A fixed repurchase strategy suffers from two drawbacks. The first is verifiability. A firm could announce an open market repurchase and then simply not do it. By suitably fudging its books, it would be some time before the deception was discovered. Thus, it would be necessary for shareholders to develop a monitoring mechanism, meaning some sort of way for stockholders to know for sure that the repurchase was in fact done. Such a mechanism wouldn’t be difficult to build (it could be a simple trustee relationship such as we observe in the bond markets), but it currently does not exist. Of course, a tender offer repurchase needs little or no verification, but such offers have expenses associated with them. The beauty of a cash dividend is that it needs no monitoring. A firm is forced to cut and mail checks four times a year, year in and year out.

Characteristics of a Sensible Payout Policy • • • • • •

Over time pay out all free cash flows. Avoid cutting positive NPV projects to pay dividends or buy back shares. Do not initiate dividends until the firm is generating substantial free cash flow. Set the current regular dividend consistent with a long-run target payout ratio. Set the level of dividends low enough to avoid expensive future external financing. Use repurchases to distribute transitory cash flow increases.

A second objection to a fixed repurchase strategy is more controversial. Suppose managers, as insiders, are better able than stockholders to judge whether their stock price is too high or too low. (Note that this idea does not conflict with semistrong market efficiency if inside information is the reason.) In this case, a fixed repurchase commitment forces management to buy back stock even in circumstances when the stock is overvalued. In other words, it forces management into making negative NPV investments. More research on the cash dividend versus share repurchase question is needed, but the historical trend seems to be favoring continued growth in repurchases relative to dividends. Total corporate payouts seem to be relatively stable over time at roughly 20 percent of aggregate earnings, but repurchases are becoming a larger portion of

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that total. The split reached about 50–50 in the latter part of the 1990s, but it looks like aggregate repurchases have recently passed aggregate dividends. One aspect of aggregate cash dividends that has not received much attention is that there may be a strong legacy effect. Before 1982, the regulatory status of stock repurchases was somewhat murky, creating a significant disincentive. In 1982, the SEC, after years of debate, created a clear set of guidelines for firms to follow, thereby making repurchases much more attractive. The legacy effect arises because many of the giant firms that pay such a large portion of aggregate dividends were paying dividends before (and perhaps long before) 1982. To the extent that these firms are unwilling to cut their dividends, aggregate cash dividends will be large, but only because of a “lock-in” effect for older firms. If locked-in, legacy payers account for much of the aggregate dividend, what we should observe is (1) a sharply reduced tendency for maturing firms to initiate dividends and (2) a growth in repurchases relative to cash dividends over time. We actually do see evidence of both of these trends; however, as the case of Microsoft clearly shows, legacy effects alone can’t account for all cash dividend payers.

19.10 Stock Dividends and Stock Splits Another type of dividend is paid out in shares of stock. This type of dividend is called a stock dividend. A stock dividend is not a true dividend because it is not paid in cash. The effect of a stock dividend is to increase the number of shares that each owner holds. Because there are more shares outstanding, each is simply worth less. A stock dividend is commonly expressed as a percentage; for example, a 20 percent stock dividend means that a shareholder receives one new share for every five currently owned (a 20 percent increase). Because every shareholder receives 20 percent more stock, the total number of shares outstanding rises by 20 percent. As we will see in a moment, the result is that each share of stock is worth about 20 percent less. A stock split is essentially the same thing as a stock dividend, except that a split is expressed as a ratio instead of a percentage. When a split is declared, each share is split up to create additional shares. For example, in a three-for-one stock split, each old share is split into three new shares.

Some Details about Stock Splits and Stock Dividends Stock splits and stock dividends have essentially the same impacts on the corporation and the shareholder They increase the number of shares outstanding and reduce the value per share. The accounting treatment is not the same, however, and it depends on two things: (1) whether the distribution is a stock split or a stock dividend and (2) the size of the stock dividend if it is called a dividend. By convention, stock dividends of less than 20 to 25 percent are called small stock dividends. The accounting procedure for such a dividend is discussed next. A stock dividend greater than this value of 20 to 25 percent is called a large stock dividend. Large stock dividends are not uncommon. For example, in April 2005, WellPoint (a health insurer) and Gentex (a manufacturer of automatic dimming rearview mirrors) both announced a 100 percent stock dividend. Except for some relatively minor accounting differences, this has the same effect as a two-for-one stock split. Example of a Small Stock Dividend The Peterson Co., a consulting firm specializing in difficult accounting problems, has 10,000 shares of stock outstanding, each

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selling at $66. The total market value of the equity is $66 × 10,000 = $660,000. With a 10 percent stock dividend, each stockholder receives one additional share for each 10 owned, and the total number of shares outstanding after the dividend is 11,000. Before the stock dividend, the equity portion of Peterson’s balance sheet might look like this: Common stock ($1 par, 10,000 shares outstanding) Capital in excess of par value Retained earnings Total owners’ equity

$ 10,000 200,000 290,000 $500,000

A seemingly arbitrary accounting procedure is used to adjust the balance sheet after a small stock dividend. Because 1,000 new shares are issued, the common stock account is increased by $1,000 (1,000 shares at $1 par value each), for a total of $11,000. The market price of $66 is $65 greater than the par value, so the “excess” of $65 × 1,000 shares = $65,000 is added to the capital surplus account (capital in excess of par value), producing a total of $265,000. Total owners’ equity is unaffected by the stock dividend because no cash has come in or out, so retained earnings are reduced by the entire $66,000, leaving $224,000. The net effect of these machinations is that Peterson’s equity accounts now look like this: Common stock ($1 par, 11,000 shares outstanding) Capital in excess of par value Retained earnings Total owners’ equity

$ 11,000 265,000 224,000 $500,000

Example of a Stock Split A stock split is conceptually similar to a stock dividend, but it is commonly expressed as a ratio. For example, in a three-for-two split, each shareholder receives one additional share of stock for each two held originally, so a three-for-two split amounts to a 50 percent stock dividend. Again, no cash is paid out, and the percentage of the entire firm that each shareholder owns is unaffected. The accounting treatment of a stock split is a little different from (and simpler than) that of a stock dividend. Suppose Peterson decides to declare a two-for-one stock split. The number of shares outstanding will double to 20,000, and the par value will be halved to $.50 per share. The owners’ equity after the split is represented as follows: For a list of recent stock splits, try www.stocksplits.net.

Common stock ($.50 par, 20,000 shares outstanding) Capital in excess of par value Retained earnings Total owners’ equity

$ 10,000 200,000 290,000 $500,000

Note that for all three of the categories, the figures on the right are completely unaffected by the split. The only changes are in the par value per share and the number of shares outstanding. Because the number of shares has doubled, the par value of each is cut in half.

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Example of a Large Stock Dividend In our example, if a 100 percent stock dividend were declared, 10,000 new shares would be distributed, so 20,000 shares would be outstanding. At a $1 par value per share, the common stock account would rise by $10,000, for a total of $20,000. The retained earnings account would be reduced by $10,000, leaving $280,000. The result would be the following: Common stock ($1 par, 20,000 shares outstanding) Capital in excess of par value Retained earnings Total owners’ equity

$ 20,000 200,000 280,000 $500,000

Value of Stock Splits and Stock Dividends The laws of logic tell us that stock splits and stock dividends can (1) leave the value of the firm unaffected, (2) increase its value, or (3) decrease its value. Unfortunately, the issues are complex enough that we cannot easily determine which of the three relationships holds. The Benchmark Case A strong case can be made that stock dividends and splits do not change either the wealth of any shareholder or the wealth of the firm as a whole. In our preceding example, the equity had a total market value of $660,000. With the small stock dividend, the number of shares increased to 11,000, so it seems that each would be worth $660,000 11,000 = $60. For example, a shareholder who had 100 shares worth $66 each before the dividend would have 110 shares worth $60 each afterward. The total value of the stock is $6,600 either way; so the stock dividend doesn’t really have any economic effect. After the stock split, there are 20,000 shares outstanding, so each should be worth $660,000 20,000 = $33. In other words, the number of shares doubles and the price halves. From these calculations, it appears that stock dividends and splits are just paper transactions. Although these results are relatively obvious, there are reasons that are often given to suggest that there may be some benefits to these actions. The typical financial manager is aware of many real-world complexities, and for that reason the stock split or stock dividend decision is not treated lightly in practice. Popular Trading Range Proponents of stock dividends and stock splits frequently argue that a security has a proper trading range. When the security is priced above this level, many investors do not have the funds to buy the common trading unit of 100 shares, called a round lot. Although securities can be purchased in odd-lot form (fewer than 100 shares), the commissions are greater. Thus, firms will split the stock to keep the price in this trading range. For example, in early 2003, Microsoft announced a two-for-one stock split. This was the ninth split for Microsoft since the company went public in 1986. The stock had split three-for-two on two occasions and two-for-one a total of seven times. So for every share of Microsoft you owned in 1986 when the company first went public, you would own 288 shares as of the most recent stock split in 2003. Similarly, since Wal-Mart went public in 1970, it has split its stock two-for-one 11 times, and Dell Computer has split three-for-two once and two-for-one six times since going public in 1988. Although this argument of a trading range is a popular one, its validity is questionable for a number of reasons. Mutual funds, pension funds, and other institutions

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have steadily increased their trading activity since World War II and now handle a sizable percentage of total trading volume (on the order of 80 percent of NYSE trading volume, for example). Because these institutions buy and sell in huge amounts, the individual share price is of little concern. Furthermore, we sometimes observe share prices that are quite large that do not appear to cause problems. To take an extreme case, consider the Swiss chocolatier Lindt. In February 2006, Lindt shares were selling for around 24,595 Swiss francs each, or about $18,818. A round lot would have cost a cool $1.88 million. This is fairly expensive, but also consider Berkshire-Hathaway, the company run by legendary investor Warren Buffett. In February 2006, each share in the company sold for about $88,000, down from a high of $95,700 in February 2004. Finally, there is evidence that stock splits may actually decrease the liquidity of the company’s shares. Following a two-for-one split, the number of shares traded should more than double if liquidity is increased by the split. This doesn’t appear to happen, and the reverse is sometimes observed.

ReverseSpl its A less frequently encountered financial maneuver is the reverse split. For example, in February 2006, Avitar, Inc., a medical products manufacturer, underwent a one-for-fifty reverse stock split, and AVANIR Pharmaceuticals undertook a one-for-four reverse stock split in January 2006. In a one-for-five reverse split, each investor exchanges five old shares for one new share. The par value is quintupled in the process. As with stock splits and stock dividends, a case can be made that a reverse split has no real effect. Given real-world imperfections, three related reasons are cited for reverse splits. First, transaction costs to shareholders may be less after the reverse split. Second, the liquidity and marketability of a company’s stock might be improved when its price is raised to the popular trading range. Third, stocks selling at prices below a certain level are not considered respectable, meaning that investors underestimate these firms’ earnings, cash flow, growth, and stability. Some financial analysts argue that a reverse split can achieve instant respectability. As was the case with stock splits, none of these reasons is particularly compelling, especially not the third one. There are two other reasons for reverse splits. First, stock exchanges have minimum price per share requirements. A reverse split may bring the stock price up to such a minimum. In 2001–2002, in the wake of a bear market, this motive became an increasingly important one. In 2001, 106 companies asked their shareholders to approve reverse splits. There were 111 reverse splits in 2002 and 75 in 2003, but only 14 by midyear 2004. The most common reason for these reverse splits is that NASDAQ delists companies whose stock price drops below $1 per share for 30 days. Many companies, particularly Internet-related technology companies, found themselves in danger of being delisted and used reverse splits to boost their stock prices. Second, companies sometimes perform reverse splits and, at the same time, buy out any stockholders who end up with less than a certain number of shares. For example, in October 2005, Sagient Research Systems, a publisher of independent financial research, announced a 1-for-101 reverse stock split. At the same time, the company would repurchase all shares held by shareholders with fewer than 100 shares. The purpose of the reverse split was to allow the company to go dark. The reverse split and share repurchase meant the company would have fewer than 300 shareholders, so it would no longer be required to file periodic reports with the SEC. What made the proposal especially imaginative was that immediately after the reverse stock split, the company underwent a 101-for-1 split to restore the stock to its original price!

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Concept Questions

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1. The dividend policy of a firm is irrelevant in a perfect capital market because the shareholder can effectively undo the firm’s dividend strategy. If a shareholder receives a greater dividend than desired, he or she can reinvest the excess. Conversely, if the shareholder receives a smaller dividend than desired, he or she can sell off extra shares of stock. This argument is due to MM and is similar to their homemade leverage concept, discussed in a previous chapter. 2. Stockholders will be indifferent between dividends and share repurchases in a perfect capitalmar ket. 3. Because dividends in the United States are taxed, companies should not issue stock to pay out a dividend. 4. Also because of taxes, firms have an incentive to reduce dividends. For example, they might consider increasing capital expenditures, acquiring other companies, or purchasing financial assets. However, due to financial considerations and legal constraints, rational firms with large cash flows will likely exhaust these activities with plenty of cash left over for dividends. 5. In a world with personal taxes, a strong case can be made for repurchasing shares instead of paying dividends. 6. Nevertheless, there are a number of justifications for dividends even in a world with personalt axes: a. Investors in no-dividend stocks incur transaction costs when selling off shares for currentc onsumption. b. Behavioral finance argues that investors with limited self-control can meet current consumption needs via high-dividend stocks while adhering to a policy of “never dipping into principal.” c. Managers, acting on behalf of stockholders, can pay dividends to keep cash from bondholders. The board of directors, also acting on behalf of stockholders, can use dividends to reduce the cash available to spendthrift managers. 7. The stock market reacts positively to increases in dividends (or an initial payment) and negatively to decreases in dividends. This suggests that there is information content in dividendp ayments. 8. High (low) dividend firms should arise to meet the demands of dividend-preferring (capital gains–preferring) investors. Because of these clienteles, it is not clear that a firm can create value by changing its dividend policy.

1. 2. 3.

4.

Dividend Policy Irrelevance How is it possible that dividends are so important, but at the same time dividend policy is irrelevant? Stock Repurchases What is the impact of a stock repurchase on a company’s debt ratio? Does this suggest another use for excess cash? Dividend Policy It is sometimes suggested that firms should follow a “residual” dividend policy. With such a policy, the main idea is that a firm should focus on meeting its investment needs and maintaining its desired debt–equity ratio. Having done so, a firm pays out any leftover, or residual, income as dividends. What do you think would be the chief drawback to a residual dividend policy? Dividend Chronology On Tuesday, December 8, Hometown Power Co.’s board of directors declares a dividend of 75 cents per share payable on Wednesday, January 17, to shareholders of record as of Wednesday, January 3. When is the exdividend date? If a shareholder buys stock before that date, who gets the dividends on those shares—the buyer or the seller?

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Alternative Dividends Some corporations, like one British company that offers its large shareholders free crematorium use, pay dividends in kind (that is, offer their services to shareholders at below-market cost). Should mutual funds invest in stocks that pay these dividends in kind? (The fundholders do not receive these services.) 6. Dividends and Stock Price If increases in dividends tend to be followed by (immediate) increases in share prices, how can it be said that dividend policy is irrelevant? 7. Dividends and Stock Price Last month, Central Virginia Power Company, which had been having trouble with cost overruns on a nuclear power plant that it had been building, announced that it was “temporarily suspending payments due to the cash flow crunch associated with its investment program.” The company’s stock price dropped from $28.50 to $25 when this announcement was made. How would you interpret this change in the stock price? (That is, what would you say caused it?) 8. Dividend Reinvestment Plans The DRK Corporation has recently developed a dividend reinvestment plan, or DRIP. The plan allows investors to reinvest cash dividends automatically in DRK in exchange for new shares of stock. Over time, investors in DRK will be able to build their holdings by reinvesting dividends to purchase additional shares of the company. Over 1,000 companies offer dividend reinvestment plans. Most companies with DRIPs charge no brokerage or service fees. In fact, the shares of DRK will be purchased at a 10 percent discount from the market price. A consultant for DRK estimates that about 75 percent of DRK’s shareholders will take part in this plan. This is somewhat higher than the average. Evaluate DRK’s dividend reinvestment plan. Will it increase shareholder wealth? Discuss the advantages and disadvantages involved here. 9. Dividend Policy For initial public offerings of common stock, 2007 was a relatively slow year, with only about $35.6 billion raised by the process. Relatively few of the 159 firms involved paid cash dividends. Why do you think that most chose not to pay cashd ividends? 10. Investment and Dividends The Phew Charitable Trust pays no taxes on its capital gains or on its dividend income or interest income. Would it be irrational for it to have low-dividend, high-growth stocks in its portfolio? Would it be irrational for it to have municipal bonds in its portfolio? Explain. Use the following information to answer the next two questions: Historically, the U.S. tax code treated dividend payments made to shareholders as ordinary income. Thus, dividends were taxed at the investor’s marginal tax rate, which was as high as 38.6 percent in 2002. Capital gains were taxed at a capital gains tax rate, which was the same for most investors and fluctuated through the years. In 2002, the capital gains tax rate stood at 20 percent. In an effort to stimulate the economy, President George W. Bush presided over a tax plan overhaul that included changes in dividend and capital gains tax rates. The new tax plan, which was implemented in 2003, called for a 15 percent tax rate on both dividends and capital gains for investors in higher tax brackets. For lower tax bracket investors, the tax rate on dividends and capital gains was set at 5 percent through 2007, dropping to zero in 2008. 11. Ex-Dividend Stock Prices How do you think this tax law change affects ex-dividend stockp rices? 12. Stock Repurchases How do you think this tax law change affected the relative attractiveness of stock repurchases compared to dividend payments? 13. Dividends and Stock Value The growing perpetuity model expresses the value of a share of stock as the present value of the expected dividends from that stock. How can you conclude that dividend policy is irrelevant when this model is valid? 5.

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20.

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2. BASIC (Questions 1–10)

Capital Structure and Dividend Policy

Bird-in-the-Hand Argument The bird-in-the-hand argument, which states that a dividend today is safer than the uncertain prospect of a capital gain tomorrow, is often used to justify high dividend payout ratios. Explain the fallacy behind this argument. Dividends and Income Preference The desire for current income is not a valid explanation of preference for high current dividend policy because investors can always create homemade dividends by selling a portion of their stocks. Is this statement true or false? Why? Dividends and Clientele Cap Henderson owns Neotech stock because its price has been steadily rising over the past few years and he expects this performance to continue. Cap is trying to convince Sarah Jones to purchase some Neotech stock, but she is reluctant because Neotech has never paid a dividend. She depends on steady dividends to provide her with income. a. What preferences are these two investors demonstrating? b. What argument should Cap use to convince Sarah that Neotech stock is the stock forh er? c. Why might Cap’s argument not convince Sarah? Dividends and Taxes Your aunt is in a high tax bracket and would like to minimize the tax burden of her investment portfolio. She is willing to buy and sell to maximize her aftertax returns, and she has asked for your advice. What would you suggest she do? Dividends versus Capital Gains If the market places the same value on $1 of dividends as on $1 of capital gains, then firms with different payout ratios will appeal to different clienteles of investors. One clientele is as good as another; therefore, a firm cannot increase its value by changing its dividend policy. Yet empirical investigations reveal a strong correlation between dividend payout ratios and other firm characteristics. For example, small, rapidly growing firms that have recently gone public almost always have payout ratios that are zero; all earnings are reinvested in the business. Explain this phenomenon if dividend policy is irrelevant. Dividend Irrelevancy In spite of the theoretical argument that dividend policy should be irrelevant, the fact remains that many investors like high dividends. If this preference exists, a firm can boost its share price by increasing its dividend payout ratio. Explain the fallacy in this argument. Dividends and Stock Price Empirical research has found that there have been significant increases in stock price on the day an initial dividend (i.e., the first time a firm pays a cash dividend) is announced. What does this finding imply about the information content of initial dividends?

Dividends and Taxes Lee Ann, Inc., has declared a $5.60 per-share dividend. Suppose capital gains are not taxed, but dividends are taxed at 15 percent. New IRS regulations require that taxes be withheld when the dividend is paid. Lee Ann sells for $75 per share, and the stock is about to go ex dividend. What do you think the ex-dividend price will be? Stock Dividends The owners’ equity accounts for Hexagon International are shown here: Common stock ($1 par value) Capital surplus Retained earnings Total owners’ equity

$ 20,000 210,000 735,300 $965,300

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a. If Hexagon stock currently sells for $48 per share and a 10 percent stock dividend is declared, how many new shares will be distributed? Show how the equity accounts would change. b. If Hexagon declared a 25 percent stock dividend, how would the accounts change? Stock Splits For the company in Problem 2, show how the equity accounts will change if: a. Hexagon declares a four-for-one stock split. How many shares are outstanding now? What is the new par value per share? b. Hexagon declares a one-for-five reverse stock split. How many shares are outstanding now? What is the new par value per share? Stock Splits and Stock Dividends Roll Corporation (RC) currently has 260,000 shares of stock outstanding that sell for $78 per share. Assuming no market imperfections or tax effects exist, what will the share price be after: a. RC has a five-for-three stock split? b. RC has a 15 percent stock dividend? c. RC has a 42.5 percent stock dividend? d. RC has a four-for-seven reverse stock split? Determine the new number of shares outstanding in parts (a) through (d). Regular Dividends The balance sheet for Levy Corp. is shown here in market value terms. There are 8,000 shares of stock outstanding.

Cash

$ 30,000

Fixed assets

$380,000

Total

6.

7.

Equity

$380,000

350,000 Total

$380,000

The company has declared a dividend of $1.60 per share. The stock goes ex dividend tomorrow. Ignoring any tax effects, what is the stock selling for today? What will it sell for tomorrow? What will the balance sheet look like after the dividends are paid? Share Repurchase In the previous problem, suppose Levy has announced it is going to repurchase $12,800 worth of stock. What effect will this transaction have on the equity of the firm? How many shares will be outstanding? What will the price per share be after the repurchase? Ignoring tax effects, show how the share repurchase is effectively the same as a cash dividend. Stock Dividends The market value balance sheet for Outbox Manufacturing is shown here. Outbox has declared a 25 percent stock dividend. The stock goes ex dividend tomorrow (the chronology for a stock dividend is similar to that for a cash dividend). There are 20,000 shares of stock outstanding. What will the ex-dividend price be? Market Value Balance Sheet Cash Fixed assets Total

8.

$230,000

Debt

415,000

Equity

$645,000

Total

$190,000 455,000 $645,000

Stock Dividends The company with the common equity accounts shown here has declared a 12 percent stock dividend when the market value of its stock is $45 per

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share. What effects on the equity accounts will the distribution of the stock dividend have? Common stock ($1 par value) Capital surplus Retained earnings Total owners’ equity

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INTERMEDIATE (Questions 11–16)

11.

12. 13.

14.

$ 380,000 1,750,000 4,150,000 $6,280,000

Stock Splits In the previous problem, suppose the company instead decides on a five-for-one stock split. The firm’s 60 cent per share cash dividend on the new (postsplit) shares represents an increase of 10 percent over last year’s dividend on the presplit stock. What effect does this have on the equity accounts? What was last year’s dividend per share? Dividends and Stock Price The Mann Company belongs to a risk class for which the appropriate discount rate is 10 percent. Mann currently has 150,000 outstanding shares selling at $120 each. The firm is contemplating the declaration of a $5 dividend at the end of the fiscal year that just began. Assume there are no taxes on dividends. Answer the following questions based on the Miller and Modigliani model, which is discussed in the text. a. What will be the price of the stock on the ex-dividend date if the dividend is declared? b. What will be the price of the stock at the end of the year if the dividend is not declared? c. If Mann makes $3 million of new investments at the beginning of the period, earns net income of $1.4 million, and pays the dividend at the end of the year, how many shares of new stock must the firm issue to meet its funding needs? d. Is it realistic to use the MM model in the real world to value stock? Why or why not? Homemade Dividends You own 1,000 shares of stock in Avondale Corporation. You will receive a 95 cent per share dividend in one year. In two years, Avondale will pay a liquidating dividend of $45 per share. The required return on Avondale stock is 14 percent. What is the current share price of your stock (ignoring taxes)? If you would rather have equal dividends in each of the next two years, show how you can accomplish this by creating homemade dividends. (Hint: Dividends will be in the form of an annuity.) Homemade Dividends In the previous problem, suppose you want only $500 total in dividends the first year. What will your homemade dividend be in two years? Stock Repurchase Flychucker Corporation is evaluating an extra dividend versus a share repurchase. In either case $3,000 would be spent. Current earnings are $1.50 per share, and the stock currently sells for $58 per share. There are 600 shares outstanding. Ignore taxes and other imperfections in answering parts (a) and (b). a. Evaluate the two alternatives in terms of the effect on the price per share of the stock and shareholder wealth. b. What will be the effect on Flychucker’s EPS and PE ratio under the two different scenarios? c. In the real world, which of these actions would you recommend? Why? Dividends and Firm Value The net income of Novis Corporation is $45,000. The company has 20,000 outstanding shares and a 100 percent payout policy. The expected value of the firm one year from now is $1,635,000. The appropriate discount rate for Novis is 12 percent, and the dividend tax rate is zero. a. What is the current value of the firm assuming the current dividend has not yet beenp aid?

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17.

18.

b. What is the ex-dividend price of Novis’s stock if the board follows its current policy? c. At the dividend declaration meeting, several board members claimed that the dividend is too meager and is probably depressing Novis’s price. They proposed that Novis sell enough new shares to finance a $4.60 dividend. i. Comment on the claim that the low dividend is depressing the stock price. Support your argument with calculations. ii. If the proposal is adopted, at what price will the new shares sell? How many willb es old? Dividend Policy Gibson Co. has a current period cash flow of $1.4 million and pays no dividends. The present value of the company’s future cash flows is $20 million. The company is entirely financed with equity and has 750,000 shares outstanding. Assume the dividend tax rate is zero. a. What is the share price of the Gibson stock? b. Suppose the board of directors of Gibson Co. announces its plan to pay out 50 percent of its current cash flow as cash dividends to its shareholders. How can Jeff Miller, who owns 1,000 shares of Gibson stock, achieve a zero payout policy on his own? Dividend Smoothing The Sharpe Co. just paid a dividend of $1.50 per share of stock. Its target payout ratio is 40 percent. The company expects to have an earnings per share of $4.15 one year from now. a. If the adjustment rate is .3 as defined in the Lintner model, what is the dividend one year from now? b. If the adjustment rate is .6 instead, what is the dividend one year from now? c. Whichad justmentr ateis mo rec onservative?W hy? Expected Return, Dividends, and Taxes The Gecko Company and the Gordon Company are two firms whose business risk is the same but that have different dividend policies. Gecko pays no dividend, whereas Gordon has an expected dividend yield of 6 percent. Suppose the capital gains tax rate is zero, whereas the dividend tax rate is 35 percent. Gecko has an expected earnings growth rate of 12 percent annually, and its stock price is expected to grow at this same rate. If the aftertax expected returns on the two stocks are equal (because they are in the same risk class), what is the pretax required return on Gordon’s stock? Dividends and Taxes As discussed in the text, in the absence of market imperfections and tax effects, we would expect the share price to decline by the amount of the dividend payment when the stock goes ex dividend. Once we consider the role of taxes, however, this is not necessarily true. One model has been proposed that incorporates tax effects into determining the ex-dividend price:19 (P0 − PX) D = (1 − tP) (1 − tG) Here P0 is the price just before the stock goes ex, PX is the ex-dividend share price, D is the amount of the dividend per share, tP is the relevant marginal personal tax rate on dividends, and tG is the effective marginal tax rate on capital gains. a. If tP = tG = 0, how much will the share price fall when the stock goes ex? b. If tP = 15 percent and tG = 0, how much will the share price fall? c. If tP = 15 percent and tG = 20 percent, how much will the share price fall? d. Suppose the only owners of stock are corporations. Recall that corporations get at least a 70 percent exemption from taxation on the dividend income they receive, but they do not get such an exemption on capital gains. If the corporation’s income and capital gains tax rates are both 35 percent, what does this model predict the ex-dividend share price will be?

19 N. Elton and M. Gruber, “Marginal Stockholder Tax Rates and the Clientele Effect,” Review of Economics and Statistics 52 (February 1970).

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CHALLENGE (Questions 17–20)

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19.

20.

Mini Case

S&P Problem

Capital Structure and Dividend Policy

e. What does this problem tell you about real-world tax considerations and the dividend policy of the firm? Dividends versus Reinvestment National Business Machine Co. (NBM) has $3 million of extra cash after taxes have been paid. NBM has two choices to make use of this cash. One alternative is to invest the cash in financial assets. The resulting investment income will be paid out as a special dividend at the end of three years. In this case, the firm can invest in either Treasury bills yielding 5 percent or 7 percent preferred stock. IRS regulations allow the company to exclude from taxable income 70 percent of the dividends received from investing in another company’s stock. Another alternative is to pay out the cash now as dividends. This would allow the shareholders to invest on their own in Treasury bills with the same yield or in preferred stock. The corporate tax rate is 35 percent. Assume the investor has a 31 percent personal income tax rate, which is applied to interest income and preferred stock dividends. The personal dividend tax rate is 15 percent on common stock dividends. Should the cash be paid today or in three years? Which of the two options generates the highest aftertax income for the shareholders? Dividends versus Reinvestment After completing its capital spending for the year, Carlson Manufacturing has $1,000 extra cash. Carlson’s managers must choose between investing the cash in Treasury bonds that yield 8 percent or paying the cash out to investors who would invest in the bonds themselves. a. If the corporate tax rate is 35 percent, what personal tax rate would make the investors equally willing to receive the dividend or to let Carlson invest the money? b. Is the answer to (a) reasonable? Why or why not? c. Suppose the only investment choice is a preferred stock that yields 12 percent. The corporate dividend exclusion of 70 percent applies. What personal tax rate will make the stockholders indifferent to the outcome of Carlson’s dividend decision? d. Is this a compelling argument for a low dividend payout ratio? Why or why not?

www.mhhe.com/edumarketinsight 1. Dividend Payouts Use the annual financial statements for General Mills (GIS), Boston Beer (SAM), and US Steel (X) to find the dividend payout ratio for each company for the last three years. Why would these companies pay out a different percentage of income as dividends? Is there anything unusual about the dividends paid by US Steel? How is this possible?

ELECTRONIC TIMING, INC. Electronic Timing, Inc. (ETI), is a small company founded 15 years ago by electronics engineers Tom Miller and Jessica Kerr. ETI manufactures integrated circuits to capitalize on the complex mixed-signal design technology and has recently entered the market for frequency timing generators, or silicon timing devices, which provide the timing signals or “clocks” necessary to synchronize electronic systems. Its clock products originally were used in PC video graphics applications, but the market subsequently expanded to include motherboards, PC peripheral devices, and other digital consumer electronics, such as digital television boxes and game consoles. ETI also designs and markets custom applicationspecific integrated circuits (ASICs) for industrial customers. The ASIC’s design combines analog and digital, or mixed-signal, technology. In addition to Tom and Jessica, Nolan Pittman, who provided capital for the company, is the third primary owner. Each owns 25 percent of the 1 million shares outstanding. Several other individuals, including current employees, own the remaining company shares.

Chapter 19 Dividends and Other Payouts

615

Recently, the company designed a new computer motherboard. The company’s design is both more efficient and less expensive to manufacture, and the ETI design is expected to become standard in many personal computers. After investigating the possibility of manufacturing the new motherboard, ETI determined that the costs involved in building a new plant would be prohibitive. The owners also decided that they were unwilling to bring in another large outside owner. Instead, ETI sold the design to an outside firm. The sale of the motherboard design was completed for an aftertax payment of $30 million. 1. Tom believes the company should use the extra cash to pay a special one-time dividend. How will this proposal affect the stock price? How will it affect the value of the company? 2. Jessica believes that the company should use the extra cash to pay off debt and upgrade and expand its existing manufacturing capability. How would Jessica’s proposals affect the company? 3. Nolan is in favor of a share repurchase. He argues that a repurchase will increase the company’s P/E ratio, return on assets, and return on equity. Are his arguments correct? How will a share repurchase affect the value of the company? 4. Another option discussed by Tom, Jessica, and Nolan would be to begin a regular dividend payment to shareholders. How would you evaluate this proposal? 5. One way to value a share of stock is the dividend growth, or growing perpetuity, model. Consider the following: The dividend payout ratio is 1 minus b, where bis the “retention” or “plowback” ratio. So, the dividend next year will be the earnings next year, E1, times 1 minus the retention ratio. The most commonly used equation to calculate the sustainable growth rate is the return on equity times the retention ratio. Substituting these relationships into the dividend growth model, we get the following equation to calculate the price of a share of stock today: E1(1 − b) P0 = _____________ RS − ROE × b What are the implications of this result in terms of whether the company should pay a dividend or upgrade and expand its manufacturing capability? Explain. 6. Does the question of whether the company should pay a dividend depend on whether thec ompanyis o rganizedas ac orporationo ran L LC?

PART V

CHAPTER 20

Issuing Securities to the Public In an eagerly awaited initial public offering (IPO), credit card giant Visa went public on March 19, 2008. Assisted by JPMorgan, Goldman Sachs, and Bank of America, Visa sold about 447 million shares of stock to the public at a price of $44. In a nod to the public’s unfortunate fascination with credit, the stock price jumped to $56.50 at the end of the day, a 28 percent increase. The Visa offer raised a total of $19.65 billion, easily the largest IPO in U.S. history. The previous record-holder was the AT&T Wireless offering in 2000, which raised $10.6 billion. In this chapter, we will examine the process by which companies such as Visa sell stock to the public, the costs of doing so, and the role of investment banks in the process. Businesses large and small have one thing in common: They need long-term capital. This chapter describes how they get it. We pay particular attention to what is probably the most important stage in a company’s financial life cycle—the IPO. Such offerings are the process by which companies convert from being privately owned to publicly owned. For many people, starting a company, growing it, and taking it public is the ultimate entrepreneurial dream.

20.1 The Public Issue When firms want to raise new funds, they can do so by issuing securities publicly or privately. We first describe the public issue. The basic steps in a public offering are depicted in Table 20.1. The Securities Act of 1933 sets forth the federal regulation for all new interstate securities issues. The Securities Exchange Act of 1934 is the basis for regulating securities already outstanding. The SEC administers both acts.

The Basic Procedure for a New Issue 1. Management’s first step in any issue of securities to the public is to obtain approval from the board of directors. 2. Next, the firm must prepare and file a registration statement with the SEC. This statement contains a great deal of financial information, including a financial history, details of the existing business, proposed financing, and plans for the future. It can easily run to 50 or more pages. The document is required for all public issues of securities with two principal exceptions: a. Loans that mature within nine months. b. Issues that involve less than $5.0 million. The second exception is known as the small-issues exemption. Issues of less than $5.0 million are governed by RegulationA , for which only a brief offering statement—rather than the full registration statement—is needed. For Regulation A to be operative, no more than $1.5 million may be sold by insiders. 3. The SEC studies the registration statement during a waiting period. During this time, the firm may distribute copies of a preliminary prospectus. The preliminary 616

Chapter 20

Table 20.1

Issuing Securities to the Public

617

The Process of Raising Capital

Steps in Public Offering

Time

Activities

1. Pre-underwriting conferences

Several months

2. Registration statements filed and approved 3. Pricing the issue

A 20-day waiting period Usually not before the last day of the registration period Shortly after the last day of the registration period Usually 30 days after the offering

The amount of money to be raised and the type of security to be issued are discussed. The underwriting syndicate and selling group are put together. The underwriting contract is negotiated. Board approval is obtained. The registration statement contains all relevant financial and business information. For seasoned offerings, the price is set close to the prevailing market price. For initial public offerings, intensive research and analysis are required. In a typical firm commitment contract, the underwriter buys a stipulated amount of stock from the firm and sells it at a higher price. The selling group assists in the sale. The underwriter stands ready to place orders to buy at a specified price on the market.

4. Public offering and sale

5. Market stabilization

prospectus iis called ll d a red herring b because b bold ld red d lletters are printed i d on the h cover. A prospectus contains much of the information put into the registration statement, and it is given to potential investors by the firm. The company cannot sell the securities during the waiting period. However, oral offers can be made. A registration statement will become effective on the 20th day after its filing unless the SEC sends a letter of comment suggesting changes. After the changes are made, the 20-day waiting period starts anew. 4. The registration statement does not initially contain the price of the new issue. On the effective date of the registration statement, a price is determined and a full-fledged selling effort gets under way. A final prospectus must accompany the delivery of securities or confirmation of sale, whichever comes first. 5. Tombstone advertisements are used during and after the waiting period. An example is reproduced in Figure 20.1.

20.2 AlternativeIssueMet hods When a company decides to issue a new security, it can sell it as a public issue or a private issue. If it is a public issue, the firm is required to register the issue with the SEC. If the issue is sold to fewer than 35 investors, it can be treated as a private issue. A registration statement is not required in this case.1 There are two kinds of public issues: the general cash offer and the rights offer. Cash offers are sold to all interested investors, and rights offers are sold to existing shareholders. Equity is sold by both the cash offer and the rights offer, though almost all debt is sold by cash offer. The first public equity issue that is made by a company is referred to as an initial public offering (IPO) or an unseasoned new issue. All initial public offerings are cash offers because, if the firm’s existing shareholders wanted to buy the shares, the firm 1

However, regulation significantly restricts the resale of unregistered securities. The purchaser must hold the securities at least two years.

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Figure 20.1 An Example of a Tombstone Advertisement

Part V Long-Term Financing

This announcement is neither an offer to sell nor a solicitation of an offer to buy any of these securities. The offering is made only by the Prospectus.

New Issue

11,500,000 Shares

World Wrestling Federation Entertainment, Inc. Class A Common Stock Price $17.00 Per Share Copies of the Prospectus may be obtained in any State in which this announcement is circulated from only such of the Underwriters, including the undersigned, as may lawfully offer these securities in such State.

U.S. Offering

9,200,000 Shares This portion of the underwriting is being offered in the United States and Canada.

Bear, Stearns & Co., Inc. Credit Suisse First Boston Merrill Lynch & Co. Wit Capital Corporation Allen & Company

Banc of America Securities LLC

Incorporated

Donaldson, Lufkin & Jenrette Prudential Securities

A.G. Edwards & Sons, Inc. SG Cowen

Axiom Capital Management, Inc. Joseph Charles & Assoc., Inc. Gaines, Berland, Inc.

Deutsche Banc Alex. Brown Hambrecht & Quist

Wassertein Perella Securities, Inc. Blackford Securities Corp. Chatsworth Securities LLC

Jefferies & Company, Inc.

ING Barings Advest, Inc. J.C. Bradford & Co.

Gabelli & Company, Inc.

Josephthal & Co., Inc.

Raymond James & Associates, Inc.

Neuberger Berman, LLC Sanders Morris Mundy

Tucker Anthony Cleary Gull

Wachovia Securities, Inc.

International Offering

2,300,000 Shares This portion of the underwriting is being offered outside of the United States and Canada.

Bear, Stearns International Limited Credit Suisse First Boston Merrill Lynch International

Chapter 20

Table 20.2

Issuing Securities to the Public

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The Methods of Issuing New Securities

Method

Type

Definition

Public Traditional negotiated cash offer

Firm commitment cash offer

Company negotiates an agreement with an investment banker to underwrite and distribute the new shares. A specified number of shares are bought by underwriters and sold at a higher price. Company has investment bankers sell as many of the new shares as possible at the agreed-upon price. There is no guarantee concerning how much cash will be raised. Some best efforts offerings do not use an underwriter. Company has investment bankers auction shares to determine the highest offer price obtainable for a given number of shares to be sold. Company offers the new stock directly to its existing shareholders. Like the direct rights offer, this contains a privileged subscription arrangement with existing shareholders. The net proceeds are guaranteed by the underwriters. Qualifying companies can authorize all the shares they expect to sell over a two-year period and sell them when needed. Company can elect to award the underwriting contract through a public auction instead of negotiation. Securities are sold directly to the purchaser, who, at least until recently, generally could not resell the securities for at least two years.

Best-efforts cash offer

Dutch auction cash offer

Privileged subscription

Direct rights offer Standby rights offer

Nontraditional cash offer

Shelf cash offer

Private

Competitive firm cash offer Direct placement

would not need to sell them publicly. More than $28 billion was raised in 162 IPOs in 2005. A seasoned new issue refers to a new issue where the company’s securities have been previously issued. A seasoned new issue of common stock may be made by using a cash offer or a rights offer. These methods of issuing new securities are shown in Table 20.2 and discussed in then extfe wse ctions.2

20.3 TheCa sh Offer As just mentioned, stock is sold to all interested investors in a cash offer. If the cash offer is a public one, investment banks are usually involved. Investment banks are financial intermediaries that perform a wide variety of services. In addition to aiding in the sale of securities, they may facilitate mergers and other corporate reorganizations, act as brokers to both individual and institutional clients, and trade for their own accounts. You may well have heard of large Wall Street investment banking houses such as Goldman Sachs and Morgan Stanley.

2

Table 20.2 describes the main methods for issuing new securities in the United States. Most initial public offerings in the United States use the negotiated cash offer method known as bookbuilding.B ookbuilding refers to the way an underwriter builds a book of potential orders and uses the book to set a price. Bookbuilding is the method of equity underwriting choice in most (but not all) countries.

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For corporate issuers, investment bankers perform services such as the following: Formulating the method used to issue the securities. Pricingth en ews ecurities. Sellingth en ew securities. There are three basic methods of issuing securities for cash: 1. Firm commitment: Under this method, the investment bank (or a group of investment banks) buys the securities for less than the offering price and accepts the risk of not being able to sell them. Because this function involves risk, we say that the investment banker underwrites the securities in a firm commitment. In other words, when participating in a firm commitment offering, the investment banker acts as an underwriter. (Because firm commitments are so prevalent, we will use investment banker and underwriter interchangeably in this chapter.) To minimize the risks here, investment bankers combine to form an underwriting group (syndicate) to share the risk and to help sell the issue. In such a group, one or more managers arrange or comanage the deal. The manager is designated as the lead manager or principal manager. The lead manager typically has responsibility for all aspects of the issue. The other investment bankers in the syndicate serve primarily to sell the issue to their clients. The difference between the underwriter’s buying price and the offering price is called the spread or discount. It is the basic compensation received by the underwriter. Sometimes the underwriter will get noncash compensation in the form of warrants or stock in addition to the spread. Firm commitment underwriting is really just a purchase–sale arrangement, and the syndicate’s fee is the spread. The issuer receives the full amount of the proceeds less the spread, and all the risk is transferred to the underwriter. If the underwriter cannot sell all of the issue at the agreed-upon offering price, it may need to lower the price on the unsold shares. However, because the offering price usually is not set until the underwriters have investigated how receptive the market is to the issue, this risk is usually minimal. This is particularly true with seasoned new issues because the price of the new issue can be based on prior trades in the security. 2. Best efforts: The underwriter bears risk with a firm commitment because it buys the entire issue. Conversely, the syndicate avoids this risk under a best-efforts offering because it does not purchase the shares. Instead, it merely acts as an agent, receiving a commission for each share sold. The syndicate is legally bound to use its best efforts to sell the securities at the agreed-upon offering price. If the issue cannot be sold at the offering price, it is usually withdrawn. This form of underwriting has become relatively rare. 3. Dutch auction underwriting: With Dutch auction underwriting, the underwriter does not set a fixed price for the shares to be sold. Instead, the underwriter conducts an auction in which investors bid for shares. The offer price is determined based on the submitted bids. A Dutch auction is also known by the more descriptive name uniform price auction. This approach to selling securities to the public is relatively new in the IPO market and has not been widely used there, but it is very common in the bond markets. For example, it is the sole procedure used by the U.S. Treasury to sell enormous quantities of notes, bonds, and bills to the public. Dutch auction underwriting was much in the news in 2004 because Web search company Google elected to use this approach. The best way to understand a

Chapter 20

Issuing Securities to the Public

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Dutch or uniform price auction is to consider a simple example. Suppose the Rial Company wants to sell 400 shares to the public. The company receives five bids as follows: Bidder

Quantity

Price

A B C D E

100 shares 100 shares 100 shares 200 shares 200 shares

$16 14 12 12 10

Thus, bidder A is willing to buy 100 shares at $16 each, bidder B is willing to buy 100 shares at $14, and so on. The Rial Company examines the bids to determine the highest price that will result in all 400 shares being sold. For example, at $14, A and B would buy only 200 shares, so that price is too high. Working our way down, all 400 shares won’t be sold until we hit a price of $12, so $12 will be the offer price in the IPO. Bidders A through D will receive shares; bidder E will not. There are two additional important points to observe in our example. First, all the winning bidders will pay $12—even bidders A and B, who actually bid a higher price. The fact that all successful bidders pay the same price is the reason for the name “uniform price auction.” The idea in such an auction is to encourage bidders to bid aggressively by providing some protection against bidding a price that is too high. Second, notice that at the $12 offer price, there are actually bids for 500 shares, which exceeds the 400 shares Rial wants to sell. Thus, there has to be some sort of allocation. How this is done varies a bit; but in the IPO market the approach has been to simply compute the ratio of shares offered to shares bid at the offer price or better, which, in our example, is 400/500 = .8, and allocate bidders that percentage of their bids. In other words, bidders A through D would each receive 80 percent of the shares they bid at a price of $12 per share. In most offerings, the principal underwriter is permitted to buy shares if the market price falls below the offering price. The purpose is to support the market and stabilize the price from temporary downward pressure. If the issue remains unsold after a time (for example, 30 days), members may leave the group and sell their shares at whatever price the market will allow. Many underwriting contracts contain a Green Shoe provision, which gives the members of the underwriting group the option to purchase additional shares at the offering price.3 The stated reason for the Green Shoe option is to cover excess demand and oversubscription. Green Shoe options usually last for about 30 days and involve no more than 15 percent of the newly issued shares. The Green Shoe option is a benefit to the underwriting syndicate and a cost to the issuer. If the market price of the new issue goes above the offering price within 30 days, the underwriters can buy shares from the issuer and immediately resell the shares to the public. The period after a new issue is initially sold to the public is called the aftermarket. During this period, the members of the underwriting syndicate generally do not sell shares of the new issue for less than the offer price. 3

The Green Shoe Corp. was the first firm to allow this provision.

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Almost all underwriting agreements contain lockups. Such arrangements specify how long insiders must wait after an IPO before they can sell some of their stock. Typically, lockup periods are set at 180 days. Lockups are important because it is not unusual for the number of locked-up insider shares to be larger than the number of shares held by the public. Thus, there is the possibility that, when the lockup period ends, a large number of shares will be sold by insiders, thereby depressing share price. Beginning well before an offering and extending for 40 calendar days following an IPO, the SEC requires that a firm and its managing underwriters observe a “quiet period.” This means that all communication with the public must be limited to ordinary announcements and other purely factual matters. The SEC’s logic is that all relevant information should be contained in the prospectus. An important result of this requirement is that the underwriter’s analysts are prohibited from making recommendations to investors. As soon as the quiet period ends, however, the managing underwriters typically publish research reports, usually accompanied by a favorable “buy” recommendation. Firms that don’t stay quiet can have their IPOs delayed. For example, just before Google’s IPO, an interview with cofounders Sergey Brin and Larry Page appeared in Playboy. The interview almost caused a postponement of the IPO, but Google was able to amend its prospectus in time (by including the article!). However, in May 2004, Salesforce.com’s IPO was delayed because an interview with CEO Marc Benioff appeared in The New York Times. Salesforce.com finally went public two months later.

InvestmentB anks Investment banks are at the heart of new security issues. They provide advice, market the securities (after investigating the market’s receptiveness to the issue), and underwrite the proceeds. They accept the risk that the market price may fall between the date the offering price is set and the time the issue is sold.4 An investment banker’s success depends on reputation. A good reputation can help investment bankers retain customers and attract new ones. In other words, financial economists argue that each investment bank has a reservoir of “reputation capital.” One measure of this reputation capital is the pecking order among the investment banks. MBA students are aware of this order because they know that accepting a job with a top-tier firm is universally regarded as more prestigious than accepting a job with a lower-tier firm. Investment banks put great importance in their relative rankings and view downward movement in their placement with much distaste. While this jockeying for position may seem as unimportant as the currying of royal favor in the court of Louis XVI, it is explained by the preceding discussion. In any industry where reputation is so important, the firms in the industry must guard theirs with great vigilance. There are two basic methods for selecting the syndicate. In a competitive offer, the issuing firm can offer its securities to the underwriter bidding highest. In a negotiated offer, the issuing firm works with one underwriter. Because the firm generally does not negotiate with many underwriters concurrently, negotiated deals may suffer from lack of competition. 4

A study of how firms and underwriters match up can be found in Chitru S. Fernando, Vladimir A. Gutchers, and Paul A. Spindt, “Wanna Dance? How Firms and Underwriters Choose Each Other,” Journal of Finance (October 2005), pp. 2437–69.

Chapter 20 Issuing Securities to the Public

In Their Own Words

ROBERT S. HANSEN ON THE ECONOMIC RATIONALE FOR THE FIRM COMMITMENT OFFER Underwriters provide four main functions: Certification, monitoring, marketing, and risk bearing. Certification assures investors that the offer price is fair. Investors have concerns about whether the offer price is unfairly above the stock’s intrinsic value. Certification increases issuer value by reducing investor doubt about fairness, making a better offer price possible. Monitoring of issuing firm management and performance builds value because it adds to shareholders’ ordinary monitoring. Underwriters provide collective monitoring on behalf of both capital suppliers and current shareholders. Individual shareholder monitoring is limited because the shareholder bears the entire cost, whereas all owners collectively share the benefit, pro rata. By contrast, in underwriter monitoring all stockholders share both the costs and benefits, pro rata. Due diligence and legal liability for the proceeds give investors assurance. However, what makes certification and monitoring credible is lead bank reputation in competitive capital markets, where they are disciplined over time. Evidence that irreputable behavior is damaging to a bank’s future abounds. Capital

623

market participants punish poorly performing banks by refusing to hire them. The participants pay banks for certification and meaningful monitoring in “quasirents” in the spread, which represent the fair cost of “renting” the reputations. Marketing is finding long-term investors who can be persuaded to buy the securities at the offer price. This would not be needed if demand for new shares were “horizontal.” There is much evidence that issuers and syndicates repeatedly invest in costly marketing practices, such as expensive road shows, to identify and expand investor interest. Another is organizing members to avoid redundant pursuit of the same customers. Lead banks provide trading support in the issuer’s stock for several weeks after the offer. Underwriting risk is like the risk of selling a put option. The syndicate agrees to buy all new shares at the offer price and resell them at that price or at the market price, whichever is lower. Thus, once the offer begins, the syndicate is exposed to potential losses on unsold inventory should the market price fall below the offer price. The risk is likely to be small because offerings are typically well prepared for quick sale. Robert S. Hansen is the Freeman Senior Research Professor of Finance at Tulane University.

Whereas competitive bidding occurs frequently in other areas of commerce, it may surprise you that negotiated deals in investment banking occur with all but the largest issuing firms. Investment bankers argue that they must expend much time and effort learning about the issuer before setting an issue price and a fee schedule. Except in the case of large issues, these underwriters could not expend the time and effort without the near certainty of receiving the contract. Studies generally show that issuing costs are higher in negotiated deals than in competitive ones. However, many financial economists argue that issuing firms are not necessarily hurt by negotiated deals. They point out that the underwriter gains much information about the issuing firm through negotiation—information likely to increase the probability of a successful offering.5

TheOf feringP rice Determining the correct offering price is the most difficult thing the lead investment bank must do for an initial public offering. The issuing firm faces a potential cost if 5

This choice has been studied recently by Robert S. Hansen and Naveen Khanna, “Why Negotiation with a Single Syndicate May Be Preferred to Making Syndicates Compete: The Problem of Trapped Bidders,” Journal of Business 67 (1994); S. Bhagat, “The Effect of Management’s Choice between Negotiated and Competitive Equity Offerings on Shareholder Wealth,” Journal of Financial and Quantitative Analysis (1986); and D. Logue and R. Jarrow, “Negotiation vs. Competitive Bidding in the Sales of Securities by Public Utilities,” Financial Management 7 (1978). 623

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Table 20.3 Number of Offerings, Average First-Day Return, and Gross Proceeds of Initial Public Offerings: 1975–2007

Year

Number of Offerings*

Average First-Day Return, %†

Gross Proceeds ($ in millions)‡

1975–1979 1980–1989 1990–1999 2000–2007 1975–2007

112 2,380 4,146 1,283 7,921

5.7 6.8 21.1 24.8 17.2

1,124 61,880 291,531 259,193 613,728

*The number of offerings excludes IPOs with an offer price of less than $5.00, ADRs, best-efforts offers, unit offers, Regulation A offerings (small issues raising less than $1.5 million during the 1980s), real estate investment trusts (REITs), partnerships, and closed-end funds. †

First-day returns are computed as the percentage return from the offering price to the first closing market price.

‡

Gross proceeds data are from Securities Data Co. and exclude overallotment options but include the international tranche, if any. No adjustments for inflation have been made. SOURCE: Professor Jay R. Ritter, University of Florida.

the offering price is set too high or too low. If the issue is priced too high, it may be unsuccessful and be withdrawn. If the issue is priced below the true market price, the issuer’s existing shareholders will experience an opportunity loss. Researchers have found that unseasoned new equity issues typically have been offered at below their true market price. Underpricing helps new shareholders earn a higher return on the shares they buy. For example, Ritter examined 7,921 firms that went public from 1975 through 2007 in the United States. He found that the average IPO rose in price 17.2 percent in the first day of trading following issuance (see Table 20.3). These figures are not annualized! In a recent example, on January 21, 2006, McDonald’s sold shares in its Chipotle Mexican Grill chain through an IPO. The initial offering was for 7.9 million shares at a price of $22 per share. The stock opened at $39.51 and rose to a first-day high of $48.28 before closing at $44.00, a 100 percent gain in the first day.

Underpricing: A Possible Explanation There are several possible explanations for underpricing, but so far there is no agreement among scholars as to which explanation is correct. In our opinion, there are two important facts associated with the underpricing puzzle that are key elements to a unifying theory. First, much of the apparent underpricing is concentrated in smaller issues. This point is documented in Table 20.4, which shows that underpricing tends to be attributable to firms with few or no sales in the prior year. These firms tend to be young firms with uncertain future prospects. The increased uncertainty probably attracts risk-averse investors only if underpricing exists. Second, when the price of a new issue is too low, the issue is often oversubscribed. This means investors will not be able to buy all of the shares they want, and the underwriters will allocate the shares among investors. The average investor will find it difficult to get shares in an oversubscribed offering because there will not be enough shares to go around. Although initial public offerings have positive initial returns on average, a significant fraction of them have price drops. An investor submitting an order for all new issues may find that she will be allocated more shares in issues that go down in price.

Chapter 20

Table 20.4

Issuing Securities to the Public

625

Average First-Day Returns Categorized by Sales for IPOs: 1980–2007*

1980–1989

1990–1998

1999–2000

2001–2007

First-Day First-Day First-Day First-Day Number Average Number Average Number Average Number Average of Firms Return of Firms Return of Firms Return of Firms Return

Annual Sales of Issuing Firms $0 ≤ sales < $10m $10m ≤ sales < $20m $20m ≤ sales < $50m $50m ≤ sales < $100m $100m ≤ sales < $200m $200m ≤ sales All

392 250 469 350 238 287 1,986

10.2% 8.6 7.7 6.5 4.7 3.4 7.2

676 385 775 579 446 629 3,490

17.3% 18.5 18.8 13.0 11.8 8.7 14.8

332 139 150 89 57 86 853

69.2% 80.1 75.5 60.4 34.9 26.3 64.4

131 40 124 133 115 312 855

6.4% 8.9 12.9 16.6 15.1 11.3 12.0

*

Sales, measured in millions, are for the last 12 months prior to going public. All sales have been converted into dollars of 2003 purchasing power, using the Consumer Price Index. There are 7,184 IPOs, after excluding IPOs with an offer price of less than $5.00 per share, units, REITs, ADRs, closed-end funds, banks and S&Ls, firms not listed on CRSP within six months of the offer date, and 140 firms with missing sales. The average first-day return is 18.3 percent. SOURCE: Professor Jay R. Ritter, University of Florida.

Consider this tale of two investors. Ms. Smarts knows precisely what companies are worth when their shares are offered. Mr. Average knows only that prices usually rise one month after the IPO. Armed with this information, Mr. Average decides to buy 1,000 shares of every IPO. Does Mr. Average actually earn an abnormally high average return across all initial offerings? The answer is no, and at least one reason is Ms. Smarts. For example, because Ms. Smarts knows that company XYZ is underpriced, she invests all her money in its IPO. When the issue is oversubscribed, the underwriters must allocate the shares between Ms. Smarts and Mr. Average. If they do this on a pro rata basis and if Ms. Smarts has bid for twice as many shares as Mr. Average, she will get two shares for each one Mr. Average receives. The net result is that when an issue is underpriced, Mr. Average cannot buy as much of it as he wants. Ms. Smarts also knows that company ABC is overpriced. In this case, she avoids its IPO altogether, and Mr. Average ends up with a full 1,000 shares. To summarize, Mr. Average receives fewer shares when more knowledgeable investors swarm to buy an underpriced issue, but he gets all he wants when the smart money avoids the issue. This is called the winner’s curse, and it is one possible reason why IPOs have such a large average return. When the average investor wins and gets his allocation, it is because those who knew better avoided the issue. To counteract the winner’s curse and attract the average investor, underwriters underprice issues.6 Another reason for underpricing is risk. Although it is true that on average IPOs have positive initial returns, a significant fraction have price drops. Underwriters

6

This explanation was first suggested in K. Rock, “Why New Issues Are Underpriced,” Journal of Financial Economics15(1986).

In Their Own Words JAY RITTER ON IPO UNDERPRICING AROUND THE WORLD The United States is not the only country in which initial public offerings (IPOs) of common stock are underpriced. The phenomenon exists in every country with a stock market, although the extent of underpricing varies from country to country. In general, countries with developed capital markets have more moderate underpricing than in emerging markets. During the Internet bubble of 1999–2000, however, underpricing in the developed capital markets increased dramatically. In the United States, for example, the average first-day

Country

Sample Size

Time Period

Avg. Initial Return

Argentina Australia Austria Belgium Brazil Bulgaria Canada Chile China Cyprus Denmark Finland France Germany Greece Hong Kong India Indonesia Iran Ireland Israel Italy

20 1,103 96 114 180 9 635 65 1,394 51 145 162 686 652 363 1,008 2,713 321 279 31 348 233

1991–1994 1976–2006 1971–2006 1984–2006 1979–2006 2004–2007 1971–2006 1982–2006 1990–2005 1999–2002 1984–2006 1971–2006 1983–2006 1978–2006 1976–2005 1980–2006 1990–2004 1989–2007 1991–2004 1999–2006 1990–2006 1985–2006

4.4% 19.8 6.5 13.5 48.7 36.5 7.1 8.4 164.5 23.7 8.1 17.2 10.7 26.9 25.1 15.9 95.4 21.1 22.4 23.7 13.8 18.2

return during 1999–2000 was 65 percent. At the same time that underpricing in the developed capital markets increased, the underpricing of IPOs sold to residents of China moderated. The Chinese average has come down to a mere 164 percent, which is lower than it had been in the early and mid-1990s. After the bursting of the Internet bubble in mid-2000, the level of underpricing in the United States, Germany, and other developed capital markets has returned to more traditional levels. The following table gives a summary of the average first-day returns on IPOs in a number of countries around the world, with the figures collected from a number of studies by various authors.

Country Japan Korea Malaysia Mexico Netherlands New Zealand Nigeria Norway Philippines Poland Portugal Russia Singapore South Africa Spain Sweden Switzerland Taiwan Thailand Turkey United Kingdom United States

Sample Size

Time Period

Avg. Initial Return

2,458 1,417 350 88 181 214 114 153 123 224 28 40 441 118 128 406 147 1,312 447 282 3,986 15,649

1970–2006 1980–2007 1980–2006 1987–1994 1982–2006 1979–2006 1989–2006 1984–2006 1987–2006 1991–2006 1992–2006 1999–2006 1973–2006 1980–1991 1986–2006 1980–2006 1983–2006 1980–2006 1987–2006 1990–2004 1959–2006 1960–2007

40.1% 57.4 69.6 15.9 10.2 20.3 12.7 9.6 21.2 22.9 11.6 4.2 28.3 32.7 10.9 27.3 29.3 37.2 36.9 10.8 16.8 18.0

Jay R. Ritter is Cordell Professor of Finance at the University of Florida. An outstanding scholar, he is well known for his insightful analyses of new issues and going public.

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would suffer from the loss of value on their own holdings and also could conceivably be sued by angry customers for the overpriced securities.7 For example, consider the Visa IPO we discussed at the beginning of the chapter. The stock opened at $44 and rose to a first-day high of $69 before closing at $56.50, a gain of about 28 percent. Based on these numbers, Visa was underpriced by about $12.50 per share, which means the company missed out on an additional $5.588 billion, the largest dollar amount “left on the table” in history. Hopefully, Visa won’t be as adversely affected by the money left on the table as some other companies. In 1999, eToys’ 8.2 million share IPO was underpriced by $57 per share, or almost a half a billion dollars in all. eToys could have used the money: It was bankrupt within two years.

20.4 What CFOs Say about the IPO Process In an IPO, a firm accomplishes two important things; namely, raising capital and becoming a public company. The two major benefits to a firm going public are the better ability to raise capital and better ability of shareholders to diversify. There are substantial costs to being a public company in the United States. We have described the statutory disclosure requirements monitored by the Securities and Exchange Commission and the listing requirements of the NYSE and NASDAQ. More recently, there are the requirements of the Sarbanes-Oxley Act for more accountability in corporate governance. In 2000–2002, a large number of CFOs whose firms had recently gone public were asked about their firms’ motives. Figure 20.2 describes their responses. The motives that were cited the most for going public were the creation of public shares for use in future acquisitions and establishing a market value for the firm. Diversification was also seen as a benefit.

Figure 20.2

Survey Evidence on the Motivations for Going Public

Debt is becoming too expensive. Our company has run out of private equity. To attract analysts’ attention. To allow venture capitalists (VCs) to cash out. To minimize our cost of capital. To allow one or more principals to diversify personal holdings. To broaden the base of ownership. To enhance the reputation of our company. To establish a market price/value for our firm. To create public shares for use in future acquisitions. 0

10 20 30 40 50 60 Percent of CFOs who agree or strongly agree

70

SOURCE:: James C. Baum and Stanley E. Fawcett, “Evidence on What CFOs Think about the IPO Process: Practice, Theory and Managerial Implications,” Journal of Applied Corporate Finance 61 (2002).

7

Some researchers have hypothesized that overenthusiasm and optimism among individual investors can explain high first-day returns. (e.g., Jay Ritter and Ivo Welch, “A Review of IPO Activity, Pricing and Allocation,” Journal of Finance 57, pp. 1795–1828). See also Francesca Cornelli, David Goldreich, and Alexander Ljungqvist, “Investor Sentiment and Pre-IPO Markets,” Journal of Finance (June 2006), pp. 1187–1216. In addition, Gerard Hoberg in “The Underwriter Persistence Phenomenon,” Journal of Finance (June 2007), pp. 1169–1206, concludes that high underpricing underwriters are not “lowballing” issuers but instead have access to superior information and use this advantage.

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Figure 20.3

CFO Perceptions of IPO Underpricing

To create a large blockholder to serve as a watchdog over management. So underwriters can make spinning possible. Underperforming reduces the need for additional IPO marketing costs. To compensate investors for truthfully revealing the price they are willing to pay. So underwriters can make flipping possible. To mitigate future litigation by investors who claim the offer price was too high. Insiders are willing to underprice because the IPO creates personal wealth. To increase stock price by starting a cascade effect among investors. To increase publicity on the opening day. To ensure a wide base of owners. Underwriters underprice to incur the favor of institutional investors. To increase the post-issue trading volume of the stock. To compensate investors for taking the risk of the IPO. 0 10 20 30 40 50 60 70 Percent of CFOs who agree or strongly agree SOURCE: James C. Baum and Stanley E. Fawcett , “Evidence on What CFOs Think about the IPO Process: Practice, Theory and Managerial Implications,” Journal of Applied Corporate Finance 61 (2002).

The CFOs were also asked to describe their perceptions of IPO underpricing. Figure 20.3 shows the results of the survey. The most cited reason for IPO underpricing was to compensate investors for taking the risk of the IPO, followed by the increase of the post-issue trading volume for the stock. The reasons are consistent with our story of Ms. Smarts and Mr. Average and underwriting risk, but they also show that the quality and liquidity of the aftermarket are important.

20.5 The Announcement of NewEq uity and the Value of the Firm As mentioned, when firms return to the equity markets for more funds, they arrange for a seasoned equity offering. The basic processes for a seasoned new issue and an IPO are the same. A curious thing happens on the announcement day. It seems reasonable to believe that new long-term financing is arranged by firms after positive net present value projects are put together. As a consequence, when the announcement of external financing is made, the firm’s market value should go up. As we mentioned in an earlier chapter, this is precisely the opposite of what actually happens in the case of new equity financing. Asquith and Mullins, Masulis and Korwar, and Mikkelson and Partch have all found that the market value of existing equity drops on the announcement of a new issue of common stock.8 Plausible reasons for this strange result include these: 1. Managerial information: If managers have superior information about the market value of the firm, they may know when the firm is overvalued. If they do, they 8

P. Asquith and D. Mullins, “Equity Issues and Offering Dilution,” Journal of Financial Economics15 (1986); R. Masulis and A. N. Korwar, “Seasoned Equity Offerings: An Empirical Investigation,” Journal of Financial Economics 15 (1986); and W. H. Mikkelson and M. M. Partch, “The Valuation Effects of Security Offerings and the Issuance Process,” Journal of Financial Economics 15 (1986).

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might attempt to issue new shares of stock when the market value exceeds the correct value. This will benefit existing shareholders. However, the potential new shareholders are not stupid. They will infer overvaluation from the new issue, thereby bidding down the stock price on the announcement date of the issue. 2. Debt capacity: The stereotypical firm chooses a debt–equity ratio that balances the tax shield from the debt with the cost of financial distress. When the managers of a firm have special information that the probability of financial distress has risen, the firm is more likely to raise capital through stock than through debt. If the market infers this chain of events, the stock price should fall on the announcement date of an equity issue. 3. Falling earnings:9 When managers raise capital in amounts that are unexpectedly large (as most unanticipated financings will be) and if investors have a reasonable fix on the firm’s upcoming investments and dividend payouts (as they do because capital expenditure announcements are often well known, as are future dividends), the unanticipated financings are roughly equal to unanticipated shortfalls in earnings (this follows directly from the firm’s sources and uses of funds identity). Therefore, an announcement of a new stock issue could also reveal a future earnings shortfall. To give a recent example, in April 2008, Washington Mutual, the largest savings and loan organization in the United States at the time (better known as “WaMu”), announced a privately placed secondary offering. Its stock fell about 10.2 percent on the day, a much bigger drop than normal. Why? One reason was that the secondary offer was much larger than normal at about $7 billion at a time when WaMu’s market capitalization was about $10.5 billion. Another reason was that WaMu had three straight quarters of losses totaling $6.1 billion. The market saw the offering as a sign of weakness. WaMu was eventually bought by JPMorgan Chase on September 25, 2008, for $1.9 billion. In another example, in May 2008, Itron, which provides products and services for the energy and water industries, announced a secondary offering to raise about $321 million. Its stock dropped 2.4 percent at the news, about what we would expect from history.

20.6 The Cost of New Issues Issuing securities to the public is not free, and the costs of different issuing methods are important determinants of which will be used. The costs fall into six categories: 1. Spread, or underwriting, discount: The spread is the difference between the price the issuer receives and the price offered to the public. 2. Other direct expenses: These are costs incurred by the issuer that are not part of the compensation to underwriters. They include filing fees, legal fees, and taxes—all reported in the prospectus. 3. Indirect expenses: These costs are not reported in the prospectus and include management time spent on the newis sue. 9

Robert S. Hansen and Claire Crutchley, “Corporate Earnings and Financings: An Empirical Analysis,” Journal of Business 20 (1990). A related argument is made by Murray Carlson, Adlai Fisher, and Ronald Giammarino in “Corporate Investment and Asset Price Dynamics: Implications for Cross-Section of Returns,” Journal of Finance (2004).

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4. Abnormal returns:

5. Underpricing:

Table 20.5

In a seasoned issue of stock, the price typically drops by 3 to 4 percent upon the announcement of the issue. The drop protects new shareholders against the firm selling overpriced stock to new shareholders. For initial public offerings, the stock typically rises substantially after the issue date. This is a cost to the firm

Direct Costs as a Percentage of Gross Proceeds for Equity (IPOs and SEOs) and Straight and Convertible Bonds Offered by Domestic Operating Companies: 1990–2008

Equity IPOs Proceeds ($ in millions) 2– 9.99 10– 19.99 20– 39.99 40– 59.99 60– 79.99 80– 99.99 100–199.99 200–499.99 500 and up Total

SEOs

Number of Issues

Gross Spread

Other Direct Expense

Total Direct Cost

Number of Issues

Gross Spread

Other Direct Expenses

Total Direct Cost

624 704 1,336 771 403 245 438 197 72 4,790

9.15% 7.33 6.99 6.96 6.88 6.79 6.48 5.91 4.66 7.17%

6.21% 4.30 2.82 2.25 1.77 1.55 1.19 .81 .49 2.97%

15.36% 11.63 9.81 9.21 8.65 8.34 7.67 6.72 5.15 10.14%

267 519 904 677 489 292 657 275 83 4,163

7.56% 6.32 5.73 5.28 5.07 4.95 4.57 3.99 3.48 5.37%

5.32% 2.49 1.51 .92 .74 .61 .43 .27 .16 1.35%

12.88% 8.81 7.24 6.20 5.81 5.56 5.00 4.26 3.64 6.72%

Bonds Convertible Bonds Proceeds ($ in millions) 2– 9.99 10– 19.99 20– 39.99 40– 59.99 60– 79.99 80– 99.99 100–199.99 200–499.99 500 and up Total

Number of Issues 8 20 27 33 61 17 100 53 17 336

Straight Bonds

Gross Spread

Other Direct Expense

Total Direct Cost

Number of Issues

Gross

Other Direct Expenses

5.73% 5.26 4.74 3.29 2.70 2.16 2.56 2.34 2.05 2.99%

2.78% 2.90 1.72 1.01 .61 .56 .39 .22 .11 .77%

8.51% 8.16 6.46 4.30 3.31 2.72 2.95 2.56 2.16 3.76%

70 104 159 152 113 159 677 333 118 1,885

1.39% 1.33 1.22 .72 1.52 1.39 1.60 1.43 .62 1.36%

2.35% 1.59 .90 .63 .76 .56 .52 .37 .20 .66%

Total Direct Cost 3.74% 2.92 2.12 1.35 2.28 1.95 2.12 1.80 .82 2.02%

SOURCE: Inmoo Lee, Scott Lockhead, Jay Ritter, and Quanshui Zhao, “The Costs of Raising Capital,” Journal of Financial Research 1 (Spring 1996), calculations and updates by the authors.

Chapter 20

Issuing Securities to the Public

Table 20.6 Direct and Indirect Costs, in Percentages, of Equity IPOs: 1990–2008

Proceeds ($ in millions)

Number of Issues

Gross Spread

631

Other Direct Expenses

Total Direct Cost

Underpricing

2– 9.99 10– 19.99 20– 39.99 40– 59.99 60– 79.99 80– 99.99 100–199.99 200–499.99 500 and up

624 704 1,336 771 403 245 438 197 72

9.15% 7.33 6.99 6.96 6.88 6.79 6.48 5.91 4.66

6.21% 4.30 2.82 2.25 1.77 1.55 1.19 .81 .49

15.36% 11.63 9.81 9.21 8.65 8.34 7.67 6.72 5.15

18.18% 10.02 17.91 29.57 39.20 45.36 37.10 17.12 12.19

Total

4,790

7.17%

2.97%

10.14%

23.49%

SOURCE: Inmoo Lee, Scott Lockhead, Jay Ritter, and Quanshui Zhao, “The Costs of Raising Capital,” Journal of Financial Research 1 (Spring 1996), calculations and updates by the authors.

because the stock is sold for less than its efficient price in the aftermarket. 6. Green Shoe option: The Green Shoe option gives the underwriters the right to buy additional shares at the offer price to cover overallotments. This is a cost to the firm because the underwriter will buy additional shares only when the offer price is below the price in the aftermarket. An interesting study by Lee, Lockhead, Ritter, and Zhao reports two of these six costs—underwriting discount and other direct expenses.10 Updated versions of their findings for both equity offerings and debt offerings are presented in Tables 20.5–20.7. Three conclusions emerge from the tables: 1. The costs in each category, for both equity offerings and debt offerings, decline as the gross proceeds of the offering increase. Thus, it appears that issuance costs are subject to substantial economies of scale.11 2. The bottom line of Table 20.5 indicates that across all offerings, direct expenses are higher for equity offers than for debt offers. 3. Last, and perhaps most important, the costs of issuing securities to the public are quite large. For example, total direct expenses are approximately 15 percent for an initial public offering of less than $10,000,000. In addition, Table 20.6 establishes that underpricing costs are another 18.18 percent. This implies that going public

10 The notion of economies of scale has been contested by Oya Altinkilic and Robert S. Hansen, “Are There Scale Economies in Underwriting Spreads? Evidence of Rising External Financing Costs,” Review of Financial Studies 13 (2000). They provide data and analysis showing that underwriter cost will be U-shaped. 11 Among the most interesting developments in the initial public offering market is that almost all underwriter spreads in recent offerings have been exactly 7 percent. This is documented in H. C. Chen and Jay R. Ritter, “The Seven-Percent Solution,” Journal of Finance (June 2000); and Robert S. Hansen, “Do Investment Banks Compete in IPOs? The Advent of the ‘7% Plus Contract,’” Journal of Financial Economics (August 2001).

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Table 20.7 Average Gross Spreads and Total Direct Costs for Domestic Debt Issues: 1990–2008

Convertible Bonds Investment Grade

Non-Investment Grade

Proceeds ($ in millions)

Number of Issues

Gross Spread

Total Direct Cost

2– 9.99 10– 19.99 20– 39.99 40– 59.99 60– 79.99 80– 99.99 100–199.99 200–499.99 500 and up Total

0 0 0 3 4 3 28 26 12 76

— — — 1.92% 1.65 .89 2.22 1.99 1.96 1.99%

— — — 2.43% 2.09 1.16 2.55 2.18 2.09 2.26%

Number of Issues 0 1 11 21 47 9 50 17 1 157

Gross Spread — 4.00% 3.47 3.33 2.78 2.54 2.57 2.62 2.50 2.81%

Total Direct Cost — 5.67% 5.02 4.48 3.40 3.19 3.00 2.85 2.57 3.47%

Straight Bonds Investment Grade Proceeds ($ in millions) 2– 9.99 10– 19.99 20– 39.99 40– 59.99 60– 79.99 80– 99.99 100–199.99 200–499.99 500 and up Total

Number of Issues 40 68 119 132 68 100 341 173 97 1,138

Gross Spread .62% .50 .58 .39 .57 .66 .55 .50 .28 .51%

Non-Investment Grade

Total Direct Cost 1.90% 1.35 1.21 .86 .97 .94 .80 .81 .38 .91%

Number of Issues 0 2 13 12 43 56 321 156 20 623

Gross Spread — 2.74% 3.06 3.01 2.99 2.74 2.71 2.49 2.45 2.68%

Total Direct Cost — 4.80% 4.36 3.93 4.07 3.66 3.39 2.90 2.71 3.35%

SOURCE:: Inmoo Lee, Scott Lockhead, Jay Ritter, and Quanshui Zhao, “The Costs of Raising Capital,” Journal of Financial Research 1 (Spring 1996), calculations and updates by the authors.

for the first time is a weighty decision. Although there are many benefits, such as raising needed capital and spreading ownership, the costs cannot be ignored.

The Costs of Going Public: The Case of Symbion On February 6, 2004, Symbion, Inc., the Nashville-based owner and operator of outpatient surgery centers, went public via an IPO. Symbion issued 8.28 million shares of stock at a price of $15.00 each, 2,971,600 of which were underwritten by Symbion’s lead investment bank, Credit Suisse First Boston LLC, with the remaining 5,308,400 underwritten by a syndicate made up of seven other investment banks.

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Even though the IPO raised a gross sum of $124.2 million, Symbion got to keep only $112.296 million after expenses. The biggest expense was the 7 percent underwriter spread, which is very standard for an offering of this size. Symbion sold each of the 8.28 million shares to the underwriters for $13.95, and the underwriters in turn sold the shares to the public for $15.00 each. Thus, of the $124.2 million investors paid for the shares, Symbion received $115,506,000. But wait—there’s more. Symbion spent $10,048 in SEC registration fees, $12,000 in other filing fees, and $100,000 to be listed on the NASDAQ. The company also spent $1.29 million on accounting to obtain the necessary audits, $5,250 for a transfer agent to physically transfer the shares and maintain a list of shareholders, $565,000 for printing and engraving expenses, $1.16 million for legal fees and expenses, and, finally, $67,702 in miscellaneous expenses. As Symbion’s outlays show, an IPO can be a costly undertaking! In the end, Symbion’s expenses totaled $11,904,000, of which $8,694,000 went to the underwriters and $3,210,000 went to other parties. The total cost to Symbion was 10.6 percent of the issue proceeds, which is a little higher than might be expected. At least part of the reason is that the company had filed to go public in 2003. Midway through the process, the company and its underwriters determined that the market conditions were not favorable for an IPO, so the company withdrew its registration. The costs for this previous registration were included in the 2004 IPO.

20.7 Rights When new shares of common stock are offered to the general public in a seasoned new equity issue, the proportionate ownership of existing shareholders is likely to be reduced. However, if a preemptive right is contained in the firm’s articles of incorporation, the firm must first offer any new issue of common stock to existing shareholders. This assures each owner his proportionate owner’s share. An issue of common stock to existing stockholders is called a rights offering. Here each shareholder is issued an option to buy a specified number of new shares from the firm at a specified price within a specified time, after which the rights expire. For example, a firm whose stock is selling at $30 may let current stockholders buy a fixed number of shares at $10 per share within two months. The terms of the option are evidenced by certificates known as share warrants or rights. Such rights are often traded on securities exchanges or over the counter.

The Mechanics of a Rights Offering The various considerations confronting a financial manager in a rights offering are illustrated by the situation of the National Power Company, whose initial financial statements are given in Table 20.8. National Power earns $2 million after taxes and has 1 million shares outstanding. Earnings per share are $2, and the stock sells at 10 times earnings (that is, its price– earnings ratio is 10). The market price of each share is therefore $20. The company plans to raise $5 million of new equity funds by a rights offering. The process of issuing rights differs from the process of issuing shares of stock for cash. Existing stockholders are notified that they have been given one right for each share of stock they own. Exercise occurs when a shareholder sends payment to the firm’s subscription agent (usually a bank) and turns in the required number of rights. Shareholders of National Power will have several choices: (1) subscribe for the full number of entitled shares, (2) order all the rights sold, or (3) do nothing and let the rights expire.

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Table 20.8

NATIONAL POWER COMPANY

Financial Statement before Rights Offering

Balance Sheet and Income Statement

Balance Sheet Assets

Shareholder Equity Common stock Retained earnings

Total

$20,000,000

Total

$10,000,000 10,000,000 $20,000,000

Income Statement Earnings before taxes

$ 3,030,303

Taxes (34%)

1,030,303

Net income

$ 2,000,000

Earnings per share

$

Shares outstanding

2 1,000,000

Market price per share

$

Total market value

$20,000,000

20

The financial ncial management of National Power must answer the following ques questions: 1. What price should the existing shareholders be allowed to pay for a share of new stock? 2. How many rights will be required to purchase one share of stock? 3. What effect will the rights offering have on the existing price of the stock?

SubscriptionP rice In a rights offering, the subscription price is the price that existing shareholders are allowed to pay for a share of stock. A rational shareholder will subscribe to the rights offering only if the subscription price is below the market price of the stock on the offer’s expiration date. For example, if the stock price at expiration is $13 and the subscription price is $15, no rational shareholder will subscribe. Why pay $15 for something worth $13? National Power chooses a price of $10, which is well below the current market price of $20. As long as the market price does not fall by half before expiration, the rights offering will succeed.

Number of Rights Needed to Purchase a Share National Power wants to raise $5 million in new equity. With a subscription price of $10, it must issue 500,000 new shares. This can be determined by dividing the total amount to be raised by the subscription price: Funds to be raised $5,000,000 Numbero f n ewsh ares = ________________ = __________ =500 ,000sh ares Subscriptionp rice $10 Because stockholders typically get one right for each share of stock they own, 1 million rights will be issued by National Power. To determine how many rights must be exercised to get one share of stock, we can divide the number of existing outstanding shares of stock by the number of new shares: 1,000,000 Numbero f righ tsn eeded ____________ “Old” shares = = _________ = 2righ ts 500,000 “New”sh ares to buy a share of stock

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Thus a shareholder must give up two rights plus $10 to receive a share of new stock. If all the stockholders do this, National Power will raise the required $5 million. It should be clear that the subscription price, the number of new shares, and the number of rights needed to buy a new share of stock are interrelated. If National Power lowers the subscription price, it must issue more new shares to raise $5 million in new equity. Several alternatives appear here:

Subscription Price

Number of New Shares

Number of Rights Needed to Buy a Share of Stock

$20 10 5

250,000 500,000 1,000,000

4 2 1

Effect of Rights Offering on Price of Stock Rights clearly have value. In the case of National Power, the right to be able to buy a share of stock worth $20 for $10 is valuable. Suppose a shareholder of National Power owns two shares of stock just before the rights offering. This situation is depicted in Table 20.9. Initially, the price of National Power is $20 per share, so the shareholder’s total holding is worth 2 × $20 = $40. The stockholder who has two shares will receive two rights. The National Power rights offer gives shareholders with two rights the opportunity to purchase one additional share for $10. The holding of the shareholder who exercises these rights and buys the new share would increase to three shares. The value of the new holding would be $40 + $10 = $50 (the $40 initial value plus the $10 paid to the company). Because the stockholder now holds three shares, the price per share would drop to $50/3 = $16.67 (rounded to two decimal places).

Table 20.9 The Value to the Individual Shareholder of National Power’s Rights

The Shareholder Initial position Number of shares Share price Value of holding Terms of offer Subscription price Number of rights issued Number of rights for a share After offer Number of shares Value of holding Share price Value of a right Old price − New price New price − Subscription price Number of rights for a share

2 $20 $40 $10 2 2 3 $50 $16.67 $20 − $16.67 = $3.33 ($16.67 − $10)/2 = $3.33

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Table 20.10 National Power Company Rights Offering

The Shareholder Initial position Number of shares Share price Value of firm Terms of offer Subscription price Number of rights issued Number of rights for a share After offer Number of shares Share price Value of firm Value of one right

1 million $20 $20 million $10 1 million 2 1.5 million $16.67 $25 million $20 − $16.67 = $3.33 or ($16.67 − $10)/2 = $3.33

The difference between the old share price of $20 and the new share price of $16.67 reflects the fact that the old shares carried rights to subscribe to the new issue. The difference must be equal to the value of one right—that is, $20 − $16.67 = $3.33. Just as we learned of an ex-dividend date in the previous chapter, there is an exrights date here. An individual buying the stock prior to the ex-rights date will receive the rights when they are distributed. An individual buying the stock on or after the ex-rights date will not receive the rights. In our example, the price of the stock prior to the ex-rights date is $20. An individual buying on or after the ex-rights date is not entitled to the rights. The price on or after the ex-rights date is $16.67. Table 20.10 shows what happens to National Power. If all shareholders exercise their rights, the number of shares will increase to 1.5 million and the value of the firm will increase to $25 million. After the rights offering the value of each share will drop to $16.67 (=$25 million/1.5 million). An investor holding no shares of National Power stock who wants to subscribe to the new issue can do so by buying rights. An outside investor buying two rights will pay $3.33 × 2 = $6.67 (to account for previous rounding). If the investor exercises the rights at a subscription cost of $10, the total cost would be $10 + $6.67 = $16.67. In return for this expenditure, the investor will receive a share of the new stock, which is worth $16.67. Of course, outside investors can also buy National Power stock directly at $16.67 per share. In an efficient stock market it will make no difference whether new stock is obtained via rights or via direct purchase.

Effectso nSha reholders Shareholders can exercise their rights or sell them. In either case, the stockholder will neither win nor lose by the rights offering. The hypothetical holder of two shares of National Power has a portfolio worth $40. On the one hand, if the shareholder exercises the rights, she ends up with three shares worth a total of $50. In other words, by spending $10, the investor increases the value of the holding by $10, which means that she is neither better nor worse off. On the other hand, a shareholder who sells the two rights for $3.33 each obtains $3.33 × 2 = $6.67 in cash. Because the two shares are each worth $16.67, the holdings are valued at:

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Shares =2 × $16.67 = $33.33 Soldrigh ts = 2 × $ 3.33 =$ 6.67 Total =$ 40.00 The new $33.33 market value plus $6.67 in cash is exactly the same as the original holding of $40. Thus, stockholders can neither lose nor gain from exercising or selling rights. It is obvious that the new market price of the firm’s stock will be lower after the rights offering than it was before the rights offering. The lower the subscription price, the greater the price decline of a rights offering. However, our analysis shows that the stockholders have suffered no loss because of the rights offering.

TheUnde rwritingAr rangements Undersubscription can occur if investors throw away rights or if bad news causes the market price of the stock to fall below the subscription price. To ensure against these possibilities, rights offerings are typically arranged by standby underwriting. Here the underwriter makes a firm commitment to purchase the unsubscribed portion of the issue at the subscription price less a take-up fee. The underwriter usually receives a standby fee as compensation for this risk-bearing function. In practice, the subscription price is usually set well below the current market price, making the probability of a rights failure quite small. Though a small percentage (less than 10 percent) of shareholders fail to exercise valuable rights, shareholders are usually allowed to purchase unsubscribed shares at the subscription price. This oversubscription privilege makes it unlikely that the corporate issuer would need to turn to its underwriter for help.

20.8 The Rights Puzzle Smith calculated the issuance costs from three alternative methods: an equity issue with underwriting, a rights issue with standby underwriting, and a pure rights issue.12 The results of his study, which appear in Table 20.11, suggest that a pure rights issue is the cheapest of the three alternatives. The bottom line of the table shows that total costs as a percentage of proceeds are 6.17 percent, 6.05 percent, and 2.45 percent for the three alternatives, respectively. As the body of the table indicates, this disparity holds when issues of different sizes are separated. If corporate executives are rational, they will raise equity in the cheapest manner. Thus, the preceding evidence suggests that issues of pure rights should dominate. Surprisingly, almost all new equity issues in the United States are sold without rights. On the other hand, rights offerings are very significant around the world. This is generally viewed as an anomaly in the finance profession, though a few explanations have been advanced:13 1. Underwriters increase the stock price. This is supposedly accomplished because of increased public confidence or by the selling effort of the underwriting group.

12

C. W. Smith, Jr., “Alternative Methods for Raising Capital: Rights versus Underwritten Offerings,” Journal of Financial Economics 5 (December 1977). Myron Slovin, Marie Sushka, and Kam Wah Lai found a similar difference in the United Kingdom, “Alternative Flotation Methods, Adverse Selection, and Ownership Structure: Evidence from Seasoned Equity Issuance in the U.K.,” Journal of Financial Economics 57 (2000).

13 It is even more anomalous because rights offerings are used around the world. In fact, they are required by law in many other countries.

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Rights with Standby Underwriting

— 6.96 10.40 6.59 5.50 4.84 4.30 3.97 3.81 5.05

— 6.78 4.89 2.87 1.53 .71 .37 .21 .14 1.12

— 13.74 15.29 9.47 7.03 5.55 4.67 4.18 3.95 6.17

— 2 5 9 4 10 12 9 5 56

— 3.43 6.36 5.20 3.92 4.14 3.84 3.96 3.50 4.32

— 4.80 4.15 2.85 2.18 1.21 .90 .74 .50 1.73

— 8.24 10.51 8.06 6.10 5.35 4.74 4.70 4.00 6.05

3 2 5 7 6 3 1 2 9 38

8.99 4.59 4.90 2.85 1.39 .72 .52 .21 .13 2.45

SOURCE: Modified from C. W. Smith, Jr., “Costs of Underwritten versus Rights Issues,” Journal of Financial Economics 5 (December 1977), p. 277 (Table 1).

*Based on 578 common stock issues registered under the Securities Act of 1933 during 1971–1975. The issues are subdivided by size of issue and method of financing: Underwriting, rights with standby underwriting, and pure rights offering. Issues are included only if the company’s stock was listed on the NYSE, AMEX, or regional exchanges before the offering; any associated secondary distribution represents less than 10 percent of the total proceeds of the issue, and the offering contains no other types of securities. The costs reported are (1) compensation received by investment bankers for underwriting services rendered, (2) legal fees, (3) accounting fees, (4) engineering fees, (5) trustees’ fees, (6) printing and engraving expenses, (7) SEC registration fees, (8) federal revenue stamps, and (9) state taxes.

0 6 18 61 66 91 156 70 16 484

Total Cost as a Percentage of Proceeds

Pure Rights

Total Cost Other Compensation Total Cost Other Compensation as a Expenses as as a as a Expenses as as a Percentage of a Percentage Percentage Percentage of a Percentage Percentage of Proceeds of Proceeds Number Proceeds of Proceeds of Proceeds Number Proceeds Number

Underwriting

Costs of Flotation as a Percentage of Proceeds*

Under .50 .50 to .99 1.00 to 1.99 2.00 to 4.99 5.00 to 9.99 10.00 to 19.99 20.00 to 49.99 50.00 to 99.99 100.00 to 500.00 Total/average

Size of Issue ($ in millions)

Table 20.11

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However, Smith could find no evidence of this in an examination of 52 rights offerings and 344 underwritten offerings. 2. Because the underwriter buys the shares at the agreed-upon price, it is providing insurance to the firm. That is, the underwriter loses if it is unable to sell all the shares to the public. This potential loss might mean that the underwriter’s effective compensation is less than that measured in Table 20.11. However, the potential economic loss is probably not large. In most cases the offer price is set within 24 hours of the offering, by which time the underwriter has usually made a careful assessment of the market for the shares. 3. Other arguments include these: (a) The proceeds of underwritten issues are available sooner than are the proceeds from a rights offer; (b) underwriters provide a wider distribution of ownership than would be possible with a rights offering; (c) consulting advice from investment bankers may be beneficial; (d ) stockholders find exercising rights a nuisance; and (e) the risk that the market price might fall below the subscription price is significant. All of the preceding arguments are pieces of the puzzle, but none seems very convincing. Booth and Smith have identified a function of the underwriter that had not been taken into account in previous cost studies.14 They argue that the underwriter certifies that the offering price is consistent with the true value of the issue. This certification is implied in the underwriting relationship and is provided when the underwriting firm gets access to inside information and puts its reputation for correct pricing on the line.

20.9 Dilution A subject that comes up quite a bit in discussions involving the selling of securities is dilution. Dilution refers to a loss in existing shareholders’ value. There are several kinds: 1. Dilutiono f p ercentageo wnership. 2. Dilutiono f mar ketv alue. 3. Dilution of book value and earnings per share. The differences between these three types can be a little confusing, and there are some common misconceptions about dilution, so we discuss it in this section.

Dilution of Proportionate Ownership The first type of dilution can arise whenever a firm sells shares to the general public. For example, Joe Smith owns 5,000 shares of Merit Shoe Company. Merit Shoe currently has 50,000 shares of stock outstanding; each share gets one vote. Joe thus controls 10 percent (=5,000/50,000) of the votes and gets 10 percent of the dividends. If Merit Shoe issues 50,000 new shares of common stock to the public via a general cash offer, Joe’s ownership in Merit Shoe may be diluted. If Joe does not participate in the new issue, his ownership will drop to 5 percent (=5,000/100,000). Notice that the value of Joe’s shares is unaffected; he just owns a smaller percentage of the firm. Because a rights offering would ensure Joe Smith an opportunity to maintain his proportionate 10 percent share, dilution of the ownership of existing shareholders can be avoided by using a rights offering. 14

J. Booth and R. Smith, “The Certification Role of the Investment Banker in New Issue Pricing,” Midland Corporate Finance Journal (Spring 1986).

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Dilution of Value: Book versus Market Values We now examine dilution of value by looking at some accounting numbers. We do this to illustrate a fallacy concerning dilution; we do not mean to suggest that accounting value dilution is more important than market value dilution. As we illustrate, quite the reverse is true. Suppose Upper States Manufacturing (USM) wants to build a new electricitygenerating plant to meet future anticipated demands. As shown in Table 20.12, USM currently has 1 million shares outstanding and no debt. Each share is selling for $5, and the company has a $5 million market value. USM’s book value is $10 million total, or $10 per share. USM has experienced a variety of difficulties in the past, including cost overruns, regulatory delays in building a nuclear-powered electricity-generating plant, and below-normal profits. These difficulties are reflected in the fact that USM’s marketto-book ratio is $5/10 = .50 (successful firms rarely have market prices below book values). Net income for USM is currently $1 million. With 1 million shares, earnings per share are $1, and the return on equity is $1/10 = 10%. USM thus sells for five times earnings (the price–earnings ratio is 5). USM has 200 shareholders, each of whom holds 5,000 shares. The new plant will cost $2 million, so USM will have to issue 400,000 new shares ($5 × 400,000 = $2 million). There will thus be 1.4 million shares outstanding after the issue. The ROE on the new plant is expected to be the same as for the company as a whole. In other words, net income is expected to go up by .10 × $2 million = $200,000. Total net income will thus be $1.2 million. The following will result if the plant is built: 1. With 1.4 million shares outstanding, EPS will be $1.2/1.4 = $.857, down from $1. 2. The proportionate ownership of each old shareholder will drop to 5,000/1.4 million = .36 percent from .50 percent.

Table 20.12 New Issues and Dilution: The Case of Upper States Manufacturing

After Taking on New Project

Number of shares Book value Book value per share (B) Market value Market price (P) Net income Return on equity (ROE) Earnings per share (EPS) EPS/P P/EPS P/B Project cost $2,000,000

Initial

With Dilution

With No Dilution

1,000,000 $10,000,000 $10 $5,000,000 $5 $1,000,000 .10 $1 .20 5 .5

1,400,000 $12,000,000 $8.57 $6,000,000 $4.29 $1,200,000 .10 $.86 .20 5 .5

1,400,000 $12,000,000 $8.57 $8,000,000 $5.71 $1,600,000 .13 $1.14 .20 5 .67

NPV = −$1,000,000

NPV = $1,000,000

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3. If the stock continues to sell for five times earnings, then the value will drop to 5 × $.857 = $4.29, representing a loss of $.71 per share. 4. The total book value will be the old $10 million plus the new $2 million, for a total of $12 million. Book value per share will fall to $12 million/1.4 million = $8.57. If we take this example at face value, then dilution of proportionate ownership, accounting dilution, and market value dilution all occur. USM’s stockholders appear to suffer significant losses. A Misconception Our example appears to show that selling stock when the marketto-book ratio is less than 1 is detrimental to stockholders. Some managers claim that the resulting dilution occurs because EPS will go down whenever shares are issued when the market value is less than the book value. When the market-to-book ratio is less than 1, increasing the number of shares does cause EPS to go down. Such a decline in EPS is accounting dilution, and accounting dilution will always occur under these circumstances. Is it also true that market value dilution will necessarily occur? The answer is no. There is nothing incorrect about our example, but why the market price decreased is not obvious. We discuss this next. The Correct Arguments In this example, the market price falls from $5 per share to $4.29. This is true dilution, but why does it occur? The answer has to do with the new project. USM is going to spend $2 million on the new plant. However, as shown in Table 20.12, the total market value of the company is going to rise from $5 million to $6 million, an increase of only $1 million. This simply means that the NPV of the new project is −$1 million. With 1.4 million shares, the loss per share is $1/1.4 = $.71, as we calculated before. So, true dilution takes place for the shareholders of USM because the NPV of the project is negative, not because the market-to-book ratio is less than 1. This negative NPV causes the market price to drop, and the accounting dilution has nothing to do with it. Suppose the new project has a positive NPV of $1 million. The total market value rises by $2 million + $1 million = $3 million. As shown in Table 20.12 (third column), the price per share rise to $5.71. Notice that accounting dilution still takes place because the book value per share still falls, but there is no economic consequence of that fact. The market value of the stock rises. The $.71 increase in share value comes about because of the $1 million NPV, which amounts to an increase in value of about $.71 per share. Also, as shown, if the ratio of price to EPS remains at 5, then EPS must rise to $5.71/5 = $1.14. Total earnings (net income) rise to $1.14 per share × 1.4 million shares = $1.6 million. Finally, ROE will rise to $1.6 million/12 million =13.33%.

20.10 Shelf Registration To simplify the procedure for issuing securities, the SEC currently allows shelf registration. Shelf registration permits a corporation to register an offering that it reasonably expects to sell within the next two years. A master registration statement is filed at the time of registration. The company is permitted to sell the issue whenever it wants over those two years as long as it distributes a short-form statement.

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Not all companies are allowed shelf registration. The major qualifications are as follows: 1. The company must be rated investment grade. 2. The firm cannot have defaulted on its debt in the past 12 months. 3. The aggregate market value of the firm’s outstanding stock must be more than $75millio n. 4. The firm must not have violated the Securities Act of 1934 in the past 12 months. Firms sometimes make use of the dribble method of new equity issuance. With dribbling, a company registers the issue and hires an underwriter to be its selling agent. The company sells shares in small amounts from time to time via a stock exchange. For example, in June 2006, Internet search provider Ask Jeeves filed a $400 million shelf registration to sell a combination of common stock, debt securities, and other instruments. The rule has been controversial. Several arguments have been made against shelf registration: 1. The timeliness of disclosure is reduced with shelf registration because the master registration statement may have been prepared up to two years before the actual issueo ccurs. 2. Some investment bankers have argued that shelf registration will cause a market overhang because registration informs the market of future issues. It has been suggested that this overhang will depress market prices. However, an empirical analysis by Bhagat, Marr, and Thompson found that shelf registration is less costly than conventional underwriting and found no evidence to suggest a market overhange ffect.15

20.11 The Private Equity Market The previous sections of this chapter assumed that a company is big enough, successful enough, and old enough to raise capital in the public equity market. Of course, many firms have not reached this stage and cannot use the public equity market. For start-up firms or firms in financial trouble, the public equity market is often not available. The market for venture capital is part of the private equity market.

PrivateP lacement Private placements avoid the costly procedures associated with the registration requirements that are part of public issues. The Securities and Exchange Commission (SEC) restricts private placement issues to no more than a couple of dozen knowledgeable investors, including institutions such as insurance companies and pension funds. The biggest drawback of privately placed securities is that the securities cannot be easily resold. Most private placements involve debt securities, but equity securities can also be privately placed. In 1990, Rule 144A was adopted by the SEC to establish a framework for the issuance of private securities to certain qualified institutional investors. As illustrated in 15

S. Bhagat, M. W. Marr, and G. R. Thompson, “The Rule 415 Experiment: Equity Markets,” Journal of Finance 19 (December 1985).

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Figure 20.4 Corporate Equity Security Offerings

17.7%

Private Rule 144A placements

16.2%

Private non–Rule 144A placements

66.1%

Public equity offering

100%

Total equity offerings

SOURCE:: Jennifer E. Bethal and Erik R. Sirri, “Express Lane or Toll Booth in the D t Th iti IIssuance,”” JJournall off Appli p t Desert: The SEC FFrameworkk ffor SSecurities Appliedd C Corporate Finance (Spring 1998).

Figure 20.4, the rule has generated a substantial market for privately underwritten issues. Largely because of Rule 144A, companies raise about one-sixth of the proceeds from all new issues without registration with the SEC. To qualify to buy Rule 144A offerings, investors must have at least $100 million in assets under management. Most private placements are in straight bonds or convertible bonds. However, preferred stock is frequently issued as a private placement.

TheP rivateE quityF irm A large amount of private equity investment is undertaken by professional private equity managers representing large institutional investors such as mutual funds and pension funds. The limited partnership is the dominant form of intermediation in this market. Typically, the institutional investors act as the limited partners, and the professional managers act as general partners. The general partners are firms that specialize in funding and managing equity investments in closely held private firms. The private equity market has been important for both traditional start-up companies and established public firms. Thus, the private equity market can be divided into venture equity and nonventure equity markets. A large part of the nonventure market is made up of firms in financial distress. Firms in financial distress are not likely to be able to issue public equity and typically cannot use traditional forms of debt such as bank loans or public debt. For these firms, the best alternative is to find a private equity marketfir m.

Suppliers of Venture Capital As we have pointed out, venture capital is an important part of the private equity market. There are at least four types of suppliers of venture capital. First, a few old-line,

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wealthy families have traditionally provided start-up capital to promising businesses. For example, over the years, the Rockefeller family has made the initial capital contribution to a number of successful businesses. These families have been involved in venture capital for at least a century. Second, a number of private partnerships and corporations have been formed to provide investment funds. The organizer behind the partnership might raise capital from institutional investors, such as insurance companies and pension funds. Alternatively, a group of individuals might provide the funds to be ultimately invested with budding entrepreneurs. Arthur Rock & Co. of San Francisco may be the best known. Because of its huge success with Apple Computer and other high-tech firms, it has achieved near mythic stature in the venture capital industry. Recent estimates put the number of venture capital firms at about 4,000. The average amount invested per venture has been estimated to be between $1 million and $2 million. However, one should not make too much of this figure because the amount of financing varies considerably with the venture to be funded. Stories used to abound about how easily an individual could obtain venture capital. Though that may have been the case in an earlier era, it is certainly not the case today. Venture capital firms employ various screening procedures to prevent inappropriate funding. For example, because of the large demand for funds, many venture capitalists have at least one employee whose full-time job consists of reading business plans. Only the very best plans can expect to attract funds. Third, large industrial and financial corporations have established venture capital subsidiaries. However, subsidiaries of this type appear to make up only a small portion of the venture capital market. Fourth, participants in an informal venture capital market have recently been identified. Rather than belonging to any venture capital firm, these investors (often referred to as angels) act as individuals when providing financing. However, they should not, by any means, be viewed as isolated. There is a rich network of angels, continually relying on each other for advice. A number of researchers have stressed that in any informal network there is likely one knowledgeable and trustworthy individual who, when backing a venture, brings a few less experienced investors in with him.

Stageso fF inancing Bruno and Tyebjee identify six stages in venture capital financing:16 1. Seed money stage: A small amount of financing needed to prove a concept or develop a product. Marketing is not included in this stage. 2. Start-up: Financing for firms that started within the past year. Funds are likely to pay for marketing and product development expenditures. 3. First-round financing: Additional money to begin sales and manufacturing after a firm has spent its start-up funds. 4. Second-round financing: Funds earmarked for working capital for a firm that is currently selling its product but still losing money.

16

A. V. Bruno and T. T. Tyebjee, “The Entrepreneur’s Search for Capital,” Journal of Business Venturing (Winter 1985); see also Paul Gompers and Josh Lerner, The Venture Capital Cycle, (Cambridge, MA: MIT Press, 2002).

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Figure 20.5 Initial Public Offerings by Venture Capital–Backed Biotechnology Firms, January 1978 to January 1992

5

Biotech equity index (1/1/78=1)

1 0 9

5

Number of IPOs

0 Jan. 78

Jan. 79

Jan. 80

Jan. 81

Jan. 82

Jan. 83

Jan. 84

Jan. 85

Jan. 86

Jan. 87

Jan. 88

Jan. 89

Jan. 90

Jan. 91

Jan. 92

SOURCE:: Joshua Lerner, “Venture Capitalists and the Decision to Go Public,” Journal of Financial Economics 35 (June 1994).

5. Third-round financing: Financing for a company that is at least breaking even and is contemplating an expansion. This is also known as mezzanine financing. 6. Fourth-round financing: Money provided for firms that are likely to go public within half a year. This round is also known as bridge financing. Although these categories may seem vague to the reader, we have found that the terms are well-accepted within the industry. For example, the venture capital firms listed in Pratt’s Guide to Venture Capital indicate which of these stages they are interested in financing. The penultimate stage in venture capital finance is the initial public offering.17 Venture capitalists are very important participants in initial public offerings. Venture capitalists rarely sell all of the shares they own at the time of the initial public offering. Instead, they usually sell out in subsequent public offerings. However, there is considerable evidence that venture capitalists can successfully time IPOs by taking firms public when the market values are at their highest. Figure 20.5 shows the number of IPOs of privately held venture capital–backed biotechnology companies in each month from 1978 to 1992. The venture capital–backed IPOs clearly coincide with the ups and downs in the biotech market index in the top panel.

17

A very influential paper by Christopher Barry, Chris J. Muscarella, John W. Peavy III, and Michael R. Vetsuypens, “The Role of Venture Capital in the Creation of Public Companies: Evidence from the Going Public Process,” Journal of Financial Economics 27 (1990), shows that venture capitalists do not usually sell shares at the time of the initial public offering, but they usually have board seats and act as advisers to managers.

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Part V Long-Term Financing

This chapter looked closely at how equity is issued. The main points follow: 1. Large issues have proportionately much lower costs of issuing equity than small ones. 2. Firm commitment underwriting is far more prevalent for large issues than is bestefforts underwriting. Smaller issues probably primarily use best efforts because of the greater uncertainty of these issues. For an offering of a given size, the direct expenses of best-efforts underwriting and firm-commitment underwriting are of the same magnitude. 3. Rights offerings are cheaper than general cash offers and eliminate the problem of underpricing. Yet most new equity issues are underwritten general cash offers. 4. Shelf registration is a new method of issuing new debt and equity. The direct costs of shelf issues seem to be substantially lower than those of traditional issues. 5. Venture capitalists are an increasingly important influence in start-up firms and subsequentf inancing.

Debt versus Equity Offering Size In the aggregate, debt offerings are much more common than equity offerings and typically much larger as well. Why? 2. Debt versus Equity Flotation Costs Why are the costs of selling equity so much larger than the costs of selling debt? 3. Bond Ratings and Flotation Costs Why do noninvestment-grade bonds have much higher direct costs than investment-grade issues? 4. Underpricing in Debt Offerings Why is underpricing not a great concern with bond offerings? Use the following information to answer the next three questions. Eyetech Pharmaceuticals, Inc., a company that develops treatments for eye problems, went public in January 2004. Assisted by the investment bank Merrill Lynch, Eyetech sold 6.5 million shares at $21 each, thereby raising a total of $136.5 million. At the end of the first day of trading, the stock sold for $32.40 per share, down slightly from a high of $33.00. Based on the endof-day numbers, Eyetech shares were apparently underpriced by about $11 each, meaning that the company missed out on an additional $71.5 million. 5. IPO Pricing The Eyetech IPO was underpriced by about 54 percent. Should Eyetech be upset at Merrill Lynch over the underpricing? 6. IPO Pricing In the previous question, would it affect your thinking to know that the company was incorporated less than four years earlier, had only $30 million in revenues for the first nine months of 2003, and had never earned a profit? Additionally, the company had only one product, Macugen, which had won fast-track status from the FDA but still did not have approval to be sold. 7. IPO Pricing In the previous two questions, how would it affect your thinking to know that in addition to the 6.5 million shares offered in the IPO, Eyetech had an additional 32 million shares outstanding? Of the 32 million shares, 10 million shares were owned by pharmaceutical giant Pfizer, and 12 million shares were owned by the 13 directors and executive officers. 8. Cash Offer versus Rights Offer Ren-Stimpy International is planning to raise fresh equity capital by selling a large new issue of common stock. Ren-Stimpy is currently a publicly traded corporation, and it is trying to choose between an underwritten cash offer and a rights offering (not underwritten) to current shareholders. Ren-Stimpy management is interested in minimizing the selling costs and has asked you for advice on the choice of issue methods. What is your recommendation and why? 1.

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PROSPECTUS

PICC 200,000 shares PESTINVE STIGATION CONTROL CORPORATION

Of the shares being offered hereby, all 200,000 are being sold by the Pest Investigation Control Corporation, Inc. (“the Company”). Before the offering there has been no public market for the shares of PICC, and no guarantee can be given that any such market will develop. These securities have not been approved or disapproved by the SEC, nor has the commission passed judgment upon the accuracy or adequacy of this prospectus. Any representation to the contrary is a criminal offense.

Per share Total

Price to Public

Underwriting Discount

Proceeds to Company*

$11.00 $2,200,000

$1.10 $220,000

$9.90 $1,980,000

*Before deducting expenses estimated at $27,000 and payable by the company.

This is an initial public offering. The common shares are being offered, subject to prior sale, when, as, and if delivered to and accepted by the Underwriters and subject to approval of certain legal matters by their Counsel and by Counsel for the Company. The Underwriters reserve the right to withdraw, cancel, or modify such offer and to reject offers in whole or in part. (continued )

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IPO Underpricing In 1980, a certain assistant professor of finance bought 12 initial public offerings of common stock. He held each of these for approximately one month and then sold. The investment rule he followed was to submit a purchase order for every firm commitment initial public offering of oil and gas exploration companies. There were 22 of these offerings, and he submitted a purchase order for approximately $1,000 in stock for each of the companies. With 10 of these, no shares were allocated to this assistant professor. With 5 of the 12 offerings that were purchased, fewer than the requested number of shares were allocated. The year 1980 was very good for oil and gas exploration company owners: On average, for the 22 companies that went public, the stocks were selling for 80 percent above the offering price a month after the initial offering date. The assistant professor looked at his performance record and found that the $8,400 invested in the 12 companies had grown to $10,000, representing a return of only about 20 percent (commissions were negligible). Did he have bad luck, or should he have expected to do worse than the average initial public offering investor? Explain. IPO Pricing The following material represents the cover page and summary of the prospectus for the initial public offering of the Pest Investigation Control Corporation (PICC), which is going public tomorrow with a firm commitment initial public offering managed by the investment banking firm of Erlanger and Ritter. Answer the following questions: a. Assume that you know nothing about PICC other than the information contained in the prospectus. Based on your knowledge of finance, what is your prediction for the price of PICC tomorrow? Provide a short explanation of why you think this will occur. b. Assume that you have several thousand dollars to invest. When you get home from class tonight, you find that your stockbroker, whom you have not talked to for weeks, has called. She has left a message that PICC is going public tomorrow and that she can get you several hundred shares at the offering price if you call her back first thing in the morning. Discuss the merits of this opportunity.

Part V Long-Term Financing

648

Erlanger and Ritter, Investment Bankers July 13, 2009 Prospectus Summary TheCo mpany TheOff ering Listing SharesOu tstanding Use of Proceeds

The Pest Investigation Control Corporation (PICC) breeds and markets toads and tree frogs as ecologically safe insect-control mechanisms. 200,000 shares of common stock, no par value. The Company will seek listing on NASDAQ and will trade over the counter. As of June 30, 2009, 400,000 shares of common stock were outstanding. After the offering, 600,000 shares of common stock will be outstanding. To finance expansion of inventory and receivables and general working capital, and to pay for country club memberships for certain finance professors. Selected Financial Information (amounts in thousands except per-share data) As of June 30, 2009 As Adjusted for Actual This Offering

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Fiscal Year Ended June 30 2007 2008 2009 Revenues Net earnings Earnings per share

$60.00 3.80 .01

11. 12. 13.

14. 15.

Questions and Problems BASIC (Questions 1–9)

1.

2.

$120.00 15.90 .04

$240.00 36.10 .09

Working capital Total assets Stockholders’ equity

$

8 511 423

$1,961 2,464 2,376

Competitive and Negotiated Offers What are the comparative advantages of a competitive offer and a negotiated offer, respectively? Seasoned Equity Offers What are the possible reasons why the stock price typically drops on the announcement of a seasoned new equity issue? Raising Capital Megabucks Industries is planning to raise fresh equity capital by selling a large new issue of common stock. Megabucks, a publicly traded corporation, is trying to choose between an underwritten cash offer and a rights offering (not underwritten) to current shareholders. Megabucks’ management is interested in maximizing the wealth of current shareholders and has asked you for advice on the choice of issue methods. What is your recommendation? Why? Shelf Registration Explain why shelf registration has been used by many firms instead of syndication. IPOs Every IPO is unique, but what are the basic empirical regularities in IPOs?

Rights Offerings Again, Inc., is proposing a rights offering. Presently, there are 450,000 shares outstanding at $90 each. There will be 80,000 new shares offered at $84 each. a. What is the new market value of the company? b. How many rights are associated with one of the new shares? c. What is the ex-rights price? d. What is the value of a right? e. Why might a company have a rights offering rather than a general cash offer? Rights Offering The Clifford Corporation has announced a rights offer to raise $40 million for a new journal, the Journal of Financial Excess. This journal will review

Chapter 20 Issuing Securities to the Public

649

potential articles after the author pays a nonrefundable reviewing fee of $5,000 per page. The stock currently sells for $34 per share, and there are 3.4 million shares outstanding. a. What is the maximum possible subscription price? What is the minimum? b. If the subscription price is set at $30 per share, how many shares must be sold? How many rights will it take to buy one share? c. What is the ex-rights price? What is the value of a right? d. Show how a shareholder with 1,000 shares before the offering and no desire (or money) to buy additional shares is not harmed by the rights offer. Rights Stone Shoe Co. has concluded that additional equity financing will be needed to expand operations and that the needed funds will be best obtained through a rights offering. It has correctly determined that as a result of the rights offering, the share price will fall from $75 to $70.25 ($75 is the “rights-on” price; $70.25 is the ex-rights price, also known as the when-issued price). The company is seeking $15 million in additional funds with a per-share subscription price equal to $50. How many shares are there currently, before the offering? (Assume that the increment to the market value of the equity equals the gross proceeds from the offering.)

4.

IPO Underpricing The Woods Co. and the Garcia Co. have both announced IPOs at $40 per share. One of these is undervalued by $8, and the other is overvalued by $5, but you have no way of knowing which is which. You plan on buying 1,000 shares of each issue. If an issue is underpriced, it will be rationed, and only half your order will be filled. If you could get 1,000 shares in Woods and 1,000 shares in Garcia, what would your profit be? What profit do you actually expect? What principle have you illustrated?

5.

Calculating Flotation Costs The St. Anger Corporation needs to raise $35 million to finance its expansion into new markets. The company will sell new shares of equity via a general cash offering to raise the needed funds. If the offer price is $31 per share and the company’s underwriters charge an 8 percent spread, how many shares need to be sold?

6.

Calculating Flotation Costs In the previous problem, if the SEC filing fee and associated administrative expenses of the offering are $900,000, how many shares need to bes old?

7.

Calculating Flotation Costs The Green Hills Co. has just gone public. Under a firm commitment agreement, Green Hills received $22.10 for each of the 8 million shares sold. The initial offering price was $24 per share, and the stock rose to $29.50 per share in the first few minutes of trading. Green Hills paid $950,000 in direct legal and other costs and $250,000 in indirect costs. What was the flotation cost as a percentage of funds raised?

8.

Price Dilution Raggio, Inc., has 100,000 shares of stock outstanding. Each share is worth $80, so the company’s market value of equity is $8,000,000. Suppose the firm issues 20,000 new shares at the following prices: $80, $75, and $65. What will the effect be of each of these alternative offering prices on the existing price per share?

9.

Stock Offerings The Newton Company has 30,000 shares of stock that each sell for $40. Suppose the company issues 8,000 shares of new stock at the following prices: $40, $20, and $10. What is the effect of each of the alternative offering prices on the existingp ricep ers hare?

10.

Dilution Teardrop, Inc., wishes to expand its facilities. The company currently has 8 million shares outstanding and no debt. The stock sells for $65 per share, but the book value per share is $20. Net income for Teardrop is currently $11.5 million. The new facility will cost $40 million, and it will increase net income by $600,000. a. Assuming a constant price–earnings ratio, what will the effect be of issuing new equity to finance the investment? To answer, calculate the new book value per

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INTERMEDIATE (Questions 10–18)

3.

650

Part V Long-Term Financing

11.

share, the new total earnings, the new EPS, the new stock price, and the new market-to-book ratio. What is going on here? b. What would the new net income for Teardrop have to be for the stock price to remainu nchanged? Dilution The Metallica Heavy Metal Mining (MHMM) Corporation wants to diversify its operations. Some recent financial information for the company is shown here: Stock price Number of shares Total assets Total liabilities Net income

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12.

13.

14.

15.

16.

$73 45,000 $6,500,000 $2,600,000 $630,000

MHMM is considering an investment that has the same PE ratio as the firm. The cost of the investment is $1,100,000, and it will be financed with a new equity issue. The return on the investment will equal MHMM’s current ROE. What will happen to the book value per share, the market value per share, and the EPS? What is the NPV of this investment? Does dilution take place? Dilution In the previous problem, what would the ROE on the investment have to be if we wanted the price after the offering to be $73 per share? (Assume the PE ratio remains constant.) What is the NPV of this investment? Does any dilution take place? Rights A company’s stock currently sells for $63 per share. Last week the firm issued rights to raise new equity. To purchase a new share, a stockholder must remit $12 and three rights. a. What is the ex-rights stock price? b. What is the price of one right? c. When will the price drop occur? Why will it occur then? Rights Summit Corp.’s stock is currently selling at $27 per share. There are 1 million shares outstanding. The firm is planning to raise $2 million to finance a new project. What are the ex-rights stock price, the value of a right, and the appropriate subscription prices under the following scenarios? a. Two shares of outstanding stock are entitled to purchase one additional share of the new issue. b. Four shares of outstanding stock are entitled to purchase one additional share of the new issue. c. How does the stockholders’ wealth change from part (a) to part (b)? Rights Hoobastink Mfg. is considering a rights offer. The company has determined that the ex-rights price will be $61. The current price is $68 per share, and there are 10 million shares outstanding. The rights offer would raise a total of $60 million. What is the subscription price? Value of a Right Show that the value of a right can be written as: Valueo f ar ight = PRO − PX = (PRO − PS)/(N + 1)

17.

where PRO, PS, and PX stand for the “rights-on” price, the subscription price, and the ex-rights price, respectively, and N is the number of rights needed to buy one new share at the subscription price. Selling Rights Wuttke Corp. wants to raise $4,125,000 via a rights offering. The company currently has 750,000 shares of common stock outstanding that sell for $45 per share. Its underwriter has set a subscription price of $25 per share and will charge Wuttke a 6 percent spread. If you currently own 6,000 shares of stock in the

Mini Case

18.

651

company and decide not to participate in the rights offering, how much money can you get by selling your rights? Valuing a Right Mitsi Inventory Systems, Inc., has announced a rights offer. The company has announced that it will take four rights to buy a new share in the offering at a subscription price of $40. At the close of business the day before the ex-rights day, the company’s stock sells for $75 per share. The next morning you notice that the stock sells for $68 per share and the rights sell for $6 each. Are the stock and/or the rights correctly priced on the ex-rights day? Describe a transaction in which you could use these prices to create an immediate profit.

EAST COAST YACHTS GOES PUBLIC Larissa Warren and Dan Ervin have been discussing the future of East Coast Yachts. The company has been experiencing fast growth, and the future looks like clear sailing. However, the fast growth means that the company’s growth can no longer be funded by internal sources, so Larissa and Dan have decided the time is right to take the company public. To this end, they have entered into discussions with the investment bank of Crowe & Mallard. The company has a working relationship with Robin Perry, the underwriter who assisted with the company’s previous bond offering. Crowe & Mallard have helped numerous small companies in the IPO process, so Larissa and Dan feel confident with this choice. Robin begins by telling Larissa and Dan about the process. Although Crowe & Mallard charged an underwriter fee of 4 percent on the bond offering, the underwriter fee is 7 percent on all initial stock offerings of the size of East Coast Yachts’ initial offering. Robin tells Larissa and Dan that the company can expect to pay about $1,500,000 in legal fees and expenses, $15,000 in SEC registration fees, and $20,000 in other filing fees. Additionally, to be listed on the NASDAQ, the company must pay $100,000. There are also transfer agent fees of $8,500 and engraving expenses of $525,000. The company should also expect to pay $75,000 for other expenses associated with the IPO. Finally, Robin tells Larissa and Dan that to file with the SEC, the company must provide three years’ worth of audited financial statements. She is unsure of the costs of the audit. Dan tells Robin that the company provides audited financial statements as part of its bond indenture, and the company pays $300,000 per year for the outside auditor. 1. At the end of the discussion Dan asks Robin about the Dutch auction IPO process. What are the differences in the expenses to East Coast Yachts if it uses a Dutch auction IPO versus a traditional IPO? Should the company go public with a Dutch auction or use a traditional underwritten offering? 2. During the discussion of the potential IPO and East Coast Yachts’ future, Dan states that he feels the company should raise $60 million. However, Larissa points out that if the company needs more cash soon, a secondary offering close to the IPO would be potentially problematic. Instead, she suggests that the company should raise $90 million in the IPO. How can we calculate the optimal size of the IPO? What are the advantages and disadvantages of increasing the size of the IPO to $90 million? 3. After deliberation, Larissa and Dan have decided that the company should use a firm commitment offering with Crowe & Mallard as the lead underwriter. The IPO will be for $70 million. Ignoring underpricing, how much will the IPO cost the company as a percentage of the funds received? 4. Many of the employees of East Coast Yachts have shares of stock in the company because of an existing employee stock purchase plan. To sell the stock, the employees can tender their shares to be sold in the IPO at the offering price, or the employees can retain their stock and sell it in the secondary market after East Coast Yachts goes public (once the 180-day lockup period expires). Larissa asks you to advise the employees aboutw hicho ptionis b est.W hatw ouldy ous uggestt ot hee mployees?

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Chapter 20 Issuing Securities to the Public

CHAPTER 21

Leasing Have you ever flown on GE Airlines? Probably not; but with 1,494 planes, GE Commercial Finance, part of General Electric, owns one of the largest aircraft fleets in the world. In fact, the financing arm of GE owns more than $572 billion in assets and generated $8.6 billion in profits during 2008. In addition to airplanes, the company leases ships, drilling rigs, trucks, and real estate. So why is GE Commercial Finance in the business of buying assets, only to lease them out? And why don’t the companies that lease from GE Commercial Finance simply purchase the assets themselves? This chapter answers these and other questions associated with leasing.

21.1 Typeso fL eases TheB asics A lease is a contractual agreement between a lessee and lessor. The agreement establishes that the lessee has the right to use an asset and in return must make periodic payments to the lessor, the owner of the asset. The lessor is either the asset’s manufacturer or an independent leasing company. If the lessor is an independent leasing company, it must buy the asset from a manufacturer. Then the lessor delivers the asset to the lessee, and the lease goes into effect. As far as the lessee is concerned, it is the use of the asset that is most important, not who owns the asset. The use of an asset can be obtained by a lease contract. Because the user can also buy the asset, leasing and buying involve alternative financing arrangements for the use of an asset. This is illustrated in Figure 21.1. The specific example in Figure 21.1 happens often in the computer industry. Firm U, the lessee, might be a hospital, a law firm, or any other firm that uses computers. The lessor is an independent leasing company that purchased the equipment from a manufacturer such as IBM or Apple. Leases of this type are called direct leases. In the figure the lessor issued both debt and equity to finance the purchase. Of course, a manufacturer like IBM could lease its own computers, though we do not show this situation in the example. Leases of this type are called sales-type leasing. In this case IBM would compete with the independent computer leasing company.

OperatingL eases Years ago, a lease where the lessee received an operator along with the equipment was called an operating lease. Though the operating lease defies an exact definition today, this form of leasing has several important characteristics: 1. Operating leases are usually not fully amortized. This means that the payments required under the terms of the lease are not enough to recover the full cost of the asset for the lessor. This occurs because the term, or life, of the operating lease 652

Chapter 21

Figure 21.1

Leasing

653

Buying versus Leasing Buy

Lease

Firm U buys asset and uses asset; financing ancing raised by debt and equity.

Firm U leases asset from lessor; the lessor owns the asset. Manufacturer of asset

Manufacturer of asset

Firm U buys asset from manufacturer.

Lessor buys asset. Lessor 1. Owns asset. 2. Does not use asset.

Firm U 1. Uses asset. 2. Owns asset. Creditors and equity shareholders supply financing to m U. Firm

Firm U Lessee (Firm U) leases asset 1. Uses asset. 2. Does not own asset. from lessor.

Creditors and shareholders supply financing to lessor.

Equity shareholders

Creditors

Equity shareholders

Creditors

is usually less than the economic life of the asset. Thus, the lessor must expect to recover the costs of the asset by renewing the lease or by selling the asset for its residualv alue. 2. Operating leases usually require the lessor to maintain and insure the leased assets. 3. Perhaps the most interesting feature of an operating lease is the cancellation option. This option gives the lessee the right to cancel the lease contract before the expiration date. If the option to cancel is exercised, the lessee must return the equipment to the lessor. The value of a cancellation clause depends on whether future technological or economic conditions are likely to make the value of the asset to the lessee less than the value of the future lease payments under the lease. To leasing practitioners, the preceding characteristics constitute an operating lease. However, accountants use the term in a slightly different way, as we will see shortly.

FinancialL eases Financial leases are the exact opposite of operating leases, as is seen from their important characteristics: 1. 2. 3. 4.

Financial leases do not provide for maintenance or service by the lessor. Financial leases are fully amortized. The lessee usually has a right to renew the lease on expiration. Generally, financial leases cannot be canceled. In other words, the lessee must make all payments or face the risk of bankruptcy.

654

Part V Long-Term Financing

Because of these characteristics, particularly (2), this lease provides an alternative method of financing to purchase. Hence, its name is a sensible one. Two special types of financial leases are the sale and leaseback arrangement and the leveraged lease arrangement. Sale and Leaseback A sale and leaseback occurs when a company sells an asset it owns to another firm and immediately leases it back. In a sale and leaseback two things happen: 1. The lessee receives cash from the sale of the asset. 2. The lessee makes periodic lease payments, thereby retaining use of the asset. For example, in January 2006, Franklin Electronic Publishers, distributor of Rolodex electronic organizers, closed the sale and leaseback of its corporate headquarters building. The company sold the building for $10.3 million, and at the same time agreed to a 10-year lease with the purchaser with an initial annual payment of $736,000. Leveraged Leases A leveraged lease is a three-sided arrangement among the lessee, the lessor, and the lenders: 1. As in other leases, the lessee uses the assets and makes periodic lease payments. 2. As in other leases, the lessor purchases the assets, delivers them to the lessee, and collects the lease payments. However, the lessor puts up no more than 40 to 50 percent of the purchase price. 3. The lenders supply the remaining financing and receive interest payments from the lessor. Thus, the arrangement on the right side of Figure 21.1 would be a leveraged lease if the bulk of the financing was supplied by creditors. The lenders in a leveraged lease typically use a nonrecourse loan. This means that the lessor is not obligated to the lender in case of a default. However, the lender is protected in two ways: 1. The lender has a first lien on the asset. 2. In the event of loan default, the lease payments are made directly to the lender. The lessor puts up only part of the funds but gets the lease payments and all the tax benefits of ownership. These lease payments are used to pay the debt service of the nonrecourse loan. The lessee benefits because, in a competitive market, the lease payment is lowered when the lessor saves taxes.

21.2 Accounting and Leasing Before November 1976, a firm could arrange to use an asset through a lease and not disclose the asset or the lease contract on the balance sheet. Lessees needed to report information on leasing activity only in the footnotes of their financial statements. Thus, leasing led to off–balance sheet financing. In November 1976, the Financial Accounting Standards Board (FASB) issued its Statement of Financial Accounting Standards No. 13 (FAS 13), “Accounting for Leases.” Under FAS 13, certain leases are classified as capital leases. For a capital lease, the present value of the lease payments appears on the right side of the balance sheet. The identical value appears on the left side of the balance sheet as an asset. FASB classifies all other leases as operating leases, though FASB’s definition differs from that of non-accountants. No mention of the lease appears on the balance sheet for operating leases.

Chapter 21

Table 21.1 Examples of Balance Sheets under FAS 13

Leasing

655

Balance Sheet Truck is purchased with debt (the company owns a $100,000 truck): Truck $100,000 Debt 100,000 Equity Land Total assets $200,000 Total debt plus equity Operating lease (the company has an operating lease for the truck): Truck $ 0 Debt 100,000 Equity Land Total assets $100,000 Total debt plus equity Capital lease (the company has a capital lease for the truck): Assets under capital lease $100,000 Obligations under capital lease 100,000 Equity Land Total assets $200,000 Total debt plus equity

$100,000 100,000 $200,000 $

0 100,000 $100,000 $100,000 100,000 $200,000

The accounting implications of this distinction are illustrated in Table 21.1. Imagine a firm that, years ago, issued $100,000 of equity to purchase land. It now wants to use a $100,000 truck, which it can either purchase or lease. The balance sheet reflecting purchase of the truck is shown at the top of the table. (We assume that the truck is financed entirely with debt.) Alternatively, imagine that the firm leases the truck. If the lease is judged to be an operating one, the middle balance sheet is created. Here, neither the lease liability nor the truck appears on the balance sheet. The bottom balance sheet reflects a capital lease. The truck is shown as an asset and the lease is shown as a liability. Accountants generally argue that a firm’s financial strength is inversely related to the amount of its liabilities. Because the lease liability is hidden with an operating lease, the balance sheet of a firm with an operating lease looks stronger than the balance sheet of a firm with an otherwise identical capital lease. Given the choice, firms would probably classify all their leases as operating ones. Because of this tendency, FAS 13 states that a lease must be classified as a capital one if at least one of the following four criteria is met: 1. The present value of the lease payments is at least 90 percent of the fair market value of the asset at the start of the lease. 2. The lease transfers ownership of the property to the lessee by the end of the term of the lease. 3. The lease term is 75 percent or more of the estimated economic life of the asset. 4. The lessee can purchase the asset at a price below fair market value when the lease expires. This is frequently called a bargain purchase price option. These rules capitalize leases that are similar to purchases. For example, the first two rules capitalize leases where the asset is likely to be purchased at the end of the lease period. The last two rules capitalize long-term leases. Some firms have tried to cook the books by exploiting this classification scheme. Suppose a trucking firm wants to lease a $200,000 truck that it expects to use for 15 years. A clever financial manager could try to negotiate a lease contract for 10 years with lease payments having a present value of $178,000. These terms would get around criteria (1) and (3). If criteria (2) and (4) could be circumvented, the arrangement would be an operating lease and would not show up on the balance sheet.

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Part V Long-Term Financing

Does this sort of gimmickry pay? The semistrong form of the efficient capital markets hypothesis implies that stock prices reflect all publicly available information. As we discussed earlier in this text, the empirical evidence generally supports this form of the hypothesis. Though operating leases do not appear in the firm’s balance sheet, information about these leases must be disclosed elsewhere in the annual report. Because of this, attempts to keep leases off the balance sheet will not affect stock price in an efficient capital market.

21.3 Taxes, the IRS, and Leases The lessee can deduct lease payments for income tax purposes if the lease is qualified by the Internal Revenue Service. Because tax shields are critical to the economic viability of any lease, all interested parties generally obtain an opinion from the IRS before agreeing to a major lease transaction. The opinion of the IRS will reflect the following guidelines: 1. The term of the lease must be less than 30 years. If the term is greater than 30 years, the transaction will be regarded as a conditional sale. 2. The lease should not have an option to acquire the asset at a price below its fair market value. This type of bargain option would give the lessee the asset’s residual scrap value, implying an equity interest. 3. The lease should not have a schedule of payments that is very high at the start of the lease term and thereafter very low. Early balloon payments would be evidence that the lease was being used to avoid taxes and not for a legitimate business purpose. 4. The lease payments must provide the lessor with a fair market rate of return. The profit potential of the lease to the lessor should be apart from the deal’s tax benefits. 5. The lease should not limit the lessee’s right to issue debt or pay dividends while the lease is operative. 6. Renewal options must be reasonable and reflect the fair market value of the asset. This requirement can be met by granting the lessee the first option to meet a competingo utsideo ffer. The reason the IRS is concerned about lease contracts is that many times they appear to be set up solely to avoid taxes. To see how this could happen, suppose a firm plans to purchase a $1 million bus that has a five-year class life. Depreciation expense would be $200,000 per year, assuming straight-line depreciation. Now suppose the firm can lease the bus for $500,000 per year for two years and buy the bus for $1 at the end of the two-year term. The present value of the tax benefits from acquiring the bus would clearly be less than if the bus were leased. The speedup of lease payments would greatly benefit the firm and give it a form of accelerated depreciation. If the tax rates of the lessor and lessee are different, leasing can be a form of tax avoidance.

21.4 The Cash Flows of Leasing In this section we identify the basic cash flows used in evaluating a lease. Consider the decision confronting the Xomox corporation, which manufactures pipe. Business has been expanding, and Xomox currently has a five-year backlog of pipe orders for the Trans-Honduran Pipeline. The International Boring Machine Corporation (IBMC) makes a pipe-boring machine that can be purchased for $10,000. Xomox has determined that it needs a new machine, and the IBMC model will save Xomox $6,000 per year in reduced electricity

Chapter 21

Leasing

657

Table 21.2

Year 0

Cash Flows to Xomox from Using the IBMC Pipe-Boring Machine: Buy versus Lease

Year 1

Year 2

Year 3

Year 4

Year 5

Buy −$10,000 Cost of machine Aftertax operating savings [$3,960 = $6,000 × (1 − .34)] $3,960 $3,960 $3,960 $3,960 $3,960 Depreciation tax benefit 680 680 680 680 680 −$10,000 $4,640 $4,640 $4,640 $4,640 $4,640 Lease −$2,500 −$2,500 −$2,500 −$2,500 −$2,500 Lease payments Tax benefits of lease payments ($850 = $2,500 × .34) 850 850 850 850 850 Aftertax operating savings 3,960 3,960 3,960 3,960 3,960 Total $2,310 $2,310 $2,310 $2,310 $2,310 Depreciation is straight-line. Because the depreciable base is $10,000, depreciation expense per year is $10,000/5 = $2,000. The depreciation tax benefit per year is equal to: Tax rate × Depreciation expense per year = Depreciation tax benefit .34

×

$2,000

=

$680

bills for the next five years. These savings are known with certainty because Xomox has a long-term electricity purchase agreement with State Electric Utilities, Inc. Xomox has a corporate tax rate of 34 percent. We assume that five-year straightline depreciation is used for the pipe-boring machine, and the machine will be worthlessafte rfi vey ears.1 However, Friendly Leasing Corporation has offered to lease the same pipe-boring machine to Xomox for $2,500 per year for five years. With the lease, Xomox would remain responsible for maintenance, insurance, and operating expenses.2 Simon Smart, a recently hired MBA, has been asked to calculate the incremental cash flows from leasing the IBMC machine in lieu of buying it. He has prepared Table 21.2, which shows the direct cash flow consequences of buying the pipe-boring machine and also signing the lease agreement with Friendly Leasing. To simplify matters, Simon Smart has prepared Table 21.3, which subtracts the direct cash flows of buying the pipe-boring machine from those of leasing it. Noting that only the net advantage of leasing is relevant to Xomox, he concludes the following from his analysis: 1. Operating costs are not directly affected by leasing. Xomox will save $3,960 (after taxes) from use of the IBMC boring machine regardless of whether the machine is owned or leased. Thus, this cash flow stream does not appear in Table 21.3. 2. If the machine is leased, Xomox will save the $10,000 it would have used to purchase the machine. This saving shows up as an initial cash inflow of $10,000 in year 0. 1

This is a simplifying assumption because current tax law allows the accelerated method as well. The accelerated method will almost always be the best choice.

2

For simplicity, we have assumed that lease payments are made at the end of each year. Actually, most leases require lease payments to be made at the beginning of the year.

Part V Long-Term Financing

658

Table 21.3 Incremental Cash Flow Consequences for Xomox from Leasing instead of Purchasing

Lease Minus Buy Lease Lease payments Tax benefits of lease payments Buy (minus) Cost of machine Lost depreciation tax benefit Total

Year 0

Year 1

Year 2

Year 3

Year 4

Year 5

−$2,500 −$2,500 −$2,500 −$2,500 −$2,500 850

850

850

850

850

−(−$10,000) −680 −680 −680 −680 −680 $10,000 −$2,330 −$2,330 −$2,330 −$2,330 −$2,330

The bottom line presents the cash flows from leasing relative to the cash flows from purchase. The cash flows would be exactly the opposite if we considered the purchase relative to the lease.

3. If Xomox leases the pipe-boring machine, it will no longer own this machine and must give up the depreciation tax benefits. These lost tax benefits show up as an outflow. 4. If Xomox chooses to lease the machine, it must pay $2,500 per year for five years. The first payment is due at the end of the first year. (This is a break: Sometimes the first payment is due immediately.) The lease payments are tax deductible and, as a consequence, generate tax benefits of $850 (=.34 ×$2,500). The net cash flows have been placed in the bottom line of Table 21.3. These numbers represent the cash flows from leasing relative to the cash flows from the purchase. It is arbitrary that we express the cash flows in this way. We could have expressed the cash flows from the purchase relative to the cash flows from leasing. These cash flows would look like this:

Net cash flows from purchase alternative relative to lease alternative

Year 0

Year 1

Year 2 Year 3

Year 4

Year 5

−$10,000

$2,330

$2,330

$2,330

$2,330

$2,330

Of course, the cash flows here are the opposite of those in the bottom line of Table 21.3. Depending on our purpose, we may look at either the purchase relative to the lease or vice versa. Thus, the student should become comfortable with either viewpoint. Now that we have the cash flows, we can make our decision by discounting the cash flows properly. However, because the discount rate is tricky, we take a detour in the next section before moving back to the Xomox case. In this next section, we show that cash flows in the lease-versus-buy decision should be discounted at the aftertax interest rate (i.e., the aftertax cost of debt capital).

21.5 A Detour for Discounting and Debt Capacity with Corporate Taxes The analysis of leases is difficult, and both financial practitioners and academics have made conceptual errors. These errors revolve around taxes. We hope to avoid their mistakes by beginning with the simplest type of example: a loan for one year. Though this example is unrelated to our lease-versus-buy situation, principles developed here will apply directly to lease–buy analysis.

Chapter 21

Table 21.4

Leasing

659

Date 0

Lending and Borrowing in a World with Corporate Taxes (Interest Rate Is 10 Percent and Corporate Tax Rate Is 34 Percent)

Date 1

Lending example Lend − $100

Receive + $100.00 of principal Receive + $ 10.00 of interest 6.6% lending

Pay

rate Aftertax lending rate is 6.6%. Borrowing example Borrow + $100

3.40 (=−.34 × $10) in taxes

+$106.60

Pay Pay 6.6% borrowing rate

−$

−$100.00 of principal −$ 10.00 of interest

Receive +$ 3.40 (=.34 × $10) as a tax rebate −$106.60

Aftertax borrowing rate is 6.6%. General principle: In a world with corporate taxes, riskless cash flows should be discounted at the aftertax interest rate.

Present Value of Riskless Cash Flows Consider a corporation that lends $100 for a year. If the interest rate is 10 percent, the firm will receive $110 at the end of the year. Of this amount, $10 is interest and the remaining $100 is the original principal. A corporate tax rate of 34 percent implies taxes on the interest of $3.40 (=.34 × $10). Thus, the firm ends up with $106.60 (=$110 − $3.40) after taxes on a $100 investment. Now consider a company that borrows $100 for a year. With a 10 percent interest rate, the firm must pay $110 to the bank at the end of the year. However, the borrowing firm can take the $10 of interest as a tax deduction. The corporation pays $3.40 (=.34 × $10) less in taxes than it would have paid had it not borrowed the money at all. Thus, considering this reduction in taxes, the firm must pay $106.60 (=$110 − $3.40) on a $100 loan. The cash flows from both lending and borrowing are displayed in Table 21.4. The previous two paragraphs show a very important result: The firm could not care less whether it received $100 today or $106.60 next year.3 If it received $100 today, it could lend it out, thereby receiving $106.60 after corporate taxes at the end of the year. Conversely, if it knows today that it will receive $106.60 at the end of the year, it could borrow $100 today. The aftertax interest and principal payments on the loan would be paid with the $106.60 that the firm will receive at the end of the year. Because of this interchangeability, we say that a payment of $106.60 next year has a present value of $100. Because $100 = $106.60/1.066, a riskless cash flow should be discounted at the aftertax interest rate of .066 [=.10 × (1 − .34)]. Of course, the preceding discussion considered a specific example. The general principle is this: In a world with corporate taxes, the firm should discount riskless cash flows at the aftertax riskless rateof inte rest. 3

For simplicity, assume that the firm received $100 or $106.60 after corporate taxes. Because .66 = 1 − .34, the pretax inflows would be $151.52 ($100/.66) and $161.52 ($106.60/.66), respectively.

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Optimal Debt Level and Riskless Cash Flows In addition, our simple example can illustrate a related point concerning optimal debt level. Consider a firm that has just determined that the current level of debt in its capital structure is optimal. Immediately following that determination, it is surprised to learn that it will receive a guaranteed payment of $106.60 in one year from, say, a tax-exempt government lottery. This future windfall is an asset that, like any asset, should raise the firm’s optimal debt level. How much does this payment raise the firm’s optimal level? Our analysis implies that the firm’s optimal debt level must be $100 more than it previously was. That is, the firm could borrow $100 today, perhaps paying the entire amount out as a dividend. It would owe the bank $110 at the end of the year. However, because it receives a tax rebate of $3.40 (=.34 × $10), its net repayment will be $106.60. Thus, its borrowing of $100 today is fully offset by next year’s government lottery proceeds of $106.60. In other words, the lottery proceeds act as an irrevocable trust that can service the increased debt. Note that we need not know the optimal debt level before the lottery was announced. We are merely saying that whatever this prelottery optimal level was, the optimal debt level is $100 more after the lottery announcement. Of course, this is just one example. The general principle is this:4 In a world with corporate taxes, we determine the increase in the firm’s optimal debt level by discounting a future guaranteed aftertax inflow at the aftertax riskless interest rate.

Conversely, suppose that a second, unrelated firm is surprised to learn that it must pay $106.60 next year to the government for back taxes. Clearly, this additional liability impinges on the second firm’s debt capacity. By the previous reasoning, it follows that the second firm’s optimal debt level must be lowered by exactly $100.

21.6 NPV Analysis of the Lease-versus-Buy Decision Our detour leads to a simple method for evaluating leases: Discount all cash flows at the aftertax interest rate. From the bottom line of Table 21.3, Xomox’s incremental cash flows from leasing versus purchasing are these:

Net cash flows from lease alternative relative to purchase alternative

Year 0

Year 1

$10,000

−$2,330

Year 2

Year 3

Year 4

Year 5

−$2,330 −$2,330 −$2,330 −$2,330

Let us assume that Xomox can either borrow or lend at the interest rate of 7.57575 percent. If the corporate tax rate is 34 percent, the correct discount rate is the aftertax rate of 5 percent [=7.57575% × (1 − .34)]. When 5 percent is used to compute the NPV of the lease, we have: 5 NPV = $10,000 − $2,330 × A.05 = −$87.68

(21.1)

Because the net present value of the incremental cash flows from leasing relative to purchasing is negative, Xomox prefers to purchase. Equation 21.1 is the correct approach to lease-versus-buy analysis. However, students are often bothered by two things. First, they question whether the cash flows 4 This principle holds for riskless or guaranteed cash flows only. Unfortunately, there is no easy formula for determining the increase in optimal debt level from a risky cash flow.

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in Table 21.3 are truly riskless. We examine this issue next. Second, they feel that this approach lacks intuition. We address this concern a little later.

TheDi scountR ate Because we discounted at the aftertax riskless rate of interest, we have implicitly assumed that the cash flows in the Xomox example are riskless. Is this appropriate? A lease payment is like the debt service on a secured bond issued by the lessee, and the discount rate should be approximately the same as the interest rate on such debt. In general, this rate will be slightly higher than the riskless rate considered in the previous section. The various tax shields could be somewhat riskier than the lease payments for two reasons. First, the value of the depreciation tax benefits depends on the ability of Xomox to generate enough taxable income to use them. Second, the corporate tax rate may change in the future, just as it fell in 1986 and increased in 1993. For these two reasons, a firm might be justified in discounting the depreciation tax benefits at a rate higher than that used for the lease payments. However, our experience is that real-world companies discount both the depreciation shield and lease payments at the same rate. This implies that financial practitioners view these two risks as minor. We adopt the real-world convention of discounting the two flows at the same rate. This rate is the aftertax interest rate on secured debt issued by the lessee. At this point some students still question why we do not use RWACC as the discount rate in lease-versus-buy analysis. Of course, RWACC should not be used for lease analysis because the cash flows are more like debt service cash flows than operating cash flows and, as such, the risk is much less. The discount rate should reflect the risk of the incremental cash flows.

21.7 Debt Displacement and Lease Valuation The Basic Concept of Debt Displacement The previous analysis allows us to calculate the right answer in a simple manner. This clearly must be viewed as an important benefit. However, the analysis has little intuitive appeal. To remedy this, we hope to make lease–buy analysis more intuitive by considering the issue of debt displacement. A firm that purchases equipment will generally issue debt to finance the purchase. The debt becomes a liability of the firm. A lessee incurs a liability equal to the present value of all future lease payments. Because of this, we argue that leases displace debt. The balance sheets in Table 21.5 illustrate how leasing might affect debt. Suppose a firm initially has $100,000 of assets and a 150 percent optimal debt– equity ratio. The firm’s debt is $60,000, and its equity is $40,000. As in the Xomox case, suppose the firm must use a new $10,000 machine. The firm has two alternatives: 1. The firm can purchase the machine. If it does, it will finance the purchase with a secured loan and with equity. The debt capacity of the machine is assumed to be the same as for the firm as a whole. 2. The firm can lease the asset and get 100 percent financing. That is, the present value of the future lease payments will be $10,000. If the firm finances the machine with both secured debt and new equity, its debt will increase by $6,000 and its equity by $4,000. Its optimal debt–equity ratio of 150 percent will be maintained. Conversely, consider the lease alternative. Because the lessee views the lease payment as a liability, the lessee thinks in terms of a liability-to-equity ratio, not just a debt-toequity ratio. As just mentioned, the present value of the lease liability is $10,000. If the

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Table 21.5

Assets

Debt Displacement Elsewhere in the Firm When a Lease Is Instituted

Initial situation Current Fixed Total Buy with secured loan Current Fixed Machine Total Lease Current Fixed Machine Total

Liabilities

$ 50,000 50,000 $100,000

Debt Equity Total

$ 60,000 40,000 $ 100,000

$ 50,000 50,000 10,000 $110,000

Debt Equity Total

$ 66,000 44,000 $110,000

$ 50,000 50,000 10,000 $110,000

Lease Debt Equity Total

$ 10,000 56,000 44,000 $110,000

This example shows that leases reduce the level of debt elsewhere in the firm. Though the example illustrates a point, it is not meant to show a precise method for calculating debt displacement.

leasing firm is to maintain a liability-to-equity ratio of 150 percent, debt elsewhere in the firm must fall by $4,000 when the lease is instituted. Because debt must be repurchased, net liabilities rise by only $6,000 (=$10,000 − $4,000) when $10,000 of assets arep lacedu nderle ase.5 Debt displacement is a hidden cost of leasing. If a firm leases, it will not use as much regular debt as it would otherwise. The benefits of debt capacity will be lost— particularly the lower taxes associated with interest expense.

Optimal Debt Level in the Xomox Example The previous section showed that leasing displaces debt. Though the section illustrated a point, it was not meant to show the precise method for calculating debt displacement. Here we describe the precise method for calculating the difference in optimal debt levels between purchase and lease in the Xomox example. From the last line of Table 21.3, we know these cash flows from the purchase alternative relative to the cash flows from the lease alternative:6

Net cash flows from purchase alternative relative to lease alternative

Year 0

Year 1

Year 2 Year 3

Year 4

Year 5

−$10,000

$2,330

$2,330

$2,330

$2,330

$2,330

An increase in the optimal debt level at year 0 occurs because the firm learns at that time of guaranteed cash flows beginning at year 1. Our detour into discounting and 5

Growing firms in the real world will not generally repurchase debt when instituting a lease. Rather, they will issue less debt in the future than they would have without the lease. 6 The last line of Table 21.3 presents the cash flows from the lease alternative relative to the purchase alternative. As pointed out earlier, our cash flows are now reversed because we are now presenting the cash flows from the purchase alternative relative to the lease alternative.

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debt capacity told us to calculate this increased debt level by discounting the future riskless cash inflows at the aftertax interest rate.7 Thus, the additional debt level of the purchase alternative relative to the lease alternative is: $2,330 $2,330 $2,330 $2,330 $2,330 $10,087.68 = ______ + ______2 + ______3 + ______4 + ______5 1.05 (1.05) (1.05) (1.05) (1.05) That is, whatever the optimal amount of debt would be under the lease alternative, the optimal amount of debt would be $10,087.68 more under the purchase alternative. This result can be stated in another way. Imagine there are two identical firms except that one firm purchases the boring machine and the other leases it. From Table 21.3, we know that the purchasing firm generates $2,330 more cash flow after taxes in each of the five years than does the leasing firm. Further imagine that the same bank lends money to both firms. The bank should lend the purchasing firm more money because it has a greater cash flow each period. How much extra money should the bank lend the purchasing firm so that the incremental loan can be paid off by the extra cash flows of $2,330 per year? The answer is exactly $10,087.68—the increase in the optimal debt level we calculated earlier. To see this, let us work through the example year by year. Because the purchasing firm borrows $10,087.68 more at year 0 than does the leasing firm, the purchasing firm will pay interest of $764.22 (=$10,087.68 × .0757575) at year 1 on the additional debt. The interest allows the firm to reduce its taxes by $259.83 (=$764.22 × .34), leaving an aftertax outflow of $504.39 (=$764.22 − $259.83) at year 1. We know from Table 21.3 that the purchasing firm generates $2,330 more cash at year 1 than does the leasing firm. Because the purchasing firm has the extra $2,330 coming in at year 1 but must pay interest on its loan, how much of the loan can the firm repay at year 1 and still have the same cash flow as the leasing firm? The purchasing firm can repay $1,825.61 (=$2,330 − $504.39) of the loan at year 1 and still have the same net cash flow that the leasing firm has. After the repayment, the purchasing firm will have a remaining balance of $8,262.07 (=$10,087.68 − $1,825.61) at year 1. For each of the five years, this sequence of cash flows is displayed in Table 21.6. The outstanding balance goes to zero over the five years. Thus, the annual cash flow of $2,330, which represents the extra cash from purchasing instead of leasing, fully amortizes the loan of $10,087.68. Our analysis of debt capacity has two purposes. First, we want to show the additional debt capacity from purchasing. We just completed this task. Second, we want to determine whether the lease is preferred to the purchase. This decision rule follows easily from our discussion. By leasing the equipment and having $10,087.68 less debt than under the purchase alternative, the firm has exactly the same cash flow in years 1 to 5 that it would have through a levered purchase. Thus, we can ignore cash flows beginning in year 1 when comparing the lease alternative to the purchase-with-debt alternative. However, the cash flows differ between the alternatives at year 0: 1. The purchase cost at year 0 of $10,000 is avoided by leasing. This should be viewed as a cash inflow under the leasing alternative.

7

Though our detour considered only riskless cash flows, the cash flows in a leasing example are not necessarily riskless. As we explained earlier, we therefore adopt the real-world convention of discounting at the aftertax interest rate on secured debt issued by the lessee.

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Table 21.6

Calculation of Increase in Optimal Debt Level If Xomox Purchases instead of Leases

Outstanding balance of loan Interest Tax deduction on interest Aftertax interest expense Extra cash that purchasing firm generates over leasing firm (from Table 21.3) Repayment of loan

Year 0

Year 1

Year 2

Year 3

Year 4

Year 5

$10,087.68

$8,262.07* 764.22 259.83 $ 504.39

$6,345.17 625.91 212.81 $ 413.10

$4,332.42 480.69 163.44 $ 317.25

$2,219.05 328.22 111.59 $ 216.63

$

$2,330.00 $1,825.61†

$2,330.00 $1,916.90

$2,330.00 $2,012.75

$2,330.00 $2,113.37

$2,330.00 $2,219.05

0 168.11 57.16 $ 110.95

Assume that there are two otherwise identical firms: One leases and the other purchases. The purchasing firm can borrow $10,087.68 more than the leasing firm. The extra cash flow each year of $2,330 from purchasing instead of leasing can be used to pay off the loan in five years. *

$8,262.07 = $10,087.68 − $1,825.61.

†

$1,825.61 = $2,330 − $504.39.

2. The firm borrows $10,087.68 less at year 0 under the lease alternative than it can under the purchase alternative. This should be viewed as a cash outflow under the leasingalte rnative. Because the firm borrows $10,087.68 less by leasing but saves only $10,000 on the equipment, the lease alternative requires an extra cash outflow at year 0 relative to the purchase alternative of −$87.68 (=$10,000 − $10,087.68). Because cash flows in later years from leasing are identical to those from purchasing with debt, the firm should purchase. This is exactly the same answer we got when, earlier in this chapter, we discounted all cash flows at the aftertax interest rate. Of course, this is no coincidence: The increase in the optimal debt level is also determined by discounting all cash flows at the aftertax interest rate. The accompanying box presents both methods. The numbers in the box are in terms of the NPV of the lease relative to the purchase. Thus, a negative NPV indicates that the purchase alternative should be taken. The NPV of a lease is often called the net advantage of leasing, or NAL.

Two Methods for Calculating Net Present Value of Lease Relative to Purchase* Method 1: Discount all cash flows at the aftertax interest rate: −$87.68 = $10,000 − $2,330 × A 5.05 Method 2: Compare purchase price with reduction in optimal debt level under leasing alternative: −$87.68 = $10,000 − $10,087.68 Purchase Reduction in price optimal debt levelif le asing *Because we are calculating the NPV of the lease relative to the purchase, a negative value indicates that the purchase alternative is preferred.

Chapter 21

Leasing

665

21.8 Does Leasing Ever Pay? The Base Case We previously looked at the lease–buy decision from the point of view of the potential lessee, Xomox. Let’s now look at the decision from the point of view of the lessor, Friendly Leasing. This firm faces three cash flows, all of which are displayed in Table 21.7. First, Friendly purchases the machine for $10,000 at year 0. Second, because the asset is depreciated straight-line over five years, the depreciation expense at the end of each of the five years is $2,000 (=$10,000/5). The yearly depreciation tax shield is $680 (=$2,000 × .34). Third, because the yearly lease payment is $2,500, the aftertax lease payment is $1,650 [=$2,500 × (1 − .34)]. Now examine the total cash flows to Friendly Leasing displayed in the bottom line of Table 21.7. Those of you with a healthy memory will notice something interesting. These cash flows are exactly the opposite of those of Xomox displayed in the bottom line of Table 21.3. Those of you with a healthy sense of skepticism may be thinking something interesting: “If the cash flows of the lessor are exactly the opposite of those of the lessee, the combined cash flow of the two parties must be zero each year. Thus, there does not seem to be any joint benefit to this lease. Because the net present value to the lessee was −$87.68, the NPV to the lessor must be $87.68. The joint NPV is $0 (=−$87.68 + $87.68). There does not appear to be any way for the NPV of both the lessor and the lessee to be positive at the same time. Because one party would inevitably lose money, the leasing deal could never fly.” This is one of the most important results of leasing. Though Table 21.7 concerns one particular leasing deal, the principle can be generalized. As long as (1) both parties are subject to the same interest and tax rates and (2) transaction costs are ignored, there can be no leasing deal that benefits both parties. However, there is a lease payment for which both parties would calculate an NPV of zero. Given that fee, Xomox would be indifferent to whether it leased or bought, and Friendly Leasing would be indifferent to whether it leased or not.8 A student with an even healthier sense of skepticism might be thinking, “This textbook appears to be arguing that leasing is not beneficial. Yet we know that leasing occurs frequently in the real world. Maybe, just maybe, the textbook is wrong.”

Table 21.7

Cash Flows to Friendly Leasing as Lessor of IBMC Pipe-Boring Machine

Year 0 Cash for machine Depreciation tax benefit ($680 = $2,000 × .34) Aftertax lease payment [$1,650 = $2,500 × (1 − .34)] Total

Year 1

Year 2

Year 3

Year 4

Year 5

$ 680

$ 680

$ 680

$ 680

$ 680

1,650 $2,330

1,650 $2,330

1,650 $2,330

1,650 $2,330

1,650 $2,330

−$10,000

−$10,000

These cash flows are the opposite of the cash flows to Xomox, the lessee (see the bottom line of Table 21.3).

8

The break-even lease payment is $2,469.32 in our example. Both the lessor and lessee can solve for this as follows: $10,000 = $680 × A 5.05 + L × (1 − .34) × A 5.05

In this case, L = $2,469.32.

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Although we will not admit to being wrong (what authors would?!), we freely admit that our explanation is incomplete at this point. The next section considers factors that give benefits to leasing.

21.9 Reasons for Leasing Proponents of leasing make many claims about why firms should lease assets rather than buy them. Some of the reasons given to support leasing are good, and some are not. Here we discuss good reasons for leasing and those we think are not.

Good Reasons for Leasing Leasing is a good choice if at least one of the following is true: 1. Taxes will be reduced by leasing. 2. The lease contract will reduce certain types of uncertainty. 3. Transaction costs will be higher for buying an asset and financing it with debt or equity than for leasing the asset. Tax Advantages The most important reason for long-term leasing is tax reduction. If the corporate income tax were repealed, long-term leasing would probably disappear. The tax advantages of leasing exist because firms are in different tax brackets. Should a user in a low tax bracket purchase, he will receive little tax benefit from depreciation and interest deductions. Should the user lease, the lessor will receive the depreciation shield and the interest deductions. In a competitive market, the lessor must charge a low lease payment to reflect these tax shields. Thus, the user is likely to lease rather than purchase. In our example with Xomox and Friendly Leasing, the value of the lease to Friendly was $87.68: $87.68 = −$10,000 + $2,330 × A 5.05 However, the value of the lease to Xomox was exactly the opposite (−$87.68). Because the lessor’s gains came at the expense of the lessee, no deal could be arranged. However, if Xomox pays no taxes and the lease payments are reduced to $2,475 from $2,500, both Friendly and Xomox will find positive NPVs in leasing. Xomox can rework Table 21.3 with tC = 0, finding that its cash flows from leasing are now these: Year 0 Cost of machine Lease payment

Year 1

Year 2

Year 3

Year 4

Year 5

−$2,475

−$2,475

−$2,475

−$2,475

−$2,475

$10,000

The value of the lease to Xomox is: Value of lease = $10,000 − $2,475 × A 5.0757575 = $6.55

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Notice that the discount rate is the interest rate of 7.57575 percent because tax rates are zero. In addition, the full lease payment of $2,475—and not some lower aftertax number—is used because there are no taxes. Finally, note that depreciation is ignored, also because no taxes apply. Given a lease payment of $2,475, the cash flows to Friendly Leasing look like this:

Year 0 Cost of machine Depreciation tax shield ($680 = $2,000 × .34) Aftertax lease payment [$1,633.50 = $2,475 × (1 − .34)] Total

Year 1

Year 2

Year 3

Year 4

Year 5

−$10,000 $ 680

$ 680

$ 680

$ 680

$ 680

$1,633.50 $2,313.50

$1,633.50 $2,313.50

$1,633.50 $2,313.50

$1,633.50 $ 2,313.50

$1,633.50 $2,313.50

The value of the lease to Friendly is: Value of lease = −$10,000 + $2,313.50 × A5.05 = −$10,000 + $10,016.24 =$16.24 As a consequence of different tax rates, the lessee (Xomox) gains $6.55 and the lessor (Friendly) gains $16.24. Both the lessor and the lessee can gain if their tax rates are different because the lessor uses the depreciation and interest tax shields that cannot be used by the lessee. The IRS loses tax revenue, and some of the tax gains of the lessor are passed on to the lessee in the form of lower lease payments. Because both parties can gain when tax rates differ, the lease payment is agreed upon through negotiation. Before negotiation begins, each party needs to know the reservation payment of both parties. This is the payment that will make one party indifferent to whether it enters the lease deal. In other words, this is the payment that makes the value of the lease zero. These payments are calculated next. Reservation Payment of Lessee We now solve for LMAX, the payment that makes the value of the lease to the lessee zero. When the lessee is in a zero tax bracket, his cash flows, in terms of LMAX, are as follows:

Year 0 Cost of machine Lease payment

Year 1

Year 2

Year 3

Year 4

Year 5

−L MAX

−L MAX

−L MAX

−L MAX

−L MAX

$10,000

This chart implies that: Value of lease = $10,000 − LMAX × A5.0757575

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The value of the lease equals zero when: $10,000 = $2,476.62 LMAX = _______ A5.0757575 After performing this calculation, the lessor knows that he will never be able to charge a payment above $2,476.62. Reservation Payment of Lessor We now solve for LMIN, the payment that makes the value of the lease to the lessor zero. The cash flows to the lessor, in terms of LMIN, are these: Year 0 Cost of machine Depreciation tax shield ($680 = $2,000 × .34) Aftertax lease payment (tC = .34)

Year 1

Year 2

Year 3

Year 4

Year 5

$680

$680

$680

$680

$680

LMIN × (.66)

LMIN × (.66)

LMIN × (.66)

LMIN × (.66)

LMIN × (.66)

−$10,000

This chart implies that: Value of lease = −$10,000 + $680 × A5.05 + LMIN × (.66) × A5.05 The value of the lease equals zero when: $10,000 $680 LMIN = _________ − _____ .66 .66 × A5.05 = $3,499.62 − $1,030.30 =$2,469.32 After performing this calculation, the lessee knows that the lessor will never agree to a lease payment below $2,469.32. A Reduction of Uncertainty We have noted that the lessee does not own the property when the lease expires. The value of the property at this time is called the residual value, and the lessor has a firm claim to it. When the lease contract is signed, there may be substantial uncertainty about what the residual value of the asset will be. Thus, under a lease contract, this residual risk is borne by the lessor. Conversely, the user bears this risk when purchasing. It is common sense that the party best able to bear a particular risk should do so. If the user has little risk aversion, she will not suffer by purchasing. However, if the user is highly averse to risk, she should find a third-party lessor more capable of assuming this burden. This latter situation frequently arises when the user is a small or newly formed firm. Because the risk of the entire firm is likely to be quite high and because the principal stockholders are likely to be undiversified, the firm desires to minimize risk wherever possible. A potential lessor, such as a large, publicly held financial institution, is far more capable of bearing the risk. Conversely, this situation is not expected to happen when the user is a blue chip corporation. That potential lessee is more able to bear risk.

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Transaction Costs The costs of changing an asset’s ownership are generally greater than the costs of writing a lease agreement. Consider the choice that confronts a person who lives in Los Angeles but must do business in New York for two days. It would clearly be cheaper to rent a hotel room for two nights than it would be to buy an apartment condominium for two days and then to sell it. Unfortunately, leases generate agency costs as well. For example, the lessee might misuse or overuse the asset because she has no interest in the asset’s residual value. This cost will be implicitly paid by the lessee through a high lease payment. Although the lessor can reduce these agency costs through monitoring, monitoring itself is costly. Thus, leasing is most beneficial when the transaction costs of purchase and resale outweigh the agency costs and monitoring costs of a lease. Flath argues that this occurs in short-term leases but not in long-term leases.9

Bad Reasons for Leasing Leasing and Accounting Income In our discussion of accounting and leasing we pointed out that a firm’s balance sheet shows fewer liabilities with an operating lease than with either a capitalized lease or a purchase financed with debt. We indicated that a firm desiring to project a strong balance sheet might select an operating lease. In addition, the firm’s return on assets (ROA) is generally higher with an operating lease than with either a capitalized lease or a purchase. To see this, we look at the numerator and denominator of the ROA formula in turn. With an operating lease, lease payments are treated as an expense. If the asset is purchased, both depreciation and interest charges are expenses. At least in the early part of the asset’s life, the yearly lease payment is generally less than the sum of yearly depreciation and yearly interest. Thus, accounting income, the numerator of the ROA formula, is higher with an operating lease than with a purchase. Because accounting expenses with a capitalized lease are analogous to depreciation and interest with a purchase, the increase in accounting income does not occur when a lease is capitalized. In addition, leased assets do not appear on the balance sheet with an operating lease. Thus, the total asset value of a firm, the denominator of the ROA formula, is less with an operating lease than it is with either a purchase or a capitalized lease. The two preceding effects imply that the firm’s ROA should be higher with an operating lease than with either a purchase or a capitalized lease. Of course, in an efficient capital market, accounting information cannot be used to fool investors. It is unlikely, then, that leasing’s impact on accounting numbers should create value for the firm. Savvy investors should be able to see through attempts by management to improve the firm’s financial statements. One Hundred Percent Financing It is often claimed that leasing provides 100 percent financing, whereas secured equipment loans require an initial down payment. However, we argued earlier that leases tend to displace debt elsewhere in the firm. Our earlier analysis suggests that leases do not permit a greater level of total liabilities than do purchases with borrowing. Other Reasons There are, of course, many special reasons that some companies find advantages in leasing. In one celebrated case, the U.S. Navy leased a fleet of 9

D. Flath, “The Economics of Short-Term Leasing,” Economic Inquiry 18 (April 1980).

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tankers instead of asking Congress for appropriations. Thus, leasing may be used to circumvent capital expenditure control systems set up by bureaucratic firms.

21.10 Some Unanswered Questions Our analysis suggests that the primary advantage of long-term leasing results from the differential tax rates of the lessor and the lessee. Other valid reasons for leasing are lower contracting costs and risk reduction. There are several questions our analysis has not specifically answered.

Are the Uses of Leases and Debt Complementary? Ang and Peterson find that firms with high debt tend to lease frequently as well.10 This result should not be puzzling. The corporate attributes that provide high debt capacity may also make leasing advantageous. Thus, even though leasing displaces debt (that is, leasing and borrowing are substitutes) for an individual firm, high debt and high leasing can be positively associated when we look at a number of firms.

Why Are Leases Offered by Both Manufacturers and Third-Party Lessors? The offsetting effects of taxes can explain why both manufacturers (for example, computer firms) and third-party lessors offer leases. 1. For manufacturer lessors, the basis for determining depreciation is the manufacturer’s cost. For third-party lessors, the basis is the sales price that the lessor paid to the manufacturer. Because the sales price is generally greater than the manufacturer’s cost, this is an advantage to third-party lessors. 2. However, the manufacturer must recognize a profit for tax purposes when selling the asset to the third-party lessor. The manufacturer’s profit for some equipment can be deferred if the manufacturer becomes the lessor. This provides an incentive forman ufacturerst ole ase.

Why Are Some Assets Leased More Than Others? Certain assets appear to be leased more frequently than others. Smith and Wakeman have looked at nontax incentives affecting leasing.11 Their analysis suggests many asset and firm characteristics that are important in the lease-or-buy decision. The following are among the things they mention: 1. The more sensitive the value of an asset is to use and maintenance decisions, the more likely it is that the asset will be purchased instead of leased. They argue that ownership provides a better incentive to minimize maintenance costs than does leasing. 2. Price discrimination opportunities may be important. Leasing may be a way of circumventing laws against charging too lowap rice.

10

J. Ang and P. P. Peterson, “The Leasing Puzzle,” Journal of Finance 39 (September 1984). C. W. Smith, Jr., and L. M. Wakeman, “Determinants of Corporate Leasing Policy,” Journal of Finance 40 (July 1985). 11

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We also documented a number of bad reasons for leasing.

Concept Questions

1. 2.

3. 4.

5.

Leasing versus Borrowing What are the key differences between leasing and borrowing? Are they perfect substitutes? Leasing and Taxes Taxes are an important consideration in the leasing decision. Which is more likely to lease: a profitable corporation in a high tax bracket or a less profitable one in a low tax bracket? Why? Leasing and IRR What are some of the potential problems with looking at IRRs when evaluating a leasing decision? Leasing Comment on the following remarks: a. Leasing reduces risk and can reduce a firm’s cost of capital. b. Leasing provides 100 percent financing. c. If the tax advantages of leasing were eliminated, leasing would disappear. Accounting for Leases Discuss the accounting criteria for determining whether a lease must be reported on the balance sheet. In each case give a rationale for the criterion.

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A large fraction of America’s equipment is leased rather than purchased. This chapter both described the institutional arrangements surrounding leases and showed how to evaluate leases financially. 1. Leases can be separated into two polar types. Though operating leases allow the lessee to use the equipment, ownership remains with the lessor. Although the lessor in a financial lease legally owns the equipment, the lessee maintains effective ownership because financial leases are fully amortized. 2. When a firm purchases an asset with debt, both the asset and the liability appear on the firm’s balance sheet. If a lease meets at least one of a number of criteria, it must be capitalized. This means that the present value of the lease appears as both an asset and a liability. A lease escapes capitalization if it does not meet any of these criteria. Leases not meeting the criteria are called operating leases, though the accountant’s definition differs somewhat from the practitioner’s definition. Operating leases do not appear on the balance sheet. For cosmetic reasons, many firms prefer that a lease be called operating. 3. Firms generally lease for tax purposes. To protect its interests, the IRS allows financial arrangements to be classified as leases only if a number of criteria are met. 4. We showed that risk-free cash flows should be discounted at the aftertax risk-free rate. Because both lease payments and depreciation tax shields are nearly riskless, all relevant cash flows in the lease–buy decision should be discounted at a rate near this aftertax rate. We use the real-world convention of discounting at the aftertax interest rate on the lessee’s secured debt. 5. Though this method is simple, it lacks certain intuitive appeal. We presented an alternative method in the hopes of increasing the reader’s intuition. Relative to a lease, a purchase generates debt capacity. This increase in debt capacity can be calculated by discounting the difference between the cash flows of the purchase and the cash flows of the lease by the aftertax interest rate. The increase in debt capacity from a purchase is compared to the extra outflow at year 0 from a purchase. 6. If the lessor is in the same tax bracket as the lessee, the cash flows to the lessor are exactly the opposite of the cash flows to the lessee. Thus, the sum of the value of the lease to the lessee plus the value of the lease to the lessor must be zero. Although this suggests that leases can never fly, there are actually at least three good reasons for leasing: a. Differences in tax brackets between the lessor and lessee. b. Shift of risk bearing to the lessor. c. Minimizationo f t ransactionc osts.

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IRS Criteria Discuss the IRS criteria for determining whether a lease is tax deductible. In each case give a rationale for the criterion. 7. Off–Balance Sheet Financing What is meant by the term off–balance sheet financing? When do leases provide such financing, and what are the accounting and economic consequences of such activity? 8. Sale and Leaseback Why might a firm choose to engage in a sale and leaseback transaction? Give two reasons. 9. Leasing Cost Explain why the aftertax borrowing rate is the appropriate discount rate to use in lease evaluation. Refer to the following example for Questions 10 through 12. In June 2008, Genesis Lease Limited announced a deal to purchase a Boeing 767-300ER passenger aircraft. Genesis then signed a lease contract on the plane with Japan Airlines International until 2020. This new plane gave Genesis 54 aircraft leased to 36 airlines in 19 countries. 10. Leasing versus Purchase Why wouldn’t Japan Airlines purchase the plane if it was obviously needed for the company’s operations? 11. Reasons to Lease Why would Genesis Lease Limited be willing to buy a plane from Boeing and then lease it to Japan Airlines? How is this different from just lending money to Japan Airlines to buy the plane? 12. Leasing What do you suppose happens to the plane at the end of the lease period?

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6.

Questions and Problems BASIC (Questions 1–8)

Use the following information to work Problems 1–6. You work for a nuclear research laboratory that is contemplating leasing a diagnostic scanner (leasing is a common practice with expensive, high-tech equipment). The scanner costs $4,500,000, and it would be depreciated straight-line to zero over four years. Because of radiation contamination, it will actually be completely valueless in four years. You can lease it for $1,350,000 per year for four years. 1. Lease or Buy Assume that the tax rate is 35 percent. You can borrow at 8 percent before taxes. Should you lease or buy? 2. Leasing Cash Flows What are the cash flows from the lease from the lessor’s viewpoint? Assume a 35 percent tax bracket. 3. Finding the Break-Even Payment What would the lease payment have to be for both the lessor and the lessee to be indifferent about the lease? 4. Taxes and Leasing Cash Flows Assume that your company does not contemplate paying taxes for the next several years. What are the cash flows from leasing in this case? 5. Setting the Lease Payment In the previous question, over what range of lease payments will the lease be profitable for both parties? 6. MACRS Depreciation and Leasing Rework Problem 1 assuming that the scanner will be depreciated as three-year property under MACRS (see Chapter 6 for the depreciation allowances). 7. Lease or Buy Super Sonics Entertainment is considering buying a machine that costs $435,000. The machine will be depreciated over five years by the straight-line method and will be worthless at that time. The company can lease the machine with year-end payments of $107,500. The company can issue bonds at a 9 percent interest rate. If the corporate tax rate is 35 percent, should the company buy or lease? 8. Setting the Lease Payment Quartz Corporation is a relatively new firm. Quartz has experienced enough losses during its early years to provide it with at least eight years of tax loss carryforwards. Thus, Quartz’s effective tax rate is zero. Quartz plans to

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lease equipment from New Leasing Company. The term of the lease is five years. The purchase cost of the equipment is $780,000. New Leasing Company is in the 35 percent tax bracket. There are no transaction costs to the lease. Each firm can borrow at 7 percent. a. What is Quartz’s reservation price? b. What is New Leasing Company’s reservation price? c. Explain why these reservation prices determine the negotiating range of the lease. INTERMEDIATE (Questions 9–16)

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Use the following information to work Problems 9–11. The Wildcat Oil Company is trying to decide whether to lease or buy a new computer-assisted drilling system for its oil exploration business. Management has decided that it must use the system to stay competitive; it will provide $1.1 million in annual pretax cost savings. The system costs $7 million and will be depreciated straight-line to zero over five years. Wildcat’s tax rate is 34 percent, and the firm can borrow at 9 percent. Lambert Leasing Company has offered to lease the drilling equipment to Wildcat for payments of $1,650,000 per year. Lambert’s policy is to require its lessees to make payments at the start of the year. 9. Lease or Buy What is the NAL for Wildcat? What is the maximum lease payment that would be acceptable to the company? 10. Leasing and Salvage Value Suppose it is estimated that the equipment will have an aftertax residual value of $700,000 at the end of the lease. What is the maximum lease payment acceptable to Wildcat now? 11. Deposits in Leasing Many lessors require a security deposit in the form of a cash payment or other pledged collateral. Suppose Lambert requires Wildcat to pay a $500,000 security deposit at the inception of the lease. If the lease payment is still $1,650,000, is it advantageous for Wildcat to lease the equipment now? 12. Setting the Lease Price Raymond Rayon Corporation wants to expand its manufacturing facilities. Liberty Leasing Corporation has offered Raymond Rayon the opportunity to lease a machine for $2,600,000 for six years. The machine will be fully depreciated by the straight-line method. The corporate tax rate for Raymond Rayon is 25 percent, whereas Liberty Leasing has a corporate tax rate of 40 percent. Both companies can borrow at 9 percent. Assume lease payments occur at year-end. What is Raymond’s reservation price? What is Liberty’s reservation price? 13. Setting the Lease Price An asset costs $475,000 and will be depreciated in a straightline manner over its three-year life. It will have no salvage value. The corporate tax rate is 34 percent, and the appropriate interest rate is 10 percent. a. What set of lease payments will make the lessee and the lessor equally well off ? b. Show the general condition that will make the value of a lease to the lessor the negative of the value to the lessee. c. Assume that the lessee pays no taxes and the lessor is in the 34 percent tax bracket. For what range of lease payments does the lease have a positive NPV for both parties? 14. Lease or Buy Wolfson Corporation has decided to purchase a new machine that costs $5.1 million. The machine will be depreciated on a straight-line basis and will be worthless after four years. The corporate tax rate is 35 percent. The Sur Bank has offered Wolfson a four-year loan for $5.1 million. The repayment schedule is four yearly principal repayments of $1,275,000 and an interest charge of 9 percent on the outstanding balance of the loan at the beginning of each year. Both principal repayments and interest are due at the end of each year. Cal Leasing Corporation offers to lease the same machine to Wolfson. Lease payments of $1.5 million per year are due at the beginning of each of the four years of the lease. a. Should Wolfson lease the machine or buy it with bank financing? b. What is the annual lease payment that will make Wolfson indifferent to whether it leases the machine or purchases it? 15. Setting the Lease Price An asset costs $330,000 and will be depreciated in a straight-line manner over its three-year life. It will have no salvage value. The lessor

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16.

CHALLENGE (Questions1 7–18)

17.

18.

can borrow at 7 percent and the lessee can borrow at 9 percent. The corporate tax rate is 34 percent for both companies. a. How does the fact that the lessor and lessee have different borrowing rates affect the calculation of the NAL? b. What set of lease payments will make the lessee and the lessor equally well off ? c. Assume that the lessee pays no taxes and the lessor is in the 34 percent tax bracket. For what range of lease payments does the lease have a positive NPV for both parties? Automobile Lease Payments Automobiles are often leased, and there are several terms unique to auto leases. Suppose you are considering leasing a car. The price you and the dealer agree on for the car is $28,000. This is the base capitalized cost. Other costs added to the capitalized cost price include the acquisition (bank) fee, insurance, or extended warranty. Assume these costs are $450. Capitalization cost reductions include any down payment, credit for trade-in, or dealer rebate. Assume you make a down payment of $2,000, and there is no trade-in or rebate. If you drive 12,000 miles per year, the lease-end residual value for this car will be $16,500 after three years. The lease or “money” factor, which is the interest rate on the loan, is the APR of the loan divided by 2,400. (We’re not really sure where the 2,400 comes from either.) The lease factor the dealer quotes you is .00342. The monthly lease payment consists of three parts: a depreciation fee, a finance fee, and sales tax. The depreciation fee is the net capitalization cost minus the residual value divided by the term of the lease. The net capitalization cost is the cost of the car minus any cost reductions plus any additional costs. The finance fee is the net capitalization cost plus the residual times the money factor, and the monthly sales tax is simply the monthly lease payment times the tax rate. What APR is the dealer quoting you? What is your monthly lease payment for a 36-month lease if the sales tax is 7 percent? Lease versus Borrow Return to the case of the diagnostic scanner discussed in Problems 1 through 6. Suppose the entire $4,500,000 purchase price of the scanner is borrowed. The rate on the loan is 8 percent, and the loan will be repaid in equal installments. Create a lease-versus-buy analysis that explicitly incorporates the loan payments. Show that the NPV of leasing instead of buying is not changed from what it was in Problem 1. Why is this so? Lease or Buy High electricity costs have made Farmer Corporation’s chickenplucking machine economically worthless. Only two machines are available to replace it. The International Plucking Machine (IPM) model is available only on a lease basis. The lease payments will be $27,000 for five years, due at the beginning of each year. This machine will save Farmer $12,000 per year through reductions in electricity costs in every year. As an alternative, Farmer can purchase a more energy-efficient machine from Basic Machine Corporation (BMC) for $150,000. This machine will save $20,000 per year in electricity costs. A local bank has offered to finance the machine with a $150,000 loan. The interest rate on the loan will be 10 percent on the remaining balance and will require five annual principal payments of $30,000. Farmer has a target debt-to-asset ratio of 67 percent. Farmer is in the 34 percent tax bracket. After five years, both machines will be worthless. The machines will be depreciated on a straight-line basis. a. Should Farmer lease the IPM machine or purchase the more efficient BMC machine? b. Does your answer depend on the form of financing for direct purchase? c. Howm uchd ebtis d isplacedb yt hisle ase?

Appendix 21A APV Approach to Leasing To access the appendix for this chapter, please visit www.mhhe.com/rwj.

Mini Case

THE DECISION TO LEASE OR BUY AT WARF COMPUTERS Warf Computers has decided to proceed with the manufacture and distribution of the virtual keyboard (VK) the company has developed. To undertake this venture, the company needs to obtain equipment for the production of the microphone for the keyboard. Because of the required sensitivity of the microphone and its small size, the company needs specialized equipment for production. Nick Warf, the company president, has found a vendor for the equipment. Clapton Acoustical Equipment has offered to sell Warf Computers the necessary equipment at a price of $2.5 million. Because of the rapid development of new technology, the equipment falls in the three-year MACRS depreciation class. At the end of four years, the market value of the equipment is expected to be $300,000. Alternatively, the company can lease the equipment from Hendrix Leasing. The lease contract calls for four annual payments of $650,000, due at the beginning of the year. Additionally, Warf Computers must make a security deposit of $150,000 that will be returned when the lease expires. Warf Computers can issue bonds with a yield of 11 percent, and the company has a marginal tax rate of 35 percent. 1. Should Warf buy or lease the equipment? 2. Nick mentions to James Hendrix, the president of Hendrix Leasing, that although the company will need the equipment for four years, he would like a lease contract for two years instead. At the end of the two years, the lease could be renewed. Nick would also like to eliminate the security deposit, but he would be willing to increase the lease payments to $1,150,000 for each of the two years. When the lease is renewed in two years, Hendrix would consider the increased lease payments in the first two years when calculating the terms of the renewal. The equipment is expected to have a market value of $1 million in two years. What is the NAL of the lease contract under these terms? Why might Nick prefer this lease? What are the potential ethical issues concerning the new lease terms? 3. In the leasing discussion, James informs Nick that the contract could include a purchase option for the equipment at the end of the lease. Hendrix Leasing offers three purchase options: a. An option to purchase the equipment at the fair market value. b. An option to purchase the equipment at a fixed price. The price will be negotiated before the lease is signed. c. An option to purchase the equipment at a price of $125,000. How would the inclusion of a purchase option affect the value of the lease? 4. James also informs Nick that the lease contract can include a cancellation option. The cancellation option would allow Warf Computers to cancel the lease on any anniversary date of the contract. In order to cancel the lease, Warf Computers would be required to give 30 days’ notice prior to the anniversary date. How would the inclusion of ac ancellationo ptionaf fectt hev alueo f t hele ase?

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CHAPTER 22

OptionsandCo rporate Finance On January 9, 2009, the closing stock prices for PepsiCo, 3M, and Amazon.com were $52.57, $57.74, and $55.51, respectively. Each company had a call option trading on the Chicago Board Options Exchange with a $55 strike price and an expiration date of February 21—43 days away. You might expect that the prices on these call options would be similar, but they weren’t. The PepsiCo options sold for $1.30, 3M options traded at $5, and Amazon.com options traded at $6.20. Why would options on these three similarly priced stocks be priced so differently when the strike prices and the time to expiration were exactly the same? A big reason is that the volatility of the underlying stock is an important determinant of an option’s underlying value; and, in fact, these three stocks had very different volatilities. In this chapter, we explore this issue—and many others—in much greater depth using the Nobel Prize–winning Black–Scholes option pricing model.

22.1 Options The Options Industry Council has a Web page with lots of educational material at www.888options.com.

An option is a contract giving its owner the right to buy or sell an asset at a fixed price on or before a given date. For example, an option on a building might give the buyer the right to buy the building for $1 million on or anytime before the Saturday prior to the third Wednesday in January 2010. Options are a unique type of financial contract because they give the buyer the right, but not the obligation, to do something. The buyer uses the option only if it is advantageous to do so; otherwise the option can be thrown away. There is a special vocabulary associated with options. Here are some important definitions: 1. Exercising the option: The act of buying or selling the underlying asset via the optionc ontract. 2. Strike, or exercise, price: The fixed price in the option contract at which the holder can buy or sell the underlying asset. 3. Expiration date: The maturity date of the option; after this date, the option is dead. 4. American and European options: An American option may be exercised anytime up to the expiration date. A European option differs from an American option in that it can be exercised only on the expiration date.

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22.2 Call Options The most common type of option is a call option. A call option gives the owner the right to buy an asset at a fixed price during a particular period. There is no restriction on the kind of asset, but the most common ones traded on exchanges are options on stocks and bonds. For example, call options on IBM stock can be purchased on the Chicago Board Options Exchange. IBM does not issue (that is, sell) call options on its common stock. Instead, individual investors are the original buyers and sellers of call options on IBM common stock. Suppose it is April 1. A representative call option on IBM stock enables an investor to buy 100 shares of IBM on or before September 19 (options expire on the Saturday after the third Friday of the month) at an exercise price of $100. This is a valuable option if there is some probability that the price of IBM common stock will exceed $100 on or before September 19.

The Value of a Call Option at Expiration What is the value of a call option contract on common stock at expiration? The answer depends on the value of the underlying stock at expiration. Let’s continue with the IBM example. Suppose the stock price is $130 at expiration. The buyer1 of the call option has the right to buy the underlying stock at the exercise price of $100. In other words, he has the right to exercise the call. Having the right to buy something for $100 when it is worth $130 is obviously a good thing. The value of this right is $30 (=$130 − $100) on the expiration day.2 The call would be worth even more if the stock price was higher on the expiration day. For example, if IBM were selling for $150 on the date of expiration, the call would be worth $50 (=$150 − $100) at that time. In fact, the call’s value increases $1 for every $1 rise in the stock price. If the stock price is greater than the exercise price, we say that the call is in the money. Of course, it is also possible that the value of the common stock will turn out to be less than the exercise price, in which case we say that the call is out of the money. The holder will not exercise in this case. For example, if the stock price at the expiration date is $90, no rational investor would exercise. Why pay $100 for stock worth only $90? Because the option holder has no obligation to exercise the call, she can walk away from the option. As a consequence, if IBM’s stock price is less than $100 on the expiration date, the value of the call option will be $0. In this case the value of the call option is not the difference between IBM’s stock price and $100, as it would be if the holder of the call option had the obligation to exercise the call. Here is the payoff of this call option at expiration: Payoff on the Expiration Date

Call option value

If Stock Price Is Less Than $100

If Stock Price Is Greater Than $100

$0

Stock price − $100

We use buyer, owner, and holder interchangeably. This example assumes that the call lets the holder purchase one share of stock at $100. In reality, one call option contract would let the holder purchase 100 shares. The profit would then equal $3,000 [= ($130 − $100) × 100].

1 2

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Figure 22.1 Value of call option at expiration ($)

The Value of a Call Option on the Expiration Date

0

$100 Value of common stock at expiration ($)

A call option gives the owner the right to buy an asset at a fixed price during a particular time period. If, at the expiration date, IBM’s stock price is greater than the exercise price of $100, the call’s value is: Stock price − $100 If IBM’s stock price is less than $100 at this time, the value of the call is zero.

Figure 22.1 plots the value of the call option at expiration against the value of IBM’s stock. This is referred to as the hockey stick diagram of call option values. If the stock price is less than $100, the call is out of the money and worthless. If the stock price is greater than $100, the call is in the money and its value rises one-for-one with increases in the stock price. Notice that the call can never have a negative value. It is a limited liability instrument, which means that all the holder can lose is the initial amount she paid for it.

EXAMPLE 22.1 Call Option Payoffs Suppose Mr. Optimist holds a one-year call option on TIX common stock. It is a European call option and can be exercised at $150. Assume that the expiration date has arrived. What is the value of the TIX call option on the expiration date? If TIX is selling for $200 per share, Mr. Optimist can exercise the option—purchase TIX at $150—and then immediately sell the share at $200. Mr. Optimist will have made $50 (=$200 − $150). Thus, the price of this call option must be $50 at expiration. Instead, assume that TIX is selling for $100 per share on the expiration date. If Mr. Optimist still holds the call option, he will throw it out.The value of the TIX call option on the expiration date will bez erointhisc ase.

22.3 Put Options A put option can be viewed as the opposite of a call option. Just as a call gives the holder the right to buy the stock at a fixed price, a put gives the holder the right to sell the stock for a fixed exercise price.

The Value of a Put Option at Expiration The circumstances that determine the value of the put are the opposite of those for a call option because a put option gives the holder the right to sell shares. Let

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us assume that the exercise price of the put is $50 and the stock price at expiration is $40. The owner of this put option has the right to sell the stock for more than it is worth, something that is clearly profitable. That is, he can buy the stock at the market price of $40 and immediately sell it at the exercise price of $50, generating a profit of $10 (=$50 − $40). Thus, the value of the option at expiration must be $10. The profit would be greater still if the stock price were lower. For example, if the stock price were only $30, the value of the option would be $20 (=$50 − $30). In fact, for every $1 that the stock price declines at expiration, the value of the put rises by $1. However, suppose that the stock at expiration is trading at $60—or any price above the exercise price of $50. The owner of the put option would not want to exercise here. It is a losing proposition to sell a stock for $50 when it trades in the open market at $60. Instead, the owner of the put will walk away from the option. That is, he will let the put option expire. Here is the payoff of this put option:

Payoff on the Expiration Date

Put option value

If Stock Price Is Less Than $50

If Stock Price Is Greater Than $50

$50 − Stock price

$0

Figure 22.2 plots the values of a put option for all possible values of the underlying stock. It is instructive to compare Figure 22.2 to Figure 22.1 for the call option. The call option is valuable when the stock price is above the exercise price, and the put option is valuable when the stock price is below the exercise price.

The Value of a Put Option on the Expiration Date

Value of put option at expiration ($)

Figure 22.2 50

0

50 Value of common stock at expiration ($)

A put option gives the owner the right to sell an asset at a fixed price during a particular period. If the stock price is greater than the exercise price of $50, the put value is zero. If the stock price is less than $50, the put value is: $50 − Stock price

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EXAMPLE 22.2 Put Option Payoffs Ms. Pessimist believes that BMI will fall from its current $160 per-share price. She buys a put. Her put option contract gives her the right to sell a share of BMI stock at $150 one year from now. If the price of BMI is $200 on the expiration date, she will tear up the put option contract because it is worthless. That is, she will not want to sell stock worth $200 for the exercise price of $150. On the other hand, if BMI is selling for $100 on the expiration date, she will exercise the option. In this case she can buy a share of BMI in the market for $100 per share and turn around and sell the share at the exercise price of $150. Her profit will be $50 (=$150 − $100). Therefore, the value of the put option on the expiration date will be $50.

22.4 Selling Options

Check out these option exchanges: www.cboe.com www.nasdaq.com www.kcbt.com www.euronext.com

An investor who sells (or writes) a call on common stock must deliver shares of the common stock if required to do so by the call option holder. Notice that the seller is obligated to do so. If, at the expiration date, the price of the common stock is greater than the exercise price, the holder will exercise the call and the seller must give the holder shares of stock in exchange for the exercise price. The seller loses the difference between the stock price and the exercise price. For example, assume that the stock price is $60 and the exercise price is $50. Knowing that exercise is imminent, the option seller buys stock in the open market at $60. Because she is obligated to sell at $50, she loses $10 (=$50 − $60). Conversely, if at the expiration date the price of the common stock is below the exercise price, the call option will not be exercised and the seller’s liability is zero. Why would the seller of a call place himself in such a precarious position? After all, the seller loses money if the stock price ends up above the exercise price, and he merely avoids losing money if the stock price ends up below the exercise price. The answer is that the seller is paid to take this risk. On the day that the option transaction takes place, the seller receives the price that the buyer pays. Now let’s look at the seller of puts. An investor who sells a put on common stock agrees to purchase shares of common stock if the put holder should so request. The seller loses on this deal if the stock price falls below the exercise price. For example, assume that the stock price is $40 and the exercise price is $50. The holder of the put will exercise in this case. In other words, she will sell the underlying stock at the exercise price of $50. This means that the seller of the put must buy the underlying stock at the exercise price of $50. Because the stock is worth only $40, the loss here is $10 (=$40 − $50). The values of the “sell-a-call” and “sell-a-put” positions are depicted in Figure 22.3. The graph on the left side of the figure shows that the seller of a call loses nothing when the stock price at the expiration date is below $50. However, the seller loses a dollar for every dollar that the stock rises above $50. The graph in the center of the figure shows that the seller of a put loses nothing when the stock price at expiration date is above $50. However, the seller loses a dollar for every dollar that the stock falls below $50. It is worthwhile to spend a few minutes comparing the graphs in Figure 22.3 to those in Figures 22.1 and 22.2. The graph of selling a call (the graph in the left side

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Figure 22.3

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The Payoffs to Sellers of Calls and Puts and to Buyers of Common Stock

Sell a Call

Value of a share of common stock ($)

Value of seller’s position at expiration ($)

Value of seller’s position at expiration ($) 0

50

Buy a Common Stock

Sell a Put

0

50

50

0

50

ⴚ50 Share price at expiration ($)

Share price at expiration ($)

Share price ($)

of Figure 22.3) is the mirror image of the graph of buying a call (Figure 22.1).3 This occurs because options are a zero-sum game. The seller of a call loses what the buyer makes. Similarly, the graph of selling a put (the middle graph in Figure 22.3) is the mirror image of the graph of buying a put (Figure 22.2). Again, the seller of a put loses what the buyer makes. Figure 22.3 also shows the value at expiration of simply buying common stock. Notice that buying the stock is the same as buying a call option on the stock with an exercise price of zero. This is not surprising. If the exercise price is zero, the call holder can buy the stock for nothing, which is really the same as owning it.

22.5 Option Quotes For more about option ticker symbols, go to the “Symbol Directory” link under “Trading Tools” at www.cboe.com.

Now that we understand the definitions for calls and puts, let’s see how these options are quoted. Table 22.1 presents information about Intel Corporation options expiring in September 2008, obtained from finance.yahoo.com. At the time of these quotes, Intel was selling for $23.57. On the left in the table are the available strike prices. On the top are call option quotes; put option quotes are on the bottom. The second column contains ticker symbols, which uniquely indicate the underlying stock; the type of option; the expiration month; and the strike price. Next, we have the most recent prices on the options (“Last”) and the change from the previous day (“Chg”). Bid and ask prices follow. Note that option prices are quoted on a per-option basis, but trading actually occurs in standardized contracts, where each contract calls for the purchase (for calls) or sale (for puts) of 100 shares. Thus, the call option with a strike price of $25 last traded at $.14 per option, or $14 per contract. The final two columns contain volume (“Vol”), quoted in contracts, and the open interest (“Open Int”), which is the number of contractsc urrentlyo utstanding. Actually, because of differing exercise prices, the two graphs are not quite mirror images of each other. The exercise price in Figure 22.1 is $100, and the exercise price in Figure 22.3 is $50.

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Table 22.1

View By Expiration: Sep 08 Oct 08 Jan 09 Apr 09 Jan 10 Expire at close Fri, Sep 19, 2008 CALL OPTIONS

Information about the Options of Intel Corporation

Strike

Symbol

Last

Chg

Bid

18.00 19.00 20.00 21.00 22.00 23.00 24.00 25.00 26.00 27.00 28.00 29.00

NQIR.X NQIT.X NQID.X NQIU.X NQIZ.X NQIY.X NQIB.X INQIE.X INQIA.X INQID.X INQIB.X INQIC.X

5.35 3.90 3.40 2.43 1.70 0.97 0.45 0.14 0.03 0.01 0.02 0.01

0.25 0.00 0.30 0.17 0.22 0.17 0.10 0.04 0.01 0.00 0.00 0.00

5.50 4.45 3.55 2.59 1.77 0.99 0.45 0.14 0.03 N/A N/A N/A

Vol

Open Int

5.60 35 4.55 80 3.60 202 2.62 139 1.79 209 1.00 1,092 0.46 880 0.15 172 0.04 54 0.02 29 0.01 69 0.01 2

Ask

221 2,518 906 4,093 11,292 19,646 25,547 40,478 14,855 11 50 98

Expire at close Fri, Sep 19, 2008

PUT OPTIONS Strike

Symbol

Last

Chg

Bid

18.00 19.00 20.00 21.00 22.00 23.00 24.00 25.00 26.00

NQUR.X NQUT.X NQUD.X NQUU.X NQUZ.X NQUY.X NQUB.X INQUE.X INQUA.X

0.02 0.04 0.06 0.09 0.22 0.46 0.93 1.66 2.89

0.00 0.00 0.00 0.04 0.08 0.16 0.27 0.45 0.31

N/A 0.01 0.03 0.07 0.19 0.43 0.91 1.61 2.45

Vol

Open Int

0.01 8 0.02 20 0.04 171 0.09 562 0.20 124 0.44 699 0.93 1,079 1.64 275 2.48 218

Ask

443 1,475 3,248 11,826 21,402 13,893 10,789 3,114 1,091

22.6 Combinations of Options Puts and calls can serve as building blocks for more complex option contracts. For example, Figure 22.4 illustrates the payoff from buying a put option on a stock and simultaneously buying the stock. If the share price is greater than the exercise price, the put option is worthless, and the value of the combined position is equal to the value of the common stock. If, instead, the exercise price is greater than the share price, the decline in the value of the shares will be exactly offset by the rise in the value of the put. Payoff to the Combination of Buying a Put and Buying the Underlying Stock

50 ⴙ

0

50 Value of common stock at expiration ($)

Buy Put

ⴙ

50 ⴝ

0

50 Value of common stock at expiration ($)

Combination

ⴝ Value of combination of stock and put positions at expiration ($)

Value of stock position at expiration ($)

Buy Stock

Value of put position at expiration ($)

Figure 22.4

50

0

50 Value of common stock at expiration ($)

Chapter 22

50 Value of common stock at expiration ($)

Buy zero coupon bond 50

50 Value of common stock at expiration ($)

Value of combination of call and zero coupon bond at expiration ($)

Buy call

0

683

Payoff to the Combination of Buying a Call and Buying a Zero Coupon Bond

Value of zero coupon bond at expiration ($)

Value of call position at expiration ($)

Figure 22.5

Options and Corporate Finance

Combination

50

50 Value of common stock at expiration ($)

The graph of buying a call and buying a zero coupon bond is the same as the graph of buying a put and buying the stock in Figure 22.4

The Th strategy off buying b i a put and db buying i the h underlying d l i stock k is i called ll d a protective put. It is as if we are buying insurance for the stock. The stock can always be sold at the exercise price, regardless of how far the market price of the stock falls. Note that the combination of buying a put and buying the underlying stock has the same shape in Figure 22.4 as the call purchase in Figure 22.1. To pursue this point, let’s consider the graph for buying a call, which is shown at the far left of Figure 22.5. This graph is the same as Figure 22.1, except that the exercise price is $50 here. Now let’s try the strategy of: (Leg A) Buying a call. (Leg B) Buying a risk-free, zero coupon bond (i.e., a T-bill) with a face value of $50 that matures on the same day that the option expires. We have drawn the graph of leg A of this strategy at the far left of Figure 22.5, but what does the graph of leg B look like? It looks like the middle graph of the figure. That is, anyone buying this zero coupon bond will be guaranteed to receive $50, regardless of the price of the stock at expiration. What does the graph of simultaneously buying both leg A and leg B of this strategy look like? It looks like the far right graph of Figure 22.5. That is, the investor receives a guaranteed $50 from the bond, regardless of what happens to the stock. In addition, the investor receives a payoff from the call of $1 for every $1 that the price of the stock rises above the exercise price of $50. The far right graph of Figure 22.5 looks exactly like the far right graph of Figure 22.4. Thus, an investor gets the same payoff from the strategy of Figure 22.4 and the strategy of Figure 22.5, regardless of what happens to the price of the underlying stock. In other words, the investor gets the same payoff from: 1. Buying a put and buying the underlying stock. 2. Buying a call and buying a risk-free, zero coupon bond. If investors have the same payoffs from the two strategies, the two strategies must have the same cost. Otherwise, all investors will choose the strategy with the lower cost and avoid the strategy with the higher cost. This leads to the following interesting result: Price of underlying Price of Price of Present value of + put = call + exercise price stock Cost of first strategy = Cost of second strategy

(22.1)

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This relationship is known as put–call parity and is one of the most fundamental relationships concerning options. It says that there are two ways of buying a protective put. You can buy a put and buy the underlying stock simultaneously. Here, your total cost is the price of the underlying stock plus the price of the put. Or you can buy the call and buy a zero coupon bond. Here, your total cost is the price of the call plus the price of the zero coupon bond. The price of the zero coupon bond is equal to the present value of the exercise price—that is, the present value of $50 in our example. Equation (22.1) is a very precise relationship. It holds only if the put and the call have both the same exercise price and the same expiration date. In addition, the maturity date of the zero coupon bond must be the same as the expiration date of the options. To see how fundamental put–call parity is, let’s rearrange the formula, yielding: Price of underlying Price of Price of Present value of = call − + exercise price stock put This relationship now states that you can replicate the purchase of a share of stock by buying a call, selling a put, and buying a zero coupon bond. (Note that because a minus sign comes before “Price of put,” the put is sold, not bought.) Investors in this three-legged strategy are said to have purchased a syntheticsto ck. Let’s do one more transformation: Covered Call Strategy Price of underlying Price Present value of −Price − of call = + exercise price stock of put Many investors like to buy a stock and write the call on the stock simultaneously. This is a conservative strategy known as selling a covered call. The preceding put–call parity relationship tells us that this strategy is equivalent to selling a put and buying a zero coupon bond. Figure 22.6 develops the graph for the covered call. You can verify that the covered call can be replicated by selling a put and simultaneously buying a zero coupon bond.

Value of stock at expiration ($)

Buy a stock

0

Sell a call

Value of combination of buying a stock and selling a call at expiration

Payoff to the Combination of Buying a Stock and Selling a Call

Value of selling a call at expiration ($)

Figure 22.6

Buy a stock plus sell a call

50

50

50

Value of stock at expiration ($)

Value of stock at expiration ($)

Value of stock at expiration ($)

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Of course, there are other ways of rearranging the basic put–call relationship. For each rearrangement, the strategy on the left side is equivalent to the strategy on the right side. The beauty of put–call parity is that it shows how any strategy in options can be achieved in two different ways. To test your understanding of put–call parity, suppose shares of stock in Joseph– Belmont, Inc., are selling for $80. A three-month call option with an $85 strike price goes for $6. The risk-free rate is .5 percent per month. What’s the value of a threemonth put option with an $85 strike price? We can rearrange the put–call parity relationship to solve for the price of the put as follows: −Price of underlying Price of Price of Present value = + stock put call + of strike price = −$80 + $6 + $85/1.0053 = $9.74 As shown, the value of the put is $9.74.

EXAMPLE 22.3

A Synthetic T-Bill Suppose shares of stock in Smolira Corp. are selling for $110. A call option on Smolira with one year to maturity and a $110 strike price sells for $15. A put with the same terms sells for $5. What’s the risk-free rate? To answer, we need to use put–call parity to determine the price of a risk-free, zero coupon bond: Price of underlying stock + Price of put − Price of call = Present value of exercise price Plugging in the numbers, we get: $110 + $5 − $15 = $100 Because the present value of the $110 strike price is $100, the implied risk-free rate is 10 percent.

22.7 Valuing Options In the last section we determined what options are worth on the expiration date. Now we wish to determine the value of options when you buy them well before expiration.4 We begin by considering the lower and upper bounds on the value of a call.

Bounding the Value of a Call Lower Bound Consider an American call that is in the money prior to expiration. For example, assume that the stock price is $60 and the exercise price is $50. In this

Our discussion in this section is of American options because they are more commonly traded in the real world. As necessary, we will indicate differences for European options.

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case the option cannot sell below $10. To see this, note the following simple strategy if the option sells at, say, $9: Date

Transaction

Today Today

(1) (2)

Today

(3)

Buy call. Exercise call—that is, buy underlying stock at exercise price. Sell stock at current market price.

Arbitrage profit

−$ 9 −$50

+$60 +$ 1

The type of profit that is described in this transaction is an arbitrage profit. Arbitrage profits come from transactions that have no risk or cost and cannot occur regularly in normal, well-functioning financial markets. The excess demand for these options would quickly force the option price up to at least $10 (=$60 − $50). Of course, the price of the option is likely to be above $10. Investors will rationally pay more than $10 because of the possibility that the stock will rise above $60 before expiration. For example, suppose the call actually sells for $12. In this case we say that the intrinsic value of the option is $10, meaning it must always be worth at least this much. The remaining $12 − $10 = $2 is sometimes called the time premium, and it represents the extra amount that investors are willing to pay because of the possibility that the stock price will rise before the option expires. Upper Bound Is there an upper boundary for the option price as well? It turns out that the upper boundary is the price of the underlying stock. That is, an option to buy common stock cannot have a greater value than the common stock itself. A call option can be used to buy common stock with a payment of the exercise price. It would be foolish to buy stock this way if the stock could be purchased directly at a lower price. The upper and lower bounds are represented in Figure 22.7.

The Upper and Lower Boundaries of Call Option Values

Value of call prior to expiration date

Figure 22.7

Upper ⴝ Price bound of stock Lower ⴝ Price ⴚ Exercise bound of stock price

Exercise price Value of common stock prior to expiration date The value of the call must lie in the colored region.

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The Factors Determining Call Option Values The previous discussion indicated that the price of a call option must fall somewhere in the shaded region of Figure 22.7. We now will determine more precisely where in the shaded region it should be. The factors that determine a call’s value can be broken into two sets. The first set contains the features of the option contract. The two basic contractual features are the exercise price and the expiration date. The second set of factors affecting the call price concerns characteristics of the stock and the market. Exercise Price An increase in the exercise price reduces the value of the call. For example, imagine that there are two calls on a stock selling at $60. The first call has an exercise price of $50 and the second one has an exercise price of $40. Which call would you rather have? Clearly, you would rather have the call with an exercise price of $40 because that one is $20 (=$60 − $40) in the money. In other words, the call with an exercise price of $40 should sell for more than an otherwise identical call with an exercise price of $50. Expiration Date The value of an American call option must be at least as great as the value of an otherwise identical option with a shorter term to expiration. Consider two American calls: One has a maturity of nine months and the other expires in six months. Obviously, the nine-month call has the same rights as the six-month call, and it also has an additional three months within which these rights can be exercised. It cannot be worth less and will generally be more valuable.5 The Philadelphia Stock Exchange has a good discussion of options at www.nasdaqtrader. com.

Stock Price Other things being equal, the higher the stock price, the more valuable the call option will be. For example, if a stock is worth $80, a call with an exercise price of $100 isn’t worth very much. If the stock soars to $120, the call becomes much more valuable. Now consider Figure 22.8, which shows the relationship between the call price and the stock price prior to expiration. The curve indicates that the call price increases as the stock price increases. Furthermore, it can be shown that the relationship is represented not by a straight line, but by a convex curve. That is, the increase in the call price for a given change in the stock price is greater when the stock price is high than when the stock price is low. There are two special points regarding the curve in Figure 22.8: 1. The stock is worthless. The call must be worthless if the underlying stock is worthless. That is, if the stock has no chance of attaining any value, it is not worthwhile to pay the exercise price to obtain the stock. 2. The stock price is very high relative to the exercise price. In this situation the owner of the call knows that she will end up exercising the call. She can view herself as the owner of the stock now with one difference: She must pay the exercise price at expiration.

5 This relationship need not hold for a European call option. Consider a firm with two otherwise identical European call options, one expiring at the end of May and the other expiring a few months later. Further assume that a huge dividend is paid in early June. If the first call is exercised at the end of May, its holder will receive the underlying stock. If he does not sell the stock, he will receive the large dividend shortly thereafter. However, the holder of the second call will receive the stock through exercise after the dividend is paid. Because the market knows that the holder of this option will miss the dividend, the value of the second call option could be less than the value of the first.

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Figure 22.8

Maximum value of call Value of call prior to expiration date

Value of an American Call as a Function of Stock Price

Minimum value of call

Value of call as function of stock price Exercise price Value of stock prior to expiration date

The call price is positively related to the stock price. In addition, the change in the call price for a given change in the stock price is greater when the stock price is high than when it is low.

Thus, the value of her position—that is, the value of the call—is: Stockp rice − Present value of exercise price These two points on the curve are summarized in the bottom half of Table 22.2. The Key Factor: The Variability of the Underlying Asset The greater the variability of the underlying asset, the more valuable the call option will be. Consider the following example. Suppose that just before the call expires, the stock price will be either $100 with probability .5 or $80 with probability .5. What will be the value of a call with an exercise price of $110? Clearly, it will be worthless because no matter what happens to the stock, its price will always be below the exercise price.

Table 22.2 Factors Affecting American Option Values

Increase in

Call Option*

Put Option*

Value of underlying asset (stock price) + − Exercise price − + Stock volatility + + Interest rate + − Time to expiration + + In addition to the preceding, we have presented the following four relationships for American calls: 1. The call price can never be greater than the stock price (upper bound). 2. The call price can never be less than either zero or the difference between the stock price and the exercise price (lower bound). 3. The call is worth zero if the stock is worth zero. 4. When the stock price is much greater than the exercise price, the call price tends toward the difference between the stock price and the present value of the exercise price. *The signs (+, −) indicate the effect of the variables on the value of the option. For example, the two +s for stock volatility indicate that an increase in volatility will increase both the value of a call and the value of a put.

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Distribution of Common Stock Price at Expiration for Both Security A and Security B. Options on the Two Securities Have the Same Exercise Price.

Probability

Figure 22.9 A

B

Exercise price Price of common stock at expiration The call on stock B is worth more than the call on stock A because stock B is more volatile. At expiration, a call that is deep in the money is more valuable than a call that is only slightly in the money. However, at expiration, a call way out of the money is worth zero, just as is a call only slightly out of the money.

For an option-oriented site focusing on volatilities, visit www.ivolatility.com.

What happens if the stock is more variable? Suppose we add $20 to the best case and take $20 away from the worst case. Now the stock has a one-half chance of being worth $60 and a one-half chance of being worth $120. We have spread the stock returns, but, of course, the expected value of the stock has stayed the same: (1 2 × $80) + (1 2 × $100) = $90 = (1 2 × $60) + (1 2 ×$120) Notice that the call option has value now because there is a one-half chance that the stock price will be $120, or $10 above the exercise price of $110. This illustrates an important point. There is a fundamental distinction between holding an option on an underlying asset and holding the underlying asset. If investors in the marketplace are risk-averse, a rise in the variability of the stock will decrease its market value. However, the holder of a call receives payoffs from the positive tail of the probability distribution. As a consequence, a rise in the variability of the underlying stock increases the market value of the call. This result can also be seen from Figure 22.9. Consider two stocks, A and B, each of which is normally distributed. For each security, the figure illustrates the probability of different stock prices on the expiration date. As can be seen from the figure, stock B has more volatility than does stock A. This means that stock B has a higher probability of both abnormally high returns and abnormally low returns. Let us assume that options on each of the two securities have the same exercise price. To option holders, a return much below average on stock B is no worse than a return only moderately below average on stock A. In either situation the option expires out of the money. However, to option holders, a return much above average on stock B is better than a return only moderately above average on stock A. Because a call’s price at the expiration date is the difference between the stock price and the exercise price, the value of the call on B at expiration will be higher in this case. The Interest Rate Call prices are also a function of the level of interest rates. Buyers of calls do not pay the exercise price until they exercise the option, if they do so at all. The ability to delay payment is more valuable when interest rates are high and less valuable when interest rates are low. Thus, the value of a call is positively related to interest rates.

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A Quick Discussion of Factors Determining Put Option Values Given our extended discussion of the factors influencing a call’s value, we can examine the effect of these factors on puts very easily. Table 22.2 summarizes the five factors influencing the prices of both American calls and American puts. The effect of three factors on puts are the opposite of the effect of these three factors on calls: 1. The put’s market value decreases as the stock price increases because puts are in the money when the stock sells below the exercise price. 2. The value of a put with a high exercise price is greater than the value of an otherwise identical put with a low exercise price for the reason given in (1). 3. A high interest rate adversely affects the value of a put. The ability to sell a stock at a fixed exercise price sometime in the future is worth less if the present value of the exercise price is reduced by a high interest rate. The effect of the other two factors on puts is the same as the effect of these factors on calls: 4. The value of an American put with a distant expiration date is greater than an otherwise identical put with an earlier expiration.6 The longer time to maturity gives the put holder more flexibility, just as it did in the case of a call. 5. Volatility of the underlying stock increases the value of the put. The reasoning is analogous to that for a call. At expiration, a put that is way in the money is more valuable than a put only slightly in the money. However, at expiration, a put way out of the money is worth zero, just as is a put only slightly out of the money.

22.8 An Option Pricing Formula We have explained qualitatively that the value of a call option is a function of five variables: 1. The current price of the underlying asset, which for stock options is the price of a share of common stock. 2. Thee xercisep rice. 3. The time to the expiration date. 4. The variance of the underlying asset. 5. Therisk -freein terestr ate. It is time to replace the qualitative model with a precise option valuation model. The model we choose is the famous Black–Scholes option pricing model. You can put numbers into the Black–Scholes model and get values back. The Black–Scholes model is represented by a rather imposing formula. A derivation of the formula is simply not possible in this textbook, as many students will be happy to learn. However, some appreciation for the achievement as well as some intuitive understanding are in order. In the early chapters of this book, we showed how to discount capital budgeting projects using the net present value formula. We also used this approach to value stocks and bonds. Why, students sometimes ask, can’t the same NPV formula be used to value Though this result must hold in the case of an American put, it need not hold for a European put.

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puts and calls? This is a good question: The earliest attempts at valuing options used NPV. Unfortunately, the attempts were not successful because no one could determine the appropriate discount rate. An option is generally riskier than the underlying stock, but no one knew exactly how much riskier. Black and Scholes attacked the problem by pointing out that a strategy of borrowing to finance a stock purchase duplicates the risk of a call. Then, knowing the price of a stock already, we can determine the price of a call such that its return is identical to that of the stock-with-borrowing alternative. We illustrate the intuition behind the Black–Scholes approach by considering a simple example where a combination of a call and a stock eliminates all risk. This example works because we let the future stock price be one of only two values. Hence, the example is called a two-state, or binomial option, model. By eliminating the possibility that the stock price can take on other values, we are able to duplicate the call exactly.

A Two-State Option Model Consider the following example. Suppose the current market price of a stock is $50 and the stock will either be $60 or $40 at the end of the year. Further, imagine a call option on this stock with a one-year expiration date and a $50 exercise price. Investors can borrow at 10 percent. Our goal is to determine the value of the call. To value the call correctly, we need to examine two strategies. The first is to simply buy the call. The second is to: 1. Buy one-half a share of stock. 2. Borrow $18.18, implying a payment of principal and interest at the end of the year of $20 (=$18.18 ×1.10). As you will see shortly, the cash flows from the second strategy match the cash flows from buying a call. (A little later we will show how we came up with the exact fraction of a share of stock to buy and the exact borrowing amount.) Because the cash flows match, we say that we are duplicating the call with the second strategy. At the end of the year, the future payoffs are set out as follows: Future Payoffs Initial Transactions

If Stock Price Is $60

1. Buy a call 1 2. Buy __ 2 share of stock Borrow $18.18 at 10% Total from stock and borrowing strategy

$60 − $50 = $10 1 __ 2 × $60 = $30 −($18.18 × 1.10) = −$20 $10

If Stock Price Is $40 $ 0 1 __

2 × $40 = $20 −$20 $ 0

Note that the future payoff structure of the “buy-a-call” strategy is duplicated by the strategy of “buy stock and borrow.” That is, under either strategy an investor would end up with $10 if the stock price rose and $0 if the stock price fell. Thus these two strategies are equivalent as far as traders are concerned. If two strategies always have the same cash flows at the end of the year, how must their initial costs be related? The two strategies must have the same initial cost.

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Otherwise, there will be an arbitrage possibility. We can easily calculate this cost for our strategy of buying stock and borrowing: 1 Buy __ 2 share of stock Borrow $18.18

1 __

2 × $50 =

$25.00 −$18.18 $ 6.82

Because the call option provides the same payoffs at expiration as does the strategy of buying stock and borrowing, the call must be priced at $6.82. This is the value of the call option in a market without arbitrage profits. We left two issues unexplained in the preceding example. Determining the Delta How did we know to buy one-half share of stock in the duplicating strategy? Actually, the answer is easier than it might first appear. The call price at the end of the year will be either $10 or $0, whereas the stock price will be either $60 or $40. Thus, the call price has a potential swing of $10 (=$10 − $0) next period, whereas the stock price has a potential swing of $20 (=$60 − $40). We can write this in terms of the following ratio: Swing of call $10 − $0 1 Delta = _____________ = _________ = __ Swing of stock $60 − $40 2 As indicated, this ratio is called the delta of the call. In words, a $1 swing in the price of the stock gives rise to a $.50 swing in the price of the call. Because we are trying to duplicate the call with the stock, it seems sensible to buy one-half share of stock instead of buying one call. In other words, the risk of buying one-half share of stock should be the same as the risk of buying one call. Determining the Amount of Borrowing How did we know how much to borrow? Buying one-half share of stock brings us either $30 or $20 at expiration, which is exactly $20 more than the payoffs of $10 and $0, respectively, from the call. To duplicate the call through a purchase of stock, we should also borrow enough money so that we have to pay back exactly $20 of interest and principal. This amount of borrowing is merely the present value of $20, which is $18.18 (=$20 1.10). Now that we know how to determine both the delta and the borrowing, we can write the value of the call as follows: Value of call = Stock price × Delta − Amount borrowed 1 $6.82 = $50 × __ − $18.18 2 We will find this intuition useful in explaining the Black–Scholes model.

(22.2)

Risk-Neutral Valuation Before leaving this simple example, we should comment on a remarkable feature. We found the exact value of the option without even knowing the probability that the stock would go up or down! If an optimist thought the probability of an up move was high and a pessimist thought it was low, they would still agree on the option value. How can that be? The answer is that the current $50 stock price already balances the views of the optimists and the pessimists. The option reflects that balance because its value depends on the stock price.

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This insight provides us with another approach to valuing the call. If we don’t need the probabilities of the two states to value the call, perhaps we can select any probabilities we want and still come up with the right answer. Suppose we selected probabilities such that the expected return on the stock is equal to the risk-free rate of 10 percent. We know that the stock return given a rise is 20 percent (=$60/$50 − 1) and the stock return given a fall is −20 percent (=$40/$50 − 1). Thus, we can solve for the probability of a rise necessary to achieve an expected return of 10 percent as follows: 10% = Probability of a rise × 20% + (1 − Probability of rise) × −20% Solving this formula, we find that the probability of a rise is 3/4 and the probability of a fall is 1/4. If we apply these probabilities to the call, we can value it as: _ _ 4 × $10 + 4 × $0 Value of call = _______________ =$6.82 1.10 the same value we got from the duplicating approach. Why did we select probabilities such that the expected return on the stock is 10 percent? We wanted to work with the special case where investors are risk-neutral. This case occurs when the expected return on any asset (including both the stock and the call) is equal to the risk-free rate. In other words, this case occurs when investors demand no additional compensation beyond the risk-free rate, regardless of the risk of the asset in question. What would have happened if we had assumed that the expected return on a stock was greater than the risk-free rate? The value of the call would still be $6.82. However, the calculations would be difficult. For example, if we assumed that the expected return on the stock was 11 percent, we would have had to derive the expected return on the call. Although the expected return on the call would have been higher than 11 percent, it would have taken a lot of work to determine the expected return precisely. Why do any more work than you have to? Because we can’t think of any good reason, we (and most other financial economists) choose to assume risk neutrality. Thus, the preceding material allows us to value a call in the following two ways: 3

1

1. Determine the cost of a strategy duplicating the call. This strategy involves an investment in a fractional share of stock financed by partial borrowing. 2. Calculate the probabilities of a rise and a fall in stock prices under the assumption of risk neutrality. Use these probabilities in conjunction with the risk-free rate to discount the payoffs of the call at expiration.

TheB lack–ScholesMo del

There’s a Black– Scholes calculator (and a lot more) at www.numa.com.

The preceding example illustrates the duplicating strategy. Unfortunately, a strategy such as this will not work in the real world over, say, a one-year time frame because there are many more than two possibilities for next year’s stock price. However, the number of possibilities is reduced as the period is shortened. Is there a time period over which the stock price can only have two outcomes? Academics argue that the assumption that there are only two possibilities for the stock price over the next infinitesimalin stantisq uitep lausible.7 In our opinion, the fundamental insight of Black and Scholes is to shorten the time period. They show that a specific combination of stock and borrowing can indeed duplicate a call over an infinitesimal time horizon. Because the price of the stock will A full treatment of this assumption can be found in John C. Hull, Options, Futures and Other Derivatives, 6th ed. (Upper Saddle River, NJ: Prentice Hall, 2005).

7

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change over the first instant, another combination of stock and borrowing is needed to duplicate the call over the second instant and so on. By adjusting the combination from moment to moment, they can continually duplicate the call. It may boggle the mind that a formula can (1) determine the duplicating combination at any moment and (2) value the option based on this duplicating strategy. Suffice it to say that their dynamic strategy allows them to value a call in the real world, just as we showed how to value the call in the two-state model. This is the basic intuition behind the Black–Scholes (BS) model. Because the actual derivation of their formula is, alas, far beyond the scope of this text, we simply present the formula itself: Black–Scholes Model C = SN(d1) − Ee−RtN( d2) where: ___ d1 = [ln(S E) + (R + σ2 2)t] √σ2t ___ d2 = d1 − √σ2t This formula for the value of a call, C, is one of the most complex in finance. However, it involves only five parameters: 1. S = Current stock price. 2. E = Exercise price of call. 3. R = Annual risk-free rate of return, continuously compounded. 4. σ2 = Variance (per year) of the continuous return on the stock. 5. t = Time (in years) to expiration date. In addition, there is this statistical concept: N(d ) = Probability that a standardized, normally distributed, random variable will be less than or equal to d. Rather than discuss the formula in its algebraic state, we illustrate the formula with an example.

EXAMPLE22.4

Black–Scholes Consider Private Equipment Company (PEC). On October 4 of year 0, the PEC April 49 call option had a closing value of $4. The stock itself was selling at $50. On October 4, the option had 199 days to expiration (maturity date = April 21, year 1). The annual risk-free interest rate, continuously compounded, was 7 percent. This information determines three variables directly: 1. The stock price, S, is $50. 2. The exercise price, E, is $49. 3. The risk-free rate, R, is .07. In addition, the time to maturity, t, can be calculated quickly: The formula calls for t to be expressed in years. 4. We express the 199-day interval in years as t = 199/365. In the real world, an option trader would know S and E exactly. Traders generally view U.S. Treasury bills as riskless, so a current quote from The Wall Street Journal or a similar source would be obtained for the interest rate. The trader would also know (or could count) the number of days to expiration exactly. Thus, the fraction of a year to expiration, t, could be calculated quickly.

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The problem comes in determining the variance of the stock’s return. The formula calls for the variance between the purchase date of October 4 and the expiration date. Unfortunately, this represents the future, so the correct value for variance is not available. Instead, traders frequently estimate variance from past data, just as we calculated variance in an earlier chapter. In addition, some traders may use intuition to adjust their estimate. For example, if anticipation of an upcoming event is likely to increase the volatility of the stock, the trader might adjust her estimate of variance upward to reflect this. (This problem was most severe right after the October 19, 1987, crash. The stock market was quite risky in the aftermath, so estimates using precrash data were too low.) The preceding discussion was intended merely to mention the difficulties in variance estimation, not to present a solution. For our purposes, we assume that a trader has come up with an estimate of variance: 5. The variance of Private Equipment Co. has been estimated to be .09 per year. Using these five parameters, we calculate the Black–Scholes value of the PEC call option in three steps: Step 1: Calculate d1 and d2. These values can be determined by a straightforward, albeit tedious, insertion of our parameters into the basic formula. We have: ___ S 2 √ 2 d1 = ln __ E + (R + σ 2)t σ t 50 199 ____ = ln ___ 49 + (.07 + .09/2) × 365

[( ) [( )

]/

_________

199 ]/√.09 × ____ 365

= [.0202 ___ + .0627]/.2215 = .3742 d2 = d1 − √σ2t = .1527 Step 2: Calculate N(d1) and N(d2).We can best understand the values N(d1) and N(d2) by examining Figure 22.10. The figure shows the normal distribution with an expected value of 0 and a standard deviation of 1. This is frequently called the standardized normal distribution. We mentioned in an earlier chapter that the probability that a drawing from this distribution will be between −1 and +1 (within one standard deviation of its mean, in other words) is 68.26 percent. Now let us ask a different question: What is the probability that a drawing from the standardized normal distribution will be below a particular value? For example, the probability that a drawing will be below 0 is clearly 50 percent because the normal distribution is symmetric. Using statistical

Figure 22.10

Probability

Graph of Cumulative Probability

ⴚ1

0 .3742 Value

1

The shaded area represents cumulative probability. Because the probability is .6459 that a drawing from the standard normal distribution will be below .3742, we say that N(.3742) = .6459. That is, the cumulative probability of .3742 is .6459. (continued )

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terminology, we say that the cumulative probability of 0 is 50 percent. Statisticians also say that N(0) = 50%. It turns out that: N(d1) = N(.3742) = .6459 N(d2) = N(.1527) = .5607 The first value means that there is a 64.59 percent probability that a drawing from the standardized normal distribution will be below .3742. The second value means that there is a 56.07 percent probability that a drawing from the standardized normal distribution will be below .1527. More generally, N(d) is the probability that a drawing from the standardized normal distribution will be below d. In other words, N(d) is the cumulative probability of d. Note that d1 and d2 in our example are slightly above zero, so N(d1) and N(d2) are slightly greater than .50. Perhaps the easiest way to determine N(d1) and N(d2) is from the EXCEL function NORMSDIST. In our example, NORMSDIST(.3742) and NORMSDIST(.1527) are .6459 and .5607, respectively. We can also determine the cumulative probability from Table 22.3. For example, consider d = .37. This can be found in the table as .3 on the vertical and .07 on the horizontal. The value in the table

Table 22.3 d .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0

Cumulative Probabilities of the Standard Normal Distribution Function

.00

.01

.02

.03

.04

.05

.06

.07

.08

.09

.0000 .0398 .0793 .1179 .1554 .1915 .2257 .2580 .2881 .3159 .3413 .3643 .3849 .4032 .4192 .4332 .4452 .4554 .4641 .4713 .4773 .4821 .4861 .4893 .4918 .4938 .4953 .4965 .4974 .4981 .4987

.0040 .0438 .0832 .1217 .1591 .1950 .2291 .2611 .2910 .3186 .3438 .3665 .3869 .4049 .4207 .4345 .4463 .4564 .4649 .4719 .4778 .4826 .4866 .4896 .4920 .4940 .4955 .4966 .4975 .4982 .4987

.0080 .0478 .0871 .1255 .1628 .1985 .2324 .2642 .2939 .3212 .3461 .3686 .3888 .4066 .4222 .4357 .4474 .4573 .4656 .4726 .4783 .4830 .4868 .4898 .4922 .4941 .4956 .4967 .4976 .4982 .4987

.0120 .0517 .0910 .1293 .1664 .2019 .2357 .2673 .2967 .3238 .3485 .3708 .3907 .4082 .4236 .4370 .4484 .4582 .4664 .4732 .4788 .4834 .4871 .4901 .4925 .4943 .4957 .4968 .4977 .4982 .4988

.0160 .0557 .0948 .1331 .1700 .2054 .2389 .2704 .2995 .3264 .3508 .3729 .3925 .4099 .4251 .4382 .4495 .4591 .4671 .4738 .4793 .4838 .4875 .4904 .4927 .4945 .4959 .4969 .4977 .4984 .4988

.0199 .0596 .0987 .1368 .1736 .2088 .2422 .2734 .3023 .3289 .3531 .3749 .3944 .4115 .4265 .4394 .4505 .4599 .4678 .4744 .4798 .4842 .4878 .4906 .4929 .4946 .4960 .4970 .4978 .4984 .4989

.0239 .0636 .1026 .1406 .1772 .2123 .2454 .2764 .3051 .3315 .3554 .3770 .3962 .4131 .4279 .4406 .4515 .4608 .4686 .4750 .4803 .4846 .4881 .4909 .4931 .4948 .4961 .4971 .4979 .4985 .4989

.0279 .0675 .1064 .1443 .1808 .2157 .2486 .2794 .3078 .3340 .3577 .3790 .3980 .4147 .4292 .4418 .4525 .4616 .4693 .4756 .4808 .4850 .4884 .4911 .4932 .4949 .4962 .4972 .4979 .4985 .4989

.0319 .0714 .1103 .1480 .1844 .2190 .2517 .2823 .3106 .3365 .3599 .3810 .3997 .4162 .4306 .4429 .4535 .4625 .4699 .4761 .4812 .4854 .4887 .4913 .4934 .4951 .4963 .4973 .4980 .4986 .4990

.0359 .0753 .1141 .1517 .1879 .2224 .2549 .2852 .3133 .3389 .3621 .3830 .4015 .4177 .4319 .4441 .4545 .4633 .4706 .4767 .4817 .4857 .4890 .4916 .4936 .4952 .4964 .4974 .4981 .4986 .4990

N(d) represents areas under the standard normal distribution function. Suppose that d1 = .24. The table implies a cumulative probability of .5000 + .0948 = .5948. If d1 is equal to .2452, we must estimate the probability by interpolating between N(.25) and N(.24).

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for d =.37 is .1443. This value is not the cumulative probability of .37. We must first make an adjustment to determine cumulative probability. That is: N(.37) = .50 + .1443 = .6443 N(−.37) = .50 − .1443 = .3557 Unfortunately, our table handles only two significant digits, whereas our value of .3742 has four significant digits. Hence we must interpolate to find N(.3742). Because N(.37) = .6443 and N(.38) = .6480, the difference between the two values is .0037 (=.6480 − .6443). Since .3742 is 42 percent of the way between .37 and .38, we interpolate as:8 N(.3742) = .6443 + .42 × .0037 = .6459 Step 3: Calculate C. We have: C = S × [N(d1)] − Ee−Rt × [N(d2)] = $50 × [N(d1)] − $49 × [e−.07 × (199/365)] × N(d2) = ($50 × .6459) − ($49 × .9626 × .5607) = $32.295 − $26.447 = $5.85 The estimated price of $5.85 is greater than the $4 actual price, implying that the call option is underpriced. A trader believing in the Black–Scholes model would buy a call. Of course, the Black– Scholes model is fallible. Perhaps the disparity between the model’s estimate and the market price reflects error in the trader’s estimate of variance.

The previous example stressed the calculations involved in using the Black–Scholes formula. Is there any intuition behind the formula? Yes, and that intuition follows from the stock purchase and borrowing strategy in our binomial example. The first line of the Black–Scholes equation is: C = S × N(d1) – Ee–Rt N(d2) which is exactly analogous to Equation 22.2: Valueo f c all = Stock price × Delta – Amount borrowed Another good options calculator can be found at www.margrabe.com/ optionpricing.html.

(22.2)

We presented this equation in the binomial example. It turns out that N(d1) is the delta in the Black–Scholes model. N(d1) is .6459 in the previous example. In addition, Ee−Rt N(d2) is the amount that an investor must borrow to duplicate a call. In the previous example, this value is $26.45 (=$49 × .9626 × .5607). Thus, the model tells us that we can duplicate the call of the preceding example by both: 1. Buying.6459sh areo f sto ck. 2. Borrowing$26.45. It is no exaggeration to say that the Black–Scholes formula is among the most important contributions in finance. It allows anyone to calculate the value of an option given a few parameters. The attraction of the formula is that four of the parameters are observable: the current price of stock, S; the exercise price, E; the interest rate, R; and the time to expiration date, t. Only one of the parameters must be estimated: the variance of return, σ2. 8

This method is called linear interpolation. It is only one of a number of possible methods of interpolation.

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To see how truly attractive this formula is, note what parameters are not needed. First, the investor’s risk aversion does not affect value. The formula can be used by anyone, regardless of willingness to bear risk. Second, it does not depend on the expected return on the stock! Investors with different assessments of the stock’s expected return will nevertheless agree on the call price. As in the two-state example, this is because the call depends on the stock price, and that price already balances investors’ divergent views.

22.9 Stocks and Bonds as Options The previous material in this chapter described, explained, and valued publicly traded options. This is important material to any finance student because much trading occurs in these listed options. The study of options has another purpose for the student of corporate finance. You may have heard the one-liner about the elderly gentleman who was surprised to learn that he had been speaking prose all of his life. The same can be said about the corporate finance student and options. Although options were formally defined for the first time in this chapter, many corporate policies discussed earlier in the text were actually options in disguise. Though it is beyond the scope of this chapter to recast all of corporate finance in terms of options, the rest of the chapter considers three examples of implicit options: 1. Stocksan db ondsaso ptions. 2. Capital structure decisions as options. 3. Capitalb udgetingd ecisionsas o ptions. We begin by illustrating the implicit options in stocks and bonds.

EXAMPLE22.5

Stocks and Bonds as Options The Popov Company has been awarded the concessions at next year’s Olympic Games in Antarctica. Because the firm’s principals live in Antarctica and because there is no other concession business on that continent, their enterprise will disband after the games. The firm has issued debt to help finance this venture. Interest and principal due on the debt next year will be $800, at which time the debt will be paid off in full.The firm’s cash flows next year are forecast as follows: Popov’s Cash Flow Schedule Very Successful Games

Moderately Moderately Successful Unsuccessful Games Games

Outright Failure

Cash flow before interest and principal

$1,000

$ 850

$ 700

$ 550

−interest and principal Cash flow to stockholders

−800 $ 200

−800 $ 50

−700 $ 0

−550 $ 0

As can be seen, the principals forecast four equally likely scenarios. If either of the first two scenarios occurs, the bondholders will be paid in full. The extra cash flow goes to the stockholders. However, if either of the last two scenarios occurs, the bondholders will not be paid in full. Instead, they will receive the firm’s entire cash flow, leaving the stockholders with nothing.

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Cash Flow to Stockholders of Popov Company as a Function of Cash Flow to Firm

Cash flow to stockholders ($)

Figure 22.11

0

45ⴗ

800 Cash flow to firm ($) The stockholders can be viewed as having a call option on the firm. If the cash flows of the firm exceed $800, the stockholders pay $800 in order to receive the firm’s cash flows. If the cash flows of the firm are less than $800, the stockholders do not exercise their option. They walk away from the firm, receiving nothing.

This example is similar to the bankruptcy examples presented in our chapters about capital structure. Our new insight is that the relationship between the common stock and the firm can be expressed in terms of options. We consider call options first because the intuition is easier. The put option scenario is treated next.

The Firm Expressed in Terms of Call Options The Stockholders We now show that stock can be viewed as a call option on the firm. To illustrate this, Figure 22.11 graphs the cash flow to the stockholders as a function of the cash flow to the firm. The stockholders receive nothing if the firm’s cash flows are less than $800; here all of the cash flows go to the bondholders. However, the stockholders earn a dollar for every dollar that the firm receives above $800. The graph looks exactly like the call option graphs that we considered earlier in this chapter. But what is the underlying asset upon which the stock is a call option? The underlying asset is the firm itself. That is, we can view the bondholders as owning the firm. However, the stockholders have a call option on the firm with an exercise price of $800. If the firm’s cash flow is above $800, the stockholders would choose to exercise this option. In other words, they would buy the firm from the bondholders for $800. Their net cash flow is the difference between the firm’s cash flow and their $800 payment. This would be $200 (=$1,000 − $800) if the games are very successful and $50 (=$850 − $800) if the games are moderately successful. Should the value of the firm’s cash flows be less than $800, the stockholders would not choose to exercise their option. Instead, they would walk away from the firm, as any call option holder would do. The bondholders would then receive the firm’s entire cash flow. This view of the firm is a novel one, and students are frequently bothered by it on first exposure. However, we encourage students to keep looking at the firm in this way until the view becomes second nature to them. The Bondholders What about the bondholders? Our earlier cash flow schedule showed that they would get the entire cash flow of the firm if the firm generates less cash than $800. Should the firm earn more than $800, the bondholders would receive

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Figure 22.12 Cash flow to bondholders ($)

Cash Flow to Bondholders of Popov Company as a Function of Cash Flow to Firm

800

0 800 Cash flow to firm ($)

The bondholders can be viewed as owning the firm but writing a call option on the firm to the stockholders as well. If the cash flows of the firm exceed $800, the call is exercised against the bondholders. The bondholders give up the firm and receive $800. If the cash flows are less than $800, the call expires. The bondholders receive the cash flows of the firm in this case.

only $800. That iis, they h are entitled i l d only l to iinterest and d principal. i i l Thi This schedule is graphed in Figure 22.12. In keeping with our view that the stockholders have a call option on the firm, what does the bondholders’ position consist of ? The bondholders’ position can be described by two claims: 1. Theyo wnth efir m. 2. They have written a call on the firm with an exercise price of $800. As we mentioned before, the stockholders walk away from the firm if cash flows are less than $800. Thus, the bondholders retain ownership in this case. However, if the cash flows are greater than $800, the stockholders exercise their option. They call the stock away from the bondholders for $800.

The Firm Expressed in Terms of Put Options The preceding analysis expresses the positions of the stockholders and the bondholders in terms of call options. We can now express the situation in terms of put options. TheSto ckholders

The stockholders’ position can be expressed by three claims:

1. Theyo wnth efir m. 2. They owe $800 in interest and principal to the bondholders. If the debt were risk-free, these two claims would fully describe the stockholders’ situation. However, because of the possibility of default, we have a third claim as well: 3. The stockholders own a put option on the firm with an exercise price of $800. The group of bondholders is the seller of the put. Now consider two possibilities. Cash Flow Is Less Than $800 Because the put has an exercise price of $800, the put is in the money. The stockholders “put”—that is, sell—the firm to the bondholders. Normally, the holder of a put receives the exercise price when the asset is sold. However,

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the stockholders already owe $800 to the bondholders. Thus, the debt of $800 is simply canceled—and no money changes hands—when the stock is delivered to the bondholders. Because the stockholders give up the stock in exchange for extinguishing the debt, the stockholders end up with nothing if the cash flow is below $800. Cash Flow Is Greater Than $800 Because the put is out of the money here, the stockholders do not exercise. Thus, the stockholders retain ownership of the firm but pay $800 to the bondholders as interest and principal. TheBo ndholders

The bondholders’ position can be described by two claims:

1. Theb ondholdersar eo wed$800. 2. They have sold a put option on the firm to the stockholders with an exercise price of $800. Cash Flow Is Less Than $800 As mentioned before, the stockholders will exercise the put in this case. This means that the bondholders are obligated to pay $800 for the firm. Because they are owed $800, the two obligations offset each other. Thus, the bondholders simply end up with the firm in this case. Cash Flow Is Greater Than $800 Here, the stockholders do not exercise the put. Thus, the bondholders merely receive the $800 that is due them. Expressing the bondholders’ position in this way is illuminating. With a riskless default-free bond, the bondholders are owed $800. Thus, we can express the risky bond in terms of a riskless bond and a put: Value of risky Value of Value of = – bond default-free bond put option That is, the value of the risky bond is the value of the default-free bond less the value of the stockholders’ option to sell the company for $800.

A Resolution of the Two Views We have argued that the positions of the stockholders and the bondholders can be viewed either in terms of calls or in terms of puts. These two viewpoints are summarized in Table 22.4.

Table 22.4 Positions of Stockholders and Bondholders in Popov Company in Terms of Calls and Puts

Stockholders

Bondholders

Positions viewed in terms of call options 1. Stockholders own a call on the 1. Bondholders own the firm. firm with an exercise price of $800. 2. Bondholders have sold a call on the firm to the stockholders. Positions viewed in terms of put options 1. Bondholders are owed $800 in interest and 1. Stockholders own the firm. principal. 2. Stockholders owe $800 in 2. Bondholders have sold a put on the firm to interest and principal to the stockholders. bondholders. 3. Stockholders own a put option on the firm with an exercise price of $800.

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We have found from experience that it is generally harder for students to think of the firm in terms of puts than in terms of calls. Thus, it would be helpful if there were a way to show that the two viewpoints are equivalent. Fortunately, there is put–call parity. In an earlier section, we presented the put–call parity relationship as Equation 22.1, which we now repeat: Price of underlying Price Price Present value + = + stock of put of call of exercise price

(22.1)

Using the results of this section, Equation 22.1 can be rewritten like this: Value of call Value of Value of put Value of = + – on firm firm on firm default-free bond Stockholders’ position in terms = Stockholders’ position in terms of put options of call options

(22.3)

Going from Equation 22.1 to Equation 22.3 involves a few steps. First, we treat the firm, not the stock, as the underlying asset in this section. (In keeping with common convention, we refer to the value of the firm and the price of the stock.) Second, the exercise price is now $800, the principal and interest on the firm’s debt. Taking the present value of this amount at the riskless rate yields the value of a default-free bond. Third, the order of the terms in Equation 22.1 is rearranged in Equation 22.3. Note that the left side of Equation 22.3 is the stockholders’ position in terms of call options, as shown in Table 22.4. The right side of Equation 22.3 is the stockholders’ position in terms of put options, as shown in the same table. Thus, put–call parity shows that viewing the stockholders’ position in terms of call options is equivalent to viewing the stockholders’ position in terms of put options. Now let’s rearrange the terms in Equation 22.3 to yield the following: Value of Value of call Value of Value of put – = – firm on firm default-free bond on firm Bondholders’ position in Bondholders’ position in = terms of call options terms of put options

(22.4)

The left side of Equation 22.4 is the bondholders’ position in terms of call options, as shown in Table 22.4. (The minus sign on this side of the equation indicates that the bondholders are writing a call.) The right side of the equation is the bondholders’ position in terms of put options, as shown in Table 22.4. Thus, put–call parity shows that viewing the bondholders’ position in terms of call options is equivalent to viewing the bondholders’ position in terms of put options.

A Note about Loan Guarantees In the Popov example given earlier, the bondholders bore the risk of default. Of course, bondholders generally ask for an interest rate that is high enough to compensate them for bearing risk. When firms experience financial distress, they can no longer attract new debt at moderate interest rates. Thus, firms experiencing distress have frequently sought loan guarantees from the government. Our framework can be used to understand these guarantees. If the firm defaults on a guaranteed loan, the government must make up the difference. In other words, a government guarantee converts a risky bond into a riskless bond. What is the value of this guarantee?

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Recall that with option pricing: Value of Value of Value of = + default-free bond risky bond put option This equation shows that the government is assuming an obligation that has a cost equal to the value of a put option. This analysis differs from that of both politicians and company spokespeople. They generally say that the guarantee will cost the taxpayers nothing because the guarantee enables the firm to attract debt, thereby staying solvent. However, it should be pointed out that although solvency may be a strong possibility, it is never a certainty. Thus, when the guarantee is made, the government’s obligation has a cost in terms of present value. To say that a government guarantee costs the government nothing is like saying a put on the stock of Microsoft has no value because the stock is likely to rise in price. Actually, the U.S. government has had good fortune with loan guarantees. Its two biggest guarantees before the current financial crisis were to the Lockheed Corporation in 1971 and the Chrysler Corporation in 1980. Both firms nearly ran out of cash and defaulted on loans. In both cases the U.S. government came to the rescue by agreeing to guarantee new loans. Under the guarantees, if Lockheed and Chrysler had defaulted on new loans, the lenders could have obtained the full value of their claims from the U.S. government. From the lender’s point of view, the loans became as risk-free as Treasury bonds. These guarantees enabled Lockheed and Chrysler to borrow large amounts of cash and to get through a difficult time. As it turned out, neither firm defaulted. Who benefits from a typical loan guarantee? 1. If existing risky bonds are guaranteed, all gains accrue to the existing bondholders. The stockholders gain nothing because the limited liability of corporations absolves the stockholders of any obligation in bankruptcy. 2. If new debt is issued and guaranteed, the new debtholders do not gain. Rather, in a competitive market, they must accept a low interest rate because of the debt’s low risk. The stockholders gain here because they are able to issue debt at a low interest rate. In addition, some of the gains accrue to the old bondholders because the firm’s value is greater than would otherwise be true. Therefore, if shareholders want all the gains from loan guarantees, they should renegotiate or retire existing bonds before the guarantee is in place. This happened in the Chrysler case.

22.10 Options and Corporate Decisions: Some Applications In this section we explore the implications of options analysis in two key areas: Capital budgeting and mergers. We start with mergers and show a very surprising result. We then go on to show that the net present value rule has some important wrinkles in a leveraged firm.

Mergersa ndDi versification Elsewhere in this book, we discuss mergers and acquisitions. There we mention that diversification is frequently cited as a reason for two firms to merge. Is diversification a good reason to merge? It might seem so. After all, in an earlier chapter, we spent a lot of time explaining why diversification is valuable for investors in their own portfolios because of the elimination of unsystematic risk.

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To investigate this issue, let’s consider two companies, Sunshine Swimwear (SS) and Polar Winterwear (PW). For obvious reasons, both companies have highly seasonal cash flows; and, in their respective off-seasons, both companies worry about cash flow. If the two companies were to merge, the combined company would have a much more stable cash flow. In other words, a merger would diversify away some of the seasonal variation and, in fact, make bankruptcy much less likely. Notice that the operations of the two firms are very different, so the proposed merger is a purely “financial” merger. This means that there are no “synergies” or other value-creating possibilities except, possibly, gains from risk reduction. Here is some premerger information:

Market value of assets Face value of pure discount debt Debt maturity Asset return standard deviation

Sunshine Swimwear

Polar Winterwear

$30 million $12 million 3 years 50%

$10 million $4 million 3 years 60%

The risk-free rate, continuously compounded, is 5 percent. Given this, we can view the equity in each firm as a call option and calculate the following using Black–Scholes to determine equity values (check these for practice): Sunshine Swimwear

Polar Winterwear

$20.424 million $ 9.576 million

$7.001 million $2.999 million

Market value of equity Market value of debt

If you check these, you may get slightly different answers if you use Table 22.3 (we used a spreadsheet). Notice that we calculated the market value of debt using the balance sheet identity. After the merger, the combined firm’s assets will simply be the sum of the premerger values ($30 + $10 = $40 million) because no value was created or destroyed. Similarly, the total face value of the debt is now $16 million. However, we will assume that the combined firm’s asset return standard deviation is 40 percent. This is lower than for either of the two individual firms because of the diversification effect. So, what is the impact of this merger? To find out, we compute the postmerger value of the equity. Based on our discussion, here is the relevant information: Combined Firm Market value of assets Face value of pure discount debt Debt maturity Asset return standard deviation

$40 million $16 million 3 years 40%

Once again, we can calculate equity and debt values: Combined Firm Market value of equity Market value of debt

$26.646 million $13.354 million

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What we notice is that this merger is a terrible idea, at least for the stockholders! Before the merger, the stock in the two separate firms was worth a total of $20.424 + 7.001 = $27.425 million compared to only $26.646 million postmerger; so the merger vaporized $27.425 − 26.646 = $.779 million, or almost $1 million, in equity. Where did the $1 million in equity go? It went to the bondholders. Their bonds were worth $9.576 + 2.999 = $12.575 million before the merger and $13.354 million after, a gain of exactly $.779 million. Thus, this merger neither created nor destroyed value, but it shifted it from the stockholders to the bondholders. Our example shows that pure financial mergers are a bad idea, and it also shows why. The diversification works in the sense that it reduces the volatility of the firm’s return on assets. This risk reduction benefits the bondholders by making default less likely. This is sometimes called the “coinsurance” effect. Essentially, by merging, the firms insure each other’s bonds. The bonds are thus less risky, and they rise in value. If the bonds increase in value and there is no net increase in asset values, then the equity must decrease in value. Thus, pure financial mergers are good for creditors but not for stockholders. Another way to see this is that because the equity is a call option, a reduction in return variance on the underlying asset has to reduce its value. The reduction in value in the case of a purely financial merger has an interesting interpretation. The merger makes default (and thus bankruptcy) less likely to happen. That is obviously a good thing from a bondholder’s perspective, but why is it a bad thing from a stockholder’s perspective? The answer is simple: The right to go bankrupt is a valuable stockholder option. A purely financial merger reduces the value of that option.

Options and Capital Budgeting We now consider two issues regarding capital budgeting. What we will show is that, for a leveraged firm, the shareholders might prefer a lower NPV project to a higher one. We then show that they might even prefer a negative NPV project to a positive NPV project. As usual, we will illustrate these points first with an example. Here is the basic background information for the firm: Market value of assets Face value of pure discount debt Debt maturity Asset return standard deviation

$20 million $40 million 5 years 50%

The risk-free rate is 4 percent. As we have now done several times, we can calculate equity and debt values: Market value of equity Market value of debt

$ 5.744 million $14.256 million

This firm has a fairly high degree of leverage: The debt–equity ratio based on market values is $14.256 5.744 = 2.48, or 248 percent. This is high, but not unheard of. Notice also that the option here is out of the money; as a result, the delta is .547.

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The firm has two mutually exclusive investments under consideration. The projects affect both the market value of the firm’s assets and the firm’s asset return standard deviation as follows:

NPV Market value of firm’s assets ($20 + NPV) Firm’s asset return standard deviation

Project A

Project B

$4 $24 40%

$2 $22 60%

Which project is better? It is obvious that project A has the higher NPV, but by now you are wary of the change in the firm’s asset return standard deviation. One project reduces it; the other increases it. To see which project the stockholders like better, we have to go through our now familiar calculations:

Market value of equity Market value of debt

Project A

Project B

$ 5.965 $18.035

$ 8.751 $13.249

There is a dramatic difference between the two projects. Project A benefits both the stockholders and the bondholders, but most of the gain goes to the bondholders. Project B has a huge impact on the value of equity, plus it reduces the value of the debt. Clearly the stockholders prefer B. What are the implications of our analysis? Basically, we have discovered two things. First, when the equity has a delta significantly smaller than 1.0, any value created will go partially to the bondholders. Second, stockholders have a strong incentive to increase the variance of the return on the firm’s assets. More specifically, stockholders will have a strong preference for variance-increasing projects as opposed to variancedecreasing ones, even if that means a lower NPV. Let’s do one final example. Here is a different set of numbers: Market value of assets Face value of pure discount debt Debt maturity Asset return standard deviation

$20 million $100 million 5 years 50%

The risk-free rate is 4 percent, so the equity and debt values are these: Market value of equity Market value of debt

$ 2.012 million $17.988 million

Notice that the change from our previous example is that the face value of the debt is now $100 million, so the option is far out of the money. The delta is only .24, so most of any value created will go to the bondholders.

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The firm has an investment under consideration that must be taken now or never. The project affects both the market value of the firm’s assets and the firm’s asset return standard deviation as follows: Project NPV Market value of firm’s assets ($20 million + NPV) Firm’s asset return standard deviation

−$ 1 million $19 million 70%

Thus, the project has a negative NPV, but it increases the standard deviation of the firm’s return on assets. If the firm takes the project, here is the result: Market value of equity Market value of debt

$ 4.834 million $14.166 million

This project more than doubles the value of the equity! Once again, what we are seeing is that stockholders have a strong incentive to increase volatility, particularly when the option is far out of the money. What is happening is that the shareholders have relatively little to lose because bankruptcy is the likely outcome. As a result, there is a strong incentive to go for a long shot, even if that long shot has a negative NPV. It’s a bit like using your very last dollar on a lottery ticket. It’s a bad investment, but there aren’t a lot of other options!

22.11 Investment in Real Projects and Options Let us quickly review the material about capital budgeting presented earlier in the text. We first considered projects where forecasts for future cash flows were made at date 0. The expected cash flow in each future period was discounted at an appropriate risky rate, yielding an NPV calculation. For independent projects, a positive NPV meant acceptance and a negative NPV meant rejection. This approach treated risk through the discount rate. We later considered decision tree analysis, an approach that handles risk in a more sophisticated way. We pointed out that the firm will make investment and operating decisions on a project over its entire life. We value a project today, assuming that future decisions will be optimal. However, we do not yet know what these decisions will be because much information remains to be discovered. The firm’s ability to delay its investment and operating decisions until the release of information is an option. We now illustrate this option through an example.

EXAMPLE 22.6

Options and Capital Budgeting Exoff Oil Corporation is considering the purchase of an oil field in a remote part of Alaska. The seller has listed the property for $10,000 and is eager to sell immediately. Initial drilling costs are $500,000. Exoff anticipates that 10,000 barrels of oil can be extracted each year for many decades. Because the termination date is so far in the future and so hard to estimate, the firm views the cash flow stream from the oil as a perpetuity. With oil prices at $50 per barrel and extraction costs at $46 a barrel, the firm anticipates a net margin of $4 per barrel. Because oil prices are expected to rise at the inflation rate, the firm assumes that its cash flow per barrel will always be $4 in real terms. The appropriate real discount rate is 10 percent. The firm has (continued)

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enough tax credits from bad years in the past that it will not need to pay taxes on any profits from the oil field. Should Exoff buy the property? The NPV of the oil field to Exoff is: $4 × 10,000 −$110,000 = −$10,000 − $500,000 + ___________ .10 According to this analysis, Exoff should not purchase the land. Though this approach uses the standard capital budgeting techniques of this and other textbooks, it is actually inappropriate for this situation. To see this, consider the analysis of Kirtley Thornton, a consultant to Exoff. He agrees that the price of oil is expected to rise at the rate of inflation. However, he points out that the next year will be quite perilous for oil prices. On the one hand, OPEC is considering a long-term agreement that would raise oil prices to $65 per barrel in real terms for many years in the future. On the other hand, National Motors recently indicated that cars using a mixture of sand and water for fuel are currently being tested. Thornton argues that oil will be priced at $35 per barrel in real terms for many years should this development prove successful. Full information about both these developments will be released in exactly one year. Should oil prices rise to $65 a barrel, the NPV of the project would be: ( $65 – $46 ) × 10,000 $1,390,000 = −$10,000 − $500,000 + ___________________ .10

However, should oil prices fall to $35 a barrel, the NPV of the oil field will be even more negative than it is today. Mr. Thornton makes two recommendations to Exoff’s board. He argues that: 1. The land should be purchased. 2. The drilling decision should be delayed until information about both OPEC’s new agreement and National Motors’ new automobile is released. Mr. Thornton explains his recommendations to the board by first assuming that the land has already been purchased. He argues that under this assumption, the drilling decision should be delayed. Second, he investigates his assumption that the land should have been purchased in the first place. This approach of examining the second decision (whether to drill) after assuming that the first decision (to buy the land) has been made was also used in our earlier presentation on decision trees. Let us now work through Mr. Thornton’s analysis. Assume the land has already been purchased. If the land has already been purchased, should drilling begin immediately? If drilling begins immediately, the NPV is −$110,000: If the drilling decision is delayed until new information is released in a year, the optimal choice can be made at that time. If oil prices drop to $35 a barrel, Exoff should not drill. Instead, the firm should walk away from the project, losing nothing beyond its $10,000 purchase price for the land. If oil prices rise to $65, drilling should begin. Mr. Thornton points out that by delaying, the firm will invest the $500,000 of drilling costs only if oil prices rise. Thus, by delaying, the firm saves $500,000 in the case where oil prices drop. Kirtley concludes that once the land is purchased, the drilling decision should be delayed.9

Actually, there are three separate effects here. First, the firm avoids drilling costs in the case of low oil prices by delaying the decision. This is the effect discussed by Mr. Thornton. Second, the present value of the $500,000 payment is less when the decision is delayed, even if drilling eventually takes place. Third, the firm loses one year of cash inflows through delay. The first two effects support delaying the decision. The third effect supports immediate drilling. In this example, the first effect greatly outweighs the other two effects. Thus, Mr. Thornton avoided the second and third effects in his presentation.

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Should the land have been purchased in the first place? We now know that if the land has been purchased, it is optimal to defer the drilling decision until the release of information. Given that we know this optimal decision concerning drilling, should the land be purchased in the first place? Without knowing the exact probability that oil prices will rise, Mr.Thornton is nevertheless confident that the land should be purchased. The NPV of the project at $65 per barrel oil prices is $1,390,000, whereas the cost of the land is only $10,000. Mr. Thornton believes that an oil price rise is possible, though by no means probable. Even so, he argues that the high potential return is clearly worth the risk.

This example presents an approach that is similar to our decision tree analysis of the Solar Equipment Company in a previous chapter. Our purpose in this section is to discuss this type of decision in an option framework. When Exoff purchases the land, it is actually purchasing a call option. That is, once the land has been purchased, the firm has an option to buy an active oil field at an exercise price of $500,000. As it turns out, one should generally not exercise a call option immediately.10 In this case the firm should delay exercise until relevant information concerning future oil prices is released. This section points out a serious deficiency in classical capital budgeting: Net present value calculations typically ignore the flexibility that real-world firms have. In our example the standard techniques generated a negative NPV for the land purchase. Yet by allowing the firm the option to change its investment policy according to new information, the land purchase can easily be justified. We encourage the reader to look for hidden options in projects. Because options are beneficial, managers are shortchanging their firm’s projects if capital budgeting calculationsign oref lexibility. Actually, it can be shown that a call option on a stock that pays no dividend should never be exercised before expiration. However, for a dividend-paying stock, it may be optimal to exercise prior to the ex-dividend date. The analogy applies to our example of an option in real assets. The firm would receive cash flows from oil earlier if drilling begins immediately. This is equivalent to the benefit from exercising a call on a stock prematurely in order to capture the dividend. However, in our example, this dividend effect is far outweighed by the benefits from waiting.

10

Summary and Conclusions

Value of Value of Value of Present value of + – = stock put call exercise price

3. The value of an option depends on five factors: a. The price of the underlying asset. b. The exercise price. c. The expiration date.

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This chapter serves as an introduction to options. 1. The most familiar options are puts and calls. These options give the holder the right to sell or buy shares of common stock at a given exercise price. American options can be exercised any time up to and including the expiration date. European options can be exercised only on the expiration date. 2. We showed that a strategy of buying a stock and buying a put is equivalent to a strategy of buying a call and buying a zero coupon bond. From this, the put–call parity relationship was established:

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d. The variability of the underlying asset. e. The interest rate on risk-free bonds. The Black–Scholes model can determine the intrinsic price of an option from these five factors. 4. Much of corporate financial theory can be presented in terms of options. In this chapter, we pointed out that: a. Common stock can be represented as a call option on the firm. b. Stockholders enhance the value of their call by increasing the risk of their firm. c. Real projectsh aveh iddeno ptionst hate nhancev alue.

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Concept Questions

1. 2.

3. 4. 5.

6. 7.

8.

9.

10.

11. 12.

Options What is a call option? A put option? Under what circumstances might you want to buy each? Which one has greater potentialp rofit?W hy? Options Complete the following sentence for each of these investors: a. Ab uyero f c allo ptions. b. A buyer of put options. c. A seller (writer) of call options. d. As eller( writer)o f puto ptions. “The (buyer/seller) of a (put/call) option (pays/receives) money for the (right/ obligation) to (buy/sell) a specified asset at a fixed price for a fixed length of time.” American and European Options What is the difference between an American option and a European option? Intrinsic Value What is the intrinsic value of a call option? Of a put option? How do we interpret these values? Option Pricing You notice that shares of stock in the Patel Corporation are going for $50 per share. Call options with an exercise price of $35 per share are selling for $10. What’s wrong here? Describe how you can take advantage of this mispricing if the option expires today. Options and Stock Risk If the risk of a stock increases, what is likely to happen to the price of call options on the stock? To the price of put options? Why? Option Risk True or false: The unsystematic risk of a share of stock is irrelevant for valuing the stock because it can be diversified away; therefore, it is also irrelevant for valuing a call option on the stock. Explain. Option Pricing Suppose a certain stock currently sells for $30 per share. If a put option and a call option are available with $30 exercise prices, which do you think will sell for more? Explain. Option Price and Interest Rates Suppose the interest rate on T-bills suddenly and unexpectedly rises. All other things being the same, what is the impact on call option values? On put option values? Contingent Liabilities When you take out an ordinary student loan, it is usually the case that whoever holds that loan is given a guarantee by the U.S. government, meaning that the government will make up any payments you skip. This is just one example of the many loan guarantees made by the U.S. government. Such guarantees don’t show up in calculations of government spending or in official deficit figures. Why not? Should they show up? Options and Expiration Dates What is the impact of lengthening the time to expiration on an option’s value? Explain. Options and Stock Price Volatility What is the impact of an increase in the volatility of the underlying stock’s return on an option’s value? Explain.

Chapter 22

13.

14.

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16.

17.

18.

1.

BASIC (Questions 1–17)

2.

711

Insurance as an Option An insurance policy is considered analogous to an option. From the policyholder’s point of view, what type of option is an insurance policy? Why? Equity as a Call Option It is said that the equityholders of a levered firm can be thought of as holding a call option on the firm’s assets. Explain what is meant by this statement. Option Valuation and NPV You are the CEO of Titan Industries and have just been awarded a large number of employee stock options. The company has two mutually exclusive projects available. The first project has a large NPV and will reduce the total risk of the company. The second project has a small NPV and will increase the total risk of the company. You have decided to accept the first project when you remember your employee stock options. How might this affect your decision? Put–Call Parity You find a put and a call with the same exercise price and maturity. What do you know about the relative prices of the put and call? Prove your answer and provide an intuitive explanation. Put–Call Parity A put and a call have the same maturity and strike price. If they have the same price, which one is in the money? Prove your answer and provide an intuitivee xplanation. Put–Call Parity One thing put–call parity tells us is that given any three of a stock, a call, a put, and a T-bill, the fourth can be synthesized or replicated using the other three. For example, how can we replicate a share of stock using a call, a put, and a T-bill?

Two-State Option Pricing Model T-bills currently yield 5.5 percent. Stock in Nina Manufacturing is currently selling for $70 per share. There is no possibility that the stock will be worth less than $65 per share in one year. a. What is the value of a call option with a $60 exercise price? What is the intrinsic value? b. What is the value of a call option with a $50 exercise price? What is the intrinsic value? c. What is the value of a put option with a $60 exercise price? What is the intrinsic value? Understanding Option Quotes Use the option quote information shown here to answer the questions that follow. The stock is currently selling for $83. Option and NY Close

Expiration

Strike Price

Vol.

Calls Last

Puts Vol. Last

230 170 139 60

2.80 6 8.05 10.20

160 127 43 11

RWJ March April July October

80 80 80 80

.80 1.40 3.90 3.65

a. Are the call options in the money? What is the intrinsic value of an RWJ Corp. callo ption? b. Are the put options in the money? What is the intrinsic value of an RWJ Corp. put option? c. Two of the options are clearly mispriced. Which ones? At a minimum, what should the mispriced options sell for? Explain how you could profit from the mispricing in each case.

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Calculating Payoffs Use the option quote information shown here to answer the questions that follow. The stock is currently selling for $114. Option and NY Close

Expiration

Strike Price

Calls Vol.

Last

85 61 22 3

7.60 8.80 10.25 13.05

Puts Vol. Last

Macrosoft

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February March May August

4.

5.

6.

7.

8.

9.

110 110 110 110

40 22 11 3

.60 1.55 2.85 4.70

a. Suppose you buy 10 contracts of the February 110 call option. How much will you pay, ignoring commissions? b. In part (a), suppose that Macrosoft stock is selling for $140 per share on the expiration date. How much is your options investment worth? What if the terminal stock price is $125? Explain. c. Suppose you buy 10 contracts of the August 110 put option. What is your maximum gain? On the expiration date, Macrosoft is selling for $104 per share. How much is your options investment worth? What is your net gain? d. In part (c), suppose you sell 10 of the August 110 put contracts. What is your net gain or loss if Macrosoft is selling for $103 at expiration? For $132? What is the break-even price—that is, the terminal stock price that results in a zero profit? Two-State Option Pricing Model The price of Ervin Corp. stock will be either $65 or $85 at the end of the year. Call options are available with one year to expiration. T-bills currently yield 6 percent. a. Suppose the current price of Ervin stock is $70. What is the value of the call option if the exercise price is $60 per share? b. Suppose the exercise price is $80 in part (a). What is the value of the call option now? Two-State Option Pricing Model The price of Tara, Inc., stock will be either $50 or $70 at the end of the year. Call options are available with one year to expiration. T-bills currently yield 5 percent. a. Suppose the current price of Tara stock is $60. What is the value of the call option if the exercise price is $35 per share? b. Suppose the exercise price is $60 in part (a). What is the value of the call option now? Put–Call Parity A stock is currently selling for $47 per share. A call option with an exercise price of $45 sells for $3.80 and expires in three months. If the risk-free rate of interest is 2.6 percent per year, compounded continuously, what is the price of a put option with the same exercise price? Put–Call Parity A put option that expires in six months with an exercise price of $60 sells for $4.89. The stock is currently priced at $57, and the risk-free rate is 3.6 percent per year, compounded continuously. What is the price of a call option with the same exercise price? Put–Call Parity A put option and a call option with an exercise price of $85 and three months to expiration sell for $3.15 and $6.12, respectively. If the risk-free rate is 4.8 percent per year, compounded continuously, what is the current stock price? Put–Call Parity A put option and a call option with an exercise price of $45 expire in two months and sell for $2.65 and $5.32, respectively. If the stock is currently priced at $47.30, what is the annual continuously compounded rate of interest?

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Black–Scholes What are the prices of a call option and a put option with the following characteristics? Stock price = $46 Exercise price = $50 Risk-free rate = 6% per year, compounded continuously Maturity = 3 months Standard deviation = 54% per year

11.

Black–Scholes What are the prices of a call option and a put option with the following characteristics? Stock price = $93 Exercise price = $90 Risk-free rate = 4% per year, compounded continuously Maturity = 8 months Standard deviation = 62% per year

12.

Delta What are the deltas of a call option and a put option with the following characteristics? What does the delta of the option tell you?

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Black–Scholes and Asset Value You own a lot in Key West, Florida, that is currently unused. Similar lots have recently sold for $1.9 million. Over the past five years, the price of land in the area has increased 12 percent per year, with an annual standard deviation of 25 percent. A buyer has recently approached you and wants an option to buy the land in the next 12 months for $2.1 million. The risk-free rate of interest is 5 percent per year, compounded continuously. How much should you charge for the option? Black–Scholes and Asset Value In the previous problem, suppose you wanted the option to sell the land to the buyer in one year. Assuming all the facts are the same, describe the transaction that would occur today. What is the price of the transaction today? Time Value of Options You are given the following information concerning options on a particular stock: Stock price = $74 Exercise price = $80 Risk-free rate = 6% per year, compounded continuously Maturity = 6 months Standard deviation = 53% per year

a. What is the intrinsic value of the call option? Of the put option? b. What is the time value of the call option? Of the put option? c. Does the call or the put have the larger time value component? Would you expect this to be true in general?

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Stock price = $74 Exercise price = $70 Risk-free rate = 5% per year, compounded continuously Maturity = 9 months Standard deviation = 56% per year

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16.

Risk-Neutral Valuation A stock is currently priced at $54. The stock will either increase or decrease by 15 percent over the next year. There is a call option on the stock with a strike price of $50 and one year until expiration. If the risk-free rate is 8 percent, what is the risk-neutral value of the call option?

17.

Risk-Neutral Valuation In the previous problem, assume the risk-free rate is only 5 percent. What is the risk-neutral value of the option now? What happens to the risk-neutral probabilities of a stock price increase and a stock price decrease?

18.

Black–Scholes A call option matures in six months. The underlying stock price is $75, and the stock’s return has a standard deviation of 30 percent per year. The riskfree rate is 4 percent per year, compounded continuously. If the exercise price is $0, what is the price of the call option?

19.

Black–Scholes A call option has an exercise price of $80 and matures in six months. The current stock price is $86, and the risk-free rate is 5 percent per year, compounded continuously. What is the price of the call if the standard deviation of the stock is 0 percent per year?

20.

Black–Scholes A stock is currently priced at $35. A call option with an expiration of one year has an exercise price of $50. The risk-free rate is 7 percent per year, compounded continuously, and the standard deviation of the stock’s return is infinitely large. What is the price of the call option?

21.

Equity as an Option Sunburn Sunscreen has a zero coupon bond issue outstanding with a $15,000 face value that matures in one year. The current market value of the firm’s assets is $15,800. The standard deviation of the return on the firm’s assets is 38 percent per year, and the annual risk-free rate is 5 percent per year, compounded continuously. Based on the Black–Scholes model, what is the market value of the firm’s equity and debt?

22.

Equity as an Option and NPV Suppose the firm in the previous problem is considering two mutually exclusive investments. Project A has an NPV of $1,200, and project B has an NPV of $1,600. As a result of taking project A, the standard deviation of the return on the firm’s assets will increase to 55 percent per year. If project B is taken, the standard deviation will fall to 34 percent per year. a. What is the value of the firm’s equity and debt if project A is undertaken? If project Bis u ndertaken? b. Which project would the stockholders prefer? Can you reconcile your answer with the NPV rule? c. Suppose the stockholders and bondholders are, in fact, the same group of investors. Would this affect your answer to (b)? d. What does this problem suggest to you about stockholder incentives?

23.

Equity as an Option Frostbite Thermalwear has a zero coupon bond issue outstanding with a face value of $25,000 that matures in one year. The current market value of the firm’s assets is $27,200. The standard deviation of the return on the firm’s assets is 53 percent per year, and the annual risk-free rate is 5 percent per year, compounded continuously. Based on the Black–Scholes model, what is the market value of the firm’s equity and debt? What is the firm’s continuously compounded cost of debt?

24.

Mergers and Equity as an Option Suppose Sunburn Sunscreen and Frostbite Thermalwear in the previous problems have decided to merge. Because the two companies have seasonal sales, the combined firm’s return on assets will have a standard deviation of 29 percent per year. a. What is the combined value of equity in the two existing companies? The value of debt? b. What is the value of the new firm’s equity? The value of debt? c. What was the gain or loss for shareholders? For bondholders? d. Whath appenedt os hareholderv alueh ere?

Chapter 22 Options and Corporate Finance

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26.

28.

Equity as an Option and NPV A company has a single zero coupon bond outstanding that matures in 10 years with a face value of $25 million. The current value of the company’s assets is $21 million, and the standard deviation of the return on the firm’s assets is 39 percent per year. The risk-free rate is 6 percent per year, compounded continuously. a. What is the current market value of the company’s equity? b. What is the current market value of the company’s debt? c. What is the company’s continuously compounded cost of debt? d. The company has a new project available. The project has an NPV of $1,200,000. If the company undertakes the project, what will be the new market value of equity? Assume volatility is unchanged. e. Assuming the company undertakes the new project and does not borrow any additional funds, what is the new continuously compounded cost of debt? What ish appeningh ere? Two-State Option Pricing Model Ken is interested in buying a European call option written on Southeastern Airlines, Inc., a non-dividend–paying common stock, with a strike price of $85 and one year until expiration. Currently, Southeastern’s stock sells for $80 per share. In one year Ken knows that Southeastern’s stock will be trading at either $98 per share or $70 per share. Ken is able to borrow and lend at the risk-free EAR of 2.5 percent. a. What should the call option sell for today? b. If no options currently trade on the stock, is there a way to create a synthetic call option with identical payoffs to the call option just described? If there is, how would you do it? c. How much does the synthetic call option cost? Is this greater than, less than, or equal to what the actual call option costs? Does this make sense? Two-State Option Pricing Model Rob wishes to buy a European put option on BioLabs, Inc., a non-dividend–paying common stock, with a strike price of $40 and six months until expiration. BioLabs’ common stock is currently selling for $30 per share, and Rob expects that the stock price will either rise to $60 or fall to $15 in six months. Rob can borrow and lend at the risk-free EAR of 8 percent. a. What should the put option sell for today? b. If no options currently trade on the stock, is there a way to create a synthetic put option with identical payoffs to the put option just described? If there is, how would you do it? c. How much does the synthetic put option cost? Is this greater than, less than, or equal to what the actual put option costs? Does this make sense? Two-State Option Pricing Model Maverick Manufacturing, Inc., must purchase gold in three months for use in its operations. Maverick’s management has estimated that if the price of gold were to rise above $875 per ounce, the firm would go bankrupt. The current price of gold is $815 per ounce. The firm’s chief financial officer believes that the price of gold will either rise to $975 per ounce or fall to $740 per ounce over the next three months. Management wishes to eliminate any risk of the firm going bankrupt. Maverick can borrow and lend at the risk-free EAR of 6.50 percent. a. Should the company buy a call option or a put option on gold? To avoid bankruptcy, what strike price and time to expiration would the company like this option to have? b. How much should such an option sell for in the open market? c. If no options currently trade on gold, is there a way for the company to create a synthetic option with identical payoffs to the option just described? If there is, how would the firm do it? d. How much does the synthetic option cost? Is this greater than, less than, or equal to what the actual option costs? Does this make sense?

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CHALLENGE (Questions 30–38)

30.

31.

32.

Options, Futures, and Corporate Finance

Black–Scholes and Collar Cost An investor is said to take a position in a “collar” if she buys the asset, buys an out-of-the-money put option on the asset, and sells an out-of-themoney call option on the asset. The two options should have the same time to expiration. Suppose Marie wishes to purchase a collar on Hollywood, Inc., a non-dividend–paying common stock, with six months until expiration. She would like the put to have a strike price of $65 and the call to have a strike price of $110. The current price of Hollywood’s stock is $85 per share. Marie can borrow and lend at the continuously compounded riskfree rate of 7 percent per annum, and the annual standard deviation of the stock’s return is 50 percent. Use the Black–Scholes model to calculate the total cost of the collar that Marie is interested in buying. What is the effect of the collar? Debt Valuation and Time to Maturity McLemore Industries has a zero coupon bond issue that matures in two years with a face value of $40,000. The current value of the company’s assets is $19,000, and the standard deviation of the return on assets is 60 percent per year. a. Assume the risk-free rate is 5 percent per year, compounded continuously. What is the value of a risk-free bond with the same face value and maturity as the company’sb ond? b. What price would the bondholders have to pay for a put option on the firm’s assets with a strike price equal to the face value of the debt? c. Using the answers from (a) and (b), what is the value of the firm’s debt? What is the continuously compounded yield on the company’s debt? d. From an examination of the value of the assets of McLemore Industries, and the fact that the debt must be repaid in two years, it seems likely that the company will default on its debt. Management has approached bondholders and proposed a plan whereby the company would repay the same face value of debt, but the repayment would not occur for five years. What is the value of the debt under the proposed plan? What is the new continuously compounded yield on the debt? Explainw hyt hiso ccurs. Debt Valuation and Asset Variance Brozik Corp. has a zero coupon bond that matures in five years with a face value of $50,000. The current value of the company’s assets is $46,000, and the standard deviation of its return on assets is 50 percent per year. The risk-free rate is 6 percent per year, compounded continuously. a. What is the value of a risk-free bond with the same face value and maturity as the currentb ond? b. What is the value of a put option on the firm’s assets with a strike price equal to the face value of the debt? c. Using the answers from (a) and (b), what is the value of the firm’s debt? What is the continuously compounded yield on the company’s debt? d. Assume the company can restructure its assets so that the standard deviation of its return on assets increases to 60 percent per year. What happens to the value of the debt? What is the new continuously compounded yield on the debt? Reconcile your answers in (c) and (d). e. What happens to bondholders if the company restructures its assets? What happens to shareholders? How does this create an agency problem? Two-State Option Pricing and Corporate Valuation Strudler Real Estate, Inc., a construction firm financed by both debt and equity, is undertaking a new project. If the project is successful, the value of the firm in one year will be $380 million, but if the project is a failure, the firm will be worth only $210 million. The current value of Strudler is $300 million, a figure that includes the prospects for the new project. Strudler has outstanding zero coupon bonds due in one year with a face value of $320 million. Treasury bills that mature in one year yield a 7 percent EAR. Strudler pays no dividends. a. Use the two-state option pricing model to find the current value of Strudler’s debt ande quity. b. Suppose Strudler has 500,000 shares of common stock outstanding. What is the price per share of the firm’s equity?

Chapter 22 Options and Corporate Finance

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c. Compare the market value of Strudler’s debt to the present value of an equal amount of debt that is riskless with one year until maturity. Is the firm’s debt worth more than, less than, or the same as the riskless debt? Does this make sense? What factors might cause these two values to be different? d. Suppose that in place of the preceding project, Strudler’s management decides to undertake a project that is even more risky. The value of the firm will either increase to $445 million or decrease to $185 million by the end of the year. Surprisingly, management concludes that the value of the firm today will remain at exactly $300 million if this risky project is substituted for the less risky one. Use the two-state option pricing model to determine the values of the firm’s debt and equity if the firm plans on undertaking this new project. Which project do bondholdersp refer? Black–Scholes and Dividends In addition to the five factors discussed in the chapter, dividends also affect the price of an option. The Black–Scholes option pricing model with dividends is: C = S × e–dt × N(d1) – E × e–Rt × N(d2) _ d1 = [ ln(S E) + (R – d + σ2 2) × t ] (σ × √t ) _ d2 = d1 – σ × √ t

S × e−dt + P = E × e−Rt + C

35. 36.

where d is again the continuously compounded dividend yield. a. What effect do you think the dividend yield will have on the price of a put option? Explain. b. From the previous question, what is the price of a put option with the same strike price and time to expiration as the call option? Put Delta In the chapter we noted that the delta for a put option is N(d1) − 1. Is this the same thing as −N(−d1)?( Hint: Yes, but why?) Black–Scholes Put Pricing Model Use the Black–Scholes model for pricing a call, put–call parity, and the previous question to show that the Black–Scholes model for directly pricing a put can be written as follows: P = E × e−Rt × N(−d2) − S × N(−d1)

37.

38.

Black–Scholes A stock is currently priced at $50. The stock will never pay a dividend. The risk-free rate is 12 percent per year, compounded continuously, and the standard deviation of the stock’s return is 60 percent. A European call option on the stock has a strike price of $100 and no expiration date, meaning that it has an infinite life. Based on Black–Scholes, what is the value of the call option? Do you see a paradox here? Do you see a way out of the paradox? Delta You purchase one call and sell one put with the same strike price and expiration date. What is the delta of your portfolio? Why?

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34.

All of the variables are the same as the Black–Scholes model without dividends except for the variable d, which is the continuously compounded dividend yield on the stock. a. What effect do you think the dividend yield will have on the price of a call option? Explain. b. A stock is currently priced at $106 per share, the standard deviation of its return is 50 percent per year, and the risk-free rate is 5 percent per year, compounded continuously. What is the price of a call option with a strike price of $100 and a maturity of six months if the stock has a dividend yield of 2 percent per year? Put–Call Parity and Dividends The put–call parity condition is altered when dividends are paid. The dividend-adjusted put–call parity formula is:

Mini Case

CLISSOLDIN DUSTRIES OPTIONS You are currently working for Clissold Industries. The company, which went public five years ago, engages in the design, production, and distribution of lighting equipment and specialty products worldwide. Because of recent events, Mal Clissold, the company president, is concerned about the company’s risk, so he asks for your input. In your discussion with Mal, you explain that the CAPM proposes that the market risk of the company’s stock is the determinant of its expected return. Even though Mal agrees with this, he argues that his portfolio consists entirely of Clissold Industry stock and options, so he is concerned with the total risk, or standard deviation, of the company’s stock. Furthermore, even though he has calculated the standard deviation of the company’s stock for the past five years, he would like an estimate of the stock’s volatility moving forward. Mal states that you can find the estimated volatility of the stock for future periods by calculating the implied standard deviation of option contracts on the company stock. When you examine the factors that affect the price of an option, all of the factors except the standard deviation of the stock are directly observable in the market. Mal states that because you can observe all of the option factors except the standard deviation, you can simply solve the Black–Scholes model and find the implied standard deviation. To help you find the implied standard deviation of the company’s stock, Mal has provided you with the following option prices on four call options that expire in six months. The risk-free rate is 4 percent, and the current stock price is $50. Strike Price $30 40 50 55

Option Price $27.65 19.45 11.95 9.55

1. How many different volatilities would you expect to see for the stock? 2. Unfortunately, solving for the implied standard deviation is not as easy as Mal suggests. In fact, there is no direct solution for the standard deviation of the stock even if we have all the other variables for the Black–Scholes model. Mal would still like you to estimate the implied standard deviation of the stock. To do this, set up a spreadsheet using the Solver function in Excel to calculate the implied volatilities for each of the options. 3. Are all of the implied volatilities for the options the same? (Hint: No.) What are the possible reasons that can cause different volatilities for these options? 4. After you discuss the importance of volatility on option prices, your boss mentions that he has heard of the VIX. What is the VIX and what does it represent? You might need to visit the Chicago Board Options Exchange (CBOE) at www.cboe.com to help with your answer. 5. When you are on the CBOE Web site, look for the option quotes for the VIX. What does the implied volatility of a VIX option represent?

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Options and Corporate Finance Extensions and Applications The historically large stock market losses in 2008 dramatically reduced the value of millions of employee stock options, leaving many of them “underwater,” meaning that stock prices were far below the corresponding exercise prices. In fact, some analysts estimated that 72 percent of Fortune 500 employee stock options were underwater, and 93 percent of the stock options held by CEOs of these same companies were in a similar condition. In response, a record number of companies swapped underwater options for cash, stock, or restricted stock. In addition, a large number of companies “repriced,” or lowered the exercise prices on their employee stock options. This chapter explores employee stock options and a variety of other applications of option principles in corporate finance.

23.1 Executive Stock Options WhyOpti ons? Executive compensation is usually made up of a base salary plus some or all of the following elements: 1. Long-termc ompensation. 2. Annualb onuses. 3. Retirementc ontributions. 4. Options. The final component of compensation, options, is by far the biggest part of total compensation for many top executives. Table 23.1 lists the 10 CEOs who received the largest stock option grants during 2007–2008. The rank is in terms of the face value of the options granted. This is the number of options times the current stock price. Knowing the face value of an option does not automatically allow us to determine the market value of the option. We also need to know the exercise price before valuing the option according to either the Black–Scholes model or the binomial model. However, the exercise price is generally set equal to the market price of the stock on the date the executive receives the options. In the next section, we value options under the assumption that the exercise price is equal to the market price. Options in the stock of the company are increasingly being granted to executives as an alternative to increases in base pay. Some of the reasons given for using options are these: 1. Options make executives share the same interests as the stockholders. By aligning interests, executives are more likely to make decisions for the benefit of the stockholders. 719

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2007−2008 Top 10 Option Grants*

Company

CEO

Oracle Corporation Capital One Financial Corporation The Goldman Sachs Group, Inc. Wachovia Corporation American Express Company United Technologies Corporation Merrill Lynch & Co., Inc. Freeport-McMoRan Copper & Gold, Inc. Aetna, Inc. Wyeth

L. Ellison R. Fairbank L. Blankfein G.Thompson K. Chenault G. David J. Thain R. Adkerson R. Williams R. Essner

Number of Options Granted (in thousands) 7,000 1,662 322 1,494 900 769 614 500 706 370

Weighted Average Exercise Price $ 14.57 50.99 204.16 42.35 58.14 57.30 60.43 72.92 42.57 56.00

Grant Value of Options Granted (in $ millions)† $102.0 84.7 65.8 63.3 52.3 44.1 37.1 36.5 30.1 20.7

*Based on the 200 largest U.S. industrial and service corporations that filed proxy statements for fiscal year 3/1/07−2/28/08. Includes mega-grants that were annualized over their respective vesting periods. Grant value of options granted equals the number of options times the stock price.

†

SOURCE: Pearl Meyer & Partners.

2. Options allow the company to lower the executive’s base pay. This removes pressures on morale caused by disparities between the salaries of executives and those of other employees. 3. Options put an executive’s pay at risk, rather than guaranteeing it, regardless of the performance of the firm. 4. Options are a tax-efficient way to pay employees. Under current tax law, if an executive is given options to purchase company stock and the options are “at the money,” they are not considered part of taxable income to the employee. The options are taxed only when and if they are eventually exercised.

EXAMPLE23.1

Options at Starbucks Stock options are not always restricted to the highest-ranking executives. Starbucks, the coffee chain, has pushed options down to the lowest-level employees. To quote its founder, Howard Schultz, “Even though we were a private company, we would grant stock options to every employee company-wide, from the top managers to the baristas, in proportion to their level of base pay. They could then, through their efforts, help make Starbucks more successful every year, and if Starbucks someday went public, their options could eventually be worth a good sum of money.”

Valuing Executive Compensation In this section, we value executive stock options. Not surprisingly, the complexity of the total compensation package often makes valuation a difficult task. The economic value of the options depends on factors such as the volatility of the underlying stock and the exact terms of the option grant.

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We attempt to estimate the economic value of the options held by the executives listed in Table 23.1. To do so, we employ the Black–Scholes option pricing formula from Chapter 22. Of course, we are missing many features of the particular plans, and the best we can hope for is a rough estimate. Simple matters such as requiring the executive to hold the option for a fixed period, the freeze-out period, before exercising, can significantly diminish the value of a standard option. Equally important, the Black–Scholes formula has to be modified if the stock pays dividends and is no longer applicable if the volatility of the stock is changing randomly over time. Intuitively, a call option on a dividend-paying stock is worth less than a call on a stock that pays no dividends: All other things being equal, the dividends will lower the stock price. Nevertheless, let us see what we can do.

EXAMPLE 23.2

Options at Capital One Corporation According to the proxy statement filed in fiscal year 2007, Rich Fairbank, the CEO of Capital One, was granted 1.662 million stock options. The average exercise price of the options was $50.99, and we will assume that all of the options were granted at the money. We’ll also assume that the options expire in five years and that the risk-free rate is 5 percent. This information implies that: 1. The stock price (S) equals the exercise price (E), $50.99. 2. The risk-free rate, R, equals .05. 3. The time interval, t, equals 5. In addition, the stock volatility, σ, reported in Table 23.2 is given as 37.46 percent per year, which implies that the variance, σ2, equals (.3746)2 = .1403.

Table 23.2

Value of 2007−2008 Top 10 Option Grants*

Company

CEO

Oracle Corporation Capital One Financial Corporation The Goldman Sachs Group, Inc. Wyeth American Express Company United Technologies Corporation Merrill Lynch & Co., Inc. Wachovia Corporation Freeport-McMoRan Copper & Gold, Inc. Aetna Inc.

L. Ellison R. Fairbank L. Blankfein R. Essner K. Chenault G. David J. Thain G. Thompson R. Adkerson R. Williams

Grant Value of Options Granted (in $ millions)†

Annual Stock Volatility, %

As Reported Option Value (in $ millions)‡

$102.0 84.7 65.8 20.7 52.3 44.1 37.1 63.3 36.5 30.1

25.09% 37.46 32.76 23.17 28.94 18.40 35.68 26.83 45.56 22.29

$50.1 17.0 16.4 14.9 13.3 12.6 11.7 11.3 11.1 10.8

*Based on the 200 la largest argest U.S. ind industrial ustrial and service corporations that filed proxy statements for fiscal year 3/1/07–2/28/08. Includes mega-grants that were annualized over their respective vesting periods. †

Grant value of options granted equals the number of options times the stock price.

Option value is FAS 123(R) value as reported by each company. For prior year mega-grants, grant date Black–Scholes value is used when “As Reported” value was not available. Grants are annualized over their respective vesting periods. ‡

SOURCE: Pearl Meyer & Partners.

(continued )

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We now have enough information to estimate the value of Rich Fairbank’s options using the Black–Scholes model: C = SN(d1) − Ee−Rt N(d2) 1 R + ____ 2σ2t ___ d1 = ________ = .7173 √σ2t ___

d2 = d1 − √σ2t = −.1204 N(d1) = .7634 N(d2) = .4521 e−Rt = .7788 C = $50.99 × .7634 − $50.99 × (.7788 × .4521) = $20.97 Since Mr. Fairbank was granted options on 1.662 million shares, and since each option is worth $20.97, the market value of his options by the above calculations is 1.662 million × $20.97 = $34.9 million.Table 23.2 shows that the actual value reported by the company, however, was only $17.0 million. There are a lot of factors that could explain this difference. Any of the parameters we used could be incorrect and would have a significant impact on our calculations. Perhaps most importantly, Capital One paid dividends at a rate of about 7 percent per year. The dividend is a payment that the stockholder receives but that the option holder does not. Since the shareholders get both the dividends and the capital gains but the option holder only benefits from the capital gains, the option is worth less if the stock pays dividends. Since the final stock price five years later on Capital One stock is less than it would be if dividends were reinvested, the option value is less as well. Redoing the computations above to take account of the impact of the dividends gets us a value for the options granted to Fairbank of just about the $17.0 million that the company did, in fact, report.

Table 23.2 shows the grant value of the options as well as the actual option values as reported by each of the companies. Most of these companies use the Black–Scholes method to value the options, but they take into account the special features of their plans and their stock, including whether or not it pays dividends. As can be seen, these reported values, while large by ordinary standards, are significantly less than the corresponding grant values. Notice, too, that the ordering by grant value is not the same as that by the reported option value. For example, whereas Table 23.1 shows that the CEO of Wyeth received a grant value of $20.7 million, which placed him tenth on the list of the top ten, the reported value of those options in Table 23.2, $14.9 million, was fourth on the list. The values we have computed in Table 23.2 are the economic values of the options if they were to trade in the market. The real question is this: Whose value are we talking about? Are these the costs of the options to the company? Are they the values of the options to the executives? Suppose a company computes the fair market value of the options as we have done in Table 23.2. For illustration, assume that the options are in the money and that they are worth $25 each. Suppose, too, that the CEO holds 1 million such options for a total value of $25 million. This is the amount that the options would trade at in the financial markets and that traders and investors would be willing to pay for them.1 If the company were very large, it would not be unreasonable for it to view this as the cost of granting the options to the CEO. Of course, in return, the company would expect the CEO to improve We ignore warrant dilution in this example. See Chapter 24 for a discussion of warrant dilution.

1

Chapter 23 Options and Corporate Finance

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the value of the company to its shareholders by more than this amount. As we have seen, perhaps the main purpose of options is to align the interests of management with those of the shareholders of the firm. Under no circumstances, though, is the $25 million necessarily a fair measure of what the options are worth to the CEO. As an illustration, suppose that the CEO of ABC has options on 1 million shares with an exercise price of $30 per share, and the current price of ABC stock is $50 per share. If the options were exercised today, they would be worth $20 million (an underestimation of their market value). Suppose, in addition, that the CEO owns $5 million in company stock and has $5 million in other assets. The CEO clearly has a very undiversified personal portfolio. By the standards of modern portfolio theory, having 25/30, or about 83 percent, of your personal wealth in one stock and its options is unnecessarily risky. Although the CEO is wealthy by most standards, shifts in stock price impact the CEO’s economic well-being. If the price drops from $50 per share to $30 per share, the current exercise value of the options on 1 million shares drops from $20 million down to zero. Ignoring the fact that if the options had more time to mature they might not lose all of this value, we nevertheless have a rather startling decline in the CEO’s net worth from $30 million to $8 million ($5 million in other assets plus stock that is now worth $3 million). But that is the purpose of giving the options and the stock holdings to the CEO—namely, to make the CEO’s fortunes rise and fall with those of the company. It is why the company requires the executive to hold the options for at least a freeze-out period rather than letting the executive sell them to realize their value. The implication is that when options are a large portion of an executive’s net worth, the total value of the position to the executive is less than market value. As a purely financial matter, an executive might be happier with $5 million in cash rather than $20 million in options. At least the executive could then diversify his personal portfolio.

23.2 Valuing a Start-Up Ralph Simmons was not your typical MBA student. Since childhood, he’d had one ambition: To open a restaurant that sold alligator meat. He went to business school because he realized that although he knew 101 ways to cook alligator, he didn’t have the business skills necessary to run a restaurant. He was extremely focused, with each course at graduate school being important to him only to the extent that it could further his dream. While taking his school’s course in entrepreneurship, he began to develop a business plan for his restaurant, which he now called Alligator Alley. He thought about marketing; he thought about raising capital; he thought about dealing with future employees. He even devoted a great deal of time to designing the physical layout of the restaurant. Against the professor’s advice in his entrepreneurship class, he designed the restaurant in the shape of an alligator, where the front door went through the animal’s mouth. Of course, his business plan would not be complete without financial projections. After much thought, he came up with the projections shown in Table 23.3. The table starts with sales projections, which rise from $300,000 in the first year to a steady state of $1 million a year. Cash flows from operations are shown in the next line, although we leave out the intermediate calculations needed to move from line (1) to line (2). After subtracting working capital, the table shows net cash flows in line (4). Net cash flows are negative initially, as is quite common in start-ups, but they become positive by year 3. However, the rest of the table presents the unfortunate truth. The cash flows from the restaurant yield a present value of $582,561, assuming

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Options, Futures, and Corporate Finance

Financial Projections for Alligator Alley

(1) Sales (2) Cash flows from operations (3) Increase in working capital (4) Net cash flows [(2) − (3)]

Year 1

Year 2

Year 3

Year 4

All Future Years

$300,000 −100,000 50,000 −$150,000

$600,000 −50,000 20,000

$900,000 +75,000 10,000 $ 65,000

$1,000,000 +250,000 10,000 $ 240,000

$1,000,000 +250,000 0 $ 250,000

−$ 70,000

Present value of net cash flows in years 1– 4 (discounted at 20%) $250,000 ______ 1 Present value of terminal value ________ = × .20 (1.20)4 Present value of restaurant

[

− Cost of building Net present value of restaurant

]

−$ 20,255 +$602,816 $582,561 −700,000 −$117,439

a discount rate of 20 percent. Unfortunately, the cost of the building is greater, at $700,000, implying a negative net present value of −$117,439. The projections indicate that Ralph’s lifelong dream may not come to pass. He cannot expect to raise the capital needed to open his restaurant; and if he did obtain the funding, the restaurant would likely go under anyway. Ralph checked and rechecked the numbers, hoping in vain to discover either a numerical error or a cost-saving omission that would move his venture from the red to the black. In fact, Ralph saw that, if anything, his forecasts were generous: A 20 percent discount rate and an infinitely lived building are on the optimistic side. It wasn’t until Ralph took a course in corporate strategy that he saw the hidden value in his venture. In that course, his instructor repeatedly stated the importance of positioning a firm to take advantage of new opportunities. Although Ralph didn’t see the connection at first, he finally realized the implications for Alligator Alley. His financial projections were based on expectations. There was a 50 percent probability that alligator meat would be more popular than he thought, in which case actual cash flows would exceed projections. And there was a 50 percent probability that the meat would be less popular, in which case the actual flows would fall short of projections. If the restaurant did poorly, it would probably fold in a few years because he would not want to keep losing money forever. However, if the restaurant did well, he would be in a position to expand. With alligator meat being popular in one locale, it would likely prove popular in other locales as well. Thus, he noticed two options: The option to abandon under bad conditions and the option to expand under good conditions. Although both options can be valued according to the principles of the previous chapter, we focus on the option to expand because it is probably much more valuable. Ralph reasoned that as much as he personally liked alligator meat, consumer resistance in some regions of the country would doom Alligator Alley. So he developed a strategy of catering only to those regions where alligator meat is somewhat popular already. He forecast that although he could expand quickly if the first restaurant proved successful, the market would limit him to 30 additional restaurants. Ralph believes that this expansion will occur about four years from now. He believes that he will need three years of operating the first restaurant to (1) get the initial restaurant running smoothly and (2) have enough information to place an accurate value on the restaurant. If the first restaurant is successful enough, he will need another year

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to obtain outside capital. Thus, he will be ready to build the 30 additional units around the fourth year. Ralph will value his enterprise, including the option to expand, according to the Black–Scholes model. From Table 23.3, we see that each unit costs $700,000, implying a total cost over the 30 additional units of $21,000,000 (=30 × $700,000). The present value of the cash inflows from these 30 units is $17,476,830 (=30 × $582,561), according to the table. However, because the expansion will occur around the fourth year, this present value calculation is provided from the point of view of four years in the future. The present value as of today is $8,428,255 [=$17,476,830/(1.20)4], assuming a discount rate of 20 percent per year. Thus, Ralph views his potential restaurant business as an option, where the exercise price is $21,000,000 and the value of the underlying asset is $8,428,255. The option is currently out of the money, a result that follows from the negative value of a typical restaurant, as calculated in Table 23.3. Of course, Ralph is hoping that the option will move into the money within four years. Ralph needs three additional parameters to use the Black–Scholes model: R, the continuously compounded interest rate; t, the time to maturity; and σ, the standard deviation of the underlying asset. Ralph uses the yield on a four-year zero coupon bond, which is 3.5 percent, as the estimate of the interest rate. The time to maturity is four years. The estimate of standard deviation is a little trickier because there is no historical data on alligator restaurants. Ralph finds that the average annual standard deviation of the returns on publicly traded restaurants is .35. Because Alligator Alley is a new venture, he reasons that the risk here would be somewhat greater. He finds that the average annual standard deviation for restaurants that have gone public in the last few years is .45. Ralph’s restaurant is newer still, so he uses a standard deviation of .50. There is now enough data to value Ralph’s venture. The value according to the Black–Scholes model is $1,455,196. The actual calculations are shown in Table 23.4. Of course, Ralph must start his pilot restaurant before he can take advantage of this option. Thus, the net value of the call option plus the negative present value of the pilot restaurant is $1,337,757 (=$1,455,196 − $117,439). Because this value is large and positive, Ralph decides to stay with his dream of Alligator Alley. He knows that the probability that the restaurant will fail is greater than 50 percent. Nevertheless, the option to expand is important enough that his restaurant business has value. And if he needs outside capital, he probably can attract the necessary investors. This finding leads to the appearance of a paradox. If Ralph approaches investors to invest in a single restaurant with no possibility of expansion, he will probably not be able to attract capital. After all, Table 23.3 shows a net present value of −$117,439. However, if Ralph thinks bigger, he will likely be able to attract all the capital he needs. But this is really not a paradox at all. By thinking bigger, Ralph is offering investors the option—not the obligation—to expand. The example we have chosen may seem frivolous, and certainly, we added offbeat characteristics for interest. However, if you think that business situations involving options are unusual or unimportant, let us state emphatically that nothing is further from the truth. The notion of embedded options is at the heart of business. There are two possible outcomes for virtually every business idea. On the one hand, the business may fail, in which case the managers will probably try to shut it down in the most costefficient way. On the other hand, the business may prosper, in which case the managers will try to expand. Thus, virtually every business has both the option to abandon and the option to expand. You may have read pundits claiming that the net present value approach to capital budgeting is wrong or incomplete. Although criticism of this type frequently irritates the finance establishment, the pundits definitely have a

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Table 23.4 Valuing a Start-Up Firm (Alligator Alley) as an Option

Facts 1. The value of a single restaurant is negative, as indicated by the net present value calculation in Table 23.3 of −$117,439. Thus, the restaurant would not be funded if there were no possibility of expansion. 2. If the pilot restaurant is successful, Ralph Simmons plans to create 30 additional restaurants around year 4. This leads to the following observations: a. The total cost of 30 units is $21,000,000 (=30 × $700,000). b. The present value of future cash flows as of year 4 is $17,476,830 (=30 × $582,561). c. The present value of these cash flows today is $8,428,255 [=$17,476,830/(1.20)4]. Here, we assume that cash flows from the project are discounted at 20% per annum. Thus, the business is essentially a call option, where the exercise price is $21,000,000 and the underlying asset is worth $8,428,255. 3. Ralph Simmons estimates the standard deviation of the annual return on Alligator Alley’s stock to be .50. Parameters of the Black–Scholes model: S (stock price) = $8,428,255 E (exercise price) = $21,000,000 t (time to maturity) = 4 years σ (standard deviation) = .50 R (continuously compounded interest rate) = 3.5% Calculation from the Black–Scholes model: C = SN(d1) − Ee−Rt N(d2) ___ d1 = [In(S/E)___ + (R + I/2σ2)t] √σ2t d2 = d1 − √ σ2t 8,428,255 1 __ 2 d1 = In _________ 21,000,000 + .035 + 2 (.50) 4

[

(

________

________

) ] √(.50) ⋅ 4 = −.27293 2

d2 = −.27293 − √ (.50)2 ⋅ 4 = −1.27293 N(d1) = N(−.27293) = .3936 N(d2) = N(−1.27293) = .1020 C = $8,428,255 × .3936 − $21,000,000 × e−.035 × 4 × .1020 = $1,455,196 Value of business including cost of pilot restaurant = $1,455,196 − $117,439 = $1,337,757

point If virtually all projects have embedded options, point. options only an approach such as the one we have outlined can be appropriate. Ignoring the options is likely to lead to serious undervaluation.

23.3 More about the Binomial Model Earlier in this chapter, we examined two applications of options: Executive compensation and the start-up decision. In both cases we valued an option using the Black–Scholes model. Although this model is justifiably well known, it is not the only approach to option valuation. As mentioned in the previous chapter, the two-state, or binomial, model is an alternative and—in some situations—a superior approach to valuation. The rest of this chapter examines two applications of the binomial model.

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HeatingOi l Two-Date Example Consider Anthony Meyer, a typical heating oil distributor, whose business consists of buying heating oil at the wholesale level and reselling the oil to homeowners at a somewhat higher price. Most of his revenue comes from sales during the winter. Today, September 1, heating oil sells for $2.00 per gallon. Of course, this price is not fixed. Rather, oil prices will vary from September 1 until December 1, the time when his customers will probably make their big winter purchases of heating oil. Let’s simplify the situation by assuming that Mr. Meyer believes that oil prices will either be at $2.74 or $1.46 on December 1. Figure 23.1 portrays this possible price movement. This potential price range represents a great deal of uncertainty because Mr. Meyer has no idea which of the two possible prices will actually occur. However, this price variability does not translate into that much risk because he can pass price changes on to his customers. That is, he will charge his customers more if he ends up paying $2.74 per gallon than if he ends up paying $1.46 per gallon. Of course, Mr. Meyer is avoiding risk by passing on that risk to his customers. His customers accept the risk, perhaps because they are each too small to negotiate a better deal. This is not the case with CECO, a large electric utility in his area. CECO approaches Mr. Meyer with the following proposition. The utility would like to be able to buy up to 6 million gallons of oil from him at $2.10 per gallon on December 1. Although this arrangement represents a lot of oil, both Mr. Meyer and CECO know that Mr. Meyer can expect to lose money on it. If prices rise to $2.74 per gallon, the utility will happily buy all 6 million gallons at only $2.10 per gallon, clearly creating a loss for the distributor. However, if oil prices decline to $1.46 per gallon, the utility will not buy any oil. After all, why should CECO pay $2.10 per gallon to Mr. Meyer when the utility can buy all the oil it wants at $1.46 per gallon in the open market? In other words, CECO is asking for a call option on heating oil. To compensate Mr. Meyer for the risk of loss, the two parties agree that CECO will pay him $1,000,000 up front for the right to buy up to 6 million gallons of oil at $2.10 per gallon. Is this a fair deal? Although small distributors may evaluate a deal like this by gut feel, we can evaluate it more quantitatively by using the binomial model described in the previous chapter. In that chapter, we pointed out that option problems can be handled

Figure 23.1 Movement of Heating Oil Prices from September 1 to December 1 in a Two-Date Example

$2.74 ($.64 = $2.74 – 2.10)

$2.00

$1.46 ($0) September 1

December 1

The price of heating oil on December 1 will be either $2.74 or $1.46. Because the price on September 1 is $2.00, we say that u = 1.37 (=$2.74/$2.00) and d = .73 (=$1.46/$2.00). The loss per gallon to Mr. Meyer (or, equivalently, the gain per gallon to CECO) of $.64 in the up state or $0 in the down state is shown in parentheses.

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most easily by assuming risk-neutral pricing. In this approach, we first note that oil will either rise 37 percent (=$2.74/$2.00 − 1) or fall −27 percent (=$1.46/$2.00 − 1) from September 1 to December 1. We can think of these two numbers as the possible returns on heating oil. In addition, we introduce two new terms, u and d. We define u as 1 + .37 = 1.37 and d as 1− .27 = .73.2 Using the methodology of the previous chapter, we value the contract in the following two steps. Step 1: Determining the Risk-Neutral Probabilities We determine the probability of a price rise such that the expected return on oil exactly equals the risk-free rate. Assuming an 8 percent annual interest rate, which implies a 2 percent rate over the next three months, we can solve for the probability of a rise as follows:3 2% = Probability of rise × .37 + (1 − Probability of rise) × (−.27) Solving this equation, we find that the probability of a rise is approximately 45 percent, implying that the probability of a fall is 55 percent. In other words, if the probability of a price rise is 45 percent, the expected return on heating oil is 2 percent. In accordance with what we said in the previous chapter, these are the probabilities that are consistent with a world of risk neutrality. That is, under risk neutrality, the expected return on any asset would equal the riskless rate of interest. No one would demand an expected return above this riskless rate, because risk-neutral individuals do not need to be compensated for bearing risk. Step 2: Valuing the Contract If the price of oil rises to $2.74 on December 1, CECO will want to buy oil from Mr. Meyer at $2.10 per gallon. Mr. Meyer will lose $.64 per gallon because he buys oil in the open market at $2.74 per gallon, only to resell it to CECO at $2.10 per gallon. This loss of $.64 is shown in parentheses in Figure 23.1. Conversely, if the market price of heating oil falls to $1.46 per gallon, CECO will not buy any oil from Mr. Meyer. That is, CECO would not want to pay $2.10 per gallon to him when the utility could buy heating oil in the open market at $1.46 per gallon. Thus, we can say that Mr. Meyer neither gains nor loses if the price drops to $1.46. The gain or loss of zero is placed in parentheses under the price of $1.46 in Figure 23.1. In addition, as mentioned earlier, Mr. Meyer receives $1,000,000 up front. Given these numbers, the value of the contract to Mr. Meyer can be calculated as: [.45 × ($2.10 − $2.74) × 6 million + .55 × 0] 1.02 + $1,000,000 = −$694,118 Value of the call option

(23.1)

As in the previous chapter, we are valuing an option using risk-neutral pricing. The cash flows of −$.64 (=$2.10 − $2.74) and $0 per gallon are multiplied by their riskneutral probabilities. The entire first term in Equation 23.1 is then discounted at 1.02 because the cash flows in that term occur on December 1. The $1,000,000 is not discounted because Mr. Meyer receives it today, September 1. Because the present value of the contract is negative, Mr. Meyer would be wise to reject the contract. As stated before, the distributor has sold a call option to CECO. The first term in the preceding equation, which equals −$1,694,118, can be viewed as the value of this call option. It is a negative number because the equation looks at the option from As we will see later, u and d are consistent with a standard deviation of the annual return on heating oil of .63.

2

For simplicity, we ignore both storage costs and a convenience yield.

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Figure 23.2

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$3.12 ($1.02 = $3.12 – $2.10)

Movement of Heating Oil Prices in a ThreeDate Model $2.50 ($.474)

$2.00 ($0)

$2.00 ($.220)

$1.60 ($0)

September 1

October 15

$1.28 ($0) December 1

The figure shows the prices of a gallon of heating oil on three dates, given u = 1.25 and d = .80. There are three possible prices for heating oil on December 1. For each one of these three prices, we calculate the price on December 1 of a call option on a gallon of heating oil with an exercise price of $2.10. These numbers are in parentheses. Call prices at earlier dates are determined by the binomial model and are also shown in parentheses.

Mr. Meyer’s point of view. Therefore, the value of the call option would be +$1,694,118 to CECO. On a per-gallon basis, the value of the option to CECO is: [.45 ($2.74 − $2.10) + .55 × 0] 1.02 = $.282

(23.2)

Equation 23.2 shows that CECO will gain $.64 (=$2.74 − $2.10) per gallon in the up state because CECO can buy heating oil worth $2.74 for only $2.10 under the contract. By contrast, the contract is worth nothing to CECO in the down state because the utility will not pay $2.10 for oil selling for only $1.46 in the open market. Using risk-neutral pricing, the formula tells us that the value of the call option on one gallon of heating oil is $.282. Three-Date Example Although the preceding example captures a number of aspects of the real world, it has one deficiency. It assumes that the price of heating oil can take on only two values on December 1. This is clearly not plausible: Oil can take on essentially any value, in reality. Although this deficiency seems glaring at first glance, it actually is easily correctable. All we have to do is introduce more intervals over the three-month period of our example. For example, consider Figure 23.2, which shows the price movement of heating oil over two intervals of 1½ months each.4 As shown in the figure, the price will be either $2.50 or $1.60 on October 15. We refer to $2.50 as the price in the up state and $1.60 as the price in the down state. Thus, heating oil has returns of 25 percent (=$2.50/$2.00) and −20 percent (=$1.60/$2.00) in the two states. 4 Though it is not apparent at first glance, we will see later that the price movement in Figure 23.2 is consistent with the price movement in Figure 23.1.

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We assume the same variability as we move forward from October 15 to December 1. That is, given a price of $2.50 on October 15, the price on December 1 will be either $3.12 (=$2.50 × 1.25) or $2 (=$2.50 × .80). Similarly, given a price of $1.60 on October 15, the price on December 1 will be either $2 (=$1.60 × 1.25) or $1.28 (=$1.60 × .80). This assumption of constant variability is quite plausible because the rate of new information impacting heating oil (or most commodities or assets) is likely to be similar from month to month. Note that there are three possible prices on December 1, but there are two possible prices on October 15. Also, note that there are two paths to a price of $2 on December 1. The price could rise to $2.50 on October 15 before falling back down to $2 on December 1. Alternatively, the price could fall to $1.60 on October 15 before going back up to $2 on December 1. In other words, the model has symmetry, where an up movement followed by a down movement yields the same price on December 1 as a down movement followed by an up movement. How do we value CECO’s option in this three-date example? We employ the same procedure that we used in the two-date example, although we now need an extra step because of the extra date. Step 1: Determining the Risk-Neutral Probabilities As we did in the two-date example, we determine what the probability of a price rise would be such that the expected return on heating oil exactly equals the riskless rate. However, in this case we work with an interval of 1½ months. Assuming an 8 percent annual rate of interest, which implies a 1 percent rate over a 1½-month interval,5 we can solve for the probability of a rise like this: 1% = Probability of rise × .25 + (1 − Probability of rise) × (−.20) Solving the equation, we find that the probability of a rise here is 47 percent, implying that the probability of a fall is 53 percent. In other words, if the probability of a rise is 47 percent, the expected return on heating oil is 1 percent per each 1½-month interval. Again, these probabilities are determined under the assumption of risk-neutral pricing. Note that the probabilities of 47 percent and 53 percent hold for both the interval from September 1 to October 15 and the interval from October 15 to December 1. This is the case because the return in the up state is 25 percent and the return in the down state is −20 percent for each of the two intervals. Thus, the preceding equation must apply to each of the intervals separately. Step 2: Valuing the Option as of October 15 As indicated in Figure 23.2, the option to CECO will be worth $1.02 per gallon on December 1 if the price of heating oil has risen to $3.12 on that date. That is, CECO can buy oil from Mr. Meyer at $2.10 when it would otherwise have to pay $3.12 in the open market. However, the option will be worthless on December 1 if the price of a gallon of heating oil is either $2 or $1.28 on that date. Here, the option is out of the money because the exercise price of $2.10 is above either $2 or $1.28. Using these option prices on December 1, we can calculate the value of the call option on October 15. If the price of a gallon of heating oil is $2.50 on October 15, Figure 23.2 shows us that the call option will be worth either $1.02 or $0 on December 1.

5

For simplicity, we ignore interest compounding.

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Thus, if the price of heating oil is $2.50 on October 15, the value of the option on one gallon of heating oil at that time is: [.47 × $1.02 + .53 × 0] 1.01 =$.474 Here we are valuing an option using the same risk-neutral pricing approach that we used in the earlier two-date example. This value of $.474 is shown in parentheses in Figure 23.2. We also want to value the option on October 15 if the price at that time is $1.60. However, the value here is clearly zero, as indicated by this calculation: [.47 × $0 + .53 × $0] 1.01 =0 This is obvious once we look at Figure 23.2. We see from the figure that the call must end up out of the money on December 1 if the price of heating oil is $1.60 on October 15. Thus, the call must have zero value on October 15 if the price of heating oil is $1.60 on that date. Step 3: Valuing the Option on September 1 In the previous step, we saw that the price of the call on October 15 would be $.474 if the price of a gallon of heating oil were $2.50 on that date. Similarly, the price of the option on October 15 would be $0 if oil was selling at $1.60 on that date. From these values, we can calculate the call option value on September 1: [.47 × $.474 + .53 × $0] 1.01 =$.220 Notice that this calculation is completely analogous to the calculation of the option value in the previous step, as well as the calculation of the option value in the two-date example that we presented earlier. In other words, the same approach applies regardless of the number of intervals used. As we will see later, we can move to many intervals, which produces greater realism, yet still maintain the same basic methodology. The previous calculation has given us the value to CECO of its option on one gallon of heating oil. Now we are ready to calculate the value of the contract to Mr. Meyer. Given the calculations from the previous equation, the contract’s value can be written as: −$.220 × 6,000,000 + $1,000,000 = −$320,000 That is, Mr. Meyer is giving away an option worth $.220 for each of the 6 million gallons of heating oil. In return, he is receiving only $1,000,000 up front. Overall, he is losing $320,000. Of course, the value of the contract to CECO is the opposite, so the value to this utility is $320,000. Extension to Many Dates We have looked at the contract between CECO and Mr. Meyer using both a two-date example and a three-date example. The three-date case is more realistic because more possibilities for price movements are allowed here. However, why stop at just three dates? Moving to 4 dates, 5 dates, 50 dates, 500 dates, and so on should give us even more realism. Note that as we move to more dates, we are merely shortening the interval between dates without increasing the overall time period of three months (September 1 to December 1). For example, imagine a model with 90 dates over the three months. Here, each interval is approximately one day long because there are about 90 days in a threemonth period. The assumption of two possible outcomes in the binomial model is more plausible over a one-day interval than it is over a 1½-month interval, let alone

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Table 23.5 Value of a Call on One Gallon of Heating Oil

Options, Futures, and Corporate Finance

Number of Intervals*

Call Value

1 2 3 4 6 10 20 30 40 50 99 Black−Scholes Infinity

$.282 .220 .244 .232 .228 .228 .228 .228 .228 .226 .226 .226

In this example, the value of the call according to the binomial model varies as the number of intervals increases. However, the value of the call converges rapidly to the Black−Scholes value. Thus, the binomial model, even with only a few intervals, appears to be a good approximation of Black−Scholes. * The number of intervals is always one less than the number of dates.

a three-month interval. Of course, we could probably achieve greater realism still by going to an interval of, say, one hour or one minute. How do we adjust the binomial model to accommodate increases in the number of intervals? It turns out that two simple formulas relate u and d to the standard deviation of the return on the underlying asset:6 _

u = eσ/√ n

and

d = 1/u

where σ is the standard deviation of the annualized return on the underlying asset (heating oil, in this case) and n is the number of intervals over a year. When we created the heating oil example, we assumed that the annualized standard deviation of the return on heating _oil was .63 (or, equivalently, 63 percent). Because there are four quarters in a year, u = e.63/√4 = 1.37 and d = 1/1.37 = .73, as shown in the two-date example of Figure 23.1. In _ the three-date example of Figure 23.2, where each interval is 1½ months long, u = e.63/√8 = 1.25 and d = 1/1.25 = .80. Thus, the binomial model can be applied in practice if the standard deviation of the return of the underlying asset can be estimated. We stated earlier that the value of the call option on a gallon of heating oil was estimated to be $.282 in the two-date model and $.220 in the three-date model. How does the value of the option change as we increase the number of intervals while keeping the time period constant at three months (from September 1 to December 1)? We have calculated the value of the call for various time intervals in Table 23.5.7 The realism increases with the number of intervals because the restriction of only two possible outcomes is more plausible over a short interval than over a long one. Thus, the value See John C. Hull, Options, Futures, and Other Derivatives, 6th ed. (Upper Saddle River, NJ: Prentice Hall, 2005), for a derivation of these formulas.

6

In this discussion, we have used both intervalsan d dates. To keep the terminology straight, remember that the number of intervals is always one less than the number of dates. For example, if a model has two dates, it has only one interval.

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of the call when the number of intervals is 99 or infinity is likely more realistic than this value when the number of intervals is, say, 1 or 2. However, a very interesting phenomenon can be observed from the table. Although the value of the call changes as the number of intervals increases, convergence occurs quite rapidly. The call’s value with 6 intervals is almost identical to the value with 99 intervals. Thus, a small number of intervals appears serviceable for the binomial model. Six intervals in a three-month period implies that each interval is two weeks long. Of course, the assumption that heating oil can take on only one of two prices in two weeks is simply not realistic. The paradox is that this unrealistic assumption still produces a realistic call price. What happens when the number of intervals goes to infinity, implying that the length of the interval goes to zero? It can be proved mathematically that we end up with the value of the Black–Scholes model. This value is also presented in Table 23.5. Thus, we can argue that the Black–Scholes model is the best approach to value the heating oil option. It is also quite easy to apply. We can use a calculator to value options with Black–Scholes, whereas we must generally use a computer program for the binomial model. However, as shown in Table 23.5, the values from the binomial model, even with relatively few intervals, are quite close to the Black–Scholes value. Thus, although Black–Scholes may save us time, it does not materially affect our estimate of value. At this point it seems as if the Black–Scholes model is preferable to the binomial model. Who wouldn’t want to save time and still get a slightly more accurate value? However, this is not always the case. There are plenty of situations where the binomial model is preferred to the Black–Scholes model. One such situation is presented in the next section.

23.4 Shutdown and Reopening Decisions Some of the earliest and most important examples of special options have occurred in the natural resources and mining industries.

Valuing a Gold Mine The Woe Is Me gold mine was founded in 1878 on one of the richest veins of gold in the West. Thirty years later, by 1908, the mine had been played out; but occasionally, depending on the price of gold, it was reopened. Currently, gold is not actively mined at Woe Is Me, but its stock is still traded on the exchange under the ticker symbol WOE. WOE has no debt and, with about 20 million outstanding shares, its market value (stock price times number of shares outstanding) exceeds $1 billion. WOE owns about 160 acres of land surrounding the mine and has a 100-year government lease to mine gold there. However, land in the desert has a market value of only a few thousand dollars. WOE holds cash securities and other assets worth about $30 million. What could possibly explain why a company with $30 million in assets and a closed gold mine with no cash flow has the market value that WOE has? The answer lies in the options that WOE implicitly owns in the form of a gold mine. Assume that the current price of gold is about $320 per ounce, and the cost of extraction and processing at the mine is about $350 per ounce. It is no wonder that the mine is closed. Every ounce of gold extracted costs $350 and can be sold for only $320, for a loss of $30 per ounce. Presumably, if the price of gold were to rise, the mine could be opened. It costs $2 million to open the mine; when it is opened, production is 50,000 ounces per year. Geologists believe that the amount of gold in the mine is essentially unlimited, and WOE has the right to mine it for the next 100 years. Under

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the terms of its lease, WOE cannot stockpile gold and each year must sell all the gold it mines that year. Closing the mine, which costs $1 million, requires equipment to be mothballed and some environmental precautions to be put in place. We will refer to the $2 million required to open the mine as the entry fee, or investment, and the $1 million to close it as the closing or abandonment cost. (We cannot avoid the abandonment cost by simply keeping the mine open and not operating.) From a financial perspective, WOE is really just a package of options on the price of gold disguised as a company and a mine. The basic option is a call on the price of gold where the exercise price is the $350 extraction cost. The option is complicated by having an exercise fee of $2 million—the opening cost—whenever it is exercised and a closing fee of $1 million when it is abandoned. It is also complicated by the fact that it is a perpetual option with no final maturity.

The Abandonment and Opening Decisions Before valuing the option implicit in WOE, it is useful to see what we can say by just applying common sense. To begin with, the mine should be opened only when the price of gold is sufficiently above the extraction cost of $350 per ounce. Because it costs $2 million to open the mine, the mine should not be opened whenever the price of gold is only slightly above $350. At a gold price of, say, $350.10, the mine wouldn’t be opened because the ten-cent profit per ounce translates into $5,000 per year (=50,000 ounces × $.10/ounce). This would not begin to cover the $2 million opening costs. More significantly, though, the mine probably would not be opened if the price rose to $360 per ounce, even though a $10 profit per ounce—$500,000 per year—would pay the $2 million opening costs at any reasonable discount rate. The reason is that here, as in all option problems, volatility (in this case the volatility of gold) plays a significant role. Because the gold price is volatile, the price has to rise sufficiently above $350 per ounce to make it worth opening the mine. If the price at which the mine is opened is too close to the extraction price of $350 per ounce, say at $360 per ounce, we would open the mine every time the price jogged above $360. Unfortunately, we would then find ourselves operating at a loss or facing a closing decision whenever gold jogged back down $10 per ounce (or only 3 percent) to $350. The estimated volatility of the return on gold is about 15 percent per year. This means that a single annual standard deviation movement in the gold price is 15 percent of $320, or $48 per year. Surely with this amount of random movement in the gold price, a threshold of, for example, $352 is much too low at which to open the mine. Similar logic applies to the closing decision. If the mine is open, we will clearly keep it open as long as the gold price is above the extraction cost of $350 per ounce because we are profiting on every ounce of gold mined. But we also won’t close the mine down simply because the gold price drops below $350 per ounce. We will tolerate a running loss because gold may later rise back above $350. If, alternatively, we closed the mine, we would pay the $1 million abandonment cost, only to pay another $2 million to reopen the mine if the price rose again. To summarize, if the mine is currently closed, then it will be opened—at a cost of $2 million—whenever the price of gold rises sufficiently above the extraction cost of $350 per ounce. If the mine is currently operating, then it will be closed down—at a cost of $1 million—whenever the price of gold falls sufficiently below the extraction cost of $350 per ounce. WOE’s problem is to find these two threshold prices at which it opens a closed mine and closes an open mine. We call these prices popen and pclose, respectively, where: popen > $350/ounce > pclose

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In other words, WOE will open the mine if the gold price option is sufficiently in the money and will close it when the option is sufficiently out of the money. We know that the more volatile the gold price, the further away popen and pclose will be from $350 per ounce. We also know that the greater the cost of opening the mine, the higher popen will be; and the greater the cost of abandoning the mine, the lower pclose will be. Interestingly, we should also expect that popen will be higher if the abandonment cost is increased. After all, if it costs more to abandon the mine, WOE will need to be more assured that the price will stay above the extraction cost when it decides to open the mine. Otherwise, WOE will face the costly choice between abandonment and operating at a loss if the price falls below $350 per ounce. Similarly, raising the cost of opening the mine will make WOE more reluctant to close an open mine. As a result, pclose will be lower. The preceding arguments have enabled us to reduce the problem of valuing WOE to two stages. First, we have to determine the threshold prices, popen and pclose. Second, given the best choices for these thresholds, we must determine the value of a gold option that is exercised for a cost of $2 million when the gold price rises above popen and is shut down for a cost of $1 million whenever the gold price is below pclose. When the mine is open—that is, when the option is exercised—the annual cash flow is equal to the difference between the gold price and the extraction cost of $350 per ounce times 50,000 ounces. When the mine is shut down, it generates no cash flow. The following diagram describes the decisions available at each point in time: Keep mine open and keep mining. Mine is open. Pay $1 million abandonment cost and cease operations. Pay $2 million to open mine and begin mining. Mine is closed. Keep mine closed.

How do we determine the critical values for popen and pclose and then the value of the mine? It is possible to get a good approximation by using the tools we have currentlyd eveloped.

Valuing the Simple Gold Mine Here is what has to be done both to determine popen and pclose and to value the mine. Step 1 Find the risk-free interest rate and the volatility. We assume a semiannual interest rate of 3.4 percent and a volatility of 15 percent per year for gold. Step 2 Construct a binomial tree and fill it in with gold prices. Suppose, for example, that we set the steps _ of the tree six months apart. If the annual volatility is 15 percent, u is equal to e .15/√ 2 , which is approximately equal to 1.11. The other parameter, d, is .90 (=1/1.11). Figure 23.3 illustrates the tree. Starting at the current price of $320, the first 11 percent increase takes the price to $355 in six months. The first 10 percent

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Figure23 .3

$437

A Binomial Tree for GoldP rices

$394

$355

$355

$320 $320

$288 $288

$259

$233 Now

6 months

12 months

18 months

Steps of the binomial tree are six months apart. For each step, u is equal to 1.11 and d is equal to .90.

decrease takes the price to $288 $288. Subsequent steps are up 11 percent or down 10 per percent from the previous price. The tree extends for the 100-year life of the lease, or 200 six-month steps. Using our analysis from the previous section, we now compute the risk-adjusted probabilities for each step. Given a semiannual interest rate of 3.4 percent, we have: 3.4% = Probability of a rise × .11 + (1 – Probability of a rise) × –.10 Solving this equation gives us .64 for the probability of a rise, implying that the probability of a fall is .36. These probabilities are the same for each six-month interval. In other words, if the probability of a rise is .64, the expected return on gold is 3.4 percent per each six-month interval. These probabilities are determined under the assumption of risk-neutral pricing. In other words, if investors are risk-neutral, they will be satisfied with an expected return equal to the risk-free rate because the extra risk of gold will not concern them. Step 3 Now we turn the computer on and let it simulate, say, 5,000 possible paths through the tree. At each node, the computer has a .64 probability of picking an “up” movement in the price and a corresponding .36 probability of picking a “down”

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movement in the price. A typical path might be represented by whether the price rose or fell each six-month period over the next 100 years; it would be a list like: up, up, down, up, down, down, . . . , down where the first “up” means the price rose from $320 to $355 in the first six months, the next “up” means it again went up in the second half of the year from $355 to $394, and so on, ending with a down move in the last half of year 100. With 5,000 such paths, we will have a good sample of all the future possibilities for movement in the gold price. Step 4 Next, we consider possible choices for the threshold prices, popen and pclose. For popen, we let the possibilities be: popen = $360 or $370 or . . . or $500 a total of 15 values. For pclose we let the possibilities be: pclose = $340 or $330 or . . . or $100 a total of 25 values. We picked these choices because they seemed reasonable and because increments of $10 for each seemed sensible. To be precise, though, we should let the threshold prices change as we move through the tree and get closer to the end of 100 years. Presumably, for example, if we decided to open the mine with one year left on the lease, the price of gold should be at least high enough to cover the $2 million opening costs in the coming year. Because we mine 50,000 ounces per year, we will open the mine in year 99 only if the gold price is at least $40 above the extraction cost, or $390. Although this will become important at the end of the lease, using a constant threshold shouldn’t have too big an impact on the value with 100 years to go. Therefore, we will stick with our approximation of constant threshold prices. Step 5 We calculate the value of the mine for each pair of choices of popen and pclose. For example, if popen = $410 and pclose = $290, we use the computer to keep track of the cash flows if we opened the mine whenever it was previously closed and the gold price rose to $410, and closed the mine whenever it was previously open and the gold price fell to $290. We do this for each of the 5,000 paths we simulated in Step 3. For example, consider the path illustrated in Figure 23.4: up, up, down, up, up, down, down, down, down As can be seen from the figure, the price reaches a peak of $437 in 2½ years, only to fall to $288 over the following four six-month intervals. If popen = $410 and pclose = $290, the mine will be opened when the price reaches $437, necessitating a cost of $2 million. However, the firm can sell 25,000 ounces of gold at $437 per ounce at that time, producing a cash flow of $2.175 million [=25,000 × ($437 − $350)]. When the price falls to $394 six months later, the firm sells another 25,000 ounces, yielding a cash flow of $1.1 million [=25,000 × ($394 − $350)]. The price continues to fall, reaching $320 a year later. Here, the firm experiences a cash outflow because production costs are $350 per ounce. Next, the price falls to $288. Because this price is below pclose of $290, the mine is closed at a cost of $1 million. Of course, the price of gold will fluctuate in further years, leading to the possibility of future mine openings and closings. This path is just a possibility. It may or may not occur in any simulation of 5,000 paths. For each of the 5,000 paths that the computer simulated, we have a

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Figure23 .4

–$2 million (Mine opened) $437 +$2.175 million = 25,000 ($437–$350)

A Possible Path for the Price of Gold

$394

$355

$320

$394

$355

$394 +$1.1 million = 25,000 ($394–$350)

$355 +$125,000 = 25,000 ($355–$350)

$320 –$750,000 = 25,000 ($320–$350)

$288 –$1 million (Mine closed)

Imagine that this path is one of the 5,000 simulated price paths for gold. Because popen = $410 and pclose = $290, the mine is opened when the price reaches $437. The mine is closed when the price reaches $288.

sequence of semiannual cash flows using a popen of $410 and a pclose of $290. We calculate the present value of each of these cash flows, discounting at the interest rate of 3.4 percent. Summing across all the cash flows, we have the present value of the gold mine for one path. We then take the average present value of the gold mine across all the 5,000 simulated paths. This number is the expected value of the mine from following a policy of opening the mine whenever the gold price hits $410 and closing it at a price of $290. Step 6 The final step is to compare the different expected discounted cash flows from Step 5 for the range of possible choices for popen and pclose and to pick the highest one. This is the best estimate of the expected value of the mine. The values for pclose and popen corresponding to this estimate are the points at which to open a closed mine and to shut an open one. As mentioned in Step 4, there are 15 different values for popen and 25 different values for pclose, implying 375 (=15 × 25) different pairs. Consider Table 23.6, which shows the present values associated with the 20 best pairs. The table indicates that the best pair is popen = $400 and pclose = $140, with a present value of $1.467 billion. This number represents the average present value across 5,000 simulations, all assuming the preceding values of popen and pclose. The next best pair is popen = $460 and pclose = $300, with a present value of $1.459 billion. The third best pair has a somewhat lower present value, and so on.

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Table 23.6 Valuation of Woe Is Me (WOE) Gold Mine for the 20 Best Choices of popenand pclose

popen

pclose

Estimated Value of Gold Mine

$400 460 380 370 360 420 430 430 470 500 410 420 400 360 360 380 450 450 440 440

$140 300 290 100 190 150 340 110 200 320 290 290 160 320 180 280 310 280 220 240

$1,466,720,900 1,459,406,200 1,457,838,700 1,455,131,900 1,449,708,200 1,448,711,400 1,448,450,200 1,445,396,500 1,435,687,400 1,427,512,000 1,426,483,500 1,423,865,300 1,423,061,900 1,420,748,700 1,419,112,000 1,417,405,400 1,416,238,000 1,409,709,800 1,408,269,100 1,403,398,100

For our simulation, WOE opens the mine whenever the gold price rises above popen and closes the mine whenever the gold price falls below pclose.

Of course, our estimate of the value of the mine is $1.467 billion, the present value of the best pair of choices. The market capitalization (Price × Number of shares outstanding) of WOE should reach this value if the market makes the same assumptions that we did. Note that the value of the firm is quite high using an option framework. However, as stated earlier, WOE would appear worthless if a regular discounted cash flow approach were used. This occurs because the initial gold price of $320 is below the extraction cost of $350. This example is not easy, neither in concepts nor in implementation. However, the extra work involved in mastering this example is worth it because the example illustrates the type of modeling that actually occurs in corporate finance departments in the real world. Furthermore, the example illustrates the benefits of the binomial approach. We merely calculate the cash flows associated with each of a number of simulations, discount the cash flows from each simulation, and average present values across the simulations. Because the Black–Scholes model is not amenable to simulations, it cannot be used for this type of problem. In addition, there are a number of other situations where the binomial model is more appropriate than is the Black–Scholes model. For example, it is well known that the Black–Scholes model cannot properly handle options with dividend payments prior to the expiration date. This model also does not adequately handle the valuation of an American put. By contrast, the binomial model can easily handle both of these situations.

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Thus, any student of corporate finance should be well versed in both models. The Black–Scholes model should be used whenever appropriate because it is simpler to use than is the binomial model. However, for the more complex situations where the Black–Scholes model breaks down, the binomial model becomes a necessary tool.

Summary and Conclusions

Real options, which are pervasive in business, are not captured by net present value analysis. Chapter 7 valued real options via decision trees. Given the work on options in the previous chapter, we are now able to value real options according to the Black−Scholes model and the binomial model. In this chapter, we described and valued four different types of options: 1. 2. 3. 4.

Executive stock options, which are technically not real options. The embedded option in a start-up company. The option in simple business contracts. The option to shut down and reopen a project.

We tried to keep the presentation simple and straightforward from a mathematical point of view. The binomial approach to option pricing in Chapter 22 was extended to many periods. This adjustment brings us closer to the real world because the assumption of only two prices at the end of an interval is more plausible when the interval is short.

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Concept Questions

1.

2. 3. 4.

5. 6.

7.

8.

9. 10.

Employee Stock Options Why do companies issue options to executives if they cost the company more than they are worth to the executive? Why not just give cash and split the difference? Wouldn’t that make both the company and the executive bettero ff ? Real Options What are the two options that many businesses have? Project Analysis Why does a strict NPV calculation typically understate the value of a company or project? Real Options Utility companies often face a decision to build new plants that burn coal, oil, or both. If the prices of both coal and gas are highly volatile, how valuable is the decision to build a plant that can burn either coal or oil? What happens to the value of this option as the correlation between coal and oil prices increases? Real Options Your company owns a vacant lot in a suburban area. What is the advantage of waiting to develop the lot? Real Options Star Mining buys a gold mine, but the cost of extraction is currently too high to make the mine profitable. In option terminology, what type of option(s) does the company have on this mine? Real Options You are discussing real options with a colleague. During the discussion, the colleague states, “Real option analysis makes no sense because it says that a real option on a risky venture is worth more than a real option on a safe venture.’’ How should you respond to this statement? Real Options and Capital Budgeting Your company currently uses traditional capital budgeting techniques, including net present value. After hearing about the use of real option analysis, your boss decides that your company should use real option analysis in place of net present value. How would you evaluate this decision? Insurance as an Option Insurance, whether purchased by a corporation or an individual, is in essence an option. What type of option is an insurance policy? Real Options How would the analysis of real options change if a company has competitors?

Chapter 23 Options and Corporate Finance

Questions and Problems

1.

BASIC (Questions 1−5)

2.

4.

5.

INTERMEDIATE (Questions 6−8)

6.

Employee Stock Options Gary Levin is the chief executive officer of Mountainbrook Trading Company. The board of directors has just granted Mr. Levin 30,000 at-the-money European call options on the company’s stock, which is currently trading at $55 per share. The stock pays no dividends. The options will expire in five years, and the standard deviation of the returns on the stock is 45 percent. Treasury bills that mature in five years currently yield a continuously compounded interest rate of 6 percent. a. Uset heB lack–Scholes model to calculate the value of the stock options. b. You are Mr. Levin’s financial adviser. He must choose between the previously mentioned stock option package and an immediate $750,000 bonus. If he is riskneutral, which would you recommend? c. How would your answer to (b) change if Mr. Levin were risk-averse and he could not sell the options prior to expiration? Employee Stock Options Jared Lazarus has just been named the new chief executive officer of BluBell Fitness Centers, Inc. In addition to an annual salary of $375,000, his three-year contract states that his compensation will include 15,000 at-the-money European call options on the company’s stock that expire in three years. The current stock price is $34 per share, and the standard deviation of the returns on the firm’s stock is 74 percent. The company does not pay a dividend. Treasury bills that mature in three years yield a continuously compounded interest rate of 5 percent. Assume that Mr. Lazarus’s annual salary payments occur at the end of the year and that these cash flows should be discounted at a rate of 9 percent. Using the Black–Scholes model to calculate the value of the stock options, determine the total value of the compensation package on the date the contract is signed. Binomial Model Gasworks, Inc., has been approached to sell up to 5 million gallons of gasoline in three months at a price of $2.05 per gallon. Gasoline is currently selling on the wholesale market at $1.74 per gallon and has a standard deviation of 46 percent. If the risk-free rate is 6 percent per year, what is the value of this option? Real Options The Webber Company is an international conglomerate with a real estate division that owns the right to erect an office building on a parcel of land in downtown Sacramento over the next year. This building would cost $20 million to construct. Due to low demand for office space in the downtown area, such a building is worth approximately $18.5 million today. If demand increases, the building would be worth $22.4 million a year from today. If demand decreases, the same office building would be worth only $17.5 million in a year. The company can borrow and lend at the risk-free annual effective rate of 4.8 percent. A local competitor in the real estate business has recently offered $750,000 for the right to build an office building on the land. Should the company accept this offer? Use a two-state model to value the real option. Real Options Jet Black is an international conglomerate with a petroleum division and is currently competing in an auction to win the right to drill for crude oil on a large piece of land in one year. The current market price of crude oil is $58 per barrel, and the land is believed to contain 375,000 barrels of oil. If found, the oil would cost $35 million to extract. Treasury bills that mature in one year yield a continuously compounded interest rate of 4 percent, and the standard deviation of the returns on the price of crude oil is 50 percent. Use the Black–Scholes model to calculate the maximum bid that the company should be willing to make at the auction. Real Options Sardano and Sons is a large, publicly held company that is considering leasing a warehouse. One of the company’s divisions specializes in manufacturing steel, and this particlar warehouse is the only facility in the area that suits the firm’s operations. The current price of steel is $630 per ton. If the price of steel falls over the next six months, the company will purchase 400 tons of steel and produce

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8.

CHALLENGE (Questions 9−10)

9.

Mini Case

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45,000 steel rods. Each steel rod will cost $16 to manufacture, and the company plans to sell the rods for $24 each. It will take only a matter of days to produce and sell the steel rods. If the price of steel rises or remains the same, it will not be profitable to undertake the project, and the company will allow the lease to expire without producing any steel rods. Treasury bills that mature in six months yield a continuously compounded interest rate of 4.5 percent, and the standard deviation of the returns on steel is 45 percent. Use the Black–Scholes model to determine the maximum amount that the company should be willing to pay for the lease. Real Options Wet for the Summer, Inc., manufactures filters for swimming pools. The company is deciding whether to implement a new technology in its pool filters. One year from now the company will know whether the new technology is accepted in the market. If the demand for the new filters is high, the present value of the cash flows in one year will be $13.4 million. Conversely, if the demand is low, the value of the cash flows in one year will be $7 million. The value of the project today under these assumptions is $11.6 million, and the risk-free rate is 6 percent. Suppose that in one year, if the demand for the new technology is low, the company can sell the technology for $8.2 million. What is the value of the option to abandon? Binomial Model There is a European put option on a stock that expires in two months. The stock price is $58, and the standard deviation of the stock returns is 70 percent. The option has a strike price of $65, and the risk-free interest rate is a 5 percent annual percentage rate. What is the price of the put option today using onemonth steps? (Hint: How will you find the value of the option if it can be exercised early? When would you exercise the option early?) Binomial Model In the previous problem, assume that the exercise style on the option is American rather than European. What is the price of the option now? (Hint: How will you find the value of the option if it can be exercised early? When would you exercise the option early?) Real Options You are in discussions to purchase an option on an office building with a strike price of $52 million. The building is currently valued at $50 million. The option will allow you to purchase the building either six months from today or one year from today. Six months from today, accrued rent payments from the building in the amount of $650,000 will be made to the owners. If you exercise the option in six months, you will receive the accrued rent payments; otherwise, the payment will be made to the current owners. A second accrued rent payment of $650,000 will be paid one year from today with the same payment terms. The standard deviation of the value of the building is 30 percent, and the risk-free rate is a 6 percent annual percentage rate. What is the price of the option today using six-month steps? (Hint: The value of the building in six months will be reduced by the accrued rent payment if you do not exercise the option at that time.)

EXOTIC CUISINES EMPLOYEE STOCK OPTIONS As a newly minted MBA, you’ve taken a management position with Exotic Cuisines, Inc., a restaurant chain that just went public last year. The company’s restaurants specialize in exotic main dishes, using ingredients such as alligator, buffalo, and ostrich. A concern you had going in was that the restaurant business is very risky. However, after some due diligence, you discovered a common misperception about the restaturant industry. It is widely thought that 90 percent of new restaurants close within three years; however, recent evidence suggests the failure rate is closer to 60 percent over three years. So it is a risky business, although not as risky as you originally thought.

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During your interview process, one of the benefits mentioned was employee stock options. Upon signing your employment contract, you received options with a strike price of $40 for 10,000 shares of company stock. As is fairly common, your stock options have a three-year vesting period and a 10-year expiration, meaning that you cannot exercise the options for three years, and you lose them if you leave before they vest. After the three-year vesting period, you can exercise the options at any time. Thus, the employee stock options are European (and subject to forfeit) for the first three years and American afterward. Of course, you cannot sell the options, nor can you enter into any sort of hedging agreement. If you leave the company after the options vest, you must exercise within 90 days or forfeit. Exotic Cuisines stock is currently trading at $36.28 per share, a slight increase from the initial offering price last year. There are no market-traded options on the company’s stock. Because the company has been traded for only about a year, you are reluctant to use the historical returns to estimate the standard deviation of the stock’s return. However, you have estimated that the average annual standard deviation for restaurant company stocks is about 55 percent. Because Exotic Cuisines is a newer restaurant chain, you decide to use a 60 percent standard deviation in your calculations. The company is relatively young, and you expect that all earnings will be reinvested back into the company for the near future. Therefore, you expect no dividends will be paid for at least the next 10 years. A three-year Treasury note currently has a yield of 3.8 percent, and a 10-year Treasury note has a yield of 4.4 percent. 1. You’re trying to value your options. What minimum value would you assign? What is the maximum value you would assign? 2. Suppose that in three years the company’s stock is trading at $60. At that time, should you keep the options or exercise them immediately? What are some of the important determinants in making such a decision? 3. Your options, like most employee stock options, are not transferable or tradable. Does this have a significant effect on the value of the options? Why? 4. Why do you suppose employee stock options usually have a vesting provision? Why must they be exercised shortly after you depart the company even after they vest? 5. A controversial practice with employee stock options is repricing. What happens is that a company experiences a stock price decrease, which leaves employee stock options far out of the money or “underwater.’’ In such cases, many companies have “repriced’’ or “restruck’’ the options, meaning that the company leaves the original terms of the option intact but lowers the strike price. Proponents of repricing argue that because the option is very unlikely to end in the money because of the stock price decline, the motivational force is lost. Opponents argue that repricing is in essence a reward for failure. How do you evaluate this argument? How does the possibility of repricing affect the value of an employee stock option at the time it is granted? 6. As we have seen, much of the volatility in a company’s stock price is due to systematic or marketwide risks. Such risks are beyond the control of a company and its employees. What are the implications for employee stock options? In light of your answer, can your ecommendan imp rovemento vert raditionale mployees tocko ptions?

CHAPTER 24

WarrantsandCo nvertibles In February 2008, Paladin Energy, Ltd., an Australian uranium mining company, announced the pricing on a new bond issue. The company sold $325 million worth of 5 percent coupon bonds due in 2013. What might surprise you is that the yield to maturity on the bonds when they were issued was a low 5 percent, significantly less than the yield on the company’s other bonds. So how was Paladin able to issue bonds with such a low promised yield? The answer is these bonds were convertible into shares of the company’s common stock at a price of $6.59 per share. Paladin shares were trading at $5.27 when the bonds were issued, so conversion was not immediately profitable, but it could prove to be very lucrative at some point in the future if the stock were to rise in price. Another provision allows Paladin to immediately redeem (buy back) the bonds at par value if the stock price exceeds 130 percent of the conversion price of $6.59 for a specified period. So, in essence, these convertible bonds are low coupon bonds with two attached call options, one held by the bondholders and one held by the company. How do we value a financial instrument that is a combination of a bond and call options? This chapter explores this and other issues.

24.1 Warrants Warrants are securities that give holders the right, but not the obligation, to buy shares of common stock directly from a company at a fixed price for a given period. Each warrant specifies the number of shares of stock that the holder can buy, the exercise price, and the expiration date. From the preceding description of warrants, it is clear that they are similar to call options. The differences in contractual features between warrants and the call options that trade on the Chicago Board Options Exchange are small. For example, warrants have longer maturity periods.1 Some warrants are actually perpetual, meaning that they never expire. Warrants are referred to as equity kickers because they are usually issued in combination with privately placed bonds.2 In most cases, warrants are attached to the bonds when issued. The loan agreement will state whether the warrants are detachable from the bond—that is, whether they can be sold separately. Usually, the warrant can be detached immediately. For example, during a reorganization, famed banana company Chiquita Brands International issued warrants. Each warrant gave the holder the right to purchase one share of stock at an exercise price of $19.32. The warrants expired on March 19, 2009. On September 3, 2008, Chiquita Brands stock closed at $15.12, and the price of a warrant was $1.05. 1

Warrants are usually protected against stock splits and dividends in the same way that call options are.

2

Warrants are also issued with publicly distributed bonds and new issues of common stock.

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Figure 24.1

745

Value of warrant

Chiquita Warrants onS eptember3, 20 08

Upper limit on warrant value Actual warrant value curve Lower limit on warrant value Price of warrant = $1.05 Actual stock price = $15.12

Exercise price = $19.32

Value of a share of common stock

The relationship between the value of Chiquita’s warrants and its stock price can be viewed as similar to the relationship between a call option and the stock price, described in a previous chapter. Figure 24.1 depicts the relationship for Chiquita’s warrants. The lower limit on the value of the warrants is zero if Chiquita’s stock price is below $19.32 per share. If the price of Chiquita’s stock rises above $19.32 per share, the lower limit is the stock price minus $19.32. The upper limit is the price of Chiquita’s stock. A warrant to buy one share of stock cannot sell at a price above the price of the underlying stock. The price of Chiquita’s warrants on September 3, 2008, was higher than the lower limit. The height of the warrant price above the lower limit will depend on the following: 1. The variance of Chiquita’s stock returns. 2. The time to expiration date. 3. The risk-free rate of interest. 4. The stock price of Chiquita. 5. Thee xercisep rice. These are the same factors that determine the value of a call option. Warrants can also have unusual features. For example, the Montana Mills Bread Company, Inc., had warrants that expired in 2007 with an exercise price of $7.58. Each warrant could be used to purchase .15 shares of stock in Krispy Kreme Doughnuts. To purchase one share of Krispy Kreme stock, a holder gave up 6.66 warrants and $50.48. This means the exercise price on the stock was $50.48, not the $7.58 exercise price listed on the warrant.

24.2 The Difference between Warrants and Call Options From the holder’s point of view, warrants are similar to call options on common stock. A warrant, like a call option, gives its holder the right to buy common stock at a specified price. Warrants usually have an expiration date, though in most cases they are issued with longer lives than call options. From the firm’s point of view, however, a warrant is very different from a call option on the company’s common stock. The most important difference between call options and warrants is that call options are issued by individuals and warrants are issued by firms. When a warrant

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is exercised, a firm must issue new shares of stock. Each time a warrant is exercised, then, the number of shares outstanding increases. To illustrate, suppose the Endrun Company issues a warrant giving holders the right to buy one share of common stock at $25. Furthermore, suppose the warrant is exercised. Endrun must print one new stock certificate. In exchange for the stock certificate, it receives $25 from the holder. In contrast, when a call option is exercised there is no change in the number of shares outstanding. Suppose Ms. Eager holds a call option on the common stock of the Endrun Company. The call option gives Ms. Eager the right to buy one share of the common stock of the Endrun Company for $25. If Ms. Eager chooses to exercise the call option, a seller, say Mr. Swift, is obligated to give her one share of Endrun’s common stock in exchange for $25. If Mr. Swift does not already own a share, he must enter the stock market and buy one. The call option is a side bet between buyers and sellers on the value of the Endrun Company’s common stock. When a call option is exercised, one investor gains and the other loses. The total number of shares outstanding of the Endrun Company remains constant, and no new funds are made available to the company.

EXAMPLE24.1

Warrants and Firm Value To see how warrants affect the value of the firm, imagine that W Mr. Gould and Ms. Rockefeller are two investors who have together purchased six ounces of platinum. M At the time they bought the platinum, Mr. Gould and Ms. Rockefeller each contributed half of the cost, which we will assume was $3,000 for six ounces, or $500 an ounce (they each contributed $1,500). They incorporated, printed two stock certificates, and named the firm the GR Company. Each certificate represents a one-half claim to the platinum. Mr. Gould and Ms. Rockefeller each own one certificate. They have formed a company with platinum as its only asset. A Call Is Issued Suppose Mr. Gould later decides to sell to Ms. Fiske a call option issued on Mr. Gould’s share. The call option gives Ms. Fiske the right to buy Mr. Gould’s share for $1,800 within the next year. If the price of platinum rises above $600 per ounce, the firm will be worth more than $3,600, and each share will be worth more than $1,800. If Ms. Fiske decides to exercise her option, Mr. Gould must turn over his stock certificate and receive $1,800. How would the firm be affected by the exercise? The number of shares will remain the same. There will still be two shares, now owned by Ms. Rockefeller and Ms. Fiske. If the price of platinum rises to $700 an ounce, each share will be worth $2,100 (=$4,200/2). If Ms. Fiske exercises her option at this price, she will gain $300. A Warrant Is Issued Instead This story changes if a warrant is issued. Suppose that Mr. Gould does not sell a call option to Ms. Fiske. Instead, Mr. Gould and Ms. Rockefeller have a stockholders’ meeting. They vote that GR Company will issue a warrant and sell it to Ms. Fiske. The warrant will give Ms. Fiske the right to receive a share of the company at an exercise price of $1,800.3 If Ms. Fiske decides to exercise the warrant, the firm will issue another stock certificate and give it to Ms. Fiske in exchange for $1,800. From Ms. Fiske’s perspective, the call option and the warrant seem to be the same. The exercise prices of the warrant and the call are the same: $1,800. It is still advantageous for Ms. Fiske to exercise the warrant when the price of platinum exceeds $600 per ounce. However, we will show that Ms. Fiske actually makes less in the warrant situation due to dilution.

3 The sale of the warrant brings cash into the firm. We assume that the sale proceeds immediately leave the firm through a cash dividend to Mr. Gould and Ms. Rockefeller. This simplifies the analysis because the firm with warrants then has the same total value as the firm without warrants.

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The GR Company must also consider dilution. Suppose the price of platinum increases to $700 an ounce and Ms. Fiske exercises her warrant. Two things will occur: 1. Ms. Fiske will pay $1,800 to the firm. 2. The firm will print one stock certificate and give it to Ms. Fiske. The stock certificate will represent a one-third claim on the platinum of the firm. Because Ms. Fiske contributes $1,800 to the firm, the value of the firm increases. It is now worth: New value of firm = Value of platinum + Contribution to the firm by Ms. Fiske = $4,200 + $1,800 = $6,000 Because Ms. Fiske has a one-third claim on the firm’s value, her share is worth $2,000 (=$6,000/3). By exercising the warrant, Ms. Fiske gains $2,000 − $1,800 = $200. This is illustrated in Table 24.1. Dilution Why does Ms. Fiske gain only $200 in the warrant case but gain $300 in the call option case? The key is dilution—that is, the creation of another share. In the call option case, she contributes $1,800 and receives one of the two outstanding shares. That is, she receives a share worth 1 $2,100 (= _2 × $4,200). Her gain is $300 (=$2,100 − $1,800). We rewrite this gain like this: Gain on Exercise of Call $4,200 ______ 2

− $1,800 = $300

(24.1)

In the warrant case, she contributes $1,800 and receives a newly created share. She now owns one of the three outstanding shares. Because the $1,800 remains in the firm, her share is worth $2,000 [(=$4,200 + $1,800) 3]. Her gain is $200 (=$2,000 − $1,800). We rewrite this gain as follows:

Table 24.1

Effect of Call Option and Warrant on the GR Company*

Price of Platinum per Share Value of Firm If No warrant Mr. Gould’s share Ms. Rockefeller’s share Firm Call option Mr. Gould’s claim Ms. Rockefeller’s claim Ms. Fiske’s claim Firm Warrant Mr. Gould’s share Ms. Rockefeller’s share Ms. Fiske’s share Firm

$700

$600

$2,100 2,100 $4,200

$1,800 1,800 $3,600

$

0 2,100 2,100 $4,200

$1,800 1,800 0 $3,600

$2,000 2,000 2,000 $6,000

$1,800 1,800 0 $3,600

*If the price of platinum is $700, the value of the firm is equal to the value of six ounces of platinum plus the excess dollars paid into the firm by Ms. Fiske. This amount is $4,200 + $1,800 = $6,000.

(continued)

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Gain on Exercise of Warrant $4,200 + $1,800 ______________ 2+1

− $1,800 = $200

(24.2)

Warrants also affect accounting numbers. Warrants and (as we shall see) convertible bonds cause the number of shares to increase. This causes the firm’s net income to be spread over more shares, thereby decreasing earnings per share. Firms with significant amounts of warrants and convertible issues must report earnings on a primary basis and a fully diluted basis.

How the Firm Can Hurt Warrant Holders Suppose that the platinum firm owned by Mr. Gould and Ms. Rockefeller has issued a warrant to Ms. Fiske that is in the money and about to expire. One way that Mr. Gould and Ms. Rockefeller can hurt Ms. Fiske is to pay themselves a large dividend. This could be funded by selling a substantial amount of platinum. The value of the firm would fall, and the warrant would be worth much less.

24.3 Warrant Pricing and the Black–Scholes Model We now wish to express the gains from exercising a call and a warrant in more general terms. The gain on a call can be written like this: Gain from Exercising a Single Call Firm’s value net of debt _____________________ − Exercise price # (Value of a share of stock)

(24.3)

Equation 24.3 generalizes Equation 24.1. We define the firm’s value net of debt to be the total firm value less the value of the debt. The total firm value is $4,200 in our example, and there is no debt. The # stands for the number of shares outstanding, which is two in our example. The ratio on the left is the value of a share of stock. The gain on a warrant can be written as follows: Gain from Exercising a Single Warrant Firm’s value net of debt + Exercise price × # − Exercise price # + #w

________________________________________w

(24.4)

(Value of a share of stock after warrant is exercised) Equation 24.4 generalizes Equation 24.2. The numerator of the left term is the firm’s value net of debt after the warrant is exercised. It is the sum of the firm’s value net of debt prior to the warrant’s exercise plus the proceeds the firm receives from the exercise. The proceeds equal the product of the exercise price multiplied by the number of warrants. The number of warrants appears as #w. (Our analysis uses the plausible assumption that all warrants in the money will be exercised.) Note that #w = 1 in our numerical example. The denominator, # + #w, is the number of shares outstanding after the exercise of the warrants. The ratio on the left is the value of a share of stock after exercise. By rearranging terms, we can rewrite Equation 24.4 as:4 4

To derive Formula 24.5, we separate “Exercise price” in Equation 24.4. This yields: # Firm’s value net of debt _______ _____________________ − × Exercise price # + #w

By rearranging terms, we can obtain Formula 24.5.

# + #w

Chapter 24

Warrants and Convertibles

Gain from Exercising a Single Warrant Firm’s value net of debt # _______ × _____________________ − Exercise price # + #w #

(

749

)

(24.5)

(Gain from a call on a firm with no warrants) Formula 24.5 relates the gain on a warrant to the gain on a call. Note that the term within parentheses is Equation 24.3. Thus, the gain from exercising a warrant is a proportion of the gain from exercising a call in a firm without warrants. The proportion # (# + #w) is the ratio of the number of shares in the firm without warrants to the number of shares after all the warrants have been exercised. This ratio must always be less than 1. Thus, the gain on a warrant must be less than the gain on an identical call 2 in a firm without warrants. Note that # (# + #w) = _3 in our example, which explains why Ms. Fiske gains $300 on her call yet gains only $200 on her warrant. The preceding implies that the Black–Scholes model must be adjusted for warrants. When a call option is issued to Ms. Fiske, we know that the exercise price is $1,800 and the time to expiration is one year. Though we have not posited the price of the stock, the variance of the stock, or the interest rate, we could easily provide these data for a realworld situation. Thus, we could use the Black–Scholes model to value Ms. Fiske’s call. Suppose that the warrant is to be issued tomorrow to Ms. Fiske. We know the number of warrants to be issued, the warrant’s expiration date, and the exercise price. Using our assumption that the warrant proceeds are immediately paid out as a dividend, we could use the Black–Scholes model to value the warrant. We would first calculate the value of an identical call. The warrant price is the call price multiplied by 2 the ratio # (# + #w). As mentioned earlier, this ratio is _3 in o ure xample.

24.4 Convertible Bonds A convertible bond is similar to a bond with warrants. The most important difference is that a bond with warrants can be separated into distinct securities and a convertible bond cannot. A convertible bond gives the holder the right to exchange it for a given number of shares of stock anytime up to and including the maturity date of the bond. Preferred stock can frequently be converted into common stock. A convertible preferred stock is the same as a convertible bond except that it has an infinite maturity date.

EXAMPLE 24.2

Convertibles Oceandoor Technology is one of the most important manufacturers of rigid magC nnetic disk drives for computers. Its stock is traded over the counter (OTC). On November 1, 2009, Oceandoor raised $300 million by issuing 6.75 percent convertible subordinated debentures due in 2025. It planned to use the proceeds to invest in new plant and equipment. Like typical debentures, they had a sinking fund and were callable. Oceandoor’s bonds differed from other debentures in their convertible feature: Each bond was convertible into 23.53 shares of common stock of Oceandoor anytime before maturity. The number of shares received for each bond (23.53 in this example) is called the conversion ratio. Bond traders also speak of the conversion price of the bond. This is calculated as the ratio of the face value of the bond to the conversion ratio. Because the face value of each Oceandoor bond was $1,000, the conversion price was $42.50 (=$1,000 23.53). The bondholders of Oceandoor could give up bonds with a face value of $1,000 and receive 23.53 shares of Oceandoor common stock. This was equivalent to paying $42.50 (=$1,000 23.53) for each share of Oceandoor common stock received. When Oceandoor issued its convertible bonds, its common stock was trading at $22.625 per share. The conversion price of $42.50 was 88 percent higher than the actual common stock price. (continued)

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This 88 percent is referred to as the conversion premium. It reflects the fact that the conversion option in Oceandoor convertible bonds was out of the money. This conversion premium is typical. Convertibles are almost always protected against stock splits and stock dividends. If Oceandoor’s common stock had been split two for one, the conversion ratio would have been increased from 23.53to 47.06.

Conversion ratio, conversion price, and conversion premium are well-known terms in the real world. For that reason alone, the student should master the concepts. However, conversion price and conversion premium implicitly assume that the bond is selling at par. If the bond is selling at another price, the terms have little meaning. By contrast, conversion ratio can have a meaningful interpretation regardless of the price of the bond. To give an example of these ideas, consider Amgen convertible bonds. When these bonds were issued in 2006, this offering was the largest convertible bond issue in history and represented about 2 percent of all convertible bonds outstanding. The conversion ratio of the bonds maturing in 2011 is 12.52. This means the conversion price is $1,000 12.52 = $79.87. In early 2009, Amgen’s stock was selling for about $44, so this represented a conversion premium of 81.5 percent. The bonds maturing in 2013 have a conversion ratio of 12.58. Check and see if you agree this represents a conversion premium of 81 percent.

24.5 The Value of Convertible Bonds The value of a convertible bond can be described in terms of three components: straight bond value, conversion value, and option value. We examine these three components next.

StraightB ondV alue The straight bond value is what the convertible bonds would sell for if they could not be converted into common stock. It will depend on the general level of interest rates and on the default risk. Suppose that straight debentures issued by Oceandoor had been rated A, and A-rated bonds were priced to yield 4 percent per six months on November 1, 2006. The straight bond value of Oceandoor convertible bonds can be determined by discounting the $33.75 semiannual coupon payment and principal amount at 4 percent: 32 $1,000 $33.75 _______ Straight bond value = ∑ ______ t + 32 1.04 (1.04) t=1 $1,000 = $33.75 × A32 + _______ .04 (1.04)32 = $603.23 + $285.06 =$888.29 The straight bond value of a convertible bond is a minimum value. The price of Oceandoor’s convertible bonds could not have gone lower than the straight bond value. Figure 24.2 illustrates the relationship between straight bond value and stock price. In Figure 24.2 we have been somewhat dramatic and implicitly assumed that the convertible bond is default free. In this case, the straight bond value does not depend on the stock price, so it is graphed as a straight line.

ConversionV alue The value of convertible bonds depends on conversion value. Conversion value is what the bonds would be worth if they were immediately converted into common stock at current prices. Typically, we compute conversion value by multiplying the number of

Chapter 24

Figure 24.2

Warrants and Convertibles

751

Minimum convertible bond value (floor value)

Minimum Value of a Convertible Bond versus the Value of the Stock for a Given Interest Rate

Conversion value Convertible bond floor value

Straight bond value

= Conversion ratio Straight bond value greater than conversion value

Straight bond value less than conversion value

Stock price

As shown, the minimum, or floor, value of a convertible bond is either its straight bond value or its conversion value, whichever is greater.

shares of common stock that will be received when the bond is converted by the current price of the common stock. On November 1, 2009, each Oceandoor convertible bond could have been converted into 23.53 shares of Oceandoor common stock. Oceandoor common stock was selling for $22.625. Thus, the conversion value was 23.53 × $22.625 = $532.37. A convertible cannot sell for less than its conversion value. Arbitrage prevents this from happening. If Oceandoor’s convertible sold for less than $532.37, investors would have bought the bonds and converted them into common stock and sold the stock. The profit would have been the difference between the value of the stock sold and the bond’s conversion value. Thus, convertible bonds have two minimum values: the straight bond value and the conversion value. The conversion value is determined by the value of the firm’s underlying common stock. This is illustrated in Figure 24.2. As the value of common stock rises and falls, the conversion value rises and falls with it. When the price of Oceandoor’s common stock increased by $1, the conversion value of its convertible bonds increased by $23.53.

OptionV alue The value of a convertible bond will generally exceed both the straight bond value and the conversion value.5 This occurs because holders of convertibles need not convert immediately. Instead, by waiting they can take advantage of whichever is greater in the future: the straight bond value or the conversion value. This option to wait has value, and it raises the value over both the straight bond value and the conversion value. When the value of the firm is low, the value of convertible bonds is most significantly influenced by their underlying value as straight debt. However, when the value of the firm is very high, the value of convertible bonds is mostly determined by their underlying conversion value. This is illustrated in Figure 24.3. 5

The most plausible exception is when conversion would provide the investor with a dividend much greater than the interest available prior to conversion. The optimal strategy here could very well be to convert immediately, implying that the market value of the bond would exactly equal the conversion value. Other exceptions occur when the firm is in default or the bondholders are forced to convert.

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Figure 24.3 Convertible bond value

Value of a Convertible Bond versus the Value of the Stock for a Given Interest Rate

Conversion value

Convertible bond values Option value

Floor value Straight bond value

Floor value

= Conversion ratio

Straight bond value greater than conversion value

Straight bond value less than conversion value

Stock price

As shown, the value of a convertible bond is the sum of its floor value and its option value.

The bottom portion of the figure implies that the value of a convertible bond is the maximum of its straight bond value and its conversion value plus its option value: Value of convertible = The greater of (Straight bond value, Conversion value) bond + Option value

EXAMPLE24.3

Conversion Suppose the Moulton Company has outstanding 1,000 shares of common stock and C 1100 bonds. Each bond has a face value of $1,000 at maturity. They are discount bonds and pay no coupons. At maturity each bond can be converted into 10 shares of newly issued common stock. What circumstances will make it advantageous for the holders of Moulton convertible bonds to convert to common stock at maturity? If the holders of the convertible bonds convert, they will receive 100 × 10 = 1,000 shares of common stock. Because there were already 1,000 shares, the total number of shares outstanding becomes 2,000 upon conversion. Thus, converting bondholders own 50 percent of the value of the firm, V. If they do not convert, they will receive $100,000 or V, whichever is less. The choice for the holders of the Moulton bonds is obvious. They should convert if 50 percent of V is greater than $100,000. This will be true whenever V is greater than $200,000. This is illustrated as follows: Payoff to Convertible Bondholders and Stockholders of the Moulton Company

Decision: Convertible bondholders Stockholders

(I) V ≤100,000

(2) $100,000 < V ≤ $200,000

(3) V > $200,000

Bondholders will not convert

Bondholders will not convert

Bondholders will convert

V 0

$100,000

.5V .5V

V − $100,000

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24.6 Reasons for Issuing Warrants and Convertibles Probably there is no other area of corporate finance where real-world practitioners get as confused as they do on the reasons for issuing convertible debt. To separate fact from fantasy, we present a rather structured argument. We first compare convertible debt to straight debt. Then we compare convertible debt to equity. For each comparison, we ask in what situations is the firm better off with convertible debt and in what situations is it worse off ?

Convertible Debt versus Straight Debt Convertible debt pays a lower interest rate than does otherwise identical straight debt. For example, if the interest rate is 10 percent on straight debt, the interest rate on convertible debt might be 9 percent. Investors will accept a lower interest rate on a convertible because of the potential gain from conversion. Imagine a firm that seriously considers both convertible debt and straight debt, finally deciding to issue convertibles. When would this decision have benefited the firm and when would it have hurt the firm? We consider two situations. The Stock Price Later Rises So That Conversion Is Indicated The firm clearly likes to see the stock price rise. However, it would have benefited even more had it previously issued straight debt instead of a convertible. Although the firm paid out a lower interest rate than it would have with straight debt, it was obligated to sell the convertible holders a chunk of the equity at a below-market price. The Stock Price Later Falls or Does Not Rise Enough to Justify Conversion The firm hates to see the stock price fall. However, as long as the stock price does fall, the firm is glad that it had previously issued convertible debt instead of straight debt. This is because the interest rate on convertible debt is lower. Because conversion does not take place, our comparison of interest rates is all that is needed. Summary Compared to straight debt, the firm is worse off having issued convertible debt if the underlying stock subsequently does well. The firm is better off having issued convertible debt if the underlying stock subsequently does poorly. In an efficient market, we cannot predict future stock price. Thus, we cannot argue that convertibles either dominate or are dominated by straight debt.

Convertible Debt versus Common Stock Next, imagine a firm that seriously considers both convertible debt and common stock but finally decides to issue convertibles. When would this decision benefit the firm and when would it hurt the firm? We consider our two situations. The Stock Price Later Rises So That Conversion Is Indicated The firm is better off having previously issued a convertible instead of equity. To see this, consider the Oceandoor case. The firm could have issued stock for $22. Instead, by issuing a convertible, the firm effectively received $42.50 for a share upon conversion. The Stock Price Later Falls or Does Not Rise Enough to Justify Conversion No firm wants to see its stock price fall. However, given that the price did fall, the firm would have been better off if it had previously issued stock instead of a convertible.

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Table 24.2 The Case for and against Convertible Bonds (CBs)

Convertible bonds (CBs) Compared to: Straight bonds

Common stock

If Firm Subsequently Does Poorly

If Firm Subsequently Prospers

No conversion because of low stock price.

Conversion because of high stock price.

CBs provide cheap financing because coupon rate is lower.

CBs provide expensive financing because bonds are converted, which dilutes existing equity. CBs provide cheap financing because firm issues stock at high prices when bonds are converted.

CBs provide expensive financing because firm could have issued common stock at high prices.

The firm would have benefited by issuing stock above its later market price. price That is, is the firm would have received more than the subsequent worth of the stock. However, the drop in stock price did not affect the value of the convertible much because the straight bond value serves as a floor. Summary Compared with equity, the firm is better off having issued convertible debt if the underlying stock subsequently does well. The firm is worse off having issued convertible debt if the underlying stock subsequently does poorly. We cannot predict future stock price in an efficient market. Thus, we cannot argue that issuing convertibles is better or worse than issuing equity. The preceding analysis is summarized in Table 24.2. Modigliani–Miller (MM) pointed out that, abstracting from taxes and bankruptcy costs, the firm is indifferent to whether it issues stock or issues debt. The MM relationship is a quite general one. Their pedagogy could be adjusted to show that the firm is indifferent to whether it issues convertibles or issues other instruments. To save space (and the patience of students) we have omitted a full-blown proof of MM in a world with convertibles. However, our results are perfectly consistent with MM. Now we turn to the real-world view of convertibles.

The “Free Lunch” Story The preceding discussion suggests that issuing a convertible bond is no better and no worse than issuing other instruments. Unfortunately, many corporate executives fall into the trap of arguing that issuing convertible debt is actually better than issuing alternative instruments. This is a free lunch type of explanation, of which we are quite critical.

EXAMPLE24.4

Are Convertibles Always Better? The stock price of RW Company is $20. Suppose this company can issue subordinated debentures at 10 percent. It can also issue convertible bonds at 6 percent with a conversion value of $800. The conversion value means that the holders can convert a convertible bond into 40 (=$800 $20) shares of common stock. A company treasurer who believes in free lunches might argue that convertible bonds should be issued because they represent a cheaper source of financing than both, subordinated bonds and common stock. The treasurer will point out that if the company does poorly and the price does not rise above $20, the convertible bondholders will not convert the bonds into common stock. In this case the company will have obtained debt financing at below-market rates by attaching worthless equity kickers. On the other hand, if the firm does well and the price of its common stock rises

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to $25 or above, convertible holders will convert. The company will issue 40 shares. The company will receive a bond with a face value of $1,000 in exchange for issuing 40 shares of common stock, implying a conversion price of $25. The company will have issued common stock at $25 per share, or 20 percent above the $20 common stock price prevailing when the convertible bonds were issued. This enables it to lower its cost of equity capital. Thus, the treasurer happily points out, regardless of whether the company does well or poorly, convertible bonds are the cheapest form of financing. Although this argument may sound quite plausible at first, there is a flaw. The treasurer is comparing convertible financing with straight debt when the stock subsequently falls. However, the treasurer compares convertible financing with common stock when the stock subsequently rises. This is an unfair mixing of comparisons. By contrast, our analysis in Table 24.2 was fair because we examined both stock increases and decreases when comparing a convertible with each alternative instrument. We found that no single alternative dominated convertible bonds in both up and down markets.

The “Expensive Lunch” Story Suppose we stand the treasurer’s argument on its head by comparing (1) convertible financing with straight debt when the stock rises and (2) convertible financing with equity when the stock falls. From Table 24.2, we see that convertible debt is more expensive than straight debt when the stock subsequently rises. The firm’s obligation to sell convertible holders a chunk of equity at a below-market price more than offsets the lower interest rate on a convertible. Also from Table 24.2, we see that convertible debt is more expensive than equity when the stock subsequently falls. Had the firm issued stock, it would have received a price higher than its subsequent worth. Therefore, the expensive lunch story implies that convertible debt is an inferior form of financing. Of course, we dismiss both the free lunch and the expensive lunch arguments.

AR econciliation In an efficient financial market there is neither a free lunch nor an expensive lunch. Convertible bonds can be neither cheaper nor more expensive than other instruments. A convertible bond is a package of straight debt and an option to buy common stock. The difference between the market value of a convertible bond and the value of a straight bond is the price investors pay for the call option feature. In an efficient market, this is a fair price. In general, if a company prospers, issuing convertible bonds will turn out to be worse than issuing straight bonds and better than issuing common stock. In contrast, if a company does poorly, convertible bonds will turn out to be better than issuing straight bonds and worse than issuing common stock.

24.7 Why Are Warrants and Convertibles Issued? From studies it is known that firms that issue convertible bonds are different from other firms. Here are some of the differences: 1. The bond ratings of firms using convertibles are lower than those of other firms.6 2. Convertibles tend to be used by smaller firms with high growth rates and more financialle verage.7 3. Convertiblesar eu suallysu bordinatedan du nsecured. 6 7

E. F. Brigham, “An Analysis of Convertible Debentures,” Journal of Finance 21 (1966).

W. H. Mikkelson, “Convertible Calls and Security Returns,” Journal of Financial Economics 9 (September 1981), p. 3.

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The kind of company that uses convertibles provides clues to why they are issued. Here are some explanations that make sense.

MatchingCa shF lows If financing is costly, it makes sense to issue securities whose cash flows match those of the firm. A young, risky, and (it hopes) growing firm might prefer to issue convertibles or bonds with warrants because these will have lower initial interest costs. When the firm is successful, the convertibles (or warrants) will be converted. This causes expensive dilution, but it occurs when the firm can most afford it.

RiskSyne rgy Another argument for convertible bonds and bonds with warrants is that they are useful when it is very costly to assess the risk of the issuing company. Suppose you are evaluating a new product by a start-up company. The new product is a genetically engineered virus that may increase the yields of corn crops in northern climates. It may also cause cancer. This type of product is difficult to value properly. Thus, the risk of the company is very hard to determine: It may be high, or it may be low. If you could be sure the risk of the company was high, you would price the bonds for a high yield, say 15 percent. If it was low, you would price them at a lower yield, say 10 percent. Convertible bonds and bonds with warrants can protect somewhat against mistakes of risk evaluation. Convertible bonds and bonds with warrants have two components: Straight bonds and call options on the company’s underlying stock. If the company turns out to be a low-risk company, the straight bond component will have high value and the call option will have low value. However, if the company turns out to be a high-risk company, the straight bond component will have low value and the call option will have high value. This is illustrated in Table 24.3. However, although risk has effects on value that cancel each other out in convertibles and bonds with warrants, the market and the buyer nevertheless must make an assessment of the firm’s potential to value securities, and it is not clear that the effort involved is that much less than is required for a straight bond.

AgencyCo sts Convertible bonds can resolve agency problems associated with raising money. In a previous chapter, we showed that straight bonds are like risk-free bonds minus a put option on the assets of the firm. This creates an incentive for creditors to force the firm into low-risk activities. In contrast, holders of common stock have incentives to adopt high-risk projects. High-risk projects with negative NPV transfer wealth from bondholders to stockholders. If these conflicts cannot be resolved, the firm may be forced to pass up profitable investment opportunities. However, because convertible bonds have an equity component, less expropriation of wealth can occur when convertible debt

Table 24.3

Firm Risk

A Hypothetical Case of the Yields on Convertible Bonds*

Straight bond yield Convertible bond yield

Low

High

10% 6

15% 7

*The yields on straight bonds reflect the risk of default. The yields on convertibles are not sensitive to default risk.

Chapter 24 Warrants and Convertibles

757

is issued instead of straight debt.8 In other words, convertible bonds mitigate agency costs. One implication is that convertible bonds have less restrictive debt covenants than do straight bonds in the real world. Casual empirical evidence seems to bear this out.

BackdoorE quity A popular theory of convertibles views them as backdoor equity.9 The basic story is that young, small, high-growth firms cannot usually issue debt on reasonable terms due to high financial distress costs. However, the owners may be unwilling to issue equity if current stock prices are too low. Lewis, Ragolski, and Seward examine the risk shifting and backdoor equity theories of convertible bond debt. They find evidence for both theories.

24.8 Conversion Policy There is one aspect of convertible bonds that we have omitted so far. Firms are frequently granted a call option on the bond. The typical arrangements for calling a convertible bond are simple. When the bond is called, the holder has about 30 days to choose between the following: 1. Converting the bond to common stock at the conversion ratio. 2. Surrendering the bond and receiving the call price in cash. What should bondholders do? It should be obvious that if the conversion value of the bond is greater than the call price, conversion is better than surrender; and if the conversion value is less than the call price, surrender is better than conversion. If the conversion value is greater than the call price, the call is said to force conversion. What should financial managers do? Calling the bonds does not change the value of the firm as a whole. However, an optimal call policy can benefit the stockholders at the expense of the bondholders. Because we are speaking about dividing a pie of fixed size, the optimal call policy is simple: Do whatever the bondholders do not want you to do. Bondholders would love the stockholders to call the bonds when the bonds’ market value is below the call price. Shareholders would be giving bondholders extra value. Alternatively, should the value of the bonds rise above the call price, the bondholders would love the stockholders not to call the bonds because bondholders would be allowed to hold onto a valuable asset. There is only one policy left. This is the policy that maximizes shareholder value and minimizes bondholder value: Call the bond when its value is equal to the call price.

It is puzzling that firms do not always call convertible bonds when the conversion value reaches the call price. Ingersoll examined the call policies of 124 firms between 1968 and 1975.10 In most cases he found that the company waited to call the bonds 8

A. Barnea, R. A. Haugen, and L. Senbet, Agency Problems and Financial Contracting, Prentice Hall Foundations of Science Series (New York: Prentice Hall, 1985), Chapter VI.

9

J. Stein, “Convertible Bonds as Backdoor Equity Financing,” Journal of Financial Economics 32 (1992). See also Craig M. Lewis, Richard J. Ragolski, and James K. Seward, “Understanding the Design of ConvertibleDe bt,” The Journal of Applied Corporate Finance (Spring 1998). 10 J. Ingersoll, “An Examination of Corporate Call Policies on Convertible Bonds,” Journal of Finance (May 1977). See also M. Harris and A. Raviv, “A Sequential Signalling Model of Convertible Debt Policy,” Journal of Finance (December 1985). Harris and Raviv describe a signal equilibrium that is consistent with Ingersoll’s result. They show that managers with favorable information will delay calls to avoid depressing stock prices.

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until the conversion value was much higher than the call price. The median company waited until the conversion value of its bonds was 44 percent higher than the call price. This is not even close to our optimal strategy. Why? One reason is that if firms attempt to implement the optimal strategy, it may not be truly optimal. Recall that bondholders have 30 days to decide whether to convert bonds to common stock or to surrender bonds for the call price in cash. In 30 days the stock price could drop, forcing the conversion value below the call price. If so, the convertible is “out of the money” and the firm is giving away money. The firm would be giving up cash for common stock worth much less. Because of this possibility, firms in the real world usually wait until the conversion value is substantially above the call price before they trigger the call.11T hisisse nsible. 11 See Paul Asquith, “Convertible Bonds Are Not Called Late,” Journal of Finance (September 1995). On the other hand, the stock market usually reacts negatively to the announcement of a call. For example, see A. K. Singh, A. R. Cowan, and N. Nayar, “Underwritten Calls of Convertible Bonds,” Journal of Financial Economics (March 1991); and M. A. Mazzeo and W. T. Moore, “Liquidity Costs and Stock Price Response to Convertible Security Calls,” Journal of Business (July 1992). Ederington, Caton, and Campbell tested various theories about when it is optimal to call convertibles. They found evidence consistent with the preceding 30-day “safety margin” theory. They also found that calls of in-the-money convertibles are highly unlikely if dividends to be received (after conversion) exceed the company’s interest payment. See Louis H. Ederington, Gary L. Caton, and Cynthia J. Campbell, “To Call or Not to Call Convertible Debt,” Financial Management (Spring 1997).

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Summary and Conclusions

1. A warrant gives the holder the right to buy shares of common stock at an exercise price for a given period. Typically, warrants are issued in a package with privately placed bonds. Afterwards, they become detached and trade separately. 2. A convertible bond is a combination of a straight bond and a call option. The holder can give up the bond in exchange for shares of stock. 3. Convertible bonds and warrants are like call options. However, there are some important differences: a. Warrants and convertible securities are issued by corporations. Call options are traded between individual investors. i. Warrants are usually issued privately and are combined with a bond. In most cases, the warrants can be detached immediately after the issue. In some cases, warrants are issued with preferred stock, with common stock, or in executive compensationp rograms. ii. Convertibles are usually bonds that can be converted into common stock. iii. Call options are sold separately by individual investors (called writers of call options). b. Warrants and call options are exercised for cash. The holder of a warrant gives the company cash and receives new shares of the company’s stock. The holder of a call option gives another individual cash in exchange for shares of stock. When someone converts a bond, it is exchanged for common stock. As a consequence, bonds with warrants and convertible bonds have different effects on corporate cash flow and capitals tructure. c. Warrants and convertibles cause dilution to the existing shareholders. When warrants are exercised and convertible bonds converted, the company must issue new shares of common stock. The percentage ownership of the existing shareholders will decline. New shares are not issued when call options are exercised. 4. Many arguments, both plausible and implausible, are given for issuing convertible bonds and bonds with warrants. One plausible rationale for such bonds has to do with risk.

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Convertibles and bonds with warrants are associated with risky companies. Lenders can do several things to protect themselves from high-risk companies: a. They can require high yields. b. They can lend less or not at all to firms whose risk is difficult to assess. c. They can impose severe restrictions on such debt. Another useful way to protect against risk is to issue bonds with equity kickers. This gives the lenders the chance to benefit from risks and reduces the conflicts between bondholders and stockholders concerning risk. 5. A certain puzzle particularly vexes financial researchers: Convertible bonds usually have call provisions. Companies appear to delay calling convertibles until the conversion value greatly exceeds the call price. From the shareholders’ standpoint, the optimal call policy would be to call the convertibles when the conversion value equals the call price.

Concept Questions

1. 2.

4. 5. 6.

7. 8. 9. 10.

Questions and Problems

1. 2. 3.

BASIC (Questions 1–9)

Conversion Price A convertible bond has a conversion ratio of 18.4. What is the conversionp rice? Conversion Ratio A convertible bond has a conversion price of $70.26. What is the conversion ratio of the bond? Conversion Premium Eckely, Inc., recently issued bonds with a conversion ratio of 12.8. If the stock price at the bond issue date was $61.18, what was the conversion premium?

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3.

Warrants and Options What is the primary difference between a warrant and a traded call option? Warrants Explain the following limits on the prices of warrants: a. If the stock price is below the exercise price of the warrant, the lower bound on the price of a warrant is zero. b. If the stock price is above the exercise price of the warrant, the lower bound on the price of a warrant is the difference between the stock price and the exercise price. c. An upper bound on the price of any warrant is the current value of the firm’s stock. Convertible Bonds and Stock Volatility Suppose you are evaluating a callable, convertible bond. If the stock price volatility increases, how will this affect the price of theb ond? Convertible Bond Value What happens to the price of a convertible bond if interest ratesin crease? Dilution What is dilution, and why does it occur when warrants are exercised? Warrants and Convertibles What is wrong with the simple view that it is cheaper to issue a bond with a warrant or a convertible feature because the required coupon is lower? Warrants and Convertibles Why do firms issue convertible bonds and bonds with warrants? Convertible Bonds Why will convertible bonds not be voluntarily converted to stock beforee xpiration? ConvertibleB onds When should a firm force conversion of convertibles? Why? Warrant Valuation A warrant with six months until expiration entitles its owner to buy 10 shares of the issuing firm’s common stock for an exercise price of $31 per share. If the current market price of the stock is $15 per share, will the warrant be worthless?

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5.

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Options, Futures, and Corporate Finance

Convertible Bonds Hannon Home Products, Inc., recently issued $2 million worth of 8 percent convertible debentures. Each convertible bond has a face value of $1,000. Each convertible bond can be converted into 18.5 shares of common stock anytime before maturity. The stock price is $38.20, and the market value of each bond is $1,070. a. What is the conversion ratio? b. What is the conversion price? c. What is the conversion premium? d. What is the conversion value? e. If the stock price increases by $2, what is the new conversion value? Warrant Value A warrant gives its owner the right to purchase three shares of common stock at an exercise price of $41 per share. The current market price of the stock is $47. What is the minimum value of the warrant? Convertible Bond Value An analyst has recently informed you that at the issuance of a company’s convertible bonds, one of the two following sets of relationships existed:

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Face value of bond Straight value of convertible bond Market value of convertible bond

7.

8.

9.

INTERMEDIATE (Questions 10–13)

10.

Scenario A

Scenario B

$1,000 900 1,000

$1,000 950 900

Assume the bonds are available for immediate conversion. Which of the two scenarios do you believe is more likely? Why? Convertible Bond Value Sportime Fitness Center, Inc., issued convertible bonds with a conversion price of $34. The bonds are available for immediate conversion. The current price of the company’s common stock is $29 per share. The current market price of the convertible bonds is $990. The convertible bonds’ straight value is not known. a. What is the minimum price for the convertible bonds? b. Explain the difference between the current market price of each convertible bond and the value of the common stock into which it can be immediately converted. Convertible Bonds You own a callable, convertible bond with a conversion ratio of 21.5. The stock is currently selling for $52 per share. The issuer of the bond has announced a call at a call price of $110. What are your options here? What should you do? Warrant Value General Modems has five-year warrants that currently trade in the open market. Each warrant gives its owner the right to purchase one share of common stock for an exercise price of $55. a. Suppose the stock is currently trading for $51 per share. What is the lower limit on the price of the warrant? What is the upper limit? b. Suppose the stock is currently trading for $58 per share. What is the lower limit on the price of the warrant? What is the upper limit? Convertible Bonds Bernanke Corp. has just issued a 30-year callable, convertible bond with a coupon rate of 6 percent annual coupon payments. The bond has a conversion price of $130. The company’s stock is selling for $26 per share. The owner of the bond will be forced to convert if the bond’s conversion value is ever greater than or equal to $1,100. The required return on an otherwise identical nonconvertible bond is 11 percent. a. What is the minimum value of the bond? b. If the stock price were to grow by 13 percent per year forever, how long would it take for the bond’s conversion value to exceed $1,100?

Chapter 24 Warrants and Convertibles

11.

12.

CHALLENGE (Questions 14–16)

14.

15.

16.

Convertible Bonds Rob Stevens is the chief executive officer of Isner Construction, Inc., and owns 750,000 shares of stock. The company currently has 5 million shares of stock and convertible bonds with a face value of $30 million outstanding. The convertible bonds have a conversion price of $34, and the stock is currently selling for $40. a. What percentage of the firm’s common stock does Mr. Stevens own? b. If the company decides to call the convertible bonds and force conversion, what percentage of the firm’s common stock will Mr. Stevens own? He does not own any convertibleb onds. Warrants Survivor, Inc., an all-equity firm, has eight shares of stock outstanding. Yesterday, the firm’s assets consisted of nine ounces of platinum, currently worth $850 per ounce. Today, the company issued Ms. Wu a warrant for its fair value of $850. The warrant gives Ms. Wu the right to buy a single share of the firm’s stock for $1,000 and can be exercised only on its expiration date one year from today. The firm used the proceeds from the issuance to immediately purchase an additional ounce of platinum. a. What was the price of a single share of stock before the warrant was issued? b. What was the price of a single share of stock immediately after the warrant was issued? c. Suppose platinum is selling for $975 per ounce on the warrant’s expiration date in one year. What will be the value of a single share of stock on the warrant’s expirationd ate? Warrants The capital structure of Ricketti Enterprises, Inc., consists of 15 million shares of common stock and 1 million warrants. Each warrant gives its owner the right to purchase one share of common stock for an exercise price of $19. The current stock price is $25, and each warrant is worth $7. What is the new stock price if all warrant holders decide to exercise today? Convertible Calculations You have been hired to value a new 25-year callable, convertible bond. The bond has a 6.80 percent coupon rate, payable annually. The conversion price is $150, and the stock currently sells for $35.50. The stock price is expected to grow at 12 percent per year. The bond is callable at $1,150; but based on prior experience, it won’t be called unless the conversion value is $1,250. The required return on this bond is 9 percent. What value would you assign to this bond? Warrant Value Superior Clamps, Inc., has a capital structure consisting of 6 million shares of common stock and 750,000 warrants. Each warrant gives its owner the right to purchase one share of newly issued common stock for an exercise price of $20. The warrants are European and will expire one year from today. The market value of the company’s assets is $105 million, and the annual variance of the returns on the firm’s assets is .15. Treasury bills that mature in one year yield a continuously compounded interest rate of 7 percent. The company does not pay a dividend. Use the Black–Scholes model to determine the value of a single warrant. Warrant Value Omega Airline’s capital structure consists of 3.2 million shares of common stock and zero coupon bonds with a face value of $18 million that mature in six months. The firm just announced that it will issue warrants with an exercise price of $75 and six months until expiration to raise the funds to pay off its maturing debt. Each warrant can be exercised only at expiration and gives its owner the right to buy a single newly issued share of common stock. The firm will place the proceeds from the warrant issue immediately into Treasury bills. The market value balance sheet shows that the firm will have assets worth $210 million after the announcement. The company does not pay dividends. The standard deviation of the returns on the firm’s assets is 50 percent, and Treasury bills with a six-month maturity yield 6 percent. How many warrants must the company issue today to be able to use the proceeds from the sale to pay off the firm’s debt obligation in six months?

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Mini Case

S&S AIR’S CONVERTIBLE BOND Chris Guthrie was recently hired by S&S Air, Inc., to assist the company with its shortterm financial planning and to evaluate the company’s performance. Chris graduated from college five years ago with a finance degree. He has been employed in the finance department of a Fortune 500 company since then. S&S Air was founded 10 years ago by two friends, Mark Sexton and Todd Story. The company has manufactured and sold light airplanes over this period, and the company’s products have received high reviews for safety and reliability. The company has a niche market in that it sells primarily to individuals who own and fly their own airplanes. The company has two models: The Birdie, which sells for $53,000, and the Eagle, which sells for $78,000. S&S Air is not publicly traded, but the company needs new funds for investment opportunities. In consultation with Tonisha Jones of underwriter Raines and Warren, Chris decided that a convertible bond issue with a 20-year maturity is the way to go. He met with the owners, Mark and Todd, and presented his analysis of the convertible bond issue. Because the company is not publicly traded, Chris looked at comparable publicly traded companies and determined that the average PE ratio for the industry is 12.5. Earnings per share for the company are $1.60. With this in mind, Chris concluded that the conversion price should be $25 per share. Several days later, Todd, Mark, and Chris met again to discuss the potential bond issue. Both Todd and Mark have researched convertible bonds and have questions for Chris. Todd begins by asking Chris if the convertible bond issue will have a lower coupon rate than a comparable bond without a conversion feature. Chris replies that to sell the bond at par value, the convertible bond issue would require a 6 percent coupon rate with a conversion value of $800, while a plain vanilla bond would have a 7 percent coupon rate. Todd nods in agreement, and he explains that the convertible bonds are a win–win form of financing. He states that if the value of the company stock does not rise above the conversion price, the company has issued debt at a cost below the market rate (6 percent instead of 7 percent). If the company’s stock does rise to the conversion value, the company has effectively issued stock at above the current value. Mark immediately disagrees, arguing that convertible bonds are a no-win form of financing. He argues that if the value of the company stock rises to $25, the company is forced to sell stock at the conversion price. This means the new shareholders (those who bought the convertible bonds) benefit from a bargain price. Put another way, if the company prospers, it would have been better to have issued straight debt so that the gains would not be shared. Chris has gone back to Tonisha for help. As Tonisha’s assistant, you’ve been asked to prepare another memo answering the following questions: 1. Why do you think Chris is suggesting a conversion price of $25? Given that the company is not publicly traded, does it even make sense to talk about a conversion price? 2. What is the floor value of the S&S Air convertible bond? 3. What is the conversion ratio of the bond? 4. What is the conversion premium of the bond? 5. What is the value of the option? 6. Is there anything wrong with Todd’s argument that it is cheaper to issue a bond with a convertible feature because the required coupon is lower? 7. Is there anything wrong with Mark’s argument that a convertible bond is a bad idea because it allows new shareholders to participate in gains made by the company? 8. How can you reconcile the arguments made by Todd and Mark? 9. During the debate, a question comes up concerning whether the bonds should have an ordinary (not make-whole) call feature. Chris confuses everybody by stating, “The call feature lets S&S Air force conversion, thereby minimizing the problem Mark has identified.’’W hatis h et alkinga bout?I sh emak ings ense? 762

PART III

CHAPTER 25

Derivatives and Hedging Risk The price of jet fuel can greatly affect the profitability of an airline. With rising fuel costs during 2008, fuel became the largest expense for many airlines, accounting for 40 percent or so of operating costs. Southwest Airlines became an innovator when it began to hedge its fuel costs by using a variety of sophisticated financial tools to deal with risks associated with volatile fuel costs, including heating oil futures contracts, jet fuel swaps, and call options. During periods of rising fuel costs, Southwest was often one of the few profitable airlines, saving millions of dollars through hedging. During late 2008, the cost of jet fuel dropped dramatically, and Southwest’s hedges did not perform nearly as well. Until 2008, the company had never announced a quarterly loss in 16 years, but, in the fourth quarter it announced a loss of $56 million, in large part due to a hedging loss of $117 million. But Southwest may have gotten off easy. For the same period, UAL Corp., the parent of United Airlines, lost $933 million and Cathay Pacific lost $1 billion on its hedges. In this chapter, we explore a variety of derivative contracts that allow a company’s management to control risk, and we also explain how hedging can be a doubleedged sword, as these airlines learned the hard way.

25.1 Derivatives, Hedging, and Risk The name derivatives is self-explanatory. A derivative is a financial instrument whose payoffs and values are derived from, or depend on, something else. Often, we speak of the thing that the derivative depends on as the primitive or the underlying. For example, in Chapter 22 we studied how options work. An option is a derivative. The value of a call option depends on the value of the underlying stock on which it is written. Actually, call options are quite complicated examples of derivatives. The vast majority of derivatives are simpler than call options. Most derivatives are forward or futures agreements or what are called swaps, and we will study each of these in some detail. Why do firms use derivatives? The answer is that derivatives are tools for changing the firm’s risk exposure. Someone once said that derivatives are to finance what scalpels are to surgery. By using derivatives, the firm can cut away unwanted portions of risk exposure and even transform the exposures into quite different forms. A central point in finance is that risk is undesirable. In our chapters about risk and return, we pointed out that individuals would choose risky securities only if the expected return compensated for the risk. Similarly, a firm will accept a project with high risk only if the return on the project compensates for this risk. Not surprisingly, then, firms are usually looking for ways to reduce their risk. When the firm reduces its risk exposure with the use of derivatives, it is said to be hedging. Hedging offsets the firm’s risk, such as the risk in a project, by one or more transactions in the financial markets. Derivatives can also be used to merely change or even increase the firm’s risk exposure. When this occurs, the firm is speculating on the movement of some economic 763

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variables—those that underlie the derivative. For example, if a derivative is purchased that will rise in value if interest rates rise, and if the firm has no offsetting exposure to interest rate changes, then the firm is speculating that interest rates will rise and give it a profit on its derivatives position. Using derivatives to translate an opinion about whether interest rates or some other economic variable will rise or fall is the opposite of hedging—it is risk enhancing. Speculating on your views on the economy and using derivatives to profit if that view turns out to be correct is not necessarily wrong, but the speculator should always remember that sharp tools cut deep: If the opinions on which the derivatives position is based turn out to be incorrect, then the consequences can prove costly. Efficient market theory teaches how difficult it is to predict what markets will do. Most of the sad experiences with derivatives have occurred not from their use as instruments for hedging and offsetting risk, but rather from speculation.

25.2 Forward Contracts We can begin our discussion of hedging by considering forward contracts. You have probably been dealing in forward contracts your whole life without knowing it. Suppose you walk into a bookstore on, say, February 1, to buy the best seller Eating Habits of the Rich and Famous. The cashier tells you that the book is currently sold out, but he takes your phone number, saying that he will reorder it for you. He says the book will cost $10.00. If you agree on February 1 to pick up and pay $10.00 for the book when called, you and the cashier have engaged in a forward contract. That is, you have agreed both to pay for the book and to pick it up when the bookstore notifies you. Because you are agreeing to buy the book at a later date, you are buying a forward contract on February 1. In commodity parlance, you will be taking delivery when you pick up the book. The book is called the deliverableins trument. The cashier, acting on behalf of the bookstore, is selling a forward contract. (Alternatively, we say that he is writing a forward contract.) The bookstore has agreed to turn the book over to you at the predetermined price of $10.00 as soon as the book arrives. The act of turning the book over to you is called making delivery. Table 25.1 illustrates the book purchase. Note that the agreement takes place on February 1. The price is set and the conditions for sale are set at that time. In this case, the sale will occur when the book arrives. In other cases, an exact date of sale would be given. However, no cash changes hands on February 1; cash changes hands only when the book arrives.

Table 25.1 Illustration of Book Purchase as a Forward Contract

February 1

Date When Book Arrives

Buyer Buyer agrees to: 1. Pay the purchase price of $10.00. 2. Receive book when book arrives.

Buyer: 1. Pays purchase price of $10.00. 2. Receives book.

Seller Seller agrees to: 1. Give up book when book arrives. 2. Accept payment of $10.00 when book arrives.

Seller: 1. Gives up book. 2. Accepts payment of $10.00.

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Though forward contracts may have seemed exotic to you before you began this chapter, you can see that they are quite commonplace. Dealings in your personal life probably have involved forward contracts. Similarly, forward contracts occur all the time in business. Every time a firm orders an item that cannot be delivered immediately, a forward contract takes place. Sometimes, particularly when the order is small, an oral agreement will suffice. Other times, particularly when the order is larger, a written agreement is necessary. Note that a forward contract is not an option. Both the buyer and the seller are obligated to perform under the terms of the contract. Conversely, the buyer of an option chooses whether to exercise the option. A forward contract should be contrasted with a cash transaction—that is, a transaction where exchange is immediate. Had the book been on the bookstore’s shelf, your purchase of it would constitute a cash transaction.

25.3 Futures Contracts A variant of the forward contract takes place on financial exchanges. Contracts on exchanges are usually called futures contracts. There are a number of futures exchanges in the United States and elsewhere, and more are being established. The CME Group is among the largest, combining the old Chicago Mercantile Exchange (CME) and the Chicago Board of Trade (CBT). However, the two are still seperate trading platforms. Other notable exchanges include the London International Financial Futures and Options Exchange (LIFFE) and the New York Mercantile Exchange (NYM). Table 25.2 gives a partial Wall Street Journal listing for selected futures contracts. Taking a look at the corn contracts in the left portion of the table, note that the contracts trade on the CBT, one contract calls for the delivery of 5,000 bushels of corn, and prices are quoted in cents per bushel. The months in which the contracts mature are given in the first column. For the corn contract with a March maturity, the first number in the row is the opening price (368.75 cents per bushel), the next number is the high price for the day (377.75), and the following number is the low price for the day (366.00). The settlement price is the fourth number (366.25), and it essentially is the closing price for the day. For purposes of marking to market, this is the figure used. The change, listed next, is the movement in the settlement price since the previous trading session (−2.25 cents). Finally, the open interest (214,858), the number of contracts outstanding at the end of the day, is shown. To see how large futures trading can be, look at the CBT Treasury bond contracts (under the interest rate heading). One contract is for long-term Treasury bonds with a face, or par, value of $100,000. The total open interest for all months is about 717,000 contracts. The total face value outstanding is therefore $71.7 billion for this one type of contract! Though we are discussing a futures contract, let us work with a forward contract first. Suppose you wrote a forward contract for September wheat at $4.07. From our discussion of forward contracts, this would mean that you would agree to turn over an agreed-upon number of wheat bushels for $4.07 per bushel on some specified date later in the month of September. A futures contract differs somewhat from a forward contract. First, the seller can choose to deliver the wheat on any day during the delivery month—that is, the month of September. This gives the seller leeway that he would not have with a forward contract. When the seller decides to deliver, he notifies the exchange clearinghouse that he wants to do so. The clearinghouse then notifies an individual who bought a September

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Table 25.2 Data on Futures Contracts, Thursday, February 12, 2009 Published Friday, February 12, 2009, The Wall Street Journal.

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wheat contract to stand ready to accept delivery within the next few days. Though each exchange selects the buyer in a different way, the buyer is generally chosen in a random fashion. Because there are so many buyers at any one time, the buyer selected by the clearinghouse to take delivery almost certainly did not originally buy the contract from the seller now making delivery. Second, futures contracts are traded on an exchange, whereas forward contracts are generally traded off an exchange. Because of this, there is generally a liquid market in futures contracts. A buyer can net out her futures position with a sale. A seller can net out his futures position with a purchase. If a buyer of a futures contract does not subsequently sell her contract, she must take delivery. Third, and most important, the prices of futures contracts are marked to the market daily. That is, suppose the price falls to $4.05 on Friday’s close. Because all buyers lost two cents per bushel on that day, they each must turn over the two cents per bushel to their brokers within 24 hours, who subsequently remit the proceeds to the clearinghouse. All sellers gained two cents per bushel on that day, so they each receive two cents per bushel from their brokers. Their brokers are subsequently compensated by the clearinghouse. Because there is a buyer for every seller, the clearinghouse must break even every day. Now suppose that the price rises to $4.12 on the close of the following Monday. Each buyer receives seven cents ($4.12 − $4.05) per bushel, and each seller must pay

Illustration of Example Involving Marking to Market in Futures Contracts Both buyer and seller originally transact at Thursday’s closing price. Delivery takes place at Monday’s closing price.* Thursday, September 19

Friday, September 20

Monday, September 23

Closing price

$4.07

$4.05

$4.12

Buyer

Buyer purchases futures contract at closing price of $4.07/bushel.

Buyer must pay two cents/bushel to clearinghouse within one business day.

Buyer receives seven cents/bushel from clearinghouse within one business day.

Delivery (Notification Given by Seller on Monday)

Buyer pays $4.12 per bushel and receives grain within one business day.

Buyer’s net payment of −$4.07 (=−$.02 + $.07 − $4.12) is the same as if buyer purchased a forward contract for $4.07/bushel. Seller

Seller sells futures contract at closing price of $4.07/bushel.

Seller receives two cents/bushel from clearinghouse within one business day.

Seller pays seven cents/bushel to clearinghouse within one business day.

Seller receives $4.12 per bushel and delivers grain within two business days.

Seller’s net receipts of $4.07 (=$.02 − $.07 + $4.12) are the same as if seller sold a forward contract for $4.07/bushel. *For simplicity, we assume that buyer and seller both (1) initially transact at the same time and (2) meet in the delivery process. This is actually very unlikely to occur in the real world because the clearinghouse assigns the buyer to take delivery in a random manner.

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seven cents per bushel. Finally, suppose that on Monday a seller notifies his broker of his intention to deliver.1 The delivery price will be $4.12, which is Monday’s close. There are clearly many cash flows in futures contracts. However, after all the dust settles, the net price to the buyer must be the price at which she bought originally. That is, an individual buying at Thursday’s closing price of $4.07 and being called to take delivery on Monday pays two cents per bushel on Friday, receives seven cents per bushel on Monday, and takes delivery at $4.12. Her net outflow per bushel is −$4.07 (=−$0.02 + $.07 − $4.12), which is the price at which she contracted on Thursday. (Our analysis ignores the time value of money.) Conversely, an individual selling at Thursday’s closing price of $4.07 and notifying his broker concerning delivery the following Monday receives two cents per bushel on Friday, pays seven cents per bushel on Monday, and makes delivery at $4.12. His net inflow per bushel is $4.07 (=$.02 − $.07 + $4.12), which is the price at which he contracted on Thursday. These details are presented in a nearby box. For simplicity, we assumed that the buyer and seller who initially transact on Thursday’s close meet in the delivery process.2 The point in the example is that the buyer’s net payment of $4.07 per bushel is the same as if she purchased a forward contract for $4.07. Similarly, the seller’s net receipt of $4.07 per bushel is the same as if he sold a forward contract for $4.07 per bushel. The only difference is the timing of the cash flows. The buyer of a forward contract knows that he will make a single payment of $4.07 on the expiration date. He will not need to worry about any other cash flows in the interim. Conversely, though the cash flows to the buyer of a futures contract will net to exactly $4.07 as well, the pattern of cash flows is not known ahead of time. The mark-to-the-market provision on futures contracts has two related effects. The first concerns differences in net present value. For example, a large price drop immediately following purchase means an immediate outpayment for the buyer of a futures contract. Though the net outflow of $4.07 is still the same as under a forward contract, the present value of the cash outflows is greater to the buyer of a futures contract. Of course, the present value of the cash outflows is less to the buyer of a futures contract if a price rise follows purchase.3 Though this effect could be substantial in certain theoretical circumstances, it appears to be of quite limited importance in the real world.4 Second, the firm must have extra liquidity to handle a sudden outflow prior to expiration. This added risk may make the futures contract less attractive. Students frequently ask, “Why in the world would managers of the commodity exchanges ruin perfectly good contracts with these bizarre mark-to-the-market provisions?” Actually, the reason is a very good one. Consider the forward contract in Table 25.1 concerning the bookstore. Suppose the public quickly loses interest in Eating Habits of the Rich and Famous. By the time the bookstore calls the buyer, other stores may have dropped the price of the book to $6.00. Because the forward contract was for $10.00, the buyer has an incentive not to take delivery on the forward contract. Conversely, should the book become a hot item selling at $15.00, the bookstore may simply not call the buyer. As indicated, forward contracts have a big flaw. Whichever way the price of the deliverable instrument moves, one party has an incentive to default. There are many cases He will deliver on Wednesday, two days later.

1

As pointed out earlier, this is actually very unlikely to occur in the real world. The direction is reversed for the seller of a futures contract. However, the general point that the net present value of cash flows may differ between forward and futures contracts holds for sellers as well.

2 3

See John C. Cox, Jonathan E. Ingersoll, and Stephen A. Ross, “The Relationship between Forward and Future Prices,” Journal of Financial Economics (1981).

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where defaults have occurred in the real world. One famous case concerned Coca-Cola. When the company began in the early 20th century, Coca-Cola made an agreement to supply its bottlers and distributors with cola syrup at a constant price forever. Of course, subsequent inflation would have caused Coca-Cola to lose large sums of money had it honored the contract. After much legal effort, Coke and its bottlers put an inflation escalator clause in the contract. Another famous case concerned Westinghouse. It seems the firm had promised to deliver uranium to certain utilities at a fixed price. The price of uranium skyrocketed in the 1970s, making Westinghouse lose money on every shipment. Westinghouse defaulted on its agreement. The utilities took Westinghouse to court but did not recover amounts anything near what Westinghouse owed them. Mark-to-the-market provisions minimize the chance of default on a futures contract. If the price rises, the seller has an incentive to default on a forward contract. However, after paying the clearinghouse, the seller of a futures contract has little reason to default. If the price falls, the same argument can be made for the buyer. Because changes in the value of the underlying asset are recognized daily, there is no accumulation of loss, and the incentive to default is reduced. Because of this default issue, forward contracts generally involve individuals and institutions who know and can trust each other. But as W. C. Fields said, “Trust everybody, but cut the cards.” Lawyers earn a handsome living writing supposedly airtight forward contracts, even among friends. The genius of the mark-to-the-market system is that it can prevent default where it is most likely to occur—among investors who do not know each other. Textbooks on futures contracts from decades ago usually include a statement such as, “No major default has ever occurred on the commodity exchanges.” No textbook published after the Hunt Brothers defaulted on silver contracts in the 1970s can make that claim. Nevertheless, the extremely low default rate in futures contracts is truly awe-inspiring.

25.4 Hedging Now that we have determined how futures contracts work, let us talk about hedging. There are two types of hedges, long and short. We discuss the short hedge first.

EXAMPLE 25.1

Futures Hedging In June, Bernard Abelman, a Midwestern farmer, anticipates a harvest of 50,000 bushels of wheat at the end of September. He has two alternatives. 1. Write futures contracts against his anticipated harvest. The September wheat contract on the Chicago Board of Trade is trading at $3.75 a bushel on June 1. He executes the following transaction: Date of Transaction June 1

Transaction Write 10 September futures contracts

Price per Bushel $3.75

He notes that transportation costs to the designated delivery point in Chicago are 30 cents/ bushel. Thus, his net price per bushel is $3.45 = $3.75 − $.30. 2. Harvest the wheat without writing a futures contract. Alternatively, Mr. Abelman could harvest the wheat without the benefit of a futures contract. The risk would be quite great here because no one knows what the cash price in September will be. If prices rise, he will profit. Conversely, he will lose if prices fall. (continued)

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We say that strategy 2 is an unhedged position because there is no attempt to use the futures markets to reduce risk. Conversely, strategy 1 involves a hedge. That is, a position in the futures market offsets the risk of a position in the physical—that is, in the actual—commodity. Though hedging may seem quite sensible to you, it should be mentioned that not everyone hedges. Mr. Abelman might reject hedging for at least two reasons. First, he may simply be uninformed about hedging. We have found that not everyone in business understands the hedging concept. Many executives have told us that they do not want to use futures markets for hedging their inventories because the risks are too great. However, we disagree. While there are large price fluctuations in these markets, hedging actually reduces the risk that an individual holding inventories bears. Second, Mr. Abelman may have a special insight or some special information that commodity prices will rise. He would not be wise to lock in a price of $3.75 if he expects the cash price in September to be well above this price. The hedge of strategy 1 is called a short hedge because Mr. Abelman reduces his risk by selling a futures contract. The short hedge is very common in business. It occurs whenever someone either anticipates receiving inventory or is holding inventory. Mr. Abelman is anticipating the harvest of grain. A manufacturer of soybean meal and oil may hold large quantities of raw soybeans that are already paid for. However, the prices to be received for meal and oil are not known because no one knows what the market prices will be when the meal and oil are produced. The manufacturer may write futures contracts in meal and oil to lock in sales prices. An oil company may hold large inventories of petroleum to be processed into heating oil. The firm could sell futures contracts in heating oil to lock in the sales price. A mortgage banker may assemble mortgages slowly before selling them in bulk to a financial institution. Movements of interest rates affect the value of the mortgages while they are in inventory. The mortgage banker could sell Treasury bond futures contracts to offset this interest rate risk. (This last example is treated later in this chapter.)

EXAMPLE 25.2

M More Hedging On April 1, Moon Chemical agreed to sell petrochemicals to the U.S. government in the future. The delivery dates and prices have been determined. Because oil is a basic ingredient in the production process, Moon Chemical will need to have large quantities of oil on hand. The firm can get the oil in one of two ways: 1. Buy the oil as the firm needs it. This is an unhedged position because, as of April 1, the firm does not know the prices it will later have to pay for the oil. Oil is quite a volatile commodity, so Moon Chemical is bearing a good bit of risk. The key to this risk bearing is that the sales price to the U.S. government has already been fixed. Thus, Moon Chemical cannot pass on increased costs to the consumer. 2. Buy futures contracts.5 The firm can buy futures contracts with expiration months corresponding to the dates the firm needs inventory. The futures contracts lock in the purchase price to Moon Chemical. Because there is a crude oil futures contract for every month, selecting the correct futures contract is not difficult. Many other commodities have only five contracts per year, frequently necessitating buying contracts one month away from the month of production. As mentioned earlier, Moon Chemical is interested in hedging the risk of fluctuating oil prices because it cannot pass any cost increases on to the consumer. Suppose, alternatively, that Moon Alternatively, the firm could buy the oil on April 1 and store it. This would eliminate the risk of price movement because the firm’s oil costs would be fixed upon the immediate purchase. However, this strategy would be inferior to strategy 2 in the common case where the difference between the futures contract quoted on April 1 and the April 1 cash price is less than the storage costs.

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Chemical was not selling petrochemicals on a fixed contract to the U.S. government. Instead, imagine that the petrochemicals were to be sold to private industry at currently prevailing prices. The price of petrochemicals should move directly with oil prices because oil is a major component of petrochemicals. Because cost increases are likely to be passed on to the consumer, Moon Chemical would probably not want to hedge in this case. Instead, the firm is likely to choose strategy 1, buying the oil as it is needed. If oil prices increase between April 1 and September 1, Moon Chemical will, of course, find that its inputs have become quite costly. However, in a competitive market, its revenues are likely to rise as well. Strategy 2 is called a long hedge because one purchases a futures contract to reduce risk. In other words, one takes a long position in the futures market. In general, a firm institutes a long hedge when it is committed to a fixed sales price. One class of situations involves actual written contracts with customers, such as the one Moon Chemical had with the U.S. government. Alternatively, a firm may find that it cannot easily pass on costs to consumers or does not want to pass on these costs. For example, a group of students opened a small meat market called What’s Your Beef near the University of Pennsylvania in the late 1970s.6 This was a time of volatile consumer prices, especially food prices. Knowing that their fellow students were particularly budget-conscious, the owners vowed to keep food prices constant regardless of price movements in either direction. They accomplished this by purchasing futures contracts in various agricultural commodities.

25.5 Interest RateF uturesCo ntracts In this section we consider interest rate futures contracts. Our examples deal with futures contracts on Treasury bonds because of their high popularity. We first price Treasury bonds and Treasury bond forward contracts. Differences between futures and forward contracts are explored. Hedging examples are provided next.

Pricing of Treasury Bonds As mentioned earlier in the text, a Treasury bond pays semiannual interest over its life. In addition, the face value of the bond is paid at maturity. Consider a 20-year, 8 percent coupon bond that was issued on March 1. The first payment is to occur in six months—that is, on September 1. The value of the bond can be determined as follows: Pricing of Treasury Bond $1,040 $40 $40 $40 $40 PTB = ______ + ________2 + ________3 + . . . + _________ + _________ 1 + R1 (1 + R2) (1 + R3) (1 + R39)39 (1 + R40)40

(25.1)

Because an 8 percent coupon bond pays interest of $80 a year, the semiannual coupon is $40. Principal and the semiannual coupons are both paid at maturity. As we mentioned in a previous chapter, the price of the Treasury bond, PTB, is determined by discounting each payment on a bond at the appropriate spot rate. Because the payments are semiannual, each spot rate is expressed in semiannual terms. That is, imagine a horizontal term structure where the effective annual yield is 8 percent for all maturities. Because each spot rate, R, is expressed in semiannual terms, each spot rate ____ is √1.12 − 1 = 3.92%. Coupon payments occur every six months, so there are 40 spot rates over the 20-year period. Ordinarily, an unusual firm name in this textbook is a tip-off that it is fictional. This, however, is a true story.

6

772

Figure 25.1 Cash Flows for Both a Treasury Bond and a Forward Contract on a Treasury Bond

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Date

0 March 1

1 2 Sept. 1 March 1

3 Sept. 1

...

39 40 Sept. 1 March 1

⫺Price of Treasury bond (⫺ PTB)

+$40

+$40

+$40

...

+$40

$1,040

+$40 ⫺Price of forward contract (⫺ PFORW.CONT.)

+$40

...

+$40

+$40

Treasury Bond

Forward Contract

41 Sept. 1

+$1,040

Pricing of Forward Contracts Now imagine a forward contract where, on March 1, you agree to buy a new 20-year, 8 percent coupon Treasury bond in six months (on September 1). As with typical forward contracts, you will pay for the bond on September 1, not March 1. The cash flows from both the Treasury bond issued on March 1 and the forward contract that you purchase on March 1 are presented in Figure 25.1. The cash flows on the Treasury bond begin exactly six months earlier than do the cash flows on the forward contract. The Treasury bond is purchased with cash on March 1 (date 0). The first coupon payment occurs on September 1 (date 1). The last coupon payment occurs at date 40, along with the face value of $1,000. The forward contract compels you to pay PFORW.CONT., the price of the forward contract, on September 1 (date 1). You receive a new Treasury bond at that time. The first coupon payment you receive from the bond occurs on March 1 of the following year (date 2). The last coupon payment occurs at date 41, along with the face value of $1,000. Given the 40 spot rates, Equation 25.1 showed how to price a Treasury bond. How do we price the forward contract on a Treasury bond? Just as we saw earlier in the text that net present value analysis can be used to price bonds, we will now show that net present value analysis can be used to price forward contracts. Given the cash flows for the forward contract in Figure 25.1, the price of the forward contract must satisfy the following equation: P $1,040 $40 $40 $40 FORW.CONT. $40 + ________ _________ = ________ + ________ + . . . + _________ + _________ (25.2) 1 + R1 (1 + R40)40 (1 + R41)41 (1 + R2)2 (1 + R3)3 (1 + R4)4 The right side of Equation 25.2 discounts all the cash flows from the delivery instrument (the Treasury bond issued on September 1) back to date 0 (March 1). Because the first cash flow occurs at date 2 (March 1 of the subsequent year), it is discounted by 1/(1 + R2)2. The last cash flow of $1,040 occurs at date 41, so it is discounted by 1/(1 + R41)41. The left side represents the cost of the forward contract as of date 0. Because the actual outpayment occurs at date 1, it is discounted by 1 (1 + R1). Students often ask, “Why are we discounting everything back to date 0 when we are actually paying for the forward contract on September 1?” The answer is simply that we apply the same techniques to Equation 25.2 that we apply to all capital budgeting problems: We want to put everything in today’s (date 0’s) dollars. Given that the spot rates are known in the marketplace, traders should have no more trouble pricing a forward contract by Equation 25.2 than they would have pricing a Treasury bond by Equation 25.1.

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Forward contracts are similar to the underlying bonds themselves. If the entire term structure of interest rates unexpectedly shifts upward on March 2, the Treasury bond issued the previous day should fall in value. This can be seen from Equation 25.1. A rise in each of the spot rates lowers the present value of each of the coupon payments. Hence, the value of the bond must fall. Conversely, a fall in the term structure of interest rates increases the value of the bond. The same relationship holds with forward contracts, as we can see by rewriting Equation 25.2 like this: $40 × (1 + R1) _____________ $40 × (1 + R1) $40 × (1 + R1) _____________ PFORW.CONT. = _____________ + + 3 2 (1 + R3) (1 + R4)4 (1 + R2) $40 × (1 + R1) ________________ $1,040 × (1 + R1) + . . . + _____________ + 40 (1 + R40) (1 + R41)41

(25.3)

We went from Equation 25.2 to 25.3 by multiplying both the left and the right sides by (1 + R1). If the entire term structure of interest rates unexpectedly shifts upward on March 2, the first term on the right side of Equation 25.3 should fall in value.7 That is, both R1 and R2 will rise an equal amount. However, R2 enters as a squared term, 1/(1 + R2)2, so an increase in R2 more than offsets the increase in R1. As we move further to the right, an increase in any spot rate, Ri, more than offsets an increase in R1. Here, Ri enters as the ith power, 1/(1 + Ri )i. Thus, as long as the entire term structure shifts upward an equal amount on March 2, the value of a forward contract must fall on that date. Conversely, as long as the entire term structure shifts downward an equal amount on March 2, the value of a forward contract must rise.

FuturesCo ntracts The previous discussion concerned a forward contract in U.S. Treasury bonds—that is, a forward contract where the deliverable instrument is a U.S. Treasury bond. What about a futures contract on a Treasury bond?8 We mentioned earlier that futures contracts and forward contracts are quite similar, though there are a few differences between the two. First, futures contracts are generally traded on exchanges, whereas forward contracts are not traded on an exchange. In this case, the Treasury bond futures contract is traded on the Chicago Board of Trade. Second, futures contracts generally allow the seller a period of time in which to deliver, whereas forward contracts generally call for delivery on a particular day. The seller of a Treasury bond futures contract can choose to deliver on any business day during the delivery month.9 Third, futures contracts are subject to the mark-to-the-market convention, whereas forward contracts are not. Traders in Treasury bill futures contracts must adhere to this convention. Fourth, there is generally a liquid market for futures contracts allowing contracts to be quickly netted out. That is, a buyer can sell his futures contract at any time, and a seller can buy back her futures contract at any time. Conversely, because forward markets are generally quite illiquid, traders cannot easily net out their positions. The popularity of the Treasury bond futures contract has produced liquidity even higher than that on other futures contracts. Positions in that contract can be netted out quite easily.

We are assuming that each spot rate shifts by the same amount. For example, suppose that on March 1 R1 = 5%, R2 = 5.4%, and R3 = 5.8%. Assuming that all rates increase by 1/2 percent on March 2, R1 becomes 5.5 percent (5% + 1/2%), R2 becomes 5.9 percent, and R3 becomes 6.3 percent. 7

8 9

Futures contracts on bonds are also called interest rate futures contracts. Delivery occurs two days after the seller notifies the clearinghouse of her intention to deliver.

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This discussion is not intended to be an exhaustive list of differences between the Treasury bond forward contract and the Treasury bond futures contract. Rather, it is intended to show that both contracts share fundamental characteristics. Though there are differences, the two instruments should be viewed as variations of the same species, not different species. Thus, the pricing of Equation 25.3, which is exact for the forward contract, should be a decent approximation for the futures contract.

Hedging in Interest Rate Futures Now that we have the basic institutional details under our belts, we are ready for examples of hedging using either futures contracts or forward contracts on Treasury bonds. Because the T-bond futures contract is extremely popular, whereas the forward contract is traded sporadically, our examples use the futures contract.

EXAMPLE 25.3

Interest Rate Hedging Ron Cooke owns a mortgage banking company. On March 1, he made a commitment to lend a total of $1 million to various homeowners on May 1. The loans are 20-year mortgages carrying a 12 percent coupon, the going interest rate on mortgages at the time. Thus, the mortgages are made at par. Though homeowners would not use the term, we could say that he is buying a forward contract on a mortgage. That is, he agrees on March 1 to give $1 million to his borrowers on May 1 in exchange for principal and interest from them every month for the next 20 years. Like many mortgage bankers, he has no intention of paying the $1 million out of his own pocket. Rather, he intends to sell the mortgages to an insurance company. Thus, the insurance company will actually lend the funds and will receive principal and interest over the next 20 years. Mr. Cooke does not currently have an insurance company in mind. He plans to visit the mortgage departments of insurance companies over the next 60 days to sell the mortgages to one or many of them. He sets April 30 as a deadline for making the sale because the borrowers expect the funds on the following day. Suppose Mr. Cooke sells the mortgages to the Acme Insurance Co. on April 15. What price will Acme pay for the bonds? You may think the insurance company will obviously pay $1 million for the loans. However, suppose interest rates have risen above 12 percent by April 15. The insurance company will buy the mortgage at a discount. For example, suppose the insurance company agrees to pay only $940,000 for the mortgages. Because the mortgage banker agreed to lend a full $1 million to the borrowers, the mortgage banker must come up with the additional $60,000 (=$1 million − $940,000) out of his own pocket. Alternatively, suppose interest rates fall below 12 percent by April 15. The mortgages can be sold at a premium under this scenario. If the insurance company buys the mortgages at $1.05 million, the mortgage banker will have made an unexpected profit of $50,000 (=$1.05 million − $1 million). Because Ron Cooke is unable to forecast interest rates, this risk is something that he would like to avoid. The risk is summarized in Table 25.3. Seeing the interest rate risk, students at this point may ask, “What does the mortgage banker get out of this loan to offset his risk bearing?” Mr. Cooke wants to sell the mortgages to the insurance company so that he can get two fees. The first is an origination fee, which is paid to the mortgage banker by the insurance company on April 15—that is, on the date the loan is sold. An industry standard in certain locales is 1 percent of the value of the loan, which is $10,000 (=1% × $1 million). In addition, Mr. Cooke will act as a collection agent for the insurance company. For this service he will receive a small portion of the outstanding balance of the loan each month. For example, if he is paid .03 percent of the loan each month, he will receive $300 (=.03% × $1 million) in the first month. As the outstanding balance of the loan declines, he will receive less. Though Mr. Cooke will earn profitable fees on the loan, he bears interest rate risk. He loses money if interest rates rise after March 1, and he profits if interest rates fall after March 1.To hedge

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Table 25.3

775

Effects of Changing Interest Rates on Ron Cooke, Mortgage Banker

Mortgage Interest Rate on April 15

Sale Price to Acme Insurance Company Effect on Mortgage Banker Dollar Gain or Loss

Above 12%

Below 12%

Below $1 million (we assume $940,000). He loses because he must lend the full $1 million to borrowers. Loss of $60,000 (=$1 million − $940,000).

Above $1 million (we assume $1.05 million). He gains because he lends only $1 million to borrowers. Gain of $50,000 (=$1.05 million − $1 million).

The interest rate on March 1, the date when the loan agreement was made with the borrowers, was 12 percent. April 15 is the date the mortgages were sold to Acme Insurance Company.

this risk, he writes June Treasury bond futures contracts on March 1. As with mortgages, Treasury bond futures contracts fall in value if interest rates rise. Because he writes the contract, he makes money on these contracts if they fall in value. Therefore, with an interest rate rise, the loss he endures on the mortgages is offset by the gain he earns in the futures market. Conversely, Treasury bond futures contracts rise in value if interest rates fall. Because he writes the contracts, he suffers losses on them when rates fall. With an interest rate fall, the profit he makes on the mortgages is offset by the loss he suffers in the futures markets. The details of this hedging transaction are presented in Table 25.4. The column on the left is labeled “Cash Markets” because the deal in the mortgage market is transacted off an exchange. The

Table 25.4

Illustration of Hedging Strategy for Ron Cooke, Mortgage Banker

March 1

April 15

If interest rates rise:

If interest rates fall:

Cash Markets

Futures Markets

Mortgage banker makes forward contracts to lend $1 million at 12 percent for 20 years. The loans are to be funded on May 1. No cash changes hands on March 1. Loans are sold to Acme Insurance Company. Mortgage banker will receive sale price from Acme on the May 1 funding date. Loans are sold at a price below $1 million. Mortgage banker loses because he receives less than the $1 million he must give to borrowers. Loans are sold at a price above $1 million. Mortgage banker gains because he receives more than the $1 million he must give to borrowers.

Mortgage banker writes 10 June Treasury bond futures contracts.

Mortgage banker buys back all the futures contracts.

Each futures contract is bought back at a price below the sales price, resulting in profit. Mortgage banker’s profit in futures market offsets loss in cash market. Each futures contract is bought back at a price above the sales price, resulting in loss. Mortgage banker’s loss in futures market offsets gain in cash market. (continued )

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column on the right shows the offsetting transactions in the futures market. Consider the first row. The mortgage banker enters into a forward contract on March 1. He simultaneously writes Treasury bond futures contracts. Ten contracts are written because the deliverable instrument on each contract is $100,000 of Treasury bonds. The total is $1 million (=10 × $100,000), which is equal to the value of the mortgages. Mr. Cooke would prefer to write May Treasury bond futures contracts. Here, Treasury bonds would be delivered on the futures contract during the same month that the loan is funded. Because there is no May T-bond futures contract, Mr. Cooke achieves the closest match through a June contract. If held to maturity, the June contract would obligate the mortgage banker to deliver Treasury bonds in June. Interest rate risk ends in the cash market when the loans are sold. Interest rate risk must be terminated in the futures market at that time. Thus, Mr. Cooke nets out his position in the futures contracts as soon as the loan is sold to Acme Insurance.

As our example shows, risk is clearly reduced via an offsetting transaction in the futures market. However, is risk totally eliminated? Risk would be totally eliminated if losses in the cash markets were exactly offset by gains in the futures markets and vice versa. This is unlikely to happen because mortgages and Treasury bonds are not identical instruments. First, mortgages may have different maturities than Treasury bonds. Second, Treasury bonds have a different payment stream than do mortgages. Principal is paid only at maturity on T-bonds, whereas principal is paid every month on mortgages. Because mortgages pay principal continuously, these instruments have a shorter effective time to maturity than do Treasury bonds of equal maturity.10 Third, mortgages have default risk whereas Treasury bonds do not. The term structure applicable to instruments with default risk may change even when the term structure for risk-free assets remains constant. Fourth, mortgages may be paid off early and hence have a shorter expected maturity than Treasury bonds of equal maturity. Because mortgages and Treasury bonds are not identical instruments, they are not identically affected by interest rates. If Treasury bonds are less volatile than mortgages, financial consultants may advise Mr. Cooke to write more than 10 T-bond futures contracts. Conversely, if these bonds are more volatile, the consultant may state that fewer than 10 futures contracts are needed. An optimal ratio of futures to mortgages will reduce risk as much as possible. However, because the price movements of mortgages and Treasury bonds are not perfectly correlated, Mr. Cooke’s hedging strategy cannot eliminate all risk. The preceding strategy is called a short hedge because Mr. Cooke sells futures contracts to reduce risk. Though it involves an interest rate futures contract, this short hedge is analogous to short hedges in agricultural and metallurgical futures contracts. We argued at the beginning of this chapter that individuals and firms institute short hedges to offset inventory price fluctuations. Once Mr. Cooke makes a contract to lend money to borrowers, the mortgages effectively become his inventory. He writes a futures contract to offset the price fluctuations of his inventory. We now consider an example where a mortgage banker institutes a long hedge.

Alternatively, we can say that mortgages have shorter duration than do Treasury bonds of equal maturity. A precise definition of duration is provided later in this chapter.

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EXAMPLE 25.4

Derivatives and Hedging Risk

777

Short versus Long Hedging Margaret Boswell is another mortgage banker. Her firm faces problems similar to those facing Mr. Cooke’s firm. However, she tackles the problems through the use of advance commitments, a strategy that is the opposite of Mr. Cooke’s. That is, she promises to deliver loans to a financial institution before she lines up borrowers. On March 1 her firm agreed to sell mortgages to No-State Insurance Co. The agreement specifies that she must turn over 12 percent coupon mortgages with a face value of $1 million to No-State by May 1. No-State is buying the mortgages at par, implying that they will pay Ms. Boswell $1 million on May 1. As of March 1, Ms. Boswell had not signed up any borrowers. Over the next two months, she will seek out individuals who want mortgages beginning May 1. As with Mr. Cooke, changing interest rates will affect Ms. Boswell. If interest rates fall before she signs up a borrower, the borrower will demand a premium on a 12 percent coupon loan. That is, the borrower will receive more than par on May 1.11 Because Ms. Boswell receives par from the insurance company, she must make up the difference. Conversely, if interest rates rise, a 12 percent coupon loan will be made at a discount. That is, the borrower will receive less than par on May 1. Because Ms. Boswell receives par from the insurance company, the difference is pure profit to her. The details are provided in Table 25.5. As did Mr. Cooke, Ms. Boswell finds the risk burdensome. Therefore, she offsets her advance commitment with a transaction in the futures markets. Because

Table 25.5

March 1

April 15

If interest rates rise:

If interest rates fall:

Illustration of Advance Commitment for Margaret Boswell, Mortgage Banker

Cash Markets

Futures Markets

Mortgage banker makes a forward contract (advance commitment) to deliver $1 million of mortgages to No-State Insurance. The insurance company will pay par to Ms. Boswell for the loans on May 1. The borrowers are to receive their funding from the mortgage banker on May 1. The mortgages are to be 12 percent coupon loans for 20 years. Mortgage banker signs up borrowers for 12 percent coupon, 20-year mortgages. She promises that the borrowers will receive funds on May 1. Mortgage banker issues mortgages to borrowers at a discount. Mortgage banker gains because she receives par from the insurance company.

Mortgage banker buys 10 June Treasury bond futures contracts.

Loans to borrowers are issued at a premium. Mortgage banker loses because she receives only par from insurance company.

Mortgage banker sells all futures contracts.

Futures contracts are sold at a price below purchase price, resulting in loss. Mortgage banker’s loss in futures market offsets gain in cash market. Futures contracts are sold at a price above purchase price, resulting in gain. Mortgage banker’s gain in futures market offsets loss in cash market. (continued )

Alternatively, the mortgage would still be at par if a coupon rate below 12 percent were used. However, this is not done because the insurance company wants to buy only 12 percent mortgages. 11

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she loses in the cash market when interest rates fall, she buys futures contracts to reduce the risk. When interest rates fall, the value of her futures contracts increases. The gain in the futures market offsets the loss in the cash market. Conversely, she gains in the cash markets when interest rates rise. The value of her futures contracts decreases when interest rates rise, offsetting her gain. We call this a long hedge because Ms. Boswell offsets risk in the cash markets by buying a futures contract. Though it involves an interest rate futures contract, this long hedge is analogous to long hedges in agricultural and metallurgical futures contracts.We argued at the beginning of this chapter that individuals and firms institute long hedges when their finished goods are to be sold at a fixed price. Once Ms. Boswell makes the advance commitment with No-State Insurance, she has fixed her sales price. She buys a futures contract to offset the price fluctuation of her raw materials—that is, hermo rtgages.

25.6 Duration Hedging The last section concerned the risk of interest rate changes. We now want to explore this risk in a more precise manner. In particular we want to show that the concept of duration is a prime determinant of interest rate risk. We begin by considering the effect of interest rate movements on bond prices.

The Case of Zero Coupon Bonds Imagine a world where the interest rate is 10 percent across all maturities. A oneyear pure discount bond pays $110 at maturity. A five-year pure discount bond pays $161.05 at maturity. Both of these bonds are worth $100, as given by the following:12 Value of One-Year Pure Discount Bond $110 $100 = _____ 1.10 Value of Five-Year Pure Discount Bond $161.05 $100 = _______ (1.10)5 Which bond will change more when interest rates move? To find out, we calculate the value of these bonds when interest rates are either 8 or 12 percent. The results are presented in Table 25.6. As can be seen, the five-year bond has greater price swings than does the one-year bond. That is, both bonds are worth $100 when interest rates are 10 percent. The five-year bond is worth more than the one-year bond when interest rates are 8 percent and worth less than the one-year bond when interest rates are 12 percent. We state that the five-year bond is subject to more price volatility. This point, which was mentioned in passing in an earlier section of the chapter, is not difficult to understand. The interest rate term in the denominator, 1 + R, is taken to the fifth power for a fiveyear bond and only to the first power for the one-year bond. Thus, the effect of a changing interest rate is magnified for the five-year bond. The general rule is this: The percentage price changes of long-term pure discount bonds are greater than the percentage price changes of short-term pure discount bonds.

12 Alternatively, we could have chosen bonds that pay $100 at maturity. Their values would be $90.91 (= $100/1.10) and $62.09 [= $100/(1.10)5]. However, our comparisons to come are made easier if both have the same initial price.

Chapter 25

Table 25.6 Value of a Pure Discount Bond as a Function of Interest Rate

Derivatives and Hedging Risk

779

Interest Rate

One-Year Pure Discount Bond

Five-Year Pure Discount Bond

8%

$110 $101.85 = _____ 1.08

10%

$110 $100.00 = _____ 1.10

12%

$110 $ 98.21 = _____ 1.12

$161.05 $109.61 = _______ (1.08)5 $161.05 $100.00 = _______ (1.10)5 $161.05 $ 91.38 = _______ (1.12)5

For a given interest rate change, a five-year pure discount bond fluctuates more in price than does a one-year pure discount bond.

The Case of Two Bonds with the Same Maturity but with Different Coupons The previous example concerned pure discount bonds of different maturities. We now want to see the effect of different coupons on price volatility. To abstract from the effect of differing maturities, we consider two bonds with the same maturity but with different coupons. Consider a five-year, 10 percent coupon bond and a five-year, 1 percent coupon bond. When interest rates are 10 percent, the bonds are priced like this: Value of Five-Year, 10 Percent Coupon Bond $10 $10 $10 $110 $10 $100 = ____ + ______2 + ______3 + ______4 + ______5 1.10 (1.10) (1.10) (1.10) (1.10) Value of Five-Year, 1 Percent Coupon Bond $1 $1 $1 $101 $1 $65.88 = ____ + ______2 + ______3 + ______4 + ______5 1.10 (1.10) (1.10) (1.10) (1.10) Which bond will change more in percentage terms if interest rates change?13 To find out, we first calculate the value of these bonds when interest rates are either 8 or 12 percent. The results are presented in Table 25.7. As we would expect, the 10 percent coupon bond always sells for more than the 1 percent coupon bond. Also as we would expect, each bond is worth more when the interest rate is 8 percent than when the interest rate is 12 percent. We calculate percentage price changes for both bonds as the interest rate changes from 10 to 8 percent and from 10 to 12 percent:

Interest rate changes from 10% to 8%: Interest rate changes from 10% to 12%:

10% Coupon Bond

1% Coupon Bond

$107.99 7.99% = _______ $100 −1

$72.05 9.37% = ______ $65.88 −1

$92.79 −7.21% = ______ $100 −1

$60.35 −8.39% = ______ $65.88 −1

As we can see, the 1 percent coupon bond has a greater percentage price increase than does the 10 percent coupon bond when the interest rate falls. Similarly, the 1 percent coupon bond has a greater percentage price decrease than does the 10 percent coupon bond when the interest rate rises. Thus, we say that the percentage price changes The bonds are at different prices initially. Thus, we are concerned with percentage price changes, not absolute price changes. 13

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Interest Rate

Five-Year, 10% Coupon Bond $10 $10 $110 $10 $10 ______ ______ _______ ______ $107.99 = ____ 1.08 + (1.08)2 + (1.08)3 + ($1.08)4 + (1.08)5 $10 $10 $10 $110 $10 ______ ______ ______ ______ $100.00 = ____ 1.10 + (1.10)2 + (1.10)3 + (1.10)4 + (1.10)5 $10 $10 $10 $110 $10 ______ ______ ______ ______ $ 92.79 = ____ 1.12 + (1.12)2 + (1.12)3 + (1.12)4 + (1.12)5

8% 10% 12% Interest Rate

Five-Year, 1% Coupon Bond $1 $1 $101 $1 $1 ______ ______ ______ ______ $72.05 = ____ 1.08 + (1.08)2 + (1.08)3 + (1.08)4 + (1.08)5 $1 $1 $1 $101 $1 ______ ______ ______ ______ $65.88 = ____ 1.10 + (1.10)2 + (1.10)3 + (1.10)4 + (1.10)5 $1 $1 $1 $101 $1 ______ ______ ______ ______ $60.35 = ____ 1.12 + (1.12)2 + (1.12)3 + (1.12)4 + (1.12)5

8% 10% 12%

on the 1 percent coupon bond are greater than are the percentage price changes on the 10 percent coupon bond.

Duration The question, of course, is “Why?” We can answer this question only after we have explored a concept called duration. We begin by noticing that any coupon bond is actually a combination of pure discount bonds. For example, the five-year, 10 percent coupon bond is made up of five pure discount bonds: 1. A pure discount bond paying $10 at the end of year 1. 2. A pure discount bond paying $10 at the end of year 2. 3. A pure discount bond paying $10 at the end of year 3. 4. A pure discount bond paying $10 at the end of year 4. 5. A pure discount bond paying $110 at the end of year 5. Similarly, the five-year, 1 percent coupon bond is made up of five pure discount bonds. Because the price volatility of a pure discount bond is determined by its maturity, we would like to determine the average maturity of the five pure discount bonds that make up a five-year coupon bond. This leads us to the concept of duration. We calculate average maturity in three steps. For the 10 percent coupon bond, we have these: 1. Calculate present value of each payment. We do this as follows:

Year

Payment

1 2 3 4 5

$ 10 10 10 10 110

Present Value of Payment by Discounting at 10% $ 9.091 8.264 7.513 6.830 68.302 $100.00

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2. Express the present value of each payment in relative terms. We calculate the relative value of a single payment as the ratio of the present value of the payment to the value of the bond. The value of the bond is $100. We obtain these values:

Year

Payment

1 2 3 4 5

$ 10 10 10 10 110

Present Value of Payment

Present Value of Payment Relative Value = ________________________ Value of Bond

$ 9.091 8.264 7.513 6.830 68.302 $100.00

$9.091/$100 = .09091 .08264 .07513 .06830 .68302 1.0

The bulk of the relative value, 68.302 percent, occurs at year 5 because the principal is paid back at that time. 3. Weight the maturity of each payment by its relative value: 4.1699y ears = 1 year × .09091 + 2 years × .08264 + 3 years × .07513 + 4 years × .06830 + 5 years ×.68302 There are many ways to calculate the average maturity of a bond. We have calculated it by weighting the maturity of each payment by the payment’s present value. We find that the effective maturity of the bond is 4.1699 years. Duration is a commonly used word for effective maturity. Thus, the bond’s duration is 4.1699 years. Note that duration is expressed in units of time.14 Because the five-year, 10 percent coupon bond has a duration of 4.1699 years, its percentage price fluctuations should be the same as those of a zero coupon bond with a duration of 4.1699 years.15 It turns out that the five-year, 1 percent coupon bond has a duration of 4.8742 years. Because the 1 percent coupon bond has a higher duration than the 10 percent bond, the 1 percent coupon bond should be subject to greater price fluctuations. This is exactly what we found earlier. In general we say the following: The percentage price changes of a bond with high duration are greater than the percentage price changes of a bond with low duration.

The mathematical formula for duration is:

14

and

PV(C1)1 + PV(C2)2 + . . . + PV(CT)T Duration = _________________________________ PV PV = PV(C1) + PV(C2) + . . . + PV(CT) CT PV(CT) = ________T (1 + R)

where CT is the cash to be received in time T, and R is the current discount rate. Also, note that in our numerical example, we discounted each payment by the interest rate of 10 percent. This was done because we wanted to calculate the duration of the bond before a change in the interest rate occurred. After a change in the rate to, say, 8 or 12 percent, all three of our steps would need to reflect the new interest rate. In other words, the duration of a bond is a function of the current interest rate. 15 Actually, this relationship exactly holds only in the case of a one-time shift in a flat yield curve, where the change in the spot rate is identical for all maturities.

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A final question: Why does the 1 percent bond have a greater duration than the 10 percent bond, even though they both have the same five-year maturity? As mentioned earlier, duration is an average of the maturity of the bond’s cash flows weighted by the present value of each cash flow. The 1 percent coupon bond receives only $1 in each of the first four years. Thus, the weights applied to years 1 through 4 in the duration formula will be low. Conversely, the 10 percent coupon bond receives $10 in each of the first four years. The weights applied to years 1 through 4 in the duration formula will be higher.

Matching Liabilities with Assets Earlier in this chapter, we argued that firms can hedge risk by trading in futures. Because some firms are subject to interest rate risk, we showed how they can hedge with interest rate futures contracts. Firms may also hedge interest rate risk by matching liabilities with assets. This ability to hedge follows from our discussion of duration.

EXAMPLE25.5

UsingD uration The Physical Bank of New York has the following market value balance sheet: PHYSICAL BANK OF NEW YORK Market Value Balance Sheet

Market Value Assets Overnight money Accounts receivable–backed loans Inventory loans Industrial loans Mortgages

$

Duration

35 million 500 million 275 million 40 million 150 million $1,000 million

0 3 months 6 months 2 years 14.8 years

$ 400 million 300 million 200 million 100 million $1,000 million

0 1 year 10 years

Liabilities and Owners’ Equity Checking a nd savings accounts Certificates of deposit Long-term financing Equity

The bank has $1,000 million of assets and $900 million of liabilities. Its equity is the difference between the two: $100 million (= $1,000 million − $900 million). Both the market value and the duration of each individual item are provided in the balance sheet. Both overnight money and checking and savings accounts have a duration of zero. This is because the interest paid on these instruments adjusts immediately to changing interest rates in the economy. The bank’s managers think that interest rates are likely to move quickly in the coming months. Because they do not know the direction of the movement, they are worried that their bank is vulnerable to changing rates. They call in a consultant, James Charest, to determine a hedging strategy.

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Mr. Charest first calculates the duration of the assets and the duration of the liabilities:16 Duration of Assets $35 million $500 million ____________ 2.56 years = 0 years × ____________ $1,000 million + ¼ year × $1,000 million

(25.4)

$40 million $275 million ____________ + ½ year × ____________ $1,000 million + 2 years × $1,000 million $150 million + 14.8 years × ____________ $1,000 million Duration of Liabilities $300 million $200 million $400 million ___________ ___________ 2.56 = 0 years × ___________ $900 million + 1 year × $900 million + 10 years × $900 million

(25.5)

The duration of the assets, 2.56 years, equals the duration of the liabilities. Because of this, Mr. Charest argues that the firm is immune to interest rate risk. Just to be on the safe side, the bank calls in a second consultant, Gail Ellert. Ms. Ellert argues that it is incorrect to simply match durations because assets total $1,000 million and liabilities total only $900 million. If both assets and liabilities have the same duration, the price change on a dollar of assets should be equal to the price change on a dollar of liabilities. However, the total price change will be greater for assets than for liabilities because there are more assets than liabilities in this bank. The firm will be immune to interest rate risk only when the duration of the liabilities is greater than the duration of the assets. Ms. Ellert states that the following relationship must hold if the bank is to be immunized—that is, immune to interest rate risk: Duration of Market value of Duration of Market value × = assets × assets liabilities of liabilities

(25.6)

She says that the bank should not equate the duration of the liabilities with the duration of the assets. Rather, using Equation 25.6, the bank should match the duration of the liabilities to the duration of the assets. She suggests two ways to achieve this match. 1. Increase the duration of the liabilities without changing the duration of the assets. Ms. Ellert argues that the duration of the liabilities could be increased to: $1,000 million Market value of assets ____________ Duration of assets × _____________________ Market value of liabilities = 2.56 years × $900 million = 2.84 years Equation 25.6 then becomes: 2.56 × $1 billion = 2.84 × $900 million 2. Decrease the duration of the assets without changing the duration of the liabilities. Alternatively, Ms. Ellert points out that the duration of the assets could be decreased to: $900 million Market value of liabilities ____________ Duration of liabilities × _____________________ Market value of assets = 2.56 years × $1,000 million = 2.30 years Equation 25.6 then becomes: 2.30 × $1 billion = 2.56 × $900 million

Note that the duration of a group of items is an average of the duration of the individual items weighted by the market value of each item. This is a simplifying step that greatly increases duration’s practicality. 16

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Though we agree with Ms. Ellert’s analysis, the bank’s current mismatch was small anyway. Huge mismatches have occurred for real-world financial institutions, particularly savings and loans. S&Ls have frequently invested large portions of their assets in mortgages. The durations of these mortgages would clearly be above 10 years. Many of the funds available for mortgage lending were financed by short-term credit, especially savings accounts. As we mentioned, the duration of such instruments is quite small. A thrift institution in this situation faces a large amount of interest rate risk because any increase in interest rates would greatly reduce the value of the mortgages. Because an interest rate rise would reduce the value of the liabilities only slightly, the equity of the firm would fall. As interest rates rose over much of the 1960s and 1970s, many S&Ls found that the market value of their equity approached zero.17 Duration and the accompanying immunization strategies are useful in other areas of finance. For example, many firms establish pension funds to meet obligations to retirees. If the assets of a pension fund are invested in bonds and other fixed-income securities, the duration of the assets can be computed. Similarly, the firm views the obligations to retirees as analogous to interest payments on debt. The duration of these liabilities can be calculated as well. The manager of a pension fund would commonly choose pension assets so that the duration of the assets is matched with the duration of the liabilities. In this way, changing interest rates would not affect the net worth of the pension fund. Life insurance companies receiving premiums today are legally obligated to provide death benefits in the future. Actuaries view these future benefits as analogous to interest and principal payments of fixed-income securities. The duration of these expected benefits can be calculated. Insurance firms frequently invest in bonds where the duration of the bonds is matched to the duration of the future death benefits. The business of a leasing company is quite simple. The firm issues debt to purchase assets, which are then leased. The lease payments have a duration, as does the debt. Leasing companies frequently structure debt financing so that the duration of the debt matches the duration of the lease. If a firm did not do this, the market value of its equity could be eliminated by a quick change in interest rates.

25.7 Swaps Contracts Swaps are close cousins to forwards and futures contracts. Swaps are arrangements between two counterparties to exchange cash flows over time. There is enormous flexibility in the forms that swaps can take, but the three basic types are interest rate swaps, currency swaps, and credit default swaps. Often these are combined when interest received in one currency is swapped for interest in another currency.

InterestR ateSw aps Like other derivatives, swaps are tools that firms can use to easily change their risk exposures and their balance sheets.18 Consider a firm that has borrowed and carried 17 Actually, the market value of the equity could easily be negative in this example. However, S&Ls in the real world have an asset not shown on our market value balance sheet: The ability to generate new, profitable loans. This should increase the market value of a thrift above the market value of its outstanding loans less its existing debt. 18 Under current accounting rules, most derivatives do not usually show up on firms’ balance sheets because they do not have a historical cost (i.e., the amount a dealer would pay on the initial transaction day).

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on its books an obligation to repay a 10-year loan for $100 million of principal with a 9 percent coupon rate paid annually. Ignoring the possibility of calling the loan, the firm expects to have to pay coupons of $9 million every year for 10 years and a balloon payment of $100 million at the end of the 10 years. Suppose, though, that the firm is uncomfortable with having this large fixed obligation on its books. Perhaps the firm is in a cyclical business where its revenues vary and could conceivably fall to a point where it would be difficult to make the debt payment. Suppose, too, that the firm earns a lot of its revenue from financing the purchase of its products. Typically, for example, a manufacturer might help its customers finance their purchase of its products through a leasing or credit subsidiary. Usually these loans are for relatively short periods and are financed at some premium over the prevailing short-term rate of interest. This puts the firm in the position of having revenues that move up and down with interest rates while its costs are relatively fixed. What the firm would really prefer is to have a floating-rate loan rather than a fixedrate loan. That way, when interest rates rise, the firm would have to pay more on the loan, but it would be making more on its product financing. An interest rate swap is ideal in this situation. Of course, the firm could also just go into the capital markets and borrow $100 million at a variable interest rate and then use the proceeds to retire its outstanding fixed-rate loan. Although this is possible, it is generally quite expensive, requiring underwriting a new loan and the repurchase of the existing loan. The ease of entering a swap is its inherent advantage. This particular swap would be one that exchanged its fixed obligation for an agreement to pay a floating rate. Every year it would agree to pay a coupon based on whatever the prevailing interest rate was at the time in exchange for an agreement from a counterparty to pay the firm’s fixed coupon. A common reference point for floating-rate commitments is called LIBOR. LIBOR stands for the London Interbank Offered Rate, and it is the rate that most international banks charge one another for dollar-denominated loans in the London market. LIBOR is commonly used as the reference rate for a floating-rate commitment, and, depending on the creditworthiness of the borrower, the rate can vary from LIBOR to LIBOR plus one point or more over LIBOR. If we assume that our firm has a credit rating that requires it to pay LIBOR plus 50 basis points, then in a swap it would be exchanging its fixed 9 percent obligation for the obligation to pay whatever the prevailing LIBOR rate is plus 50 basis points. Table 25.8

Table 25.8

Fixed for Floating Swap: Cash Flows (in $ millions)

Coupons Year

1

2

3

4

5

6

7

8

9

10

A. Swap Fixed obligation

9

9

9

9

9

9

9

9

9

9

LIBOR floating B. Original loan

−8.5

−9.5

−10.5

−11.5

−7.5

−7.5

−7.5

−7.5

−7.5

−7.5

Fixed obligation Net effect

−9 −8.5

−9 −9.5

−9 10.5

−9 11.5

−9 7.5

−9 7.5

−9 7.5

−9 7.5

−9 7.5

109 −107.5

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displays how the cash flows on this swap would work. In the table, we have assumed that LIBOR starts at 8 percent and rises for three years to 11 percent and then drops to 7 percent. As the table shows, the firm would owe a coupon of 8.5% × $100 million = $8.5 million in year 1, $9.5 million in year 2, $10.5 million in year 3, and $11.5 million in year 4. The precipitous drop to 7 percent lowers the annual payments to $7.5 million thereafter. In return, the firm receives the fixed payment of $9 million each year. Actually, rather than swapping the full payments, the cash flows would be netted. Because the firm is paying variable and receiving fixed—which it uses to pay its lender—in the first year, for example, the firm owes $8.5 million and is owed by its counterparty, who is paying fixed, $9 million. Hence, net, the firm would receive a payment of $.5 million. Because the firm has to pay its lender $9 million but gets a net payment from the swap of $.5 million, it really pays out only the difference, or $8.5 million. In each year, then, the firm would effectively pay only LIBOR plus 50 basis points. Notice, too, that the entire transaction can be carried out without any need to change the terms of the original loan. In effect, by swapping, the firm has found a counterparty that is willing to pay its fixed obligation in return for the firm paying a floatingo bligation.

CurrencySw aps FX stands for foreign exchange, and currency swaps are sometimes called FX swaps. Currency swaps are swaps of obligations to pay cash flows in one currency for obligations to pay in another currency. Currency swaps arise as a natural vehicle for hedging risk in international trade. For example, suppose a U.S. firm sells a broad range of its product line in the German market. Every year the firm can count on receiving revenue from Germany in euros. We will study international finance later in this book, but for now we can just observe that because exchange rates fluctuate, this subjects the firm to considerable risk. If the firm produces its products in the United States and exports them to Germany, then the firm has to pay its workers and its suppliers in dollars. But it is receiving some of its revenues in euros. The exchange rate between dollars and euros changes over time. As the euro rises in value, the German revenues are worth more dollars, but as it falls they decline. Suppose the firm can count on selling 100 million euros of goods each year in Germany. If the exchange rate is 2 euros for each dollar, then the firm will receive $50 million. But if the exchange rate were to rise to 3 euros for each dollar, the firm would receive only $33.333 million for its 100 million euros. Naturally the firm would like to protect itself against these currency swings. To do so the firm can enter a currency swap. We will learn more about exactly what the terms of such a swap might be, but for now we can assume that the swap is for five years at a fixed term of 100 million euros for $50 million each year. Now, no matter what happens to the exchange rate between euros and dollars over the next five years, as long as the firm makes 100 million euros each year from the sale of its products, it will swap this for $50 million each year.

Credit Default Swap (CDS) A CDS is like insurance against value loss due to a firm defaulting on a bond. As in other swaps, a person involved in a CDS is called a counterparty. There are always

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two counterparties in a CDS. In a typical CDS, counterparty 1 pays counterparty 2 a periodic payment. In exchange, counterparty 2 agrees to pay par for a particular bond issue if default occurs. Counterparty 1 is called the protection buyer and counterparty 2 is called the protection seller. The periodic payment is called the CDS spread. For example, suppose the Mizuno Company wants to borrow $200 million from United Pacific Bank and is willing to pay a spread of 50 basis points (bps) over LIBOR. United Pacific Bank is interested but cannot justify such a large loan to one company and the attendant credit risks. United Pacific can agree to the loan and buy protection for a 40–basis-point CDS spread. Midland Insurance Company agrees to be the counterparty to United Pacific and, in case the Mizuno Company defaults, will pay the par amount. In exchange, Midland Insurance will receive $800,000 per year (40 bps × $200 million) for a specified term, say 5 years. In this simple example, the terms of the CDS are clear and precise. In practice, there is no organized exchange or template. Each counterparty will attempt to negotiate the best possible agreement. Swap Pricing We have not addressed the question of how the market sets prices for swaps—either interest rate swaps, credit default swaps, or currency swaps. In the fixedfor-floating example and in the currency swap, we just quoted some terms. We won’t go into great detail on exactly how it is done, but we can stress the most important points. Swaps, like forwards and futures, are essentially zero-sum transactions, which is to say that in both cases the market sets prices at a fair level, and neither party has any substantial bargain or loss at the moment the deal is struck. For example, in the currency swap, the swap rate is some average of the market expectation of what the exchange rate will be over the life of the swap. In the interest rate swap, the rates are set as the fair floating and fixed rates for the creditor, taking into account the creditworthiness of the counterparties. We can actually price swaps fairly once we know how to price forward contracts. In our interest rate swap example, the firm swapped LIBOR plus 50 basis points for a 9 percent fixed rate, all on a principal amount of $100 million. This is equivalent to a series of forward contracts extending over the life of the swap. In year 1, for example, having made the swap, the firm is in the same position that it would be if it had sold a forward contract entitling the buyer to receive LIBOR plus 50 basis points on $100 million in return for a fixed payment of $9 million (9 percent of $100 million). Similarly, the currency swap can also be viewed as a series of forward contracts. In a credit default swap, the swap rate is a market expectation of the default rate for a particular bond over a particular time.

Exotics Up to now we have dealt with the meat and potatoes of the derivatives markets: Swaps, options, forwards, and futures. Exotics are the complicated blends of these that often produce surprising results for buyers. One of the more interesting types of exotics is called an inverse floater. In our fixedfor-floating swap, the floating payments fluctuated with LIBOR. An inverse floater is one that fluctuates inversely with some rate such as LIBOR. For example, the floater might pay an interest rate of 20 percent minus LIBOR. If LIBOR is 9 percent, then the inverse pays 11 percent, and if LIBOR rises to 12 percent, the payments on the inverse would fall to 8 percent. Clearly, the purchaser of an inverse profits from the inverse if interest rates fall.

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Both floaters and inverse floaters have supercharged versions called superfloaters and superinverses that fluctuate more than one for one with movements in interest rates. As an example of a superinverse floater, consider a floater that pays an interest rate of 30 percent minus twice LIBOR. When LIBOR is 10 percent, the inverse pays: 30% − 2 × 10% = 30% − 20% = 10% And if LIBOR falls by 3 percent to 7 percent, then the return on the inverse rises by 6 percent from 10 percent to 16 percent: 30% − 2 × 7% = 30% − 14% =16% Sometimes derivatives are combined with options to bound the impact of interest rates. The most important of these instruments are called caps and floors. A cap is so named because it puts an upper limit or a cap on the impact of a rise in interest rates. A floor, conversely, provides a floor below which the interest rate impact is insulated. To illustrate the impact of these, consider a firm that is borrowing short term and is concerned that interest rates might rise. For example, using LIBOR as the reference interest rate, the firm might purchase a 7 percent cap. The cap pays the firm the difference between LIBOR and 7 percent on some principal amount, provided that LIBOR is greater than 7 percent. As long as LIBOR is below 7 percent, the holder of the cap receives no payments. By purchasing the cap, the firm has assured itself that even if interest rates rise above 7 percent, it will not have to pay more than a 7 percent rate. Suppose that interest rates rise to 9 percent. While the firm is borrowing short term and paying 9 percent rates, this is offset by the cap, which is paying the firm the difference between 9 percent and the 7 percent limit. For any LIBOR rate above 7 percent, the firm receives the difference between LIBOR and 7 percent, and, as a consequence, it has capped its cost of borrowing at 7 percent. On the other side, consider a financial firm that is in the business of lending short term and is concerned that interest rates—and consequently its revenues—might fall. The firm could purchase a floor to protect itself from such declines. If the limit on the floor is 7 percent, then the floor pays the difference between 7 percent and LIBOR whenever LIBOR is below 7 percent, and nothing if LIBOR is above 7 percent. Thus, if interest rates were to fall to, say, 5 percent while the firm is receiving only 5 percent from its lending activities, the floor is paying it the difference between 7 percent and 5 percent, or an additional 2 percent. By purchasing the floor, the firm has assured itself of receiving no less than 7 percent from the combination of the floor and its lending activities. We have only scratched the surface of what is available in the world of derivatives. Derivatives are designed to meet marketplace needs, and the only binding limitation is the human imagination. Nowhere should the buyer’s warning caveat emptor be taken more seriously than in the derivatives markets, and this is especially true for the exotics. If swaps are the meat and potatoes of the derivatives markets, then caps and floors are the meat and potatoes of the exotics. As we have seen, they have obvious value as hedging instruments. But much attention has been focused on truly exotic derivatives, some of which appear to have arisen more as the residuals that were left over from more straightforward deals. We won’t examine these in any detail, but suffice it to say that some of these are so volatile and unpredictable that market participants have dubbed them “toxic waste.”

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25.8 Actual Use of Derivatives Because derivatives do not usually appear in financial statements, it is much more difficult to observe the use of derivatives by firms compared to, say, bank debt. Much of our knowledge of corporate derivative use comes from academic surveys. Most surveys report that the use of derivatives appears to vary widely among large publicly traded firms. Large firms are far more likely to use derivatives than are small firms. Table 25.9 shows that for firms that use derivatives, foreign currency and interest rate derivatives are the most frequently used. The prevailing view is that derivatives can be very helpful in reducing the variability of firm cash flows, which, in turn, reduces the various costs associated with financial distress. Therefore, it is somewhat puzzling that large firms use derivatives more often than small firms because large firms tend to have less cash flow variability than small firms. Also, some surveys report that firms occasionally use derivatives when they want to speculate about future prices and not just to hedge risks. However, most of the evidence is consistent with the theory that derivatives are most frequently used by firms where financial distress costs are high and access to the capitalmar ketsisc onstrained.

Table 25.9

Companies That Use Derivatives

Derivative Usage: Survey Results

12/05 12/04

Overall

Under $1 billion

Over $1 billion

68% 74

53% 67

83% 83

Do You Use Derivatives to Manage . . .?

Short-term assets Long-term assets Short-term liabilities Long-term liabilities

Overall

Under $1 billion

Over $1 billion

55% 29 59 61

35% 17 54 67

68% 37 63 57

In Which Asset Classes Do You Use Derivatives? Overall

Interest rates Currencies Credit Energy Commodities Equities

Over $1 billion

2005

2004

2005

2004

70% 67 9 17 20 7

73% 54 7 10 11 12

77% 80 12 21 30 10

76% 68 13 11 13 16

SOURCE: Adapted from Treasury & Risk Management (December/January 2006). Results are based on a survey of 190 financial executives. In the sample, 30 percent of the companies had revenues under $500 million, 18 percent were between $500 million and $1 billion, 33 percent were between $1 billion and $5 billion, and 19 percent had revenues over $5 billion.

Options, Futures, and Corporate Finance

Part VI

Summary and Conclusions

1. Firms hedge to reduce risk. This chapter showed a number of hedging strategies. 2. A forward contract is an agreement by two parties to sell an item for cash at a later date. The price is set at the time the agreement is signed. However, cash changes hands on the date of delivery. Forward contracts are generally not traded on organized exchanges. 3. Futures contracts are also agreements for future delivery. They have certain advantages, such as liquidity, that forward contracts do not. An unusual feature of futures contracts is the mark-to-the-market convention. If the price of a futures contract falls on a particular day, every buyer of the contract must pay money to the clearinghouse. Every seller of the contract receives money from the clearinghouse. Everything is reversed if the price rises. The mark-to-the-market convention prevents defaults on futures contracts. 4. We divided hedges into two types: short hedges and long hedges. An individual or firm that sells a futures contract to reduce risk is instituting a short hedge. Short hedges are generally appropriate for holders of inventory. An individual or firm that buys a futures contract to reduce risk is instituting a long hedge. Long hedges are typically used by firms with contracts to sell finished goods at a fixed price. 5. An interest rate futures contract employs a bond as the deliverable instrument. Because of their popularity, we worked with Treasury bond futures contracts. We showed that Treasury bond futures contracts can be priced using the same type of net present value analysis that is used to price Treasury bonds themselves. 6. Many firms face interest rate risk. They can reduce this risk by hedging with interest rate futures contracts. As with other commodities, a short hedge involves the sale of a futures contract. Firms that are committed to buying mortgages or other bonds are likely to institute short hedges. A long hedge involves the purchase of a futures contract. Firms that have agreed to sell mortgages or other bonds at a fixed price are likely to institute long hedges. 7. Duration measures the average maturity of all the cash flows in a bond. Bonds with high duration have high price variability. Firms frequently try to match the duration of their assets with the duration of their liabilities. 8. Swaps are agreements to exchange cash flows over time. The first major type is an interest rate swap in which one pattern of coupon payments, say, fixed payments, is exchanged for another, say, coupons that float with LIBOR. The second major type is a currency swap, in which an agreement is struck to swap payments denominated in one currency for payments in another currency over time.

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Concept Questions

1. 2. 3.

4.

5.

Hedging Strategies If a firm is selling futures contracts on lumber as a hedging strategy, what must be true about the firm’s exposure to lumber prices? Hedging Strategies If a firm is buying call options on pork belly futures as a hedging strategy, what must be true about the firm’s exposure to pork belly prices? Forwards and Futures What is the difference between a forward contract and a futures contract? Why do you think that futures contracts are much more common? Are there any circumstances under which you might prefer to use forwards instead of futures? Explain. Hedging Commodities Bubbling Crude Corporation, a large Texas oil producer, would like to hedge against adverse movements in the price of oil because this is the firm’s primary source of revenue. What should the firm do? Provide at least two reasons why it probably will not be possible to achieve a completely flat risk profile with respect to oil prices. Sources of Risk A company produces an energy-intensive product and uses natural gas as the energy source. The competition primarily uses oil. Explain why this company is exposed to fluctuations in both oil and natural gas prices.

Chapter 25 Derivatives and Hedging Risk

6.

7. 8.

9.

10. 11. 12.

14.

15.

Hedging Commodities If a textile manufacturer wanted to hedge against adverse movements in cotton prices, it could buy cotton futures contracts or buy call options on cotton futures contracts. What would be the pros and cons of the two approaches? Option Explain why a put option on a bond is conceptually the same as a call option on interest rates. Hedging Interest Rates A company has a large bond issue maturing in one year. When it matures, the company will float a new issue. Current interest rates are attractive, and the company is concerned that rates next year will be higher. What are some hedging strategies that the company might use in this case? Swaps Explain why a swap is effectively a series of forward contracts. Suppose a firm enters a swap agreement with a swap dealer. Describe the nature of the default risk faced by both parties. Swaps Suppose a firm enters a fixed for floating interest rate swap with a swap dealer. Describe the cash flows that will occur as a result of the swap. Transaction versus Economic Exposure What is the difference between transactions and economic exposure? Which can be hedged more easily? Why? Hedging Exchange Rate Risk If a U.S. company exports its goods to Japan, how would it use a futures contract on Japanese yen to hedge its exchange rate risk? Would it buy or sell yen futures? Does the way the exchange rate is quoted in the futures contractma tter? Hedging Strategies For the following scenarios, describe a hedging strategy using futures contracts that might be considered. If you think that a cross-hedge would be appropriate, discuss the reasons for your choice of contract. a. A public utility is concerned about rising costs. b. A candy manufacturer is concerned about rising costs. c. A corn farmer fears that this year’s harvest will be at record high levels across the country. d. A manufacturer of photographic film is concerned about rising costs. e. A natural gas producer believes there will be excess supply in the market this year. f. A bank derives all its income from long-term, fixed-rate residential mortgages. g. A stock mutual fund invests in large, blue-chip stocks and is concerned about a decline in the stock market. h. A U.S. importer of Swiss army knives will pay for its order in six months in Swiss francs. i. A U.S. exporter of construction equipment has agreed to sell some cranes to a German construction firm. The U.S. firm will be paid in euros in three months. Swaps In May 2004, Sysco Corporation, the distributor of food and foodrelated products (not to be confused with Cisco Systems), announced it had signed an interest rate swap. The interest rate swap effectively converted the company’s $100 million, 4.6 percent interest rate bonds for a variable rate payment, which would be the six-month LIBOR minus .52 percent. Why would Sysco use a swap agreement? In other words, why didn’t Sysco just go ahead and issue floating-rate bonds because the net effect of issuing fixed-rate bonds and then doing a swap is to create a variable rate bond? Hedging Strategies William Santiago is interested in entering the import/export business. During a recent visit with his financial advisers, he said, “If we play the game right, this is the safest business in the world. By hedging all of our transactions in the foreign exchange futures market, we can eliminate all of our risk.” Do you agree with Mr. Santiago’s assessment of hedging? Why or why not?

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791

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Questions and Problems

Part VI

16.

Hedging Strategies Kevin Nomura is a Japanese student who is planning a oneyear stay in the United States. He expects to arrive in the United States in eight months. He is worried about depreciation of the yen relative to the dollar over the next eight months and wishes to take a position in foreign exchange futures to hedge this risk. What should Mr. Nomura’s hedging position be? Assume the exchange rate between Japanese and U.S. currencies is quoted as yen/dollar.

1.

Futures Quotes Refer to Table 25.2 in the text to answer this question. Suppose you purchase a May 2009 cocoa futures contract on February 12, 2009, at the last price of the day. What will your profit or loss be if cocoa prices turn out to be $2,431 per metric ton at expiration? Futures Quotes Refer to Table 25.2 in the text to answer this question. Suppose you sell five March 2009 silver futures contracts on February 12, 2009, at the last price of the day. What will your profit or loss be if silver prices turn out to be $13.97 per ounce at expiration? What if silver prices are $12.63 per ounce at expiration? Put and Call Payoffs Suppose a financial manager buys call options on 50,000 barrels of oil with an exercise price of $35 per barrel. She simultaneously sells a put option on 50,000 barrels of oil with the same exercise price of $35 per barrel. Consider her gains and losses if oil prices are $30, $32, $35, $38, and $40. What do you notice about the payoff profile? Marking to Market You are long 10 gold futures contracts, established at an initial settle price of $951 per ounce, where each contract represents 100 ounces. Over the subsequent four trading days, gold settles at $943, $946, $953, and $957, respectively. Compute the cash flows at the end of each trading day, and compute your total profit or loss at the end of the trading period. Marking to Market You are short 25 gasoline futures contracts, established at an initial settle price of $1.41 per gallon, where each contract represents 42,000 gallons. Over the subsequent four trading days, gasoline settles at $1.37, $1.42, $1.45, and $1.51, respectively. Compute the cash flows at the end of each trading day, and compute your total profit or loss at the end of the trading period. Duration What is the duration of a bond with three years to maturity and a coupon of 8 percent paid annually if the bond sells at par? Duration What is the duration of a bond with four years to maturity and a coupon of 8 percent paid annually if the bond sells at par? Duration Blue Steel Community Bank has the following market value balance sheet:

2. BASIC (Questions 1−8)

3.

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Options, Futures, and Corporate Finance

4.

5.

6. 7. 8.

Asset or Liability Federal funds deposits Accounts receivable Short-term loans Long-term loans Mortgages Checking and savings deposits Certificates of deposit Long-term financing Equity

Market Value (in $ millions)

Duration (in years)

$ 31 630 390 98 346 585 310 305 295

0 .20 .65 5.25 12.85 0 1.60 9.80 N/A

Chapter 25 Derivatives and Hedging Risk

INTERMEDIATE (Questions9–1 5)

9.

10.

12.

13.

14.

a. What is the duration of the assets? b. What is the duration of the liabilities? c. Ist heb ankimm unet oin terestr ater isk? Hedging with Futures Refer to Table 25.2 in the text to answer this question. Suppose today is February 12, 2009, and your firm produces breakfast cereal and needs 140,000 bushels of corn in May 2009 for an upcoming promotion. You would like to lock in your costs today because you are concerned that corn prices might go up between now and May. a. How could you use corn futures contracts to hedge your risk exposure? What price would you effectively be locking in based on the closing price of the day? b. Suppose corn prices are $3.92 per bushel in May. What is the profit or loss on your futures position? Explain how your futures position has eliminated your exposure to price risk in the corn market. Interest Rate Swaps ABC Company and XYZ Company need to raise funds to pay for capital improvements at their manufacturing plants. ABC Company is a well-established firm with an excellent credit rating in the debt market; it can borrow funds either at 11 percent fixed rate or at LIBOR + 1 percent floating rate. XYZ Company is a fledgling start-up firm without a strong credit history. It can borrow funds either at 10 percent fixed rate or at LIBOR + 3 percent floating rate. a. Is there an opportunity here for ABC and XYZ to benefit by means of an interest rate swap? b. Suppose you’ve just been hired at a bank that acts as a dealer in the swaps market, and your boss has shown you the borrowing rate information for your clients, ABC and XYZ. Describe how you could bring these two companies together in an interest rate swap that would make both firms better off while netting your banka2.0p ercentp rofit. Duration Ted and Alice Hansel have a son who will begin college seven years from today. School expenses of $30,000 will need to be paid at the beginning of each of the four years that their son plans to attend college. What is the duration of this liability to the couple if they can borrow and lend at the market interest rate of 9 percent? Duration What is the duration of a bond with two years to maturity if the bond has a coupon rate of 6 percent paid semiannually, and the market interest rate is 9p ercent? Forward Pricing The forward price (F) of a contract on an asset with neither carrying costs nor convenience yield is the current spot price of the asset (S0) multiplied by 1, plus the appropriate interest rate between the initiation of the contract and the delivery date of the asset. Derive this relationship by comparing the cash flows that result from the following two strategies: Strategy 1: Buy silver on the spot market today and hold it for one year. (Hint:Do not use any of your own money to purchase the silver.) Strategy 2: Take a long position in a silver forward contract for delivery in one year. Assume that silver is an asset with neither carrying costs nor convenienceyie ld. Forward Pricing You enter into a forward contract to buy a 10-year, zero coupon bond that will be issued in one year. The face value of the bond is $1,000, and the 1-year and 11-year spot interest rates are 6 percent and 9 percent, respectively. a. What is the forward price of your contract? b. Suppose both the 1-year and 11-year spot rates unexpectedly shift downward by 2 percent. What is the new price of the forward contract?

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15.

Mini Case

CHALLENGE (Question 16)

16.

Options, Futures, and Corporate Finance

Forward Pricing This morning you agreed to buy a one-year Treasury bond in six months. The bond has a face value of $1,000. Use the spot interest rates listed here to answer the following questions: Time

EAR

6 months 12 months 18 months 24 months

3.61% 4.05% 4.73% 5.42%

a. What is the forward price of this contract? b. Suppose shortly after you purchased the forward contract all rates increased by 30 basis points. For example, the six-month rate increased from 3.61 percent to 3.91 percent. What is the price of a forward contract otherwise identical to yours givent hesec hanges? Financial Engineering Suppose there were call options and forward contracts available on coal, but no put options. Show how a financial engineer could synthesize a put option using the available contracts. What does your answer tell you about the general relationship between puts, calls, and forwards?

WILLIAMSON MORTGAGE, INC. Jennifer Williamson recently received her MBA and has decided to enter the mortgage brokerage business. Rather than work for someone else, she has decided to open her own shop. Her cousin Jerry has approached her about a mortgage for a house he is building. The house will be completed in three months, and he will need the mortgage at that time. Jerry wants a 25-year, fixed-rate mortgage in the amount of $500,000 with monthly payments. Jennifer has agreed to lend Jerry the money in three months at the current market rate of 6.5 percent. Because Jennifer is just starting out, she does not have $500,000 available for the loan, so she approaches Max Cabell, the president of MC Insurance Corporation, about purchasing the mortgage from her in three months. Max has agreed to purchase the mortgage in three months, but he is unwilling to set a price on the mortgage. Instead, he has agreed in writing to purchase the mortgage at the market rate in three months. There are Treasury bond futures contracts available for delivery in three months. A Treasury bond contract is for $100,000 in face value of Treasury bonds. 1. 2. 3. 4.

What is the monthly mortgage payment on Jerry’s mortgage? What is the most significant risk Jennifer faces in this deal? How can Jennifer hedge this risk? Suppose that in the next three months the market rate of interest rises to 7.4 percent. a. How much will Max be willing to pay for the mortgage? b. What will happen to the value of Treasury bond futures contracts? Will the long or shortp ositionin creasein v alue? 5. Suppose that in the next three months the market rate of interest falls to 5.8 percent. a. How much will Max be willing to pay for the mortgage? b. What will happen to the value of Treasury bond futures contracts? Will the long or shortp ositionin creasein v alue? 6. Are there any possible risks Jennifer faces in using Treasury bond futures contracts to hedgeh erin terestr ater isk?

PART VII

CHAPTER 26

Short-Term Finance and Planning With gasoline prices passing $4 per gallon in mid-2008, sales of hybrid automobiles really began to pick up. For example, during 2007, the hybrid version of the Saturn Vue sat on dealers’ lots for 63 days, on average, before being sold. By summer 2008, this period had fallen to 17 days. Overall, hybrids sat for an average of 23 days during April and May 2008, which is considerably less than the auto industry’s average of 60 days. And the Saturn Vue wasn’t the fastest-moving car. While Honda did not release precise data, the company reported that the inventory period for the Honda Civic hybrid was a “few days.” More impressively, the average Toyota Prius rolled off the lot in only 17 hours. Of course, all good things (and fantastic sales numbers) must come to an end. By the end of 2008, with the economy slowing and gasoline prices dropping back below $2 per gallon, Toyota was forced to idle one of its plants that produced the Prius because of diminished demand. As this chapter explores, the length of time goods are carried in inventory until they are sold is an important element of short-term financial management, and industries such as the automobile industry pay close attention to it.

Interested in a career in short-term finance? Visit the Association for Financial Professionals (AFP) Web site at www.afponline.org.

To this point, we have described many of the decisions of long-term finance, such as those of capital budgeting, dividend policy, and financial structure. In this chapter, we begin to discuss short-term finance. Short-term finance is primarily concerned with the analysis of decisions that affect current assets and current liabilities. Frequently, the term net working capital is associated with short-term financial decision making. As we have described in previous chapters, net working capital is the difference between current assets and current liabilities. Often, short-term financial management is called working capital management. These terms mean the same thing. There is no universally accepted definition of short-term finance. The most important difference between short-term and long-term finance is in the timing of cash flows. Short-term financial decisions typically involve cash inflows and outflows that occur within a year. For example, short-term financial decisions are involved when a firm orders raw materials, pays in cash, and anticipates selling finished goods in one year for cash. In contrast, long-term financial decisions are involved when a firm purchases a special machine that will reduce operating costs over, say, the next five years. What types of questions fall under the general heading of short-term finance? To name a few: 1. What is a reasonable level of cash to keep on hand (in a bank) to pay bills? 2. How much should the firm borrow in the short term? 3. How much credit should be extended to customers? 795

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Short-Term Finance

This chapter introduces the basic elements of short-term financial decisions. First, we discuss the short-term operating activities of the firm. We then identify some alternative short-term financial policies. Finally, we outline the basic elements in a shortterm financial plan and describe short-term financing instruments.

26.1 Tracing Cash and Net Working Capital In this section, we examine the components of cash and net working capital as they change from one year to the next. We have already discussed various aspects of this subject in Chapters 2 and 3. We briefly review some of that discussion as it relates to short-term financing decisions. Our goal is to describe the short-term operating activities of the firm and their impact on cash and net working capital. To begin, recall that current assets are cash and other assets that are expected to convert to cash within the year. Current assets are presented on the balance sheet in order of their accounting liquidity—the ease with which they can be converted to cash and the time it takes to convert them. Four of the most important items found in the current asset section of a balance sheet are cash and cash equivalents, marketable securities, accounts receivable, and inventories. Analogous to their investment in current assets, firms use several kinds of shortterm debt called current liabilities. Current liabilities are obligations that are expected to require cash payment within one year (or within the operating period if it is longer than one year). Three major items found as current liabilities are accounts payable, expenses payable (including accrued wages and taxes), and notes payable. Because we want to focus on changes in cash, we start off by defining cash in terms of the other elements of the balance sheet. This lets us isolate the cash account and explore the impact on cash from the firm’s operating and financing decisions. The basic balance sheet identity can be written as: Netw orkingc apital + Fixed assets = Long-term debt +E quity

(26.1)

Net working capital is cash plus other current assets, less current liabilities; that is: Netw orkingc apital = (Cash + Other current assets) −Cu rrentlia bilities

(26.2)

If we substitute this for net working capital in the basic balance sheet identity and rearrange things a bit, we see that cash is: Cash = Long-term debt + Equity + Current liabilities − Current assets other than cash −F ixedasse ts

(26.3)

This tells us in general terms that some activities naturally increase cash and some activities decrease it. We can list these various activities, along with an example of each, as follows: ActivitiesT hatIn creaseC ash Increasing long-term debt (borrowing over the long term) Increasing equity (selling some stock) Increasing current liabilities (getting a 90-day loan) Decreasing current assets other than cash (selling some inventory for cash) Decreasingfix edasse ts(se llings omep roperty)

Chapter 26

Short-Term Finance and Planning

797

Activities That Decrease Cash Decreasing long-term debt (paying off a long-term debt) Decreasing equity (repurchasing some stock) Decreasing current liabilities (paying off a 90-day loan) Increasing current assets other than cash (buying some inventory for cash) Increasing fixed assets (buying some property) Notice that our two lists are exact opposites. For example, floating a long-term bond issue increases cash (at least until the money is spent). Paying off a long-term bond issue decreases cash. Activities that increase cash are called sources of cash. Those activities that decrease cash are called uses of cash. Looking back at our list, we see that sources of cash always involve increasing a liability (or equity) account or decreasing an asset account. This makes sense because increasing a liability means that we have raised money by borrowing it or by selling an ownership interest in the firm. A decrease in an asset means that we have sold or otherwise liquidated an asset. In either case there is a cash inflow. Uses of cash are just the reverse. A use of cash involves decreasing a liability by paying it off, perhaps, or increasing assets by purchasing something. Both of these activities require that the firm spend some cash.

EXAMPLE 26.1

Sources and Uses Here is a quick check of your understanding of sources and uses: If accounts payable go up by $100, does this indicate a source or a use? What if accounts receivable go up by $100? Accounts payable are what we owe our suppliers.This is a short-term debt. If it rises by $100, we have effectively borrowed the money, which is a source of cash. Receivables are what our customers owe to us, so an increase of $100 in accounts receivable means that we have loaned the money; this is a useo fc ash.

26.2 The Operating Cycle and the Cash Cycle The primary concern in short-term finance is the firm’s short-run operating and financing activities. For a typical manufacturing firm, these short-run activities might consist of the following sequence of events and decisions: Event 1. 2. 3. 4.

Buying raw materials Paying cash Manufacturing the product Selling the product

5. Collecting cash

Decision 1. How much inventory to order 2. Whether to borrow or draw down cash balances 3. What choice of production technology to use 4. Whether credit should be extended to a particular customer 5. How to collect

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Short-Term Finance

These activities create patterns of cash inflows and cash outflows. These cash flows are both unsynchronized and uncertain. They are unsynchronized because, for example, the payment of cash for raw materials does not happen at the same time as the receipt of cash from selling the product. They are uncertain because future sales and costs cannot be precisely predicted.

Defining the Operating and Cash Cycles We can start with a simple case. One day, call it Day 0, we purchase $1,000 worth of inventory on credit. We pay the bill 30 days later, and, after 30 more days, someone buys the $1,000 in inventory for $1,400. Our buyer does not actually pay for another 45 days. We can summarize these events chronologically as follows: Day

Activity

0 30 60 105

Acquire inventory Pay for inventory Sell inventory on credit Collect on sale

Cash Effect None −$1,000 None +$1,400

The Operating Cycle There are several things to notice in our example. First, the entire cycle, from the time we acquire some inventory to the time we collect the cash, takes 105 days. This is called the operatingc ycle. As we illustrate, the operating cycle is the length of time it takes to acquire inventory, sell it, and collect for it. This cycle has two distinct components. The first part is the time it takes to acquire and sell the inventory. This period, a 60-day span in our example, is called the inventory period. The second part is the time it takes to collect on the sale, 45 days in our example. This is called the accounts receivable period. Based on our definitions, the operating cycle is obviously just the sum of the inventory and accounts receivable periods: Operatingc ycle = Inventory period + Accounts receivable period 105 days = 60 days + 45 days

(26.4)

What the operating cycle describes is how a product moves through the current asset accounts. The product begins life as inventory, it is converted to a receivable when it is sold, and it is finally converted to cash when we collect from the sale. Notice that, at each step, the asset is moving closer to cash. The Cash Cycle The second thing to notice is that the cash flows and other events that occur are not synchronized. For example, we don’t actually pay for the inventory until 30 days after we acquire it. The intervening 30-day period is called the accounts payable period. Next, we spend cash on Day 30, but we don’t collect until Day 105. Somehow, we have to arrange to finance the $1,000 for 105 − 30 = 75 days. This period is called the cashc ycle. The cash cycle, therefore, is the number of days that pass before we collect the cash from a sale, measured from when we actually pay for the inventory. Notice that, based

Chapter 26

Figure 26.1 CashFlo w Time Line and the ShortTerm Operating Activities of a Typical ManufacturingF irm

Short-Term Finance and Planning

Inventory purchased

799

Inventory sold

Accounts receivable period

Inventory period

Time Accounts payable period

Cash cycle

Cash paid for inventory

Cash received

Operating cycle The operating cycle is the time period from inventory purchase until the receipt of cash. (The operating cycle may not include the time from placement of the order until arrival of the stock.) The cash cycle is the time period from when cash is paid out to when cash is received.

on our definitions, the cash cycle is the difference between the operating cycle and the accounts payable period: Cashc ycle = Operating cycle − Accounts payable period 75 days = 105 days − 30 days

Learn more about outsourcing accounts management at www.businessdebts .com. and www.opiglobal.com.

(26.5)

Figure 26.1 depicts the short-term operating activities and cash flows of a typical manufacturing firm by way of a cash flow time line. As shown, the cash flow time line presents the operating cycle and the cash cycle in graphical form. In Figure 26.1, the need for short-term financial management is suggested by the gap between the cash inflows and the cash outflows. This is related to the lengths of the operating cycle and the accounts payable period. The gap between short-term inflows and outflows can be filled either by borrowing or by holding a liquidity reserve in the form of cash or marketable securities. Alternatively, the gap can be shortened by changing the inventory, receivable, and payable periods. These are all managerial options that we discuss in the following sections. Internet-based bookseller and retailer Amazon.com provides an interesting example of the importance of managing the cash cycle. In January 2008, the market value of Amazon.com was higher than (in fact, more than 17 times as much as) that of Barnes & Noble, king of the brick-and-mortar bookstores, even though Barnes & Noble’s sales were greater than Amazon’s. How could Amazon.com be worth so much more? There are multiple reasons, but short-term management is one factor. During 2007, Amazon turned over its inventory about 10 times per year, 4 times faster than Barnes & Noble, so its inventory period is dramatically shorter. Even more striking, Amazon charges a customer’s credit card when it ships a book, and it usually gets paid by the credit card firm within a day. This means Amazon has a negative cash cycle! In fact, during 2007, Amazon’s cash cycle was negative by almost 40 days. Every sale, therefore, generates a cash inflow that can be put to work immediately.

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Table 26.1 Managers Who Deal with Short-Term Financial Problems

Duties Related to Short-Term Financial Management

Assets/Liabilities Influenced

Collection, concentration, disbursement; short-term investments; short-term borrowing; banking relations Monitoring and control of accounts receivable; credit policy decisions Credit policy decisions Decisions on purchases, suppliers; may negotiate payment terms Setting of production schedules and materials requirements Decisions on payment policies and on whether to take discounts Accounting information on cash flows; reconciliation of accounts payable; application of payments to accounts receivable

Cash, marketable securities, short-term loans Accounts receivable

Title of Manager Cash manager

Credit manager Marketing manager Purchasing manager Production manager Payables manager Controller

Accounts receivable Inventory, accounts payable Inventory, accounts payable Accounts payable Accounts receivable, accounts payable

The Operating Cycle and the Firm’s Organization Chart Before we examine the operating and cash cycles in greater detail, it is useful for us to take a look at the people involved in managing a firm’s current assets and liabilities. As Table 26.1 illustrates, short-term financial management in a large corporation involves a number of different financial and nonfinancial managers. Examining Table 26.1, we see that selling on credit involves at least three different entities: The credit manager, the marketing manager, and the controller. Of these three, only two are responsible to the vice president of finance (the marketing function is usually associated with the vice president of marketing). Thus, there is the potential for conflict, particularly if different managers concentrate on only part of the picture. For example, if marketing is trying to land a new account, it may seek more liberal credit terms as an inducement. However, this may increase the firm’s investment in receivables or its exposure to baddebt risk, and conflict can result.

Calculating the Operating and Cash Cycles In our example, the lengths of time that made up the different periods were obvious. If all we have is financial statement information, we will have to do a little more work. We illustrate these calculations next. To begin, we need to determine various things such as how long it takes, on average, to sell inventory and how long it takes, on average, to collect receivables. We start by gathering some balance sheet information such as the following (in thousands): Item

Beginning

Ending

Average

Inventory Accounts receivable Accounts payable

$2,000 1,600 750

$3,000 2,000 1,000

$2,500 1,800 875

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Short-Term Finance and Planning

801

Also, from the most recent income statement, we might have the following figures (in thousands): Net sales Cost of goods sold

$11,500 8,200

We now need to calculate some financial ratios. We discussed these in some detail in Chapter 3; here, we just define them and use them as needed. The Operating Cycle First of all, we need the inventory period. We spent $8.2 million on inventory (our cost of goods sold). Our average inventory was $2.5 million. We thus turned our inventory over $8.2/2.5 times during the year:1 Cost of goods sold Inventorytu rnover = _________________ Average inventory $8.2 million = ___________ = 3.28 times 2.5 million Loosely speaking, this tells us that we bought and sold off our inventory 3.28 times during the year. This means that, on average, we held our inventory for: 365 days Inventoryp eriod = _________________ Inventory turnover 365 = _____ = 111.3 days 3.28 So, the inventory period is about 111 days. On average, in other words, inventory sat for about 111 days before it was sold.2 Similarly, receivables averaged $1.8 million, and sales were $11.5 million. Assuming that all sales were credit sales, the receivables turnover is:3 Credit sales Receivables turnover = ________________________ Average accounts receivable $11.5 million = _____________ = 6.4 times 1.8 million If we turn over our receivables 6.4 times a year, then the receivables period is: 365 days Receivablesp eriod = __________________ Receivables turnover 365 = ____ = 57 days 6.4 The receivables period is also called the days’ sales in receivables, or the average collection period. Whatever it is called, it tells us that our customers took an average of 57 days to pay.

1

Notice that in calculating inventory turnover here, we use the average inventory instead of using the ending inventory as we did in Chapter 3. Both approaches are used in the real world. To gain some practice using average figures, we will stick with this approach in calculating various ratios throughout this chapter.

2

This measure is conceptually identical to the days’ sales in inventory figure we discussed in Chapter 3. If less than 100 percent of our sales were credit sales, then we would just need a little more information, namely, credit sales for the year. See Chapter 3 for more discussion of this measure.

3

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The operating cycle is the sum of the inventory and receivables periods: Operatingc ycle = Inventory period + Accounts receivable period = 111 days + 57 days = 168 days This tells us that, on average, 168 days elapse between the time we acquire inventory and, having sold it, collect for the sale. The Cash Cycle We now need the payables period. From the information given earlier, we know that average payables were $875,000 and cost of goods sold was $8.2 million. Our payables turnover is: Cost of goods sold Payablest urnover = _________________ Average payables $8.2 million ___________ = = 9.4 times .875 million The payables period is: 365 days Payablesp eriod = ________________ Payables turnover 365 = ____ = 39 days 9.4 Thus, we took an average of 39 days to pay our bills. Finally, the cash cycle is the difference between the operating cycle and the payables period: Cashc ycle = Operating cycle − Accounts payable period = 168 days − 39 days = 129 days So, on average, there is a 129-day delay between the time we pay for merchandise and the time we collect on the sale.

EXAMPLE26.2 The Operating and Cash Cycles Company:

You have collected the following information for the Slowpay

Item Inventory Accounts receivable Accounts payable

Beginning

Ending

$5,000 1,600 2,700

$7,000 2,400 4,800

Credit sales for the year just ended were $50,000, and cost of goods sold was $30,000. How long does it take Slowpay to collect on its receivables? How long does merchandise stay around before it is sold? How long does Slowpay take to pay its bills? We can first calculate the three turnover ratios: Inventory turnover = $30,000 6,000 = 5 times Receivables turnover = $50,000 2,000 = 25 times Payables turnover = $30,000 3,750 = 8 times

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We use these to get the various periods: Inventory period = 365 5 = 73 days Receivables period = 365 25 = 14.6 days Payables period = 365 8 = 45.6 days All told, Slowpay collects on a sale in 14.6 days, inventory sits around for 73 days, and bills get paid after about 46 days. The operating cycle here is the sum of the inventory and receivables periods: 73 + 14.6 = 87.6 days. The cash cycle is the difference between the operating cycle and the payables period: 87.6 − 45.6 = 42 days.

Interpreting the Cash Cycle Our examples show that the cash cycle depends on the inventory, receivables, and payables periods. The cash cycle increases as the inventory and receivables periods get longer. It decreases if the company is able to defer payment of payables and thereby lengthen the payables period. Unlike Amazon.com, most firms have a positive cash cycle, and they thus require financing for inventories and receivables. The longer the cash cycle, the more financing is required. Also, changes in the firm’s cash cycle are often monitored as an earlywarning measure. A lengthening cycle can indicate that the firm is having trouble moving inventory or collecting on its receivables. Such problems can be masked, at least partially, by an increased payables cycle, so both cycles should be monitored. The link between the firm’s cash cycle and its profitability can be easily seen by recalling that one of the basic determinants of profitability and growth for a firm is its total asset turnover, which is defined as Sales/Total assets. In Chapter 3, we saw that the higher this ratio is, the greater are the firm’s accounting return on assets, ROA, and return on equity, ROE. Thus, all other things being the same, the shorter the cash cycle is, the lower is the firm’s investment in inventories and receivables. As a result, the firm’s total assets are lower, and total turnover is higher.

A Look at Operating and Cash Cycles In 2007, CFO magazine published its survey of working capital for various industries. The results of this survey highlight the marked differences in cash and operating cycles across industries. The table below shows four different industries and the median operating and cash cycles for each. Of these, the restaurant industry has the lowest operating and cash cycles. Looking at the components, it is surprising that the receivables period is as long as 10 days for the restaurant industry (most customers either pay in cash or use debit/credit cards). For example, the receivables period for McDonald’s is one of the longest in the industry at 14 days. Restaurants also have a short inventory period (we are happy to see this since we don’t like spoiled food).

Electric utilities Healthcare equipment Paper products Restaurants

Receivables Period (days)

Inventory Period (days)

Operating Cycle (days)

Payables Period (days)

Cash Cycle (days)

41 73 38 10

18 46 39 5

59 119 77 15

31 17 26 14

28 102 51 1

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Compared to the restaurant business, the healthcare equipment industry has a much longer operating cycle. Its long receivables period is the major cause. However, this does not necessarily mean the healthcare equipment industry is less efficient. Most, if not all, of the receivables in this industry are paid by medical insurance companies and government medical insurance such as Medicare, and these entities have relatively long payables periods. We’ve seen that operating and cash cycles can vary quite a bit across industries, but these cycles also can be different for companies within the same industry. Below you will find the operating and cash cycles for selected computer companies. As you can see, there are differences. Apple and Dell have the best operating and cash cycles in the industry. In fact, Dell has long been known as the worldwide leader in current asset management. Hewlett-Packard’s inventory period stands out as being dramatically different from its peers.

Apple Dell Gateway Hewlett-Packard

Receivables Period (days)

Inventory Period (days)

Operating Cycle (days)

Payables Period (days)

Cash Cycle (days)

24 36 48 43

5 4 9 29

29 39 57 72

64 65 56 48

−35 −26 1 24

By examining all parts of the cash and conversion cycles, you can see where a company is performing well, or poorly, as the case may be. Looking at the operating cycles for Gateway and Hewlett-Packard, the two companies appear fairly similar. However, Hewlett-Packard has a longer inventory period and Gateway has a longer payables period. When you look at the operating and cash cycles, consider that each is really a financial ratio. As with any financial ratio, firm and industry characteristics will have an effect, so take care in the interpretation. For example, in looking at Hewlett-Packard, we note its seemingly long inventory period. Is that a bad thing? Maybe not. HP’s business model is different from that of the other companies in this industry. By relying more on retail store sales, HP needs to keep a larger supply of inventory than Apple and Dell. Of course, such operations result in increased inventories, but, properly managed, this can be a good thing.

26.3 Some Aspects of Short-Term FinancialP olicy The policy that a firm adopts for short-term finance will be composed of at least two elements: 1. The size of the firm’s investment in current assets: This is usually measured relative to the firm’s level of total operating revenues. A flexible or accommodative short-term financial policy would maintain a high ratio of current assets to sales.

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A restrictive short-term financial policy would entail a low ratio of current assets tosale s. 2. The financing of current assets: This is measured as the proportion of short-term debt to long-term debt. A restrictive short-term financial policy means a high proportion of short-term debt relative to long-term financing, and a flexible policy means less short-term debt and more long-term debt.

The Size of the Firm’s Investment in Current Assets Flexible short-term financial policies include: 1. Keeping large balances of cash and marketable securities. 2. Making large investments in inventory. 3. Granting liberal credit terms, which results in a high level of accounts receivable. Restrictive short-term financial policies are: 1. Keeping low cash balances and no investment in marketable securities. 2. Making small investments in inventory. 3. Allowing no credit sales and no accounts receivable. Determining the optimal investment level in short-term assets requires an identification of the different costs of alternative short-term financing policies. The objective is to trade off the costs of restrictive policies against those of the flexible ones to arrive at the best compromise. Current asset holdings are highest with a flexible short-term financial policy and lowest with a restrictive policy. Thus, flexible short-term financial policies are costly in that they require higher cash outflows to finance cash and marketable securities, inventory, and accounts receivable. However, future cash inflows are highest with a flexible policy. Sales are stimulated by the use of a credit policy that provides liberal financing to customers. A large amount of inventory on hand (“on the shelf ”) provides a quick delivery service to customers and increases in sales.4 In addition, the firm can probably charge higher prices for the quick delivery service and the liberal credit terms of flexible policies. A flexible policy also may result in fewer production stoppagesb ecauseo f in ventorysh ortages.5 Managing current assets can be thought of as involving a trade-off between costs that rise with the level of investment and costs that fall with the level of investment. Costs that rise with the level of investment in current assets are called carrying costs. Costs that fall with increases in the level of investment in current assets are called shortage costs. Carrying costs are generally of two types. First, because the rate of return on current assets is low compared to that of other assets, there is an opportunity cost. Second, there is the cost of maintaining the economic value of the item. For example, the cost of warehousing inventory belongs here.

4 5

This is true of some types of finished goods. This is true of inventory of raw materials but not of finished goods.

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Determinants of Corporate Liquid Asset Holdings Firms with High Holdings of Liquid Assets Will Have

Firms with Low Holdings of Liquid Assets Will Have

High-growth opportunities High-risk investments Small firms Low-credit firms

Low-growth opportunities Low-risk investments Large firms High-credit firms

Firms will hold more liquid assets (i.e., cash and marketable securities) to ensure that they can continue investing when cash flow is low relative to positive NPV investment opportunities. Firms that have good access to capital markets will hold less liquid assets. SOURCE: Tim Opler, Lee Pinkowitz, René Stulz, and Rohan Williamson, “The Determinants and Implications of Corporate Cash Holdings,” Journal of Financial Economics 52 (1999).

Shortage costs are incurred when the investment in current assets is low. If a firm runs out of cash, it will be forced to sell marketable securities. If a firm runs out of cash and cannot readily sell marketable securities, it may need to borrow or default on an obligation. (This general situation is called cash-out.) If a firm has no inventory (a stockout) or if it cannot extend credit to its customers, it will lose customers. There are two kinds of shortage costs: 1. Trading, or order, costs: Order costs are the costs of placing an order for more cash (brokerage costs) or more inventory (production setup costs). 2. Costs related to safety reserves: These are the costs of lost sales, lost customer goodwill, and disruption of production schedules. Figure 26.2 illustrates the basic nature of carrying costs. The total costs of investing in current assets are determined by adding the carrying costs and the shortage costs. The minimum point on the total cost curve (CA*) reflects the optimal balance of current assets. The curve is generally quite flat at the optimum, and it is difficult, if not impossible, to find the precise optimal balance of shortage and carrying costs. Usually, we are content with a choice near the optimum. If carrying costs are low or shortage costs are high, the optimal policy calls for substantial current assets. In other words, the optimal policy is a flexible one. This is illustrated in the middle graph of Figure 26.2. If carrying costs are high or shortage costs are low, the optimal policy is a restrictive one. That is, the optimal policy calls for modest current assets. This is illustrated in the bottom graph of the figure. Opler, Pinkowitz, Stulz, and Williamson examine the determinants of holdings of cash and marketable securities by publicly traded firms.6 They find evidence that firms behave according to the static trade-off model described earlier. Their study focuses only on liquid assets (i.e., cash and marketable securities), so that carrying costs are the opportunity costs of holding liquid assets and shortage costs are the risks of not having cash when investment opportunities are good. 6

Tim Opler, Lee Pinkowitz, René Stulz, and Rohan Williamson, “The Determinants and Implications of Corporate Cash Holdings,” Journal of Financial Economics 52 (1999).

Chapter 26

Figure 26.2 Carrying Costs and ShortageC osts

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Dollars Total cost of holding current assets

Minimum point

Carrying costs

Shortage costs Amount of current assets (CA) CA* The optimal amount of current assets. This point minimizes costs. Flexible policy Dollars

Minimum point Total cost

Carrying costs Shortage costs Amount of current assets (CA) CA* Restrictive policy Dollars Minimum point Carrying costs Total cost

Shortage costs Amount of current assets (CA) CA*

Carrying costs increase with the level of investment in current assets. They include both opportunity costs and the costs of maintaining the asset’s economic value. Shortage costs decrease with increases in the level of investment in current assets. They include trading costs and the costs of running out of the current asset (for example, being short on cash).

808

Figure26 .3 Financing Policy for an Ideal Economy

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Dollars Current assets = Short-term debt

Long-term debt plus common stock

Fixed assets

Time 0

1

2

3

4

In an ideal world, net working capital is always zero because short-term assets are financed with short-term debt.

Alternative Financing Policies for Current Assets In the previous section, we examined the level of investment in current assets. Now we turn to the level of current liabilities, assuming the investment in current assets is optimal. An Ideal Model In an ideal economy, short-term assets can always be financed with short-term debt, and long-term assets can be financed with long-term debt and equity. In this economy, net working capital is always zero. Imagine the simple case of a grain elevator operator. Grain elevator operators buy crops after harvest, store them, and sell them during the year. They have high inventories of grain after the harvest and end with low inventories just before the next harvest. Bank loans with maturities of less than one year are used to finance the purchase of grain. These loans are paid with the proceeds from the sale of grain. The situation is shown in Figure 26.3. Long-term assets are assumed to grow over time, whereas current assets increase at the end of the harvest and then decline during the year. Short-term assets end at zero just before the next harvest. These assets are financed by short-term debt, and long-term assets are financed with long-term debt and equity. Net working capital—current assets minus current liabilities—is always zero. Different Strategies for Financing Current Assets Current assets cannot be expected to drop to zero in the real world because a long-term rising level of sales will result in some permanent investment in current assets. A growing firm can be thought of as having a permanent requirement for both current assets and long-term assets. This total asset requirement will exhibit balances over time reflecting (1) a secular growth trend, (2) a seasonal variation around the trend, and (3) unpredictable day-to-day and month-to-month fluctuations. This is depicted in Figure 26.4. (We have not tried to show the unpredictable day-to-day and month-to-month variations in the total asset requirement.) Now let us look at how this asset requirement is financed. First, consider the strategy (strategy F in Figure 26.5) where long-term financing covers more than the total asset requirement, even at seasonal peaks. The firm will have excess cash available for investment in marketable securities when the total asset requirement falls from peaks. Because this approach implies chronic short-term cash surpluses and a large investment in net working capital, it is considered a flexible strategy. When long-term financing does not cover the total asset requirement, the firm must borrow short-term to make up the deficit. This restrictive strategy is labeled strategy Rin F igure26.5.

Chapter 26

Figure 26.4 The Total Asset Requirement over Time

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Dollars

Seasonal variation

Secular growth in fixed assets and permanent current assets

Total asset requirement

Time

Figure 26.5 Alternative Asset FinancingP olicies

Strategy F Dollars Marketable securities

Total asset requirement

Long-term financing

Time

Strategy R Dollars Total asset requirement Short-term financing

Long-term financing Time

Strategy F always implies a short-term cash surplus and a large investment in cash and marketable securities. Strategy R uses long-term financing for secular asset requirements only, and short-term borrowing for seasonal variations.

WhichI sB est? What is the most appropriate amount of short-term borrowing? There is no definitive answer. Several considerations must be included in a proper analysis: 1. Cash reserves: The flexible financing strategy implies surplus cash and little shortterm borrowing. This strategy reduces the probability that a firm will experience financial distress. Firms may not need to worry as much about meeting recurring

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short-term obligations. However, investments in cash and marketable securities are zero net present value investments at best. 2. Maturity hedging: Most firms finance inventories with short-term bank loans and fixed assets with long-term financing. Firms tend to avoid financing longlived assets with short-term borrowing. This type of maturity mismatching would necessitate frequent financing and is inherently risky because short-term interest rates are more volatile than longer rates. 3. Term structure: Short-term interest rates are normally lower than long-term interest rates. This implies that, on average, it is more costly to rely on long-term borrowing than on short-term borrowing.

26.4 Cash Budgeting The cash budget is a primary tool of short-term financial planning. It allows the financial manager to identify short-term financial needs (and opportunities). It will tell the manager the required borrowing for the short term. It is the way of identifying the cash flow gap on the cash flow time line. The idea of the cash budget is simple: It records estimates of cash receipts and disbursements. We illustrate cash budgeting with the following example of Fun Toys.

EXAMPLE26.3

Cash Collections All of Fun Toys’ cash inflows come from the sale of toys. Cash budgeting for Fun Toys starts with a sales forecast for the next year by quarter: First Quarter

Second Quarter

Third Quarter

Fourth Quarter

$100

$200

$150

$100

Sales ($ in millions)

Fun Toys’ fiscal year starts on July 1. Fun Toys’ sales are seasonal and are usually very high in the second quarter due to holiday sales. But Fun Toys sells to department stores on credit, and sales do not generate cash immediately. Instead, cash comes later from collections on accounts receivable. Fun Toys has a 90-day collection period, and 100 percent of sales are collected the following quarter. In other words: Collections = Last quarter’s sales This relationship implies that: Accounts receivable at end of last quarter = Last quarter’s sales

(26.6)

We assume that sales in the fourth quarter of the previous fiscal year were $100 million. From Equation 26.6 we know that accounts receivable at the end of the fourth quarter of the previous fiscal year were $100 million, and collections in the first quarter of the current fiscal year are $100 million. The first quarter sales of the current fiscal year of $100 million are added to the accounts receivable, but $100 million of collections are subtracted. Therefore, Fun Toys ended the first quarter with accounts receivable of $100 million. The basic relation is: Ending accounts Starting accounts = + Sales − Collections receivable receivable

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Table 26.2 shows cash collections for Fun Toys for the next four quarters. Though collections are the only source of cash here, this need not always be the case. Other sources of cash could include sales of assets, investment income, and long-term financing.

Table 26.2

Sources of Cash ($ in millions)

Sales Cash collections Starting receivables Ending receivables

First Quarter

Second Quarter

Third Quarter

Fourth Quarter

$100 100 100 100

$200 100 100 200

$150 200 200 150

$100 150 150 100

CashOutf low Next, we consider cash disbursements. They can be put into four basic categories, as shown in Table 26.3. 1. Payments of accounts payable: These are payments for goods or services, such as raw materials. These payments will generally be made after purchases. Purchases will depend on the sales forecast. In the case of Fun Toys, assume that: Payments = Last quarter’s purchases Purchases = 1/2 next quarter’s sales forecast 2. Wages, taxes, and other expenses: This category includes all other normal costs of doing business that require actual expenditures. Depreciation, for example, is often thought of as a normal cost of business, but it requires no cash outflow. 3. Capital expenditures: These are payments of cash for long-lived assets. Fun Toys plans a major capital expenditure in the fourth quarter. 4. Long-term financing: This category includes interest and principal payments on long-term outstanding debt and dividend payments to shareholders. The total forecast outflow appears in the last line of Table 26.3.

Table 26.3 Disbursement of Cash ($ in millions)

Sales Purchases Uses of cash Payments of accounts payable Wages, taxes, and other expenses Capital expenditures Long-term financing expenses: interest and dividends Total uses of cash

First Quarter

Second Quarter

Third Quarter

Fourth Quarter

$100 100

$200 75

$150 50

$100 50

50 20 0

100 40 0

75 30 0

50 20 100

10 $ 80

10 $150

10 $115

10 $180

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Table 26.4 The Cash Balance ($ in millions)

Total cash receipts Total cash disbursements Net cash flow Cumulative excess cash balance Minimum cash balance Cumulative finance surplus (deficit) requirement

First Quarter

Second Quarter

Third Quarter

Fourth Quarter

$100 80 20 20 5

$100 150 (50) (30) 5

$200 115 85 55 5

$150 180 (30) 25 5

15

(35)

50

20

TheCa shB alance The net cash balance appears in Table 26.4, and a large net cash outflow is forecast in the second quarter. This large outflow is not caused by an inability to earn a profit. Rather, it results from delayed collections on sales. This results in a cumulative cash shortfall of $30 million in the second quarter. Fun Toys had established a minimum operating cash balance equal to $5 million to facilitate transactions, protect against unexpected contingencies, and maintain compensating balances at its commercial banks. This means that it has a cash shortfall in the second quarter equal to $35 million.

26.5 The Short-Term Financial Plan Fun Toys has a short-term financing problem. It cannot meet the forecast cash outflows in the second quarter from internal sources. Its financing options include (1) unsecured bank borrowing, (2) secured borrowing, and (3) other sources.

UnsecuredL oans The most common way to finance a temporary cash deficit is to arrange a short-term unsecured bank loan. Firms that use short-term bank loans usually ask their bank for either a noncommitted or a committed line of credit. A noncommitted line of credit is an informal arrangement that allows firms to borrow up to a previously specified limit without going through the normal paperwork. The interest rate on the line of credit is usually set equal to the bank’s prime lending rate plus an additional percentage. Committed lines of credit are formal legal arrangements and usually involve a commitment fee paid by the firm to the bank (usually, the fee is approximately .25 percent of the total committed funds per year). For larger firms, the interest rate is often tied to the London Interbank Offered Rate (LIBOR) or to the bank’s cost of funds, rather than the prime rate. Midsized and smaller firms often are required to keep compensating balances in the bank. Compensatingb alances are deposits the firm keeps with the bank in low-interest or non-interest-bearing accounts. Compensating balances are commonly on the order of 2 to 5 percent of the amount used. By leaving these funds with the bank without receiving interest, the firm increases the effective interest earned by the bank on the line of credit. For example, if a firm borrowing $100,000 must keep $5,000 as a compensating balance, the firm effectively receives only $95,000. A stated interest rate of 10 percent implies yearly interest payments of $10,000 (=$100,000 × .10). The effective interest rate is 10.53 percent (=$10,000/$95,000).

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SecuredL oans Banks and other finance companies often require security for a loan. Security for short-term loans usually consists of accounts receivable or inventories. Under accounts receivable financing, receivables are either assigned or factored. Under assignment, the lender not only has a lien on the receivables but also has recourse to the borrower. Factoring involves the sale of accounts receivable. The purchaser, who is called a factor, must then collect on the receivables. The factor assumes the full risk of default on bad accounts. As the name implies, an inventory loan uses inventory as collateral. Some common types of inventory loans are: 1. Blanket inventory lien: The blanket inventory lien gives the lender a lien against all the borrower’s inventories. 2. Trust receipt: Under this arrangement, the borrower holds the inventory in trust for the lender. The document acknowledging the loan is called the trust receipt. Proceeds from the sale of inventory are remitted immediately to the lender. 3. Field warehouse financing: In field warehouse financing, a public warehouse company supervises the inventory for the lender.

OtherSo urces A variety of other sources of short-term funds are employed by corporations. The most important of these are the issuance of commercial paper and financing through banker’s acceptances. Commercial paper consists of short-term notes issued by large, highly rated firms. Typically, these notes are of short maturity, ranging up to 270 days (beyond that limit the firm must file a registration statement with the SEC). Because the firm issues these directly and because it usually backs the issue with a special bank line of credit, the rate the firm obtains is often significantly below the prime rate the bank would charge it for a direct loan. A banker’s acceptance is an agreement by a bank to pay a sum of money. These agreements typically arise when a seller sends a bill or draft to a customer. The customer’s bank accepts this bill and notes the acceptance on it, which makes it an obligation of the bank. In this way a firm that is buying something from a supplier can effectively arrange for the bank to pay the outstanding bill. Of course, the bank charges the customer a fee for this service.

Summary and Conclusions

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1. This chapter introduced the management of short-term finance. Short-term finance involves short-lived assets and liabilities. We traced and examined the short-term sources and uses of cash as they appear on the firm’s financial statements. We saw how current assets and current liabilities arise in the short-term operating activities and the cash cycle of the firm. From an accounting perspective, short-term finance involves net workingc apital. 2. Managing short-term cash flows involves the minimization of costs. The two major costs are carrying costs (the interest and related costs incurred by overinvesting in short-term assets such as cash) and shortage costs (the cost of running out of short-term assets). The objective of managing short-term finance and short-term financial planning is to find the optimal trade-off between these costs. 3. In an ideal economy, a firm could perfectly predict its short-term uses and sources of cash, and net working capital could be kept at zero. In the real world, net working

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capital provides a buffer that lets the firm meet its ongoing obligations. The financial manager seeks the optimal level of each of the current assets. 4. The financial manager can use the cash budget to identify short-term financial needs. The cash budget tells the manager what borrowing is required or what lending will be possible in the short term. The firm has a number of possible ways of acquiring funds to meet short-term shortfalls, including unsecured and secured loans.

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Concept Questions

Questions and Problems BASIC (Questions 1–11)

Operating Cycle What are some of the characteristics of a firm with a long operatingc ycle? 2. Cash Cycle What are some of the characteristics of a firm with a long cash cycle? 3. Sources and Uses For the year just ended, you have gathered the following information about the Holly Corporation: a. A $200 dividend was paid. b. Accounts payable increased by $500. c. Fixed asset purchases were $900. d. Inventories increased by $625. e. Long-term debt decreased by $1,200. Label each as a source or use of cash and describe its effect on the firm’s cash balance. 4. Cost of Current Assets Grohl Manufacturing, Inc., has recently installed a justin-time (JIT) inventory system. Describe the effect this is likely to have on the company’s carrying costs, shortage costs, and operating cycle. 5. Operating and Cash Cycles Is it possible for a firm’s cash cycle to be longer than its operating cycle? Explain why or why not. 6. Shortage Costs What are the costs of shortages? Describe them. 7. Reasons for Net Working Capital In an ideal economy, net working capital is always zero. Why might net working capital be positive in a real economy? Use the following information to answer Questions 8–12: Last month, BlueSky Airline announced that it would stretch out its bill payments to 45 days from 30 days. The reason given was that the company wanted to “control costs and optimize cash flow.” The increased payables period will be in effect for all of the company’s 4,000 suppliers. 8. Operating and Cash Cycles What impact did this change in payables policy have on BlueSky’s operating cycle? Its cash cycle? 9. Operating and Cash Cycles What impact did the announcement have on BlueSky’s suppliers? 10. Corporate Ethics Is it ethical for large firms to unilaterally lengthen their payables periods, particularly when dealing with smaller suppliers? 11. Payables Period Why don’t all firms simply increase their payables periods to shorten their cash cycles? 12. Payables Period BlueSky lengthened its payables period to “control costs and optimize cash flow.” Exactly what is the cash benefit to BlueSky from this change? 1.

1.

Changes in the Cash Account Indicate the impact of the following corporate actions on cash, using the letter I for an increase, D for a decrease, or N when no change occurs. a. A dividend is paid with funds received from a sale of debt. b. Real estate is purchased and paid for with short-term debt. c. Inventory is bought on credit. d. A short-term bank loan is repaid. e. Next year’s taxes are prepaid.

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2.

3.

5.

f. Preferred stock is redeemed. g. Sales are made on credit. h. Interest on long-term debt is paid. i. Payments for previous sales are collected. j. The accounts payable balance is reduced. k. A dividend is paid. l. Production supplies are purchased and paid with a short-term note. m. Utility bills are paid. n. Cash is paid for raw materials purchased for inventory. o. Marketables ecuritiesar es old. Cash Equation McConnell Corp. has a book net worth of $10,380. Long-term debt is $7,500. Net working capital, other than cash, is $2,105. Fixed assets are $15,190. How much cash does the company have? If current liabilities are $1,450, what are currentas sets? Changes in the Operating Cycle Indicate the effect that the following will have on the operating cycle. Use the letter I to indicate an increase, the letter D for a decrease, and the letter N for no change. a. Receivables average goes up. b. Credit repayment times for customers are increased. c. Inventory turnover goes from 3 times to 6 times. d. Payables turnover goes from 6 times to 11 times. e. Receivables turnover goes from 7 times to 9 times. f. Paymentst os uppliersar eac celerated. Changes in Cycles Indicate the impact of the following on the cash and operating cycles, respectively. Use the letter I to indicate an increase, the letter D for a decrease, and the letter N for no change. a. The terms of cash discounts offered to customers are made less favorable. b. The cash discounts offered by suppliers are increased; thus, payments are made earlier. c. An increased number of customers begin to pay in cash instead of with credit. d. Fewer raw materials than usual are purchased. e. A greater percentage of raw material purchases are paid for with credit. f. More finished goods are produced for inventory instead of for order. Calculating Cash Collections The Litzenberger Company has projected the following quarterly sales amounts for the coming year:

Sales

Q1

Q2

Q3

Q4

$700

$630

$810

$930

a. Accounts receivable at the beginning of the year are $275. Litzenberger has a 45-day collection period. Calculate cash collections in each of the four quarters by completing the following: Q1

Q2

Beginning receivables Sales Cash collections Ending receivables

b. Rework (a) assuming a collection period of 60 days. c. Rework (a) assuming a collection period of 30 days.

Q3

Q4

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4.

815

816

Part VII

6.

7.

Short-Term Finance

Calculating Cycles Consider the following financial statement information for the Bulldog Icers Corporation: Item

Beginning

Ending

Inventory Accounts receivable Accounts payable Net sales Cost of goods sold

$15,382 12,169 13,408

$16,147 12,682 14,108 $143,625 105,817

Calculate the operating and cash cycles. How do you interpret your answer? Calculating Payments Lewellen Products has projected the following sales for the coming year:

Sales

Q1

Q2

Q3

Q4

$830

$745

$905

$980

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Sales in the year following this one are projected to be 15 percent greater in each quarter. a. Calculate payments to suppliers assuming that Lewellen places orders during each quarter equal to 30 percent of projected sales for the next quarter. Assume that the company pays immediately. What is the payables period in this case?

Payment of accounts

8.

Q1

Q2

Q3

Q4

$

$

$

$

b. Rework (a) assuming a 90-day payables period. c. Rework (a) assuming a 60-day payables period. Calculating Payments The Thakor Corporation’s purchases from suppliers in a quarter are equal to 75 percent of the next quarter’s forecast sales. The payables period is 60 days. Wages, taxes, and other expenses are 20 percent of sales, and interest and dividends are $73 per quarter. No capital expenditures are planned. Here are the projected quarterly sales:

Sales

Q1

Q2

Q3

Q4

$830

$1,050

$970

$860

Sales for the first quarter of the following year are projected at $970. Calculate the company’s cash outlays by completing the following: Q1 Payment of accounts Wages, taxes, and other expenses Long-term financing expenses (interest and dividends) Total

Q2

Q3

Q4

Chapter 26

9.

Short-Term Finance and Planning

Calculating Cash Collections the first quarter of 2010:

Sales budget

10.

817

The following is the sales budget for Shleifer, Inc., for January

February

March

$173,000

$184,000

$205,000

Credit sales are collected as follows: 65 percent in the month of the sale. 20 percent in the month after the sale. 15 percent in the second month after the sale. The accounts receivable balance at the end of the previous quarter was $79,800 ($57,200 of which were uncollected December sales). a. Compute the sales for November. b. Compute the sales for December. c. Compute the cash collections from sales for each month from January through March. Calculating the Cash Budget Here are some important figures from the budget of Cornell, Inc., for the second quarter of 2010: May

June

$608,000 235,200

$633,600 280,800

$700,800 320,500

63,600 18,240 132,800

77,136 18,240 145,600

80,480 18,240 0

The company predicts that 5 percent of its credit sales will never be collected, 35 percent of its sales will be collected in the month of the sale, and the remaining 60 percent will be collected in the following month. Credit purchases will be paid in the month following the purchase. In March 2010, credit sales were $336,000, and credit purchases were $249,600. Using this information, complete the following cash budget: April Beginning cash balance Cash receipts Cash collections from credit sales Total cash available Cash disbursements Purchases Wages, taxes, and expenses Interest Equipment purchases Total cash disbursements Ending cash balance

$448,000

May

June

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Credit sales Credit purchases Cash disbursements Wages, taxes, and expenses Interest Equipment purchases

April

818

Part VII

11.

Short-Term Finance

Sources and Uses Here are the most recent balance sheets for Country Kettles, Inc. Excluding accumulated depreciation, determine whether each item is a source or a use of cash, and the amount: COUNTRY KETTLES, INC. Balance Sheet December 31, 2010

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2009

Assets Cash Accounts receivable Inventory Property, plant, and equipment Less: Accumulated depreciation Total assets Liabilities and Equity Accounts payable Accrued expenses Long-term debt Common stock Accumulated retained earnings Total liabilities and equity

INTERMEDIATE (Questions 12–15)

12.

13.

2010

$ 43,800 91,050 76,000 173,840 (59,380) $325,310

$ 41,650 95,830 81,560 191,605 (65,830) $344,815

$ 60,460 9,150 45,000 30,000 180,700 $325,310

$ 62,540 8,405 55,000 35,000 183,870 $344,815

Cash Budgeting The sales budget for your company in the coming year is based on a 20 percent quarterly growth rate with the first-quarter sales projection at $150 million. In addition to this basic trend, the seasonal adjustments for the four quarters are 0, −$16, −$8, and $21 million, respectively. Generally, 50 percent of the sales can be collected within the quarter and 45 percent in the following quarter; the rest of the sales are bad debt. The bad debts are written off in the second quarter after the sales are made. The beginning accounts payable balance is $72 million. Assuming all sales are on credit, compute the cash collections from sales for each quarter. Calculating the Cash Budget Wildcat, Inc., has estimated sales (in millions) for the next four quarters as follows:

Sales

Q1

Q2

Q3

Q4

$210

$180

$245

$280

Sales for the first quarter of the year after this one are projected at $240 million. Accounts receivable at the beginning of the year were $68 million. Wildcat has a 45-day collection period. Wildcat’s purchases from suppliers in a quarter are equal to 45 percent of the next quarter’s forecast sales, and suppliers are normally paid in 36 days. Wages, taxes, and other expenses run about 30 percent of sales. Interest and dividends are $12 million per quarter.

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Short-Term Finance and Planning

819

Wildcat plans a major capital outlay in the second quarter of $80 million. Finally, the company started the year with a $64 million cash balance and wishes to maintain a $30 million minimum balance. a. Complete a cash budget for Wildcat by filling in the following:

WILDCAT, INC. Cash Budget ($ in millions)

Q1 Beginning cash balance Net cash inflow Ending cash balance Minimum cash balance Cumulative surplus (deficit)

Q2

Q3

Q4

$30

30

WILDCAT, INC. Short-Term Financial Plan ($ in millions)

Q1 Beginning cash balance Net cash inflow New short-term investments Income from short-term investments Short-term investments sold New short-term borrowing Interest on short-term borrowing Short-term borrowing repaid Ending cash balance Minimum cash balance Cumulative surplus (deficit) Beginning short-term investments Ending short-term investments Beginning short-term debt Ending short-term debt

$64

30

Q2

Q3

Q4

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b. Assume that Wildcat can borrow any needed funds on a short-term basis at a rate of 3 percent per quarter, and can invest any excess funds in short-term marketable securities at a rate of 2 percent per quarter. Prepare a short-term financial plan by filling in the following schedule. What is the net cash cost (total interest paid minus total investment income earned) for the year?

820

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14.

15.

Short-Term Finance

CashM anagementP olicy Rework Problem 13 assuming the following: a. Wildcat maintains a minimum cash balance of $50 million. b. Wildcat maintains a minimum cash balance of $10 million. Based on your answers in (a) and (b), do you think the firm can boost its profit by changing its cash management policy? Should other factors be considered as well? Explain. Short-Term Finance Policy Cleveland Compressor and Pnew York Pneumatic are competing manufacturing firms. Their financial statements are printed here. a. How are the current assets of each firm financed? b. Which firm has the larger investment in current assets? Why? c. Which firm is more likely to incur carrying costs, and which is more likely to incur shortagec osts?W hy?

CLEVELAND COMPRESSOR Balance Sheet 2009

2010

Cash . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

$ 16,339

$ 13,862

Net accounts receivable . . . . . . . . . . . . . . . . .

25,778

23,887

Inventory . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

43,287

54,867

Total current assets . . . . . . . . . . . . . . . . . . .

$ 85,404

$ 92,616

99,615

101,543

Assets

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Current assets:

Fixed assets: Plant, property, and equipment . . . . . . . . . . . .

(31,957)

Less: Accumulated depreciation . . . . . . . . . Net fixed assets . . . . . . . . . . . . . . . . . . . . . .

$ 67,658

(34,331) $ 67,212

Prepaid expenses . . . . . . . . . . . . . . . . . . . . . . . . .

1,791

1,914

Other assets. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

13,138

13,052

Total assets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

$ 167,991

$ 174,794

$

$

Liabilities and Equity Current liabilities: Accounts payable . . . . . . . . . . . . . . . . . . . . . . . Notes payable . . . . . . . . . . . . . . . . . . . . . . . . .

4,893 11,617

6,494 10,483

Accrued expenses . . . . . . . . . . . . . . . . . . . . . .

7,227

7,422

Other taxes payable. . . . . . . . . . . . . . . . . . . . .

8,460

9,924

Total current liabilities . . . . . . . . . . . . . . . . .

32,197

34,323

Long-term debt . . . . . . . . . . . . . . . . . . . . . . . . . .

22,036

22,036

Total liabilities . . . . . . . . . . . . . . . . . . . . . . . .

$ 54,233

$ 56,359

Common stock . . . . . . . . . . . . . . . . . . . . . . . .

38,000

38,000

Paid-in capital . . . . . . . . . . . . . . . . . . . . . . . . . .

12,000

12,000

Equity:

Retained earnings. . . . . . . . . . . . . . . . . . . . . . .

63,758

68,435

Total equity . . . . . . . . . . . . . . . . . . . . . . . . . .

113,758

118,435

Total liabilities and equity. . . . . . . . . . . . . . . . . . .

$167,991

$174,794

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Short-Term Finance and Planning

821

CLEVELAND COMPRESSOR Income Statement 2010 Income: Sales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

$162,749

Other income . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1,002

Total income . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

$163,751

Operating expenses: Cost of goods sold. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

103,570

Selling and administrative expenses. . . . . . . . . . . . . . . . . . . . . . .

28,495

Depreciation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2,274

Total expenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

$134,339

Pretax earnings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

29,412

Taxes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

14,890

Net earnings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

$ 14,522

Dividends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

$ 9,845

Retained earnings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

$

4,677

Balance Sheet

2009

2010

$ 3,307 22,133 44,661 $70,101

$ 5,794 26,177 46,463 $78,434

Fixed assets: Plant, property, and equipment . . . . . . . . . . . . . . Less: Accumulated depreciation . . . . . . . . . . . Net fixed assets . . . . . . . . . . . . . . . . . . . . . .

31,116 (18,143) $12,973

31,842 (19,297) $12,545

Prepaid expenses . . . . . . . . . . . . . . . . . . . . . . . . . . . Other assets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Total assets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

688 1,385 $85,147

763 1,601 $93,343

Liabilities and Equity Current liabilities: Accounts payable . . . . . . . . . . . . . . . . . . . . . . . . . $ 5,019 Bank loans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645 Accrued expenses . . . . . . . . . . . . . . . . . . . . . . . . 3,295 Other taxes payable. . . . . . . . . . . . . . . . . . . . . . . 4,951 Total current liabilities . . . . . . . . . . . . . . . . . . . $13,910

$ 6,008 3,722 4,254 5,688 $19,672

Equity: Common stock . . . . . . . . . . . . . . . . . . . . . . . . . . Paid-in capital . . . . . . . . . . . . . . . . . . . . . . . . . . . . Retained earnings. . . . . . . . . . . . . . . . . . . . . . . . . Less: Treasury stock . . . . . . . . . . . . . . . . . . . . . Total equity . . . . . . . . . . . . . . . . . . . . . . . . . .

20,576 5,624 46,164 (1,127) $71,237

20,576 5,624 48,598 (1,127) $73,671

Total liabilities and equity. . . . . . . . . . . . . . . . . . . . .

$85,147

$93,343

Assets Current assets: Cash . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Net accounts receivable . . . . . . . . . . . . . . . . . . . Inventory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Total current assets . . . . . . . . . . . . . . . . . . . . .

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PNEW YORK PNEUMATIC

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PNEW YORK PNEUMATIC Income Statement 2010

Income: Sales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

$91,374

Other income . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1,067

Total income . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

$92,441

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Operating expenses:

S&P Problems

59,042

Selling and administrative expenses. . . . . . . . . . . . . . . . . . . . . . .

18,068

Depreciation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1,154

Total expenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

$78,264

Pretax earnings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

14,177

Taxes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6,838

Net earnings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

$ 7,339

Dividends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

$ 4,905

Retained earnings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

$ 2,434

www.mhhe.com/edumarketinsight

1.

2.

Mini Case

Cost of goods sold. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Cash and Operating Cycles Find the most recent financial statements for Dell Computer (DELL) and Boeing (BA). Calculate the cash and operating cycles for each company for the most recent year. Are the numbers similar for these companies? Why or why not? Cash and Operating Cycles Download the most recent quarterly financial statements for Wal-Mart (WMT). Calculate the operating and cash cycles for Wal-Mart over each of the last four quarters. Comment on any changes in the operating or cash cycleso vert hisp eriod.

KEAFERMA NUFACTURING WORKING CAPITAL MANAGEMENT You have recently been hired by Keafer Manufacturing to work in its established treasury department. Keafer Manufacturing is a small company that produces highly customized cardboard boxes in a variety of sizes for different purchasers. Adam Keafer, the owner of the company, works primarily in the sales and production areas of the company. Currently, the company basically puts all receivables in one pile and all payables in another, and a part-time bookkeeper periodically comes in and attacks the piles. Because of this disorganized system, the finance area needs work, and that’s what you’ve been brought in to do. The company currently has a cash balance of $149,500, and it plans to purchase new machinery in the third quarter at a cost of $260,000. The purchase of the machinery will be made with cash because of the discount offered for a cash purchase. Adam wants to maintain a minimum cash balance of $90,000 to guard against unforeseen contingencies. All of Keafer’s sales to customers and purchases from suppliers are made with credit, and no discounts are offered or taken.

Chapter 26

Short-Term Finance and Planning

823

The company had the following sales each quarter of the year just ended:

Gross sales

Q1

Q2

Q3

Q4

$735,000

$761,000

$817,000

$709,000

After some research and discussions with customers, you’re projecting that sales will be 8 percent higher in each quarter next year. Sales for the first quarter of the following year are also expected to grow at 8 percent. You calculate that Keafer currently has an accounts receivable period of 57 days and an accounts receivable balance of $553,000. However, 10 percent of the accounts receivable balance is from a company that has just entered bankruptcy, and it is likely that this portion will never be collected. You’ve also calculated that Keafer typically orders supplies each quarter in the amount of 50 percent of the next quarter’s projected gross sales, and suppliers are paid in 53 days on average. Wages, taxes, and other costs run about 25 percent of gross sales. The company has a quarterly interest payment of $148,000 on its long-term debt. Finally, the company uses a local bank for its short-term financial needs. It currently pays 1.2 percent per quarter on all short-term borrowing and maintains a money market account that pays .5 percent per quarter on all short-term deposits. Adam has asked you to prepare a cash budget and short-term financial plan for the company under the current policies. He has also asked you to prepare additional plans based on changes in several inputs. 1. Use the numbers given to complete the cash budget and short-term financial plan. 2. Rework the cash budget and short-term financial plan assuming Keafer changes to a minimum cash balance of $70,000. 3. Rework the sales budget assuming an 11 percent growth rate in sales and a 5 percent growth rate in sales. Assume a $90,000 target cash balance. 4. Assuming the company maintains its target cash balance at $90,000, what sales growth rate would result in a zero need for short-term financing? To answer this question, you mayn eedt os etu pas preadsheetan du set he“S olver”f unction.

CHAPTER 27

CashManagem ent Most often, when news breaks about a firm’s bank accounts, it’s because the company is running low on cash. However, that wasn’t the case for many companies in 2008. For example, in September 2008 carmaker Ford had a cash balance of $24.9 billion, or $10.42 per share. What’s so striking about that amount is the stock was trading for only about $5 per share, so Ford’s actual cash per share was much larger than its stock price, normally not a good sign. Other companies with healthier operations also had large amounts of cash. For example, Microsoft had a cash hoard of about $21 billion, while General Electric had about $60 billion. Why would firms such as these hold such large quantities of cash? We examine cash management in this chapter to find out.

This chapter is about how firms manage cash. The basic objective of cash management is to keep the investment in cash as low as possible while still keeping the firm operating efficiently and effectively. This goal usually reduces to the dictum, “Collect early and pay late.” Accordingly, we discuss ways of accelerating collections and managing disbursements. In addition, firms must invest temporarily idle cash in short-term marketable securities. As we discuss in various places, these securities can be bought and sold in the financial markets. As a group they have very little default risk, and most are highly marketable. There are different types of these so-called money market securities, and we discuss a few of the most important ones.

27.1 Reasons for Holding Cash John Maynard Keynes, in his classic work The General Theory of Employment, Interest, and Money, identified three motives for liquidity: The speculative motive, the precautionary motive, and the transaction motive. We discuss these next.

The Speculative and Precautionary Motives The speculative motive is the need to hold cash in order to be able to take advantage of, for example, bargain purchases that might arise, attractive interest rates, and (in the case of international firms) favorable exchange rate fluctuations. For most firms, reserve borrowing ability and marketable securities can be used to satisfy speculative motives. Thus, there might be a speculative motive for maintaining liquidity, but not necessarily for holding cash per se. Think of it this way: If you have a credit card with a very large credit limit, then you can probably take advantage of any unusual bargains that come along without carrying any cash. This is also true, to a lesser extent, for precautionary motives. The precautionary motive is the need for a safety supply to act as a financial reserve. Once again, there probably is a precautionary motive for maintaining liquidity. However, given that the value of money market instruments is relatively certain and that instruments such as 824

Chapter 27 Cash Management

825

T-bills are extremely liquid, there is no real need to hold substantial amounts of cash for precautionary purposes.

TheT ransactionMo tive Cash is needed to satisfy the transaction motive: the need to have cash on hand to pay bills. Transaction-related needs come from the normal disbursement and collection activities of the firm. The disbursement of cash includes the payment of wages and salaries, trade debts, taxes, and dividends. Cash is collected from product sales, the selling of assets, and new financing. The cash inflows (collections) and outflows (disbursements) are not perfectly synchronized, and some level of cash holdings is necessary to serve as a buffer. As electronic funds transfers and other high-speed, “paperless” payment mechanisms continue to develop, even the transaction demand for cash may all but disappear. Even if it does, however, there will still be a demand for liquidity and a need to manage it efficiently.

CompensatingB alances Compensating balances are another reason to hold cash. As we discussed in the previous chapter, cash balances are kept at commercial banks to compensate for banking services the firm receives. A minimum compensating balance requirement may impose a lower limit on the level of cash a firm holds.

Costs of Holding Cash When a firm holds cash in excess of some necessary minimum, it incurs an opportunity cost. The opportunity cost of excess cash (held in currency or bank deposits) is the interest income that could be earned by the next best use, such as investment in marketable securities. Given the opportunity cost of holding cash, why would a firm hold cash in excess of its compensating balance requirements? The answer is that a cash balance must be maintained to provide the liquidity necessary for transaction needs—paying bills. If the firm maintains too small a cash balance, it may run out of cash. If this happens, the firm may have to raise cash on a short-term basis. This could involve, for example, selling marketable securities or borrowing. Activities such as selling marketable securities and borrowing involve various costs. As we’ve discussed, holding cash has an opportunity cost. To determine the appropriate cash balance, the firm must weigh the benefits of holding cash against these costs. We discuss this subject in more detail in the sections that follow.

Cash Management versus Liquidity Management Before we move on, we should note that it is important to distinguish between true cash management and a more general subject, liquidity management. The distinction is a source of confusion because the word cash is used in practice in two different ways. First of all, it has its literal meaning, actual cash on hand. However, financial managers frequently use the word to describe a firm’s holdings of cash along with its marketable securities, and marketable securities are sometimes called cash equivalents, or near-cash. In our discussion of Ford’s and GE’s cash positions at the beginning of the chapter, for example, what was actually being described was their total cash and cash equivalents.

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The distinction between liquidity management and cash management is straightforward. Liquidity management concerns the optimal quantity of liquid assets a firm should have on hand, and it is one particular aspect of the current asset management policies we discussed in our previous chapter. Cash management is much more closely related to optimizing mechanisms for collecting and disbursing cash, and it is this subject that we primarily focus on in this chapter. In general, the firm needs to balance the benefits of holding cash to meet transactions and avoid insolvency against the opportunity costs of lower returns. A sensible cash management policy is to have enough cash on hand to meet the obligations that may arise in the ordinary course of business and to invest some excess cash in marketable securities for precautionary purposes. All other excess cash should be invested in the business or paid out to investors.1

27.2 Understanding Float As you no doubt know, the amount of money you have according to your checkbook can be very different from the amount of money that your bank thinks you have. The reason is that some of the checks you have written haven’t yet been presented to the bank for payment. The same thing is true for a business. The cash balance that a firm shows on its books is called the firm’s book, or ledger, balance. The balance shown in its bank account as available to spend is called its available, or collected, balance. The difference between the available balance and the ledger balance, called the float, represents the net effect of checks in the process of clearing (moving through the banking system).

DisbursementF loat Checks written by a firm generate disbursement float, causing a decrease in the firm’s book balance but no change in its available balance. For example, suppose General Mechanics, Inc. (GMI) currently has $100,000 on deposit with its bank. On June 8, it buys some raw materials and pays with a check for $100,000. The company’s book balance is immediately reduced by $100,000 as a result. GMI’s bank, however, will not find out about this check until it is presented to GMI’s bank for payment on, say, June 14. Until the check is presented, the firm’s available balance is greater than its book balance by $100,000. In other words, before June 8, GMI has a zero float: Float = Firm’s available balance − Firm’s book balance = $100,000 − 100,000 =$0 GMI’s position from June 8 to June 14 is: Disbursementf loat = Firm’s available balance − Firm’s book balance = $100,000 − 0 =$100,000 1

There is some evidence that corporate governance has some role in the cash holdings of U.S. firms. Jarrad Harford, Sattar A. Mansi, and William F. Maxwell, in “Corporate Governance and Firm Cash Holdings in the U.S.,” Journal of Financial Economics, 2008, vol. 87, iss. 3, pp. 535–55, find that firms with weaker corporate governance systems have smaller cash reserves. The combination of excess cash and weak governance leads to more capital spending and more acquisitions.

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While the check is clearing, GMI has a balance with the bank of $100,000. It can obtain the benefit of this cash during this period. For example, the available balance could be temporarily invested in marketable securities and thus earn some interest. We will return to this subject a little later.

Collection Float and Net Float Checks received by the firm create collection float. Collection float increases book balances but does not immediately change available balances. For example, suppose GMI receives a check from a customer for $100,000 on October 8. Assume, as before, that the company has $100,000 deposited at its bank and a zero float. It deposits the check and increases its book balance by $100,000 to $200,000. However, the additional cash is not available to GMI until its bank has presented the check to the customer’s bank and received $100,000. This will occur on, say, October 14. In the meantime, the cash position at GMI will reflect a collection float of $100,000. We can summarize these events. Before October 8, GMI’s position is: Float = Firm’s available balance − Firm’s book balance = $100,000 − 100,000 =$0 GMI’s position from October 8 to October 14 is: Collectionf loat = Firm’s available balance − Firm’s book balance = $100,000 − 200,000 = −$100,000 In general, a firm’s payment (disbursement) activities generate disbursement float, and its collection activities generate collection float. The net effect—that is, the sum of the total collection and disbursement floats—is the net float. The net float at a point in time is simply the overall difference between the firm’s available balance and its book balance. If the net float is positive, then the firm’s disbursement float exceeds its collection float, and its available balance exceeds its book balance. If the available balance is less than the book balance, then the firm has a net collection float. A firm should be concerned with its net float and available balance more than with its book balance. If a financial manager knows that a check written by the company will not clear for several days, that manager will be able to keep a lower cash balance at the bank than might be possible otherwise. This can generate a great deal of money. For example, take the case of ExxonMobil. The average daily sales of ExxonMobil are about $1 billion. If ExxonMobil’s collections could be sped up by a single day, then ExxonMobil could free up $1 billion for investing. At a relatively modest .01 percent daily rate, the interest earned would be on the order of $100,000 per day.

EXAMPLE27.1

Staying Afloat Suppose you have $5,000 on deposit. One day, you write a check for $1,000 to pay for books, and you deposit $2,000. What are your disbursement, collection, and net floats? After you write the $1,000 check, you show a balance of $4,000 on your books, but the bank shows $5,000 while the check is clearing. The difference is a disbursement float of $1,000. After you deposit the $2,000 check, you show a balance of $6,000. Your available balance doesn’t rise until the check clears. This results in a collection float of −$2,000. Your net float is the sum of the collection and disbursement floats, or −$1,000. (continued)

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Overall, you show $6,000 on your books. The bank shows a $7,000 balance, but only $5,000 is available because your deposit has not been cleared. The discrepancy between your available balance and your book balance is the net float (–$1,000), and it is bad for you. If you write another check for $5,500, there may not be sufficient available funds to cover it, and it might bounce. This is why financial managers have to be more concerned with available balances than book balances.

FloatMa nagement For a real-world example of float management services. visit www.carreker.com.

Float management involves controlling the collection and disbursement of cash. The objective of cash collection is to speed up collections and reduce the lag between the time customers pay their bills and the time the cash becomes available. The objective of cash disbursement is to control payments and minimize the firm’s costs associated with making payments. Total collection or disbursement times can be broken down into three parts: Mailing time, processing delay, and availability delay: 1. Mailing time is the part of the collection and disbursement processes during which checks are trapped in the postal system. 2. Processing delay is the time it takes the receiver of a check to process the payment and deposit it in a bank for collection. 3. Availability delay refers to the time required to clear a check through the banking system. Speeding up collections involves reducing one or more of these components. Slowing up disbursements involves increasing one of them. We will describe some procedures for managing collection and disbursement times later. First, we need to discuss how float is measured. Measuring Float The size of the float depends on both the dollars and the time delay involved. For example, suppose you mail a check for $500 to another state each month. It takes five days in the mail for the check to reach its destination (the mailing time) and one day for the recipient to get over to the bank (the processing delay). The recipient’s bank holds out-of-state checks for three days (availability delay). The total delay is 5 + 1 + 3 = 9 days. In this case, what is your average daily disbursement float? There are two equivalent ways of calculating the answer. First, you have a $500 float for nine days, so we say that the total float is 9 × $500 = $4,500. Assuming 30 days in the month, the average daily float is $4,500 30 = $150. Alternatively, your disbursement float is $500 for 9 days out of the month and zero the other 21 days (again, assuming 30 days in a month). Your average daily float is thus: Average daily float = (9 × $500 + 21 × $0) 30 = 9 30 × $500 + 21 30 × $0 = $4,500 30 =$150 This means that, on an average day, your book balance is $150 less than your available balance, representing a $150 average disbursement float.

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Things are only a little more complicated when there are multiple disbursements or receipts. To illustrate, suppose Concepts, Inc., receives two items each month as follows: Amount Item 1: $5,000,000 Item 2: $3,000,000 Total: $8,000,000

Processing and availability delay ×9 ×5

Total float = $45,000,000 = $15,000,000 $60,000,000

The average daily float is equal to: Total float Average daily float = _________ Total days $60 million = __________ =$2millio n 30

(27.1)

So, on an average day, there is $2 million that is uncollected and not available. Another way to see this is to calculate the average daily receipts and multiply by the weighted average delay. Average daily receipts are: Total receipts $8 million Average daily receipts = ____________ = _________ =$266,666 .67 30 Total days Of the $8 million total receipts, $5 million, or 5⁄8 of the total, is delayed for nine days. The other 3⁄8 is delayed for five days. The weighted average delay is thus: Weighted average delay = (5 8) × 9 days + (3 8) × 5 days = 5.625 + 1.875 =7.50d ays The average daily float is thus: Average daily float = Average daily receipts × Weighted average delay = $266,666.67 × 7.50 days =$2millio n

(27.2)

Some Details In measuring float, there is an important difference to note between collection and disbursement float. We defined float as the difference between the firm’s available cash balance and its book balance. With a disbursement, the firm’s book balance goes down when the check is mailed, so the mailing time is an important component in disbursement float. However, with a collection, the firm’s book balance isn’t increased until the check is received, so mailing time is not a component of collection float. This doesn’t mean that mailing time is not important. The point is that when collection float is calculated, mailing time should not be considered. As we will discuss, when total collection time is considered, the mailing time is a crucial component. Also, when we talk about availability delay, how long it actually takes a check to clear isn’t really crucial. What matters is how long we must wait before the bank grants availability—that is, use of the funds. Banks actually use availability schedules to determine how long a check is held based on time of deposit and other factors. Beyond this, availability delay can be a matter of negotiation between the bank and a customer. In a similar vein, for outgoing checks, what matters is the date our account is debited, not when the recipient is granted availability. Cost of the Float The basic cost of collection float to the firm is simply the opportunity cost of not being able to use the cash. At a minimum, the firm could earn interest on the cash if it were available for investing.

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Figure27.1 Day

Buildup of the Float

Beginning float Checks received Checks cleared (cash available) Ending float

$

1

2

3

4

5

...

0 1,000

$1,000 1,000

$2,000 1,000

$3,000 1,000

$3,000 1,000

... ...

0 $3,000

⫺ 1,000 $3,000

⫺ 1,000 $3,000

... ...

⫺ 0 $1,000

⫺

0 $2,000

⫺

Figure27.2 Day

Effect of Eliminating the Float

t Beginning float Checks received Checks cleared (cash available) Ending float

Try www.cfoasia.com for an international view of cash management.

$3,000 1,000 ⫺ 4,000 $ 0

t ⫹1 $

0 1,000

⫺ 1,000 $ 0

t⫹2

...

0 1,000

... ...

⫺ 1,000 $ 0

... ...

$

Suppose the Lambo Corporation has average daily receipts of $1,000 and a weighted average delay of three days. The average daily float is thus 3 × $1,000 = $3,000. This means that, on a typical day, there is $3,000 that is not earning interest. Suppose Lambo could eliminate the float entirely. What would be the benefit? If it costs $2,000 to eliminate the float, what is the NPV of doing so? Figure 27.1 illustrates the situation for Lambo. Suppose Lambo starts with a zero float. On a given day, Day 1, Lambo receives and deposits a check for $1,000. The cash will become available three days later on Day 4. At the end of the day on Day 1, the book balance is $1,000 more than the available balance, so the float is $1,000. On Day 2, the firm receives and deposits another check. It will collect three days later on Day 5. At the end of Day 2, there are two uncollected checks, and the books show a $2,000 balance. The bank, however, still shows a zero available balance; so the float is $2,000. The same sequence occurs on Day 3, and the float rises to a total of $3,000. On Day 4, Lambo again receives and deposits a check for $1,000. However, it also collects $1,000 from the Day 1 check. The change in book balance and the change in available balance are identical, +$1,000; so the float stays at $3,000. The same thing happens every day after Day 4; the float therefore stays at $3,000 forever.2 Figure 27.2 illustrates what happens if the float is eliminated entirely on some day t in the future. After the float is eliminated, daily receipts are still $1,000. The firm collects the same day because the float is eliminated, so daily collections are also still $1,000. As Figure 27.2 illustrates, the only change occurs the first day. On that day, as usual, Lambo collects $1,000 from the sale made three days before. Because the float is gone, it also collects on the sales made two days before, one day before, and that same day, for an additional $3,000. Total collections on Day t are thus $4,000 instead of $1,000. 2

This permanent float is sometimes called the steady-state float.

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What we see is that Lambo generates an extra $3,000 on Day t by eliminating the float. On every subsequent day, Lambo receives $1,000 in cash just as it did before the float was eliminated. Thus, the only change in the firm’s cash flows from eliminating the float is this extra $3,000 that comes in immediately. No other cash flows are affected, so Lambo is $3,000 richer. In other words, the PV of eliminating the float is simply equal to the total float. Lambo could pay this amount out as a dividend, invest it in interest-bearing assets, or do anything else with it. If it costs $2,000 to eliminate the float, then the NPV is $3,000 − 2,000 = $1,000; so Lambo should do it.

EXAMPLE27.2

EXAMPLE27.3

Reducing the Float: Part I Instead of eliminating the float, suppose Lambo can reduce it to one day. What is the maximum Lambo should be willing to pay for this? If Lambo can reduce the float from three days to one day, then the amount of the float will fall from $3,000 to $1,000. From our immediately preceding discussion, we see right away that the PV of doing this is equal to the $2,000 float reduction. Lambo should thus be willing to pay up to $2,000.

Reducing the Float: Part II Look back at Example 27.2. A large bank is willing to provide the float reduction service for $175 per year, payable at the end of each year. The relevant discount rate is 8 percent. Should Lambo hire the bank? What is the NPV of the investment? How do you interpret this discount rate? What is the most per year that Lambo should be willing to pay? The PV to Lambo is still $2,000. The $175 would have to be paid out every year forever to maintain the float reduction; so the cost is perpetual, and its PV is $175/.08 = $2,187.50. The NPV is $2,000 − 2,187.50 = −$187.50; therefore, the service is not a good deal. Ignoring the possibility of bounced checks, the discount rate here corresponds most closely to the cost of short-term borrowing. The reason is that Lambo could borrow $1,000 from the bank every time a check was deposited and pay it back three days later. The cost would be the interest that Lambo would have to pay. The most Lambo would be willing to pay is whatever charge results in an NPV of zero. This zero NPV occurs when the $2,000 benefit exactly equals the PV of the costs—that is, when $2,000 = C/.08, where C is the annual cost. Solving for C, we find that C = .08 × $2,000 = $160 per year.

Ethical and Legal Questions The cash manager must work with collected bank cash balances and not the firm’s book balance (which reflects checks that have been deposited but not collected). If this is not done, a cash manager could be drawing on uncollected cash as a source of funds for short-term investing. Most banks charge a penalty rate for the use of uncollected funds. However, banks may not have good enough accounting and control procedures to be fully aware of the use of uncollected funds. This raises some ethical and legal questions for the firm.

Electronic Data Interchange and Check 21: The End of Float? Electronic data interchange (EDI) is a general term that refers to the growing practice of direct, electronic information exchange between all types of businesses. One important use of EDI, often called financial EDI, or FEDI, is to electronically transfer financial

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information and funds between parties, thereby eliminating paper invoices, paper checks, mailing, and handling. For example, it is now possible to arrange to have your checking account directly debited each month to pay many types of bills, and corporations now routinely directly deposit paychecks into employee accounts. More generally, EDI allows a seller to send a bill electronically to a buyer, thereby avoiding the mail. The buyer can then authorize payment, which also occurs electronically. Its bank then transfers the funds to the seller’s account at a different bank. The net effect is that the length of time required to initiate and complete a business transaction is shortened considerably, and much of what we normally think of as float is sharply reduced or eliminated. As the use of FEDI increases (which it will), float management will evolve to focus much more on issues surrounding computerized information exchange and funds transfers. One of the drawbacks of EDI (and FEDI) is that it is expensive and complex to set up. However, with the growth of the Internet, a new form of EDI has emerged: Internet e-commerce. For example, networking giant Cisco Systems books millions in orders each day on its Web site from resellers around the world. Firms are also linking to critical suppliers and customers via “extranets,” which are business networks that extend a company’s internal network. Because of security concerns and lack of standardization, don’t look for e-commerce and extranets to eliminate the need for EDI anytime soon. In fact, these are complementary systems that will most likely be used in tandem as the future unfolds. On October 29, 2004, the Check Clearing for the 21st Century Act, also known as Check 21, took effect. Before Check 21, a bank receiving a check was required to send the physical check to the customer’s bank before payment could be made. Now a bank can transmit an electronic image of the check to the customer’s bank and receive payment immediately. Previously, an out-of-state check might take three days to clear. But with Check 21, the clearing time is typically one day; and often a check can clear the same day it is written. Thus, Check 21 promises to significantly reduce float.

27.3 Cash Collection and Concentration From our previous discussion, we know that collection delays work against the firm. All other things being the same, a firm will adopt procedures to speed up collections and thereby decrease collection times. In addition, even after cash is collected, firms need procedures to funnel, or concentrate, that cash where it can be best used. We discuss some common collection and concentration procedures next.

Components of Collection Time Based on our previous discussion, we can depict the basic parts of the cash collection process as follows. The total time in this process is made up of mailing time, checkprocessing delay, and the bank’s availability delay. Customer mails payment

Company receives payment

Company deposits payment

Cash available

Time Mailing time

Processing delay Collection time

Availability delay

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The amount of time that cash spends in each part of the cash collection process depends on where the firm’s customers and banks are located and how efficient the firm is in collecting cash.

CashCo llection How a firm collects from its customers depends in large part on the nature of the business. The simplest case would be a business such as a restaurant chain. Most of its customers will pay with cash, check, or credit card at the point of sale (this is called over-the-counter collection), so there is no problem with mailing delay. Normally, the funds will be deposited in a local bank, and the firm will have some means (discussed later) of gaining access to the funds. When some or all of the payments a company receives are checks that arrive through the mail, all three components of collection time become relevant. The firm may choose to have all the checks mailed to one location; more commonly, the firm might have a number of different mail collection points to reduce mailing times. Also, the firm may run its collection operation itself or might hire an outside firm that specializes in cash collection. We discuss these issues in more detail in the following pages. Other approaches to cash collection exist. One that is becoming more common is the preauthorized payment arrangement. With this arrangement, the payment amounts and payment dates are fixed in advance. When the agreed-upon date arrives, the amount is automatically transferred from the customer’s bank account to the firm’s bank account, which sharply reduces or even eliminates collection delays. The same approach is used by firms that have online terminals, meaning that when a sale is rung up, the money is immediately transferred to the firm’s accounts.

Lockboxes When a firm receives its payments by mail, it must decide where the checks will be mailed and how the checks will be picked up and deposited. Careful selection of the number and locations of collection points can greatly reduce collection times. Many firms use special post office boxes called lockboxes to intercept payments and speed up cash collection. Figure 27.3 illustrates a lockbox system. The collection process is started by customers mailing their checks to a post office box instead of sending them to the firm. The lockbox is maintained by a local bank. A large corporation may actually maintain more than 20 lockboxes around the country. In the typical lockbox system, the local bank collects the lockbox checks several times a day. The bank deposits the checks directly to the firm’s account. Details of the operation are recorded (in some computer-usable form) and sent to the firm. A lockbox system reduces mailing time because checks are received at a nearby post office instead of at corporate headquarters. Lockboxes also reduce processing time because the corporation doesn’t have to open the envelopes and deposit checks for collection. All in all, a bank lockbox system should enable a firm to get its receipts processed, deposited, and cleared faster than if it were to receive checks at its headquarters and deliver them itself to the bank for deposit and clearing. Some firms have turned to what are called “electronic lockboxes” as an alternative to traditional lockboxes. In one version of an electronic lockbox, customers use the telephone or the Internet to access their account—say, their credit card account at a bank—review their bill, and authorize payment without paper ever having changed

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Figure 27.3 Overview of Lockbox Processing

Customer payments

Customer payments

Customer payments

Post office box 1

Customer payments

Post office box 2

Local bank collects funds from post office boxes Envelopes opened; separation of checks and receipts

Details of receivables go to firm

Deposit of checks into bank accounts

Firm processes receivables

Bank begins check-clearing process

The flow starts when a corporate customer mails remittances to a post office box instead of to the corporation. Several times a day, the bank collects the lockbox receipts from the post office. The checks are then put into the company bank accounts.

hands on either end of the transaction. Clearly, an electronic lockbox system is far superior to traditional bill payment methods, at least from the biller’s perspective. Look for systems like this to continue to grow in popularity.

CashCo ncentration As we discussed earlier, a firm will typically have a number of cash collection points; as a result, cash collections may end up in many different banks and bank accounts. From here the firm needs procedures to move the cash into its main accounts. This is called cash concentration. By routinely pooling its cash, the firm greatly simplifies its cash management by reducing the number of accounts that must be tracked. Also, by having a larger pool of funds available, a firm may be able to negotiate or otherwise obtain a better rate on any short-term investments. In setting up a concentration system, firms will typically use one or more concentration banks. A concentration bank pools the funds obtained from local banks contained within some geographic region. Concentration systems are often used in conjunction with lockbox systems. Figure 27.4 illustrates how an integrated cash collection and cash concentration system might look. As Figure 27.4 illustrates, a key part of the cash collection and concentration process is the transfer of funds to the concentration bank. There are several options available for accomplishing this transfer. The cheapest

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Figure 27.4 Lockboxesand Concentration Banks in a Cash ManagementS ystem

Customer payments

Customer payments

Firm sales office

Statements are sent by mail to firm for receivables processing Customer payments

Local bank deposits

Post office lockbox receipts Customer payments

Funds are transferred to concentration bank Concentration bank Cash manager analyzes bank balance and deposit information and makes cash allocation revision Firm cash manager

Maintenance of cash reserves

Global Treasury News has current info about cash management, especially for international issues (www.gtnews.com).

Disbursement activity

Short-term investment of cash

Maintenance of compensating balance at creditor bank

is a depository transfer check (DTC), which is a preprinted check that usually needs no signature and is valid only for transferring funds between specific accounts within the same firm. The money becomes available one to two days later. Automated clearinghouse (ACH ) transfers are basically electronic versions of paper checks. These may be more expensive, depending on the circumstances, but the funds are available the next day. The most expensive means of transfer are wire transfers, which provide sameday availability. Which approach a firm will choose depends on the number and size of payments. For example, a typical ACH transfer might be $200, whereas a typical wire transfer would be several million dollars. Firms with a large number of collection points and relatively small payments will choose the cheaper route, whereas firms that receive smaller numbers of relatively large payments may choose more expensive procedures.

Accelerating Collections: An Example The decision of whether or not to use a bank cash management service incorporating lockboxes and concentration banks depends on where a firm’s customers are located and the speed of the U.S. postal system. Suppose Atlantic Corporation, located in Philadelphia, is considering a lockbox system. Its collection delay is currently eight days.

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Atlantic does business in the southwestern part of the country (New Mexico, Arizona, and California). The proposed lockbox system would be located in Los Angeles and operated by Pacific Bank. Pacific Bank has analyzed Atlantic’s cashgathering system and has concluded that it can decrease collection time by two days. Specifically, the bank has come up with the following information on the proposed lockbox system: Reductionin mailin gtime = 1.0 day Reduction in clearing time = .5 day Reduction in firm processing time = .5 day Total =2.0d ays The following is also known: Dailyin teresto nT reasuryb ills =.025% Average number of daily payments to lockboxes =2,000 Average siz e fo ayment p =$600 The cash flows for the current collection operation are shown in the following cash flow time chart: Mailing time

Processing delay

Customer mails check 0

Availability delay

Check Deposit is is received made 1

2

3

4 Day

Cash is available

5

6

7

8

The cash flows for the lockbox collection operation will be as follows: Mailing time

Processing delay

Customer mails check 0

1

2

Check is received

Deposit is made

3

3.5

Availability delay Cash is available 4

5

6

Day

Pacific Bank has agreed to operate this lockbox system for a fee of 25 cents per check processed. Should Atlantic give the go-ahead? We first need to determine the benefit of the system. The average daily collections from the southwestern region are $1.2 million (=2,000 × $600). The collection time will be decreased by two days, so the lockbox system will increase the collected bank balance by $1.2 million × 2 = $2.4 million. In other words, the lockbox system releases $2.4 million to the firm by reducing processing, mailing, and clearing time by two days. From our earlier discussion, we know that this $2.4 million is the PV of the proposal.

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To calculate the NPV, we need to determine the PV of the costs. There are several different ways to proceed. First, at 2,000 checks per day and $.25 per check, the daily cost is $500. This cost will be incurred every day forever. At an interest rate of .025 percent per day, the PV is therefore $500 .00025 = $2 million. The NPV is thus $2.4 million − $2 million = $400,000, and the system appears to be desirable. Alternatively, Atlantic could invest the $2.4 million at .025 percent per day. The interest earned would be $2.4 million × .00025 = $600 per day. The cost of the system is $500 per day; so running it obviously generates a profit in the amount of $100 per day. The PV of $100 per day forever is $100 .00025 = $400,000, just as we calculated before. Finally, and most simply, each check is for $600 and is available two days sooner if the system is used. The interest on $600 for two days is 2 × $600 × .00025 = $.30. The cost is 25 cents per check, so Atlantic makes a nickel (=$.30 × .25) on every check. With 2,000 checks per day, the profit is $.05 × 2,000 checks = $100 per day, as we previously calculated.

EXAMPLE27.4

Accelerating Collections In our example concerning the Atlantic Corporation’s proposed lockbox system, suppose Pacific Bank wants a $20,000 fixed fee (paid annually) in addition to the 25 cents per check. Is the system still a good idea? To answer, we need to calculate the PV of the fixed fee. The daily interest rate is .025 percent. The annual rate is therefore 1.00025365 − 1 = 9.553%. The PV of the fixed fee (which is paid each year forever) is $20,000 .09553 = $209,358. Because the NPV without the fee is $400,000, the NPV with the fee is $400,000 − $209,358 = $190,642. It’s still a good idea.

27.4 Managing Cash Disbursements From the firm’s point of view, disbursement float is desirable, so the goal in managing disbursement float is to slow down disbursements. To do this, the firm may develop strategies to increase mail float, processing float, and availability float on the checks it writes. Beyond this, firms have developed procedures for minimizing cash held for payment purposes. We discuss the most common of these in this section.

Increasing Disbursement Float For a free cash budgeting spreadsheet, go to www.toolkit.cch .com/tools/tools.asp.

As we have seen, slowing down payments comes from the time involved in mail delivery, check processing, and collection of funds. Disbursement float can be increased by writing a check on a geographically distant bank. For example, a New York supplier might be paid with checks drawn on a Los Angeles bank. This will increase the time required for the checks to clear through the banking system. Mailing checks from remote post offices is another way firms slow down disbursement. Tactics for maximizing disbursement float are debatable on both ethical and economic grounds. First, as we discuss in some detail in the next chapter, payment terms frequently offer a substantial discount for early payment. The discount is usually much larger than any possible savings from “playing the float game.” In such cases, increasing mailing time will be of no benefit if the recipient dates payments based on the date received (as is common) as opposed to the postmark date.

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Beyond this, suppliers are not likely to be fooled by attempts to slow down disbursements. The negative consequences of poor relations with suppliers can be costly. In broader terms, intentionally delaying payments by taking advantage of mailing times or unsophisticated suppliers may amount to avoiding paying bills when they are due— an unethical business procedure.

ControllingDi sbursements We have seen that maximizing disbursement float is probably a poor business practice. However, a firm will still wish to tie up as little cash as possible in disbursements. Firms have therefore developed systems for efficiently managing the disbursement process. The general idea in such systems is to have no more than the minimum amount necessary to pay bills on deposit in the bank. We discuss some approaches to accomplishing this goal next. Zero-Balance Accounts With a zero-balance account system, the firm, in cooperation with its bank, maintains a master account and a set of subaccounts. When a check written on one of the subaccounts must be paid, the necessary funds are transferred in from the master account. Figure 27.5 illustrates how such a system might work. In this case, the firm maintains two disbursement accounts, one for suppliers and one for payroll. As shown, if the firm does not use zero-balance accounts, then each of these accounts must have a safety stock of cash to meet unanticipated demands. If the firm does use zero-balance accounts, then it can keep one safety stock in a master account and transfer the funds to the two subsidiary accounts as needed. The key is that the total amount of cash held as a buffer is smaller under the zero-balance arrangement, which frees up cash to be used elsewhere. Controlled Disbursement Accounts With a controlled disbursement account system, almost all payments that must be made in a given day are known in the morning. The bank informs the firm of the total, and the firm transfers (usually by wire) the amount needed.

Figure 27.5

Zero-Balance Accounts

No zero-balance accounts Payroll account

Two zero-balance accounts

Supplier account

Master account

Safety stock Safety stocks

With no zero-balance accounts, separate safety stocks must be maintained, which ties up cash unnecessarily. With zerobalance accounts, the firm keeps a single safety stock of cash in a master account. Funds are transferred into disbursement accounts as needed.

Cash transfers

Payroll account

Cash transfers

Supplier account

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27.5 Investing Idle Cash If a firm has a temporary cash surplus, it can invest in short-term securities. As we have mentioned at various times, the market for short-term financial assets is called the money market. The maturity of short-term financial assets that trade in the money market is one year or less. Most large firms manage their own short-term financial assets, carrying out transactions through banks and dealers. Some large firms and many small firms use money market mutual funds. These are funds that invest in short-term financial assets for a management fee. The management fee is compensation for the professional expertise and diversification provided by the fund manager. Among the many money market mutual funds, some specialize in corporate customers. In addition, banks offer arrangements in which the bank takes all excess available funds at the close of each business day and invests them for the firm.

TemporaryCa shSur pluses Firms have temporary cash surpluses for various reasons. Two of the most important are the financing of seasonal or cyclical activities of the firm and the financing of planned or possible expenditures. Seasonal or Cyclical Activities Some firms have a predictable cash flow pattern. They have surplus cash flows during part of the year and deficit cash flows the rest of the year. For example, Toys “ ” Us, a retail toy firm, has a seasonal cash flow pattern influenced by the holiday season. A firm such as Toys “ ” Us may buy marketable securities when surplus cash flows occur and sell marketable securities when deficits occur. Of course, bank loans are another short-term financing device. The use of bank loans and marketable securities to meet temporary financing needs is illustrated in Figure 27.6. In this case, the firm is following a compromise working capital policy in the sense we discussed in the previous chapter.

Figure 27.6 SeasonalC ash Demands

Total financing needs

Bank loans

Short-term financing

Dollars

Marketable securities

Long-term financing

0

1

2 Time (quarters)

3

Time 1: A surplus cash flow exists. Seasonal demand for assets is low. The surplus cash flow is invested in short-term marketable securities. Time 2: A deficit cash flow exists. Seasonal demand for assets is high. The financial deficit is financed by selling marketable securities and by bank borrowing.

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Planned or Possible Expenditures Firms frequently accumulate temporary investments in marketable securities to provide the cash for a plant construction program, dividend payment, or other large expenditure. Thus, firms may issue bonds and stocks before the cash is needed, investing the proceeds in short-term marketable securities and then selling the securities to finance the expenditures. Also, firms may face the possibility of having to make a large cash outlay. An obvious example would involve the possibility of losing a large lawsuit. Firms may build up cash surpluses against such a contingency.

Characteristicso fSho rt-TermSe curities Given that a firm has some temporarily idle cash, a variety of short-term securities are available for investing. The most important characteristics of these short-term marketable securities are their maturity, default risk, marketability, and taxability. Maturity From Chapter 8, we know that for a given change in the level of interest rates, the prices of longer-maturity securities will change more than those of shortermaturity securities. As a consequence, firms that invest in long-term securities are accepting greater risk than firms that invest in securities with short-term maturities. We called this type of risk interest rate risk. Firms often limit their investments in marketable securities to those maturing in less than 90 days to avoid the risk of losses in value from changing interest rates. Of course, the expected return on securities with short-term maturities is usually less than the expected return on securities with longer maturities. Default Risk Default risk refers to the probability that interest and principal will not be paid in the promised amounts on the due dates (or will not be paid at all). In Chapter 8, we observed that various financial reporting agencies, such as Moody’s Investors Service and Standard and Poor’s, compile and publish ratings of various corporate and other publicly held securities. These ratings are connected to default risk. Of course, some securities have negligible default risk, such as U.S. Treasury bills. Given the purposes of investing idle corporate cash, firms typically avoid investing in marketable securities with significant default risk. Marketability Marketability refers to how easy it is to convert an asset to cash; so marketability and liquidity mean much the same thing. Some money market instruments are much more marketable than others. At the top of the list are U.S. Treasury bills, which can be bought and sold very cheaply and very quickly. Taxes Interest earned on money market securities that are not some kind of government obligation (either federal or state) is taxable at the local, state, and federal levels. U.S. Treasury obligations such as T-bills are exempt from state taxation, but other government-backed debt is not. Municipal securities are exempt from federal taxes, but they may be taxed at the state level.

Some Different Types of Money Market Securities Money market securities are generally highly marketable and short-term. They usually have low risk of default. They are issued by the U.S. government (for example, U.S. Treasury bills), domestic and foreign banks (for example, certificates of deposit), and business corporations (for example, commercial paper). There are many types in all, and we illustrate only a few of the most common here.

Chapter 27 Cash Management

Check out short-term rates online at www.bloomberg.com.

U.S. Treasury bills are obligations of the U.S. government that mature in 30, 90, or 180 days. Bills are sold by auction every week. Short-term tax-exempts are short-term securities issued by states, municipalities, local housing agencies, and urban renewal agencies. Because these are all considered municipal securities, they are exempt from federal taxes. RANs, BANs, and TANs, for example, are revenue, bond, and tax anticipation notes, respectively. In other words, they represent short-term borrowing by municipalities in anticipation of cash receipts. Short-term tax-exempts have more default risk than U.S. Treasury issues and are less marketable. Because the interest is exempt from federal income tax, the pretax yield on tax-exempts is lower than that on comparable securities such as Treasury bills. Also, corporations face restrictions on holding tax-exempts as investments. Commercial paper consists of short-term securities issued by finance companies, banks, and corporations. Typically, commercial paper is unsecured. Maturities range from a few weeks to 270 days. There is no especially active secondary market in commercial paper. As a consequence, the marketability can be low; however, firms that issue commercial paper will often repurchase it directly before maturity. The default risk of commercial paper depends on the financial strength of the issuer. Moody’s and S&P publish quality ratings for commercial paper. These ratings are similar to the bond ratings we discussed in Chapter 8. Certificates of deposit (CDs) are short-term loans to commercial banks. The most common are jumbo CDs—those in excess of $100,000. There are active markets in CDs of 3-month, 6-month, 9-month, and 12-month maturities. Repurchase agreements (repos) are sales of government securities (for example, U.S. Treasury bills) by a bank or securities dealer with an agreement to repurchase. Typically, an investor buys some Treasury securities from a bond dealer and simultaneously agrees to sell them back at a later date at a specified higher price. Repurchase agreements usually involve a very short term—overnight to a few days. Because 70 to 80 percent of the dividends received by one corporation from another are exempt from taxation, the relatively high dividend yields on preferred stock provide a strong incentive for investment. The only problem is that the dividend is fixed with ordinary preferred stock, so the price can fluctuate more than is desirable in a shortterm investment. However, money market preferred stock is a fairly recent innovation featuring a floating dividend. The dividend is reset fairly often (usually every 49 days); so this type of preferred has much less price volatility than ordinary preferred, and it has become a popular short-term investment.

In this chapter, we have examined cash and liquidity management. We saw the following: 1. A firm holds cash to conduct transactions and to compensate banks for the various services they render. 2. The difference between a firm’s available balance and its book balance is the firm’s net float. The float reflects the fact that some checks have not cleared and are thus uncollected. The financial manager must always work with collected cash balances and not with the company’s book balance. To do otherwise is to use the bank’s cash without the bank knowing it, which raises ethical and legal questions. 3. The firm can make use of a variety of procedures to manage the collection and disbursement of cash in such a way as to speed up the collection of cash and slow down the

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payments. Some methods to speed up the collection are the use of lockboxes, concentration banking, and wire transfers. 4. Because of seasonal and cyclical activities, to help finance planned expenditures, or as a contingency reserve, firms temporarily hold a cash surplus. The money market offers a variety of possible vehicles for “parking” this idle cash.

Concept Questions

1. 2. 3. 4. 5.

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Cash Management Is it possible for a firm to have too much cash? Why would shareholders care if a firm accumulates large amounts of cash? Cash Management What options are available to a firm if it believes it has too much cash? How about too little? Agency Issues Are stockholders and creditors likely to agree on how much cash a firm should keep on hand? Cash Management versus Liquidity Management What is the difference between cash management and liquidity management? Short-Term Investments Why is a preferred stock with a dividend tied to short-term interest rates an attractive short-term investment for corporations with excess cash? Collection and Disbursement Floats Which would a firm prefer: A net collection float or a net disbursement float? Why? Float Suppose a firm has a book balance of $2 million. At the automatic teller machine (ATM), the cash manager finds out that the bank balance is $2.5 million. What is the situation here? If this is an ongoing situation, what ethical dilemma arises? Short-Term Investments For each of the short-term marketable securities given here, provide an example of the potential disadvantages the investment has for meeting a corporation’s cash management goals: a. U.S.T reasuryb ills. b. Ordinaryp referreds tock. c. Negotiable certificates of deposit (NCDs). d. Commercialp aper. e. Revenuean ticipationn otes. f. Repurchasea greements. Agency Issues It is sometimes argued that excess cash held by a firm can aggravate agency problems (discussed in Chapter 1) and, more generally, reduce incentives for shareholder wealth maximization. How would you describe the issue here? Use of Excess Cash One option a firm usually has with any excess cash is to pay its suppliers more quickly. What are the advantages and disadvantages of this use of excess cash? Use of Excess Cash Another option usually available is to reduce the firm’s outstanding debt. What are the advantages and disadvantages of this use of excess cash? Float An unfortunately common practice goes like this (Warning: Don’t try this at home): Suppose you are out of money in your checking account; however, your local grocery store will, as a convenience to you as a customer, cash a check for you. So, you cash a check for $200. Of course, this check will bounce unless you do something. To prevent this, you go to the grocery the next day and cash another check for $200. You take this $200 and deposit it. You repeat this process every day, and, in doing so, you make sure that no checks bounce. Eventually, manna from heaven arrives (perhaps in the form of money from home), and you are able to cover your outstanding checks. To make it interesting, suppose you are absolutely certain that no checks will bounce along the way. Assuming this is true, and ignoring any question of legality (what we have described is probably illegal check kiting), is there anything unethical about this? If you say yes, then why? In particular, who is harmed?

Chapter 27

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Calculating Float In a typical month, the Jeremy Corporation receives 80 checks totaling $156,000. These are delayed four days on average. What is the average daily float? Calculating Net Float Each business day, on average, a company writes checks totaling $14,000 to pay its suppliers. The usual clearing time for the checks is four days. Meanwhile, the company is receiving payments from its customers each day, in the form of checks, totaling $26,000. The cash from the payments is available to the firm after two days. a. Calculate the company’s disbursement float, collection float, and net float. b. How would your answer to part (a) change if the collected funds were available in oned ayin steado f t wo? Costs of Float Purple Feet Wine, Inc., receives an average of $19,000 in checks per day. The delay in clearing is typically three days. The current interest rate is .019 percent per day. a. Whatis thec ompany’sf loat? b. What is the most Purple Feet should be willing to pay today to eliminate its float entirely? c. What is the highest daily fee the company should be willing to pay to eliminate its floate ntirely? Float and Weighted Average Delay Your neighbor goes to the post office once a month and picks up two checks, one for $17,000 and one for $6,000. The larger check takes four days to clear after it is deposited; the smaller one takes five days. a. What is the total float for the month? b. What is the average daily float? c. What are the average daily receipts and weighted average delay? NPV and Collection Time Your firm has an average receipt size of $108. A bank has approached you concerning a lockbox service that will decrease your total collection time by two days. You typically receive 8,500 checks per day. The daily interest rate is .016 percent. If the bank charges a fee of $225 per day, should the lockbox project be accepted? What would the net annual savings be if the service were adopted? Using Weighted Average Delay A mail-order firm processes 5,300 checks per month. Of these, 60 percent are for $55 and 40 percent are for $80. The $55 checks are delayed two days on average; the $80 checks are delayed three days on average. a. What is the average daily collection float? How do you interpret your answer? b. What is the weighted average delay? Use the result to calculate the average daily float. c. How much should the firm be willing to pay to eliminate the float? d. If the interest rate is 7 percent per year, calculate the daily cost of the float. e. How much should the firm be willing to pay to reduce the weighted average float by1 .5d ays? Value of Lockboxes Paper Submarine Manufacturing is investigating a lockbox system to reduce its collection time. It has determined the following: Average number of payments per day Average value of payment Variable lockbox fee (per transaction) Daily interest rate on money market securities

385 $1,105 $.50 .02%

The total collection time will be reduced by three days if the lockbox system is adopted. a. What is the PV of adopting the system? b. What is the NPV of adopting the system? c. What is the net cash flow per day from adopting? Per check?

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Short-Term Finance

Lockboxes and Collections It takes Cookie Cutter Modular Homes, Inc., about six days to receive and deposit checks from customers. Cookie Cutter’s management is considering a lockbox system to reduce the firm’s collection times. It is expected that the lockbox system will reduce receipt and deposit times to three days total. Average daily collections are $145,000, and the required rate of return is 9 percent per year. a. What is the reduction in outstanding cash balance as a result of implementing the lockboxs ystem? b. What is the dollar return that could be earned on these savings? c. What is the maximum monthly charge Cookie Cutter should pay for this lockbox system if the payment is due at the end of the month? What if the payment is due at the beginning of the month? Value of Delay No More Pencils, Inc., disburses checks every two weeks that average $93,000 and take seven days to clear. How much interest can the company earn annually if it delays transfer of funds from an interest-bearing account that pays .015 percent per day for these seven days? Ignore the effects of compounding interest. NPV and Reducing Float No More Books Corporation has an agreement with Floyd Bank, whereby the bank handles $4 million in collections a day and requires a $400,000 compensating balance. No More Books is contemplating canceling the agreement and dividing its eastern region so that two other banks will handle its business. Banks A and B will each handle $2 million of collections a day, and each requires a compensating balance of $250,000. No More Books’ financial management expects that collections will be accelerated by one day if the eastern region is divided. Should the company proceed with the new system? What will be the annual net savings? Assume that the T-bill rate is 5 percent annually. Lockboxes and Collection Time Bird’s Eye Treehouses, Inc., a Kentucky company, has determined that a majority of its customers are located in the Pennsylvania area. It therefore is considering using a lockbox system offered by a bank located in Pittsburgh. The bank has estimated that use of the system will reduce collection time by two days. Based on the following information, should the lockbox system be adopted? Average number of payments per day Average value of payment Variable lockbox fee (per transaction) Annual interest rate on money market securities

12.

750 $980 $.35 7%

How would your answer change if there were a fixed charge of $5,000 per year in addition to the variable charge? Calculating Transactions Required Cow Chips, Inc., a large fertilizer distributor based in California, is planning to use a lockbox system to speed up collections from its customers located on the East Coast. A Philadelphia-area bank will provide this service for an annual fee of $20,000 plus 10 cents per transaction. The estimated reduction in collection and processing time is one day. If the average customer payment in this region is $5,300, how many customers are needed, on average, each day to make the system profitable for Cow Chips? Treasury bills are currently yielding 5 percent per year.

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Appendix 27A Determining the Target Cash Balance Appendix 27B Adjustable Rate Preferred Stock, Auction Rate

Preferred Stock, and Floating-Rate Certificates of Deposit

Mini Case

To access the appendixes for this chapter, please visit www.mhhe.com/rwj.

CASH MANAGEMENT AT RICHMOND CORPORATION Richmond Corporation was founded 20 years ago by its president, Daniel Richmond. The company originally began as a mail-order company but has grown rapidly in recent years, in large part due to its Web site. Because of the wide geographical dispersion of the company’s customers, it currently employs a lockbox system with collection centers in San Francisco, St. Louis, Atlanta, and Boston. Steve Dennis, the company’s treasurer, has been examining the current cash collection policies. On average, each lockbox center handles $235,000 in payments each day. The company’s current policy is to invest these payments in short-term marketable securities daily at the collection center banks. Every two weeks the investment accounts are swept, and the proceeds are wire-transferred to Richmond’s headquarters in Dallas to meet the company’s payroll. The investment accounts each pay .068 percent per day, and the wire transfers cost .20 percent of the amount transferred. Steve has been approached by Third National Bank, located just outside Dallas, about the possibility of setting up a concentration banking system for Richmond Corp. Third National will accept the lockbox centers’ daily payments via automated clearinghouse (ACH) transfers in lieu of wire transfers. The ACH-transferred funds will not be available for use for one day. Once cleared, the funds will be deposited in a short-term account, which will yield .075 percent per day. Each ACH transfer will cost $200. Daniel has asked Steve to determine which cash management system will be the best for the company. Steve has asked you, his assistant, to answer the following questions: 1. What is Richmond Corporation’s total net cash flow from the current lockbox system available to meet payroll? 2. Under the terms outlined by Third National Bank, should the company proceed with the concentration banking system? 3. What cost of ACH transfers would make the company indifferent between the two systems?

CHAPTER 28

Credit and Inventory Management Home furnishings company Linens ‘n Things was in poor shape financially in April 2008, and many suppliers stopped shipping merchandise to the retailer because of slow or no payments. In an unusual effort to keep its doors open, the company agreed to pay between 60 and 100 of its suppliers “CBD,” or cash before delivery, instead of the more typical policy of paying one to two months after delivery. Unfortunately for the company, it was still forced to declare bankruptcy. When this happened, suppliers who were owed money faced the consequences. For example, Amcor, an appliance and consumer electronics manufacturer, was owed $3.68 million on a shipment of GPS units. Because of the bankruptcy proceedings, Amcor expected to lose between $500,000 and $750,000 of the amount owed, a significant loss for the relatively small company. Other creditors included Calphalon, KitchenAid, and Yankee Candle Co. As this case shows, extending credit can lead to large losses when the customer can’t (or won’t) pay, and, consequently, credit management is an important aspect of short-term finance.

28.1 Credit and Receivables When a firm sells goods and services, it can demand cash on or before the delivery date, or it can extend credit to customers and allow some delay in payment. The next few sections provide an idea of what is involved in the firm’s decision to grant credit to its customers. Granting credit is making an investment in a customer—an investment tied to the sale of a product or service. Why do firms grant credit? Not all do, but the practice is extremely common. The obvious reason is that offering credit is a way of stimulating sales. The costs associated with granting credit are not trivial. First, there is the chance that the customer will not pay. Second, the firm has to bear the costs of carrying the receivables. The credit policy decision thus involves a trade-off between the benefits of increased sales and the costs of granting credit. From an accounting perspective, when credit is granted, an account receivable is created. Such receivables include credit to other firms, called trade credit, and credit granted consumers, called consumer credit. About one-sixth of all the assets of U.S. industrial firms are in the form of accounts receivable, so receivables obviously represent a major investment of financial resources by U.S. businesses.

Components of Credit Policy If a firm decides to grant credit to its customers, then it must establish procedures for extending credit and collecting. In particular, the firm will have to deal with the following components of credit policy: 1. Terms of sale: The terms of sale establish how the firm proposes to sell its goods and services. A basic decision is whether the firm will require cash or will extend 846

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credit. If the firm does grant credit to a customer, the terms of sale will specify (perhaps implicitly) the credit period, the cash discount and discount period, and the type of credit instrument. 2. Creditanalysis : In granting credit, a firm determines how much effort to expend trying to distinguish between customers who will pay and customers who will not pay. Firms use a number of devices and procedures to determine the probability that customers will not pay; put together, these are called credit analysis. 3. Collectionpolic y: After credit has been granted, the firm has the potential problem of collecting the cash, for which it must establish a collection policy. In the next several sections, we will discuss these components of credit policy that collectively make up the decision to grant credit.

The Cash Flows from Granting Credit In a previous chapter, we described the accounts receivable period as the time it takes to collect on a sale. There are several events that occur during this period. These events are the cash flows associated with granting credit, and they can be illustrated with a cashf lowd iagram: These companies assist businesses with working capital management: www.pnc.com and www.treasurystrat .com/corp.

The Cash Flows of Granting Credit Credit sale is made

Customer mails check

Firm deposits check in bank

Bank credits firm’s account

Time Cash collection Accounts receivable

As our time line indicates, the typical sequence of events when a firm grants credit is as follows: (1) The credit sale is made, (2) the customer sends a check to the firm, (3) the firm deposits the check, and (4) the firm’s account is credited for the amount of the check. Based on our discussion in the previous chapter, it is apparent that one of the factors influencing the receivables period is float. Thus, one way to reduce the receivables period is to speed up the check mailing, processing, and clearing. Because we cover this subject elsewhere, we will ignore float in the subsequent discussion and focus on what is likely to be the major determinant of the receivables period: Credit policy.

The Investment in Receivables For more on accounts receivable management, visit www.insidearm.com.

The investment in accounts receivable for any firm depends on the amount of credit sales and the average collection period. For example, if a firm’s average collection period, ACP, is 30 days, then, at any given time, there will be 30 days’ worth of sales outstanding. If credit sales run $1,000 per day, the firm’s accounts receivable will then be equal to 30 days × $1,000 per day = $30,000, on average. As our example illustrates, a firm’s receivables generally will be equal to its average daily sales multiplied by its average collection period: Accountsr eceivable = Average daily sales ×A CP

(28.1)

Thus, a firm’s investment in accounts receivable depends on factors that influence credit sales and collections.

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We have seen the average collection period in various places, including Chapter 3 and Chapter 26. Recall that we use the terms days’ sales in receivables, receivables period, and average collection period interchangeably to refer to the length of time it takes for the firm to collect on a sale.

28.2 Terms of the Sale As we described previously, the terms of a sale are made up of three distinct elements: 1. The period for which credit is granted (the credit period). 2. The cash discount and the discount period. 3. Thet ypeo f c reditin strument. Within a given industry, the terms of sale are usually fairly standard, but these terms vary quite a bit across industries. In many cases, the terms of sale are remarkably archaic and literally date to previous centuries. Organized systems of trade credit that resemble current practice can be easily traced to the great fairs of medieval Europe, and they almost surely existed long before then.

TheB asicF orm

For more about the credit process for small businesses, see www.newyorkfed.org/ education/addpub/ credit.html.

The easiest way to understand the terms of sale is to consider an example. Terms such as 2 10, net 60 are common. This means that customers have 60 days from the invoice date (discussed a bit later) to pay the full amount; however, if payment is made within 10 days, a 2 percent cash discount can be taken. Consider a buyer who places an order for $1,000, and assume that the terms of the sale are 2 10, net 60. The buyer has the option of paying $1,000 × (1 − .02) = $980 in 10 days, or paying the full $1,000 in 60 days. If the terms are stated as just net 30, then the customer has 30 days from the invoice date to pay the entire $1,000, and no discount is offered for early payment. In general, credit terms are interpreted in the following way: ,

Thus, 5 10, net 45 means take a 5 percent discount from the full price if you pay within 10 days, or else pay the full amount in 45 days.

TheCr editP eriod The credit period is the basic length of time for which credit is granted. The credit period varies widely from industry to industry, but it is almost always between 30 and 120 days. If a cash discount is offered, then the credit period has two components: The net credit period and the cash discount period. The net credit period is the length of time the customer has to pay. The cash discount period is the time during which the discount is available. With 2 10, net 30, for example, the net credit period is 30 days and the cash discount period is 10 days. The Invoice Date The invoice date is the beginning of the credit period. An invoice is a written account of merchandise shipped to the buyer. For individual items, by convention, the invoice date is usually the shipping date or the billing date, not the date on which the buyer receives the goods or the bill.

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Many other arrangements exist. For example, the terms of sale might be ROG, for receipt of goods. In this case, the credit period starts when the customer receives the order. This might be used when the customer is in a remote location. With EOM dating, all sales made during a particular month are assumed to be made at the end of that month. This is useful when a buyer makes purchases throughout the month, but the seller bills only once a month. For example, terms of 2 10th, EOM tell the buyer to take a 2 percent discount if payment is made by the 10th of the month; otherwise the full amount is due. Confusingly, the end of the month is sometimes taken to be the 25th day of the month. MOM, for middle of month, is another variation. Seasonal dating is sometimes used to encourage sales of seasonal products during the off-season. A product sold primarily in the summer (e.g., suntan oil) can be shipped in January with credit terms of 2 10, net 30. However, the invoice might be dated May 1 so that the credit period actually begins at that time. This practice encourages buyers to order early. Length of the Credit Period Several factors influence the length of the credit period. Two important ones are the buyer’s inventory period and operating cycle. All else equal, the shorter these are, the shorter the credit period will be. From Chapter 26, the operating cycle has two components: The inventory period and the receivables period. The buyer’s inventory period is the time it takes the buyer to acquire inventory (from us), process it, and sell it. The buyer’s receivables period is the time it then takes the buyer to collect on the sale. Note that the credit period we offer is effectively the buyer’s payables period. By extending credit, we finance a portion of our buyer’s operating cycle and thereby shorten that buyer’s cash cycle (see Figure 26.1). If our credit period exceeds the buyer’s inventory period, then we are financing not only the buyer’s inventory purchases, but part of the buyer’s receivables as well. Furthermore, if our credit period exceeds our buyer’s operating cycle, then we are effectively providing financing for aspects of our customer’s business beyond the immediate purchase and sale of our merchandise. The reason is that the buyer effectively has a loan from us even after the merchandise is resold, and the buyer can use that credit for other purposes. For this reason, the length of the buyer’s operating cycle is often cited as an appropriate upper limit to the credit period. There are a number of other factors that influence the credit period. Many of these also influence our customer’s operating cycles; so, once again, these are related subjects. Among the most important are these: 1. Perishability and collateral value: Perishable items have relatively rapid turnover and relatively low collateral value. Credit periods are thus shorter for such goods. For example, a food wholesaler selling fresh fruit and produce might use net seven days. Alternatively, jewelry might be sold for 5 30, net four months. 2. Consumer demand: Products that are well established generally have more rapid turnover. Newer or slow-moving products will often have longer credit periods associated with them to entice buyers. Also, as we have seen, sellers may choose to extend much longer credit periods for off-season sales (when customer demand is low). 3. Cost, profitability, and standardization: Relatively inexpensive goods tend to have shorter credit periods. The same is true for relatively standardized goods and raw materials. These all tend to have lower markups and higher turnover rates, both of

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which lead to shorter credit periods. However, there are exceptions. Auto dealers, for example, generally pay for cars as they are received. Credit risk: The greater the credit risk of the buyer, the shorter the credit period is likely to be (if credit is granted at all). Size of the account: If an account is small, the credit period may be shorter because small accounts cost more to manage, and the customers are less important. Competition: When the seller is in a highly competitive market, longer credit periods may be offered as a way of attracting customers. Customer type: A single seller might offer different credit terms to different buyers. A food wholesaler, for example, might supply groceries, bakeries, and restaurants. Each group would probably have different credit terms. More generally, sellers often have both wholesale and retail customers, and they frequently quote differentte rmsto th etw otyp es.

CashDi scounts As we have seen, cash discounts are often part of the terms of sale. The practice of granting discounts for cash purchases in the United States dates to the Civil War and is widespread today. One reason discounts are offered is to speed up the collection of receivables. This will have the effect of reducing the amount of credit being offered, and the firm must trade this off against the cost of the discount. Notice that when a cash discount is offered, the credit is essentially free during the discount period. The buyer pays for the credit only after the discount expires. With 2 10, net 30, a rational buyer either pays in 10 days to make the greatest possible use of the free credit or pays in 30 days to get the longest possible use of the money in exchange for giving up the discount. By giving up the discount, the buyer effectively gets 30 − 10 = 20 days’ credit. Another reason for cash discounts is that they are a way of charging higher prices to customers that have had credit extended to them. In this sense, cash discounts are a convenient way of charging for the credit granted to customers. Visit the National Association of Credit Management at www.nacm.org.

Cost of the Credit In our examples, it might seem that the discounts are rather small. With 2/10, net 30, for example, early payment gets the buyer only a 2 percent discount. Does this provide a significant incentive for early payment? The answer is yes because the implicit interest rate is extremely high. To see why the discount is important, we will calculate the cost to the buyer of not paying early. To do this, we will find the interest rate that the buyer is effectively paying for the trade credit. Suppose the order is for $1,000. The buyer can pay $980 in 10 days or wait another 20 days and pay $1,000. It’s obvious that the buyer is effectively borrowing $980 for 20 days and that the buyer pays $20 in interest on the “loan.” What’s the interest rate? This interest is ordinary discount interest, which we discussed in Chapter 4. With $20 in interest on $980 borrowed, the rate is $20 980 = 2.0408%. This is relatively low, but remember that this is the rate per 20-day period. There are 365 20 = 18.25 such periods in a year; so, by not taking the discount, the buyer is paying an effective annual rate (EAR) of: EAR = 1.02040818.25 − 1 =44.6% From the buyer’s point of view, this is an expensive source of financing!

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Given that the interest rate is so high here, it is unlikely that the seller benefits from early payment. Ignoring the possibility of default by the buyer, the decision of a customer to forgo the discount almost surely works to the seller’s advantage. Trade Discounts In some circumstances, the discount is not really an incentive for early payment but is instead a trade discount, a discount routinely given to some type of buyer. For example, with our 2 10th, EOM terms, the buyer takes a 2 percent discount if the invoice is paid by the 10th, but the bill is considered due on the 10th, and overdue after that. Thus, the credit period and the discount period are effectively the same, and there is no reward for paying before the due date. The Cash Discount and the ACP To the extent that a cash discount encourages customers to pay early, it will shorten the receivables period and, all other things being equal, reduce the firm’s investment in receivables. For example, suppose a firm currently has terms of net 30 and an average collection period (ACP) of 30 days. If it offers terms of 2 10, net 30, then perhaps 50 percent of its customers (in terms of volume of purchases) will pay in 10 days. The remaining customers will still take an average of 30 days to pay. What will the new ACP be? If the firm’s annual sales are $15 million (before discounts), what will happen to the investment in receivables? If half of the customers take 10 days to pay and half take 30, then the new average collection period will be: NewA CP = .50 × 10 days + .50 × 30 days = 20 days The ACP thus falls from 30 days to 20 days. Average daily sales are $15 million 365 = $41,096 per day. Receivables will thus fall by $41,096 × 10 =$410,960.

CreditI nstruments The credit instrument is the basic evidence of indebtedness. Most trade credit is offered on open account. This means that the only formal instrument of credit is the invoice, which is sent with the shipment of goods and which the customer signs as evidence that the goods have been received. Afterward, the firm and its customers record the exchange on their books of account. At times the firm may require that the customer sign a promissory note. This is a basic IOU and might be used when the order is large, when there is no cash discount involved, or when the firm anticipates a problem in collections. Promissory notes are not common, but they can eliminate possible controversies later about the existence of debt. One problem with promissory notes is that they are signed after delivery of the goods. One way to obtain a credit commitment from a customer before the goods are delivered is to arrange a commercial draft. Typically, the firm draws up a commercial draft calling for the customer to pay a specific amount by a specified date. The draft is then sent to the customer’s bank with the shipping invoices. If immediate payment is required on the draft, it is called a sight draft. If immediate payment is not required, then the draft is a time draft. When the draft is presented and the buyer “accepts” it, meaning that the buyer promises to pay it in the future, then it is called a trade acceptance and is sent back to the selling firm. The seller can then keep the acceptance or sell it to someone else. If a bank accepts the draft, meaning that the bank is guaranteeing payment, then the draft becomes a banker’s acceptance. This arrangement is common in international trade, and banker’s acceptances are actively traded in the money market.

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A firm can also use a conditional sales contract as a credit instrument. With such an arrangement, the firm retains legal ownership of the goods until the customer has completed payment. Conditional sales contracts usually are paid in installments and have an interest cost built into them.

28.3 AnalyzingCre dit Policy In this section, we take a closer look at the factors that influence the decision to grant credit. Granting credit makes sense only if the NPV from doing so is positive. We thus need to look at the NPV of the decision to grant credit.

CreditP olicyE ffects In evaluating credit policy, there are five basic factors to consider: 1. Revenue effects: If the firm grants credit, then there will be a delay in revenue collections as some customers take advantage of the credit offered and pay later. However, the firm may be able to charge a higher price if it grants credit and it may be able to increase the quantity sold. Total revenues may thus increase. 2. Cost effects: Although the firm may experience delayed revenues if it grants credit, it will still incur the costs of sales immediately. Whether the firm sells for cash or credit, it will still have to acquire or produce the merchandise (and pay for it). 3. The cost of debt: When the firm grants credit, it must arrange to finance the resulting receivables. As a result, the firm’s cost of short-term borrowing is a factor in the decision to grant credit.1 4. The probability of nonpayment: If the firm grants credit, some percentage of the credit buyers will not pay. This can’t happen, of course, if the firm sells for cash. 5. The cash discount: When the firm offers a cash discount as part of its credit terms, some customers will choose to pay early to take advantage of the discount.

Evaluatinga P roposedCr editP olicy To illustrate how credit policy can be analyzed, we will start with a relatively simple case. Locust Software has been in existence for two years, and it is one of several successful firms that develop computer programs. Currently, Locust sells for cash only. Locust is evaluating a request from some major customers to change its current policy to net one month (30 days). To analyze this proposal, we define the following: P = Price per unit v = Variable cost per unit Q = Current quantity sold per month Q′ = Quantity sold under new policy R = Monthly required return The cost of short-term debt is not necessarily the required return on receivables, although it is commonly assumed to be. As always, the required return on an investment depends on the risk of the investment, not the source of the financing. The buyer’s cost of short-term debt is closer in spirit to the correct rate. We will maintain the implicit assumption that the seller and the buyer have the same short-term debt cost. In any case, the time periods in credit decisions are relatively short, so a relatively small error in the discount rate will not have a large effect on our estimated NPV.

1

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For now, we ignore discounts and the possibility of default. Also, we ignore taxes because they don’t affect our conclusions. NPV of Switching Policies To illustrate the NPV of switching credit policies, suppose we have the following for Locust: P =$49 v =$20 Q =100 Q′ =110 If the required return, R, is 2 percent per month, should Locust make the switch? Currently, Locust has monthly sales of P × Q = $4,900. Variable costs each month are v × Q = $2,000, so the monthly cash flow from this activity is: Cash flow with old policy = (P – v) Q = ($49 – 20) × 100 =$2,900

(28.2)

This is not the total cash flow for Locust, of course, but it is all that we need to look at because fixed costs and other components of cash flow are the same whether or not the switch is made. If Locust does switch to net 30 days on sales, then the quantity sold will rise to Q′ = 110. Monthly revenues will increase to P × Q′, and costs will be v × Q′. The monthly cash flow under the new policy will thus be: Cashf lowwith n ewp olicy = (P − v) Q′ = ($49 − 20) × 110 = $3,190

(28.3)

Going back to Chapter 6, we know that the relevant incremental cash flow is the difference between the new and old cash flows: Incrementalc ashin flow = (P − v) (Q′ − Q) = ($49 − 20) × (110 − 100) = $290 This says that the benefit each month of changing policies is equal to the gross profit per unit sold, P − v = $29, multiplied by the increase in sales, Q′ − Q = 10. The present value of the future incremental cash flows is thus: PV = [(P − v) (Q′ − Q)] R

(28.4)

For Locust, this present value works out to be: PV = ($29 × 10) .02 =$14,500 Notice that we have treated the monthly cash flow as a perpetuity because the same benefit will be realized each month forever. Now that we know the benefit of switching, what’s the cost? There are two components to consider. First, because the quantity sold will rise from Q to Q′, Locust will have to produce Q′ − Q more units at a cost of v(Q′ − Q) = $20 × (110 − 100) = $200. Second, the sales that would have been collected this month under the current policy (P × Q = $4,900) will not be collected. Under the new policy, the sales made

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this month won’t be collected until 30 days later. The cost of the switch is the sum of these two components: Costo f s witching = PQ + v (Q′ − Q)

(28.5)

For Locust, this cost would be $4,900 + $200 = $5,100. Putting it all together, we see that the NPV of the switch is: NPVo f s witching = − [PQ + v (Q′ − Q)] + [(P − v)(Q′ − Q)] R

(28.6)

For Locust, the cost of switching is $5,100. As we saw earlier, the benefit is $290 per month, forever. At 2 percent per month, the NPV is: NPV = −$5,100 + 290 .02 = −$5,100 + 14,500 = $9,400 Therefore, the switch is very profitable.

EXAMPLE 28.1

We’d Rather Fight Than Switch Suppose a company is considering a switch from all cash to net 30, but the quantity sold is not expected to change. What is the NPV of the switch? Explain. In this case, Q′ − Q is zero, so the NPV is just −PQ.What this says is that the effect of the switch is simply to postpone one month’s collections forever, with no benefit from doing so.

A Break-Even Application Based on our discussion thus far, the key variable for Locust is Q′ – Q, the increase in unit sales. The projected increase of 10 units is only an estimate, so there is some forecasting risk. Under the circumstances, it’s natural to wonder what increase in unit sales is necessary to break even. Earlier, the NPV of the switch was defined as: NPV = − [PQ + v (Q′ − Q)] + [(P − v)(Q′ − Q)] R We can calculate the break-even point explicitly by setting the NPV equal to zero and solving for (Q′ – Q): NPV = 0 = − [PQ + v (Q′ − Q)] + [(P − v)(Q′ − Q)] R Q′ − Q = PQ [(P − v) R − v]

(28.7)

For Locust, the break-even sales increase is thus: Q′ − Q = $4,900 (29 .02 −20) = 3.43 units This tells us that the switch is a good idea as long as Locust is confident that it can sell at least 3.43 more units per month.

28.4 OptimalCre dit Policy For business reports on credit, visit www.creditworthy.com.

So far, we’ve discussed how to compute net present values for a switch in credit policy. We have not discussed the optimal amount of credit or the optimal credit policy. In principle, the optimal amount of credit is determined by the point at which the

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incremental cash flows from increased sales are exactly equal to the incremental costs of carrying the increase in investment in accounts receivable.

The Total Credit Cost Curve The trade-off between granting credit and not granting credit isn’t hard to identify, but it is difficult to quantify precisely. As a result, we can only describe an optimal credit policy. To begin, the carrying costs associated with granting credit come in three forms: 1. Ther equiredr eturno nr eceivables. 2. The losses from bad debts. 3. The costs of managing credit and credit collections. We have already discussed the first and second of these. The third cost, the cost of managing credit, consists of the expenses associated with running the credit department. Firms that don’t grant credit have no such department and no such expense. These three costs will all increase as credit policy is relaxed. If a firm has a very restrictive credit policy, then all of the associated costs will be low. In this case, the firm will have a “shortage” of credit, so there will be an opportunity cost. This opportunity cost is the extra potential profit from credit sales that are lost because credit is refused. This forgone benefit comes from two sources: The increase in quantity sold, Q′ minus Q, and (potentially) a higher price. The opportunity costs go down as credit policy is relaxed. The sum of the carrying costs and the opportunity costs of a particular credit policy is called the total credit cost curve. We have drawn such a curve in Figure 28.1. As Figure 28.1 illustrates, there is a point where the total credit cost is minimized. This point corresponds to the optimal amount of credit or, equivalently, the optimal investment in receivables.

Figure 28.1 The Costs of Granting Credit

Total costs Carrying costs

Cost ($)

Optimal amount of credit

Opportunity costs Amount of credit extended ($) Carrying costs are the cash flows that must be incurred when credit is granted. They are positively related to the amount of credit extended. Opportunity costs are the lost sales resulting from refusing credit. These costs go down when credit is granted.

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If the firm extends more credit than this minimum, the additional net cash flow from new customers will not cover the carrying costs of the investment in receivables. If the level of receivables is below this amount, then the firm is forgoing valuable profit opportunities. In general, the costs and benefits from extending credit will depend on characteristics of particular firms and industries. All other things being equal, for example, it is likely that firms with (1) excess capacity, (2) low variable operating costs, and (3) repeat customers will extend credit more liberally than other firms. See if you can explain why each of these characteristics contributes to a more liberal credit policy.

Organizingthe Cr editF unction Firms that grant credit have the expense of running a credit department. In practice, firms often choose to contract out all or part of the credit function to a factor, an insurance company, or a captive finance company. Chapter 26 discusses factoring, an arrangement in which the firm sells its receivables. Depending on the specific arrangement, the factor may have full responsibility for credit checking, authorization, and collection. Smaller firms may find such an arrangement cheaper than running a credit department. Firms that manage internal credit operations are self-insured against default. An alternative is to buy credit insurance through an insurance company. The insurance company offers coverage up to a preset dollar limit for accounts. As you would expect, accounts with a higher credit rating merit higher insurance limits. This type of insurance is particularly important for exporters, and government insurance is available for certain types of exports. Large firms often extend credit through a captive finance company, which is simply a wholly owned subsidiary that handles the credit function for the parent company. Ford Motor Credit (FMC) is a well-known example. Ford sells to car dealers, who in turn sell to customers. FMC finances the dealer’s inventory of cars and also finances customers who buy the cars. Why would a firm choose to set up a separate company to handle the credit function? There are a number of reasons, but a primary one is to separate the production and financing of the firm’s products for management, financing, and reporting. For example, the finance subsidiary can borrow in its own name, using its receivables as collateral, and the subsidiary often carries a better credit rating than the parent. This may allow the firm to achieve a lower overall cost of debt than could be obtained if production and financing were commingled.

28.5 Credit Analysis Thus far, we have focused on establishing credit terms. Once a firm decides to grant credit to its customers, it must then establish guidelines for determining who will and who will not be allowed to buy on credit. Credit analysis refers to the process of deciding whether or not to extend credit to a particular customer. It usually involves two steps: Gathering relevant information and determining creditworthiness. Credit analysis is important simply because potential losses on receivables can be substantial. On their balance sheets, companies report the amount of receivables they expect not to collect. In 2008, IBM reported that $249 million of accounts receivable were doubtful, and GE reported a staggering $4.4 billion as an allowance for losses.

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When Should Credit Be Granted? Imagine that a firm is trying to decide whether or not to grant credit to a customer. This decision can get complicated. For example, note that the answer depends on what will happen if credit is refused. Will the customer simply pay cash? Or will the customer not make the purchase at all? To avoid being bogged down by this and other difficulties, we will use some special cases to illustrate the key points. A One-Time Sale We start by considering the simplest case. A new customer wishes to buy one unit on credit at a price of P per unit. If credit is refused, the customer will not make the purchase. Furthermore, we assume that, if credit is granted, then, in one month, the customer will either pay up or default. The probability of the second of these events is π. In this case, the probability (π) can be interpreted as the percentage of new customers who will not pay. Our business does not have repeat customers, so this is strictly a one-time sale. Finally, the required return on receivables is R per month, and the variable cost is v per unit. The analysis here is straightforward. If the firm refuses credit, then the incremental cash flow is zero. If it grants credit, then it spends v (the variable cost) this month and expects to collect (1 − π)P next month. The NPV of granting credit is: NPV = –v + (1 – π) P (1 + R)

(28.8)

For example, for Locust Software, this NPV is: NPV = –$20 + (1 – π) × 49 1.02 With, say, a 20 percent rate of default, this works out to be: NPV = –$20 + .80 × 49 1.02 =$18.43 Therefore, credit should be granted. Notice that we have divided by (1 + R) here instead of by R because we now assume that this is a one-time transaction. Our example illustrates an important point. In granting credit to a new customer, a firm risks its variable cost (v). It stands to gain the full price (P). For a new customer, then, credit may be granted even if the default probability is high. For example, the break-even probability in this case can be determined by setting the NPV equal to zero and solving for π: NPV = 0 = –$20 + (1 – π) × 49 1.02 1 – π = $20 49 × 1.02 π = 58.4% Locust should extend credit as long as there is a 1 – .584 = 41.6% chance or better of collecting. This explains why firms with higher markups tend to have looser credit terms. This percentage (58.4 percent) is the maximum acceptable default probability for a new customer. If a returning, cash-paying customer wanted to switch to a credit basis, the analysis would be different, and the maximum acceptable default probability would be much lower. The important difference is that, if we extend credit to a returning customer, we risk the total sales price (P), because this is what we collect if we don’t extend credit. If we extend credit to a new customer, we risk only our variable cost. Repeat Business A second, very important factor to keep in mind is the possibility of repeat business. We can illustrate this by extending our one-time sale example. We

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make one important assumption: A new customer who does not default the first time around will remain a customer forever and never default. If the firm grants credit, it spends v this month. Next month, it gets nothing if the customer defaults, or it gets P if the customer pays. If the customer pays, then the customer will buy another unit on credit and the firm will spend v again. The net cash inflow for the month is thus P − v. In every subsequent month, this same P − v will occur as the customer pays for the previous month’s order and places a new one. It follows from our discussion that, in one month, the firm will receive $0 with probability π. With probability (1 − π), however, the firm will have a permanent new customer. The value of a new customer is equal to the present value of (P − v) every month forever: PV = (P − v) R The NPV of extending credit is therefore: NPV = −v + (1 − π)(P − v) R

(28.9)

For Locust, this is: NPV = −$20 + (1 − π) × (49 − 20) .02 = −$20 + (1 − π) × 1,450 Even if the probability of default is 90 percent, the NPV is: NPV = −$20 + .10 × 1,450 = $125 Locust should extend credit unless default is a virtual certainty. The reason is that it costs only $20 to find out who is a good customer and who is not. A good customer is worth $1,450, however, so Locust can afford quite a few defaults. Our repeat business example probably exaggerates the acceptable default probability, but it does illustrate that it will often turn out that the best way to do credit analysis is simply to extend credit to almost anyone. It also points out that the possibility of repeat business is a crucial consideration. In such cases, the important thing is to control the amount of credit initially offered to any one customer so that the possible loss is limited. The amount can be increased with time. Most often, the best predictor of whether or not someone will pay in the future is whether or not they have paid in the past.

CreditI nformation Web-surfing students should peruse the Dun & Bradstreet home page. This major supplier of credit information can be found at www.dnb.com.

If a firm wants credit information about customers, there are a number of sources. Information sources commonly used to assess creditworthiness include the following: 1. Financial statements: A firm can ask a customer to supply financial statements such as balance sheets and income statements. Minimum standards and rules of thumb based on financial ratios like the ones we discussed in Chapter 3 can then be used as a basis for extending or refusing credit. 2. Credit reports about the customer’s payment history with other firms: Quite a few organizations sell information about the credit strength and credit history of business firms. The best-known and largest firm of this type is Dun & Bradstreet, which provides subscribers with credit reports on individual firms. Experian is another well-known credit-reporting firm. Ratings and information are available for a huge number of firms, including very small ones. Equifax, Transunion, and Experian are the major suppliers of consumer credit information.

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3. Banks: Banks will generally provide some assistance to their business customers in acquiring information about the creditworthiness of other firms. 4. The customer’s payment history with the firm: The most obvious way to obtain information about the likelihood of customers not paying is to examine whether they have settled past obligations (and how quickly).

CreditE valuationa ndSco ring There are no magical formulas for assessing the probability that a customer will not pay. In very general terms, the classic five Cs of credit are the basic factors to be evaluated: 1. Character: The customer’s willingness to meet credit obligations. 2. Capacity: The customer’s ability to meet credit obligations out of operating cash flows. 3. Capital: The customer’s financial reserves. 4. Collateral: An asset pledged in the case of default. 5. Conditions: General economic conditions in the customer’s line of business. Credit scoring is the process of calculating a numerical rating for a customer based on information collected; credit is then granted or refused based on the result. For example, a firm might rate a customer on a scale of 1 (very poor) to 10 (very good) on each of the five Cs of credit using all the information available about the customer. A credit score could then be calculated by totaling these ratings. Based on experience, a firm might choose to grant credit only to customers with a score above, say, 30. Firms such as credit card issuers have developed statistical models for credit scoring. Usually, all of the legally relevant and observable characteristics of a large pool of customers are studied to find their historic relation to defaults. Based on the results, it is possible to determine the variables that best predict whether a customer will pay and then calculate a credit score based on those variables. Because credit-scoring models and procedures determine who is and who is not creditworthy, it is not surprising that they have been the subject of government regulation. In particular, the kinds of background and demographic information that can be used in the credit decision are limited.

28.6 Collection Policy Collection policy is the final element in credit policy. Collection policy involves monitoring receivables to spot trouble and obtaining payment on past-due accounts.

MonitoringR eceivables To keep track of payments by customers, most firms will monitor outstanding accounts. First of all, a firm will normally keep track of its average collection period (ACP) through time. If a firm is in a seasonal business, the ACP will fluctuate during the year; but unexpected increases in the ACP are a cause for concern. Either customers in general are taking longer to pay, or some percentage of accounts receivable are seriously overdue. To see just how important timely collection of receivables is to investors, consider the case of Art Technology Group (ATG), a company that provides Internet customer

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relationship management and e-commerce software. In late 2000, ATG announced an unusual sale of accounts receivable to a bank. The sale helped lower ATG’s reported September days’ sales outstanding, an important indicator of receivables management. However, after this information became public, investors became concerned about the quality of the firm’s sales, and ATG’s stock sank 18 percent. The aging schedule is a second basic tool for monitoring receivables. To prepare one, the credit department classifies accounts by age.2 Suppose a firm has $100,000 in receivables. Some of these accounts are only a few days old, but others have been outstanding for quite some time. The following is an example of an aging schedule: Aging Schedule Age of Account

Amount

Percentage of Total Value of Accounts Receivable

0–10 days 11–60 days 61–80 days Over 80 days

$ 50,000 25,000 20,000 5,000 $100,000

50% 25 20 5 100%

If this firm has a credit period of 60 days, then 25 percent of its accounts are late. Whether or not this is serious depends on the nature of the firm’s collections and customers. It is often the case that accounts beyond a certain age are almost never collected. Monitoring the age of accounts is very important in such cases. Firms with seasonal sales will find the percentages on the aging schedule changing during the year. For example, if sales in the current month are very high, then total receivables will also increase sharply. This means that the older accounts, as a percentage of total receivables, become smaller and might appear less important. Some firms have refined the aging schedule so that they have an idea of how it should change with peaks and valleys in their sales.

CollectionE ffort A firm usually goes through the following sequence of procedures for customers whose payments are overdue: 1. It sends out a delinquency letter informing the customer of the past-due status of theac count. 2. It makes a telephone call to the customer. 3. It employs a collection agency. 4. It takes legal action against the customer. At times, a firm may refuse to grant additional credit to customers until arrearages are cleared up. This may antagonize a normally good customer, which points to a potential conflict between the collections department and the sales department. In probably the worst case, the customer files for bankruptcy. When this happens, the credit-granting firm is just another unsecured creditor. The firm can simply wait, or it can 2

Aging schedules are also used elsewhere in business such as inventory tracking.

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sell its receivable. For example, when FoxMeyer Health filed for bankruptcy in August 1996, it owed $20 million to Bristol-Myers Squibb for drug purchases. Once FoxMeyer filed for bankruptcy, Bristol-Myers tried to sell its receivable at a discount. The purchaser would then have been the creditor in the bankruptcy proceedings and would have gotten paid when the bankruptcy was settled. Similar trade claims against FoxMeyer initially traded as high as 49 cents on the dollar, but settled to about 20 cents less than a month later. Thus, if Bristol-Myers had cashed out at that price, it would have sold its $20 million claim for about $4 million, a hefty discount. Of course, Bristol-Myers would have gotten the money immediately rather than waiting for an uncertain future amount.

28.7 Inventory Management Like receivables, inventories represent a significant investment for many firms. For a typical manufacturing operation, inventories will often exceed 15 percent of assets. For a retailer, inventories could represent more than 25 percent of assets. From our discussion in Chapter 26, we know that a firm’s operating cycle is made up of its inventory period and its receivables period. This is one reason for considering credit and inventory policy in the same chapter. Beyond this, both credit policy and inventory policy are used to drive sales, and the two must be coordinated to ensure that the process of acquiring inventory, selling it, and collecting on the sale proceeds smoothly. For example, changes in credit policy designed to stimulate sales must be accompanied by planning for adequate inventory.

The Financial Manager and Inventory Policy

Visit the Society for Inventory Management Benchmarking Analysis at www.simba.org.

Despite the size of a typical firm’s investment in inventories, the financial manager of a firm will not normally have primary control over inventory management. Instead, other functional areas such as purchasing, production, and marketing will usually share decision-making authority regarding inventory. Inventory management has become an increasingly important specialty in its own right, and financial management will often only have input into the decision. For this reason, we will just survey some basics of inventory and inventory policy.

InventoryT ypes For a manufacturer, inventory is normally classified into one of three categories. The first category is raw materials. This is whatever the firm uses as a starting point in its production process. Raw materials might be something as basic as iron ore for a steel manufacturer or something as sophisticated as disk drives for a computer manufacturer. The second type of inventory is work-in-progress, which is just what the name suggests—unfinished product. How big this portion of inventory is depends in large part on the length of the production process. For an airframe manufacturer, for example, work-in-progress can be substantial. The third and final type of inventory is finished goods—that is, products ready to ship or sell. Keep in mind three things concerning inventory types. First, the names for the different types can be a little misleading because one company’s raw materials can be another’s finished goods. For example, going back to our steel manufacturer, iron ore would be a raw material, and steel would be the final product. An auto body panel stamping operation will have steel as its raw material and auto body panels as its finished goods, and an automobile assembler will have body panels as raw materials and automobiles as finished products.

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The second thing to keep in mind is that the various types of inventory can be quite different in terms of their liquidity. Raw materials that are commodity-like or relatively standardized can be easy to convert to cash. Work-in-progress, on the other hand, can be quite illiquid and have little more than scrap value. As always, the liquidity of finished goods depends on the nature of the product. Finally, a very important distinction between finished goods and other types of inventories is that the demand for an inventory item that becomes a part of another item is usually termed derived or dependent demand because the firm’s need for these inventory types depends on its need for finished items. In contrast, the firm’s demand for finished goods is not derived from demand for other inventory items, so it is sometimes said to be independent.

InventoryCo sts As we discussed in Chapter 26, two basic types of costs are associated with current assets in general and with inventory in particular. The first of these is carrying costs. Here, carrying costs represent all of the direct and opportunity costs of keeping inventory on hand. These include: 1. Storagean dtr ackingc osts. 2. Insurancean dtax es. 3. Losses due to obsolescence, deterioration, or theft. 4. The opportunity cost of capital on the invested amount. The sum of these costs can be substantial, ranging roughly from 20 to 40 percent of inventory value per year. The other type of costs associated with inventory is shortage costs. Shortage costs are costs associated with having inadequate inventory on hand. The two components of shortage costs are restocking costs and costs related to safety reserves. Depending on the firm’s business, restocking or order costs are either the costs of placing an order with suppliers or the costs of setting up a production run. The costs related to safety reserves are opportunity losses such as lost sales and loss of customer goodwill that result from having inadequate inventory. A basic trade-off exists in inventory management because carrying costs increase with inventory levels, whereas shortage or restocking costs decline with inventory levels. The basic goal of inventory management is thus to minimize the sum of these two costs. We consider ways to reach this goal in the next section. Just to give you an idea of how important it is to balance carrying costs with shortage costs, consider the case of the Nintendo Wii. In December 2007, analysts estimated that the company could sell twice the 1.8 million units it was currently producing. The lower production was blamed on the shortage of components from suppliers, Nintendo’s just-in-time inventory management, and supply chain mismanagement by the company. As a result, the company missed out on nearly $1.3 billion in additional sales during Christmas 2007.

28.8 Inventory Management Techniques As we described earlier, the goal of inventory management is usually framed as cost minimization. Three techniques are discussed in this section, ranging from the relatively simple to the very complex.

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Figure 28.2 100 Percentage of inventory value

ABC Inventory Analysis

80 60 40 20 0

Percentage of inventory items

A Group

20

57%

B Group C Group 27%

16%

10% 40%

50%

40 60 80 100

TheAB CAppr oach The ABC approach is a simple approach to inventory management in which the basic idea is to divide inventory into three (or more) groups. The underlying rationale is that a small portion of inventory in terms of quantity might represent a large portion in terms of inventory value. For example, this situation would exist for a manufacturer that uses some relatively expensive, high-tech components and some relatively inexpensive basic materials in producing its products. Figure 28.2 illustrates an ABC comparison of items in terms of the percentage of inventory value represented by each group versus the percentage of items represented. As Figure 28.2 shows, the A Group constitutes only 10 percent of inventory by item count, but it represents over half of the value of inventory. The A Group items are thus monitored closely, and inventory levels are kept relatively low. At the other end, basic inventory items, such as nuts and bolts, also exist; but, because these are crucial and inexpensive, large quantities are ordered and kept on hand. These would be C Group items. The B Group is made up of in-between items.

The Economic Order Quantity Model The economic order quantity (EOQ) model is the best-known approach for explicitly establishing an optimal inventory level. The basic idea is illustrated in Figure 28.3, which plots the various costs associated with holding inventory (on the vertical axis) against inventory levels (on the horizontal axis). As shown, inventory carrying costs rise and restocking costs decrease as inventory levels increase. From our general discussion in Chapter 26 and our discussion of the total credit cost curve in this chapter, the general shape of the total inventory cost curve is familiar. With the EOQ model, we will attempt to specifically locate the minimum total cost point, Q*. In our discussion that follows, an important point to keep in mind is that the actual cost of the inventory itself is not included. The reason is that the total amount of inventory the firm needs in a given year is dictated by sales. What we are analyzing here is how much the firm should have on hand at any particular time. More precisely, we are trying to determine what order size the firm should use when it restocks its inventory.

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Figure28 .3

Cost of holding inventory ($)

Costs of Holding Inventory

Total costs of holding inventory Carrying costs

Restocking costs Q* Optimal size of inventory order Size of inventory orders (Q) Restocking costs are greatest when the firm holds a small quantity of inventory. Carrying costs are greatest when there is a large quantity of inventory on hand. Total costs are the sum of the carrying and restocking costs.

Inventory Depletion To develop the EOQ, we will assume that the firm’s inventory is sold off at a steady rate until it hits zero. At that point, the firm restocks its inventory back to some optimal level. For example, suppose the Eyssell Corporation starts out today with 3,600 units of a particular item in inventory. Annual sales of this item are 46,800 units, which is 900 per week. If Eyssell sells 900 units of inventory each week, all the available inventory will be sold after four weeks, and Eyssell will restock by ordering (or manufacturing) another 3,600 and start over. This selling and restocking process produces a sawtooth pattern for inventory holdings; this pattern is illustrated in Figure 28.4. As the figure shows, Eyssell always starts with 3,600 units in inventory and ends up at zero. On average, then, inventory is half of 3,600, or 1,800 units. The Carrying Costs As Figure 28.3 illustrates, carrying costs are normally assumed to be directly proportional to inventory levels. Suppose we let Q be the quantity of inventory that Eyssell orders each time (3,600 units); we will call this the restocking quantity. Average inventory would then just be Q 2, or 1,800 units. If we let CC be the carrying cost per unit per year, Eyssell’s total carrying costs will be: Total carrying costs = Average inventory × Carrying costs per unit = (Q 2) ×CC

(28.10)

In Eyssell’s case, if carrying costs were $.75 per unit per year, total carrying costs would be the average inventory of 1,800 multiplied by $.75, or $1,350 per year. The Shortage Costs For now, we will focus only on the restocking costs. In essence, we will assume that the firm never actually runs short on inventory, so that costs relating to safety reserves are not important. We will return to this issue later.

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Figure 28.4 Inventory Holdings for the Eyssell Corporation

Starting inventory: Q 3,600

Q/2

Average inventory

1,800

Ending inventory: Q 0

0

1

2

3

4 Weeks

5

6

7

8

The Eyssell Corporation starts with inventory of 3,600 units. The quantity drops to zero by the end of the fourth week. The average inventory is Q/2 3,600/2 1,800 over the period.

Restocking costs are normally assumed to be fixed. In other words, every time we place an order, fixed costs are associated with that order (remember that the cost of the inventory itself is not considered here). Suppose we let T be the firm’s total unit sales per year. If the firm orders Q units each time, then it will need to place a total of T Q orders. For Eyssell, annual sales are 46,800, and the order size is 3,600. Eyssell thus places a total of 46,800 3,600 = 13 orders per year. If the fixed cost per order is F, the total restocking cost for the year would be: Total restocking cost = Fixed cost per order × Number of orders = F × (T Q)

(28.11)

For Eyssell, order costs might be $50 per order, so the total restocking cost for 13 orders would be $50 × 13 = $650 per year. The Total Costs The total costs associated with holding inventory are the sum of the carrying costs and the restocking costs: Total costs = Carrying costs + Restocking costs = (Q 2) × CC + F × (T Q)

(28.12)

Our goal is to find the value of Q, the restocking quantity, that minimizes this cost. To see how we might go about this, we can calculate total costs for some different values of Q. For the Eyssell Corporation, we had carrying costs (CC) of $.75 per unit per year, fixed costs (F) of $50 per order, and total, sales (T) of 46,800 units.

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With these numbers, here are some possible total costs (check some of these for practice): Restocking Quantity (Q)

Carrying Costs (Q 2 × CC)

500 1,000 1,500 2,000 2,500 3,000 3,500

$ 187.5 375.0 562.5 750.0 937.5 1,125.0 1,312.5

Restocking Costs (F × T Q)

+

$4,680.0 2,340.0 1,560.0 1,170.0 936.0 780.0 668.6

=

Total Costs $ 4,867.50 2,715.00 2,122.50 1,920.00 1,873.50 1,905.00 1,981.10

Inspecting the numbers, we see that total costs start out at almost $5,000 and decline to just under $1,900. The cost-minimizing quantity is about 2,500. To find the cost-minimizing quantity, we can look back at Figure 28.3. What we notice is that the minimum point occurs right where the two lines cross. At this point, carrying costs and restocking costs are the same. For the particular types of costs we have assumed here, this will always be true; so we can find the minimum point just by setting these costs equal to each other and solving for Q*: Carryingc osts = Restocking costs (Q* 2) × CC = F × (T Q*)

(28.13)

With a little algebra, we get:

2T × F Q*2 = _______ CC To solve for Q*, we take the square root of both sides to find:

(28.14)

_______

2T × F Q* = _______ CC

√

(28.15)

This reorder quantity, which minimizes the total inventory cost, is called the economic order quantity (EOQ). For the Eyssell Corporation, the EOQ is: _______

2T × F Q* = _______ CC _________________ (2 × 46,800) × $50 = _________________ .75 _________ = √6,240,000 = 2,498 units

√

√

Thus, for Eyssell, the economic order quantity is 2,498 units. At this level, verify that the restocking costs and carrying costs are both $936.75.

EXAMPLE 28.2

Carrying Costs Thiewes Shoes begins each period with 100 pairs of hiking boots in stock. This stock is depleted each period and reordered. If the carrying cost per pair of boots per year is $3, what are the total carrying costs for the hiking boots? Inventories always start at 100 items and end up at zero, so average inventory is 50 items. At an annual cost of $3 per item, total carrying costs are $150.

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Restocking Costs In Example 28.2, suppose Thiewes sells a total of 600 pairs of boots in a year. How many times per year does Thiewes restock? Suppose the restocking cost is $20 per order. What are total restocking costs? Thiewes orders 100 items each time. Total sales are 600 items per year, so Thiewes restocks six times per year, or about every two months. The restocking costs would be 6 orders × $20 per order = $120.

The EOQ Based on our previous two examples, what size orders should Thiewes place to minimize costs? How often will Thiewes restock? What are the total carrying and restocking costs? The total costs? We know that the total number of pairs of boots ordered for the year (T) is 600. The restocking cost (F) is $20 per order, and the carrying cost (CC) is $3 per unit per year. We can calculate the EOQ for Thiewes as follows: _______

√

2T × F EOQ = ______ CC

_______________

√

(2 × 600) × $20 = _______________ 3 _____

= √8,000

= 89.44 units Because Thiewes sells 600 pairs per year, it will restock 600 89.44 = 6.71 times. The total restocking costs will be $20 × 6.71 = $134.16. Average inventory will be 89.44 2 = 44.72. The carrying costs will be $3 × 44.72 = $134.16, the same as the restocking costs. The total costs are thus $268.32.

Extensions to the EOQ Model Thus far, we have assumed that a company will let its inventory run down to zero and then reorder. In reality, a company will wish to reorder before its inventory goes to zero for two reasons. First, by always having at least some inventory on hand, the firm minimizes the risk of a stockout and the resulting losses of sales and customers. Second, when a firm does reorder, there will be some time lag before the inventory arrives. Thus, to finish our discussion of the EOQ, we consider two extensions: Safety stocks and reordering points. Safety Stocks A safety stock is the minimum level of inventory that a firm keeps on hand. Inventories are reordered whenever the level of inventory falls to the safety stock level. The top of Figure 28.5 illustrates how a safety stock can be incorporated into an EOQ model. Notice that adding a safety stock simply means that the firm does not run its inventory all the way down to zero. Other than this, the situation here is identical to that described in our earlier discussion of the EOQ. Reorder Points To allow for delivery time, a firm will place orders before inventories reach a critical level. The reorder points are the times at which the firm will actually place its inventory orders. These points are illustrated in the middle of Figure 28.5.

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Figure28 .5 A. Safety stocks

Inventory (units)

Safety Stocks and ReorderP oints

Minimum inventory level

Safety stock Time

With a safety stock, the firm reorders when inventory reaches a minimum level.

Inventory (units)

B. Reorder points

Reorder point

Delivery time

Delivery time Time

When there are lags in delivery or production times, the firm reorders when inventory reaches the reorder point.

Inventory (units)

C. Combined reorder points and safety stocks

Reorder point

Delivery time

Safety stock

Delivery time

Minimum inventory level

Time By combining safety stocks and reorder points, the firm maintains a buffer against unforeseen events.

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As shown, the reorder points simply occur some fixed number of days (or weeks or months) before inventories are projected to reach zero. One of the reasons that a firm will keep a safety stock is to allow for uncertain delivery times. We can therefore combine our reorder point and safety stock discussions in the bottom part of Figure 28.5. The result is a generalized EOQ model in which the firm orders in advance of anticipated needs and also keeps a safety stock of inventory.

ManagingDe rived-DemandI nventories The third type of inventory management technique is used to manage derived-demand inventories. As we described earlier, demand for some inventory types is derived from, or dependent on, other inventory needs. A good example is given by the auto manufacturing industry, in which the demand for finished products depends on consumer demand, marketing programs, and other factors related to projected unit sales. The demand for inventory items such as tires, batteries, headlights, and other components is then completely determined by the number of autos planned. Materials requirements planning and just-in-time inventory management are two methods for managingd emand-dependentin ventories. Materials Requirements Planning Production and inventory specialists have developed computer-based systems for ordering and/or scheduling production of demanddependent types of inventories. These systems fall under the general heading of materials requirements planning (MRP). The basic idea behind MRP is that, once finished goods inventory levels are set, it is possible to determine what levels of work-in-progress inventories must exist to meet the need for finished goods. From there, it is possible to calculate the quantity of raw materials that must be on hand. This ability to schedule backward from finished goods inventories stems from the dependent nature of work-in-progress and raw materials inventories. MRP is particularly important for complicated products for which a variety of components are needed to create the finished product. Just-in-Time Inventory Just-in-time (JIT) inventory is a modern approach to managing dependent inventories. The goal of JIT is to minimize such inventories, thereby maximizing turnover. The approach began in Japan, and it is a fundamental part of Japanese manufacturing philosophy. As the name suggests, the basic goal of JIT is to have only enough inventory on hand to meet immediate production needs. The result of the JIT system is that inventories are reordered and restocked frequently. Making such a system work and avoiding shortages requires a high degree of cooperation among suppliers. Japanese manufacturers often have a relatively small, tightly integrated group of suppliers with whom they work closely to achieve the needed coordination. These suppliers are a part of a large manufacturer’s (such as Toyota’s) industrial group, or keiretsu. Each large manufacturer tends to have its own keiretsu. It also helps to have suppliers located nearby, a situation that is common in Japan. The kanban is an integral part of a JIT inventory system, and JIT systems are sometimes called kanban systems. The literal meaning of kanban is “card” or “sign”; but, broadly speaking, a kanban is a signal to a supplier to send more inventory. For example, a kanban can literally be a card attached to a bin of parts. When a worker pulls that bin, the card is detached and routed back to the supplier, who then supplies a replacement bin. A JIT inventory system is an important part of a larger production planning process. A full discussion of it would necessarily shift our focus away from finance to production and operations management, so we will leave it here.

Short-Term Finance

Part VII

Summary and Conclusions

This chapter has covered the basics of credit and inventory policy. The major topics we discussed include these: 1. The components of credit policy: We discussed the terms of sale, credit analysis, and collection policy. Under the general subject of terms of sale, the credit period, the cash discount and discount period, and the credit instrument were described. 2. Credit policy analysis: We developed the cash flows from the decision to grant credit and showed how the credit decision can be analyzed in an NPV setting. The NPV of granting credit depends on five factors: Revenue effects, cost effects, the cost of debt, the probability of nonpayment, and the cash discount. 3. Optimal credit policy: The optimal amount of credit the firm should offer depends on the competitive conditions under which the firm operates. These conditions will determine the carrying costs associated with granting credit and the opportunity costs of the lost sales resulting from refusing to offer credit. The optimal credit policy minimizes the sum of these two costs. 4. Credit analysis: We looked at the decision to grant credit to a particular customer. We saw that two considerations are very important: The cost relative to the selling price and the possibility of repeat business. 5. Collection policy: Collection policy determines the method of monitoring the age of accounts receivable and dealing with past-due accounts. We described how an aging schedule can be prepared and the procedures a firm might use to collect on past-due accounts. 6. Inventory types: We described the different inventory types and how they differ in terms of liquidity and demand. 7. Inventory costs: The two basic inventory costs are carrying and restocking costs; we discussed how inventory management involves a trade-off between these two costs. 8. Inventory management techniques: We described the ABC approach and the EOQ model approach to inventory management. We also briefly touched on materials requirements planning (MRP) and just-in-time (JIT) inventory management.

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Concept Questions

1.

2. 3.

4. 5.

6.

CreditI nstruments Describe each of the following: a. Sightd raft. b. Timed raft. c. Banker’sac ceptance. d. Promissoryn ote. e. Tradeac ceptance. Trade Credit Forms In what form is trade credit most commonly offered? What is the credit instrument in this case? Receivables Costs What costs are associated with carrying receivables? What costs are associated with not granting credit? What do we call the sum of the costs for different levels of receivables? FiveCs of Cr edit What are the five Cs of credit? Explain why each is important. Credit Period Length What are some of the factors that determine the length of the credit period? Why is the length of the buyer’s operating cycle often considered an upper bound on the length of the credit period? Credit Period Length In each of the following pairings, indicate which firm would probably have a longer credit period and explain your reasoning. a. Firm A sells a miracle cure for baldness; firm B sells toupees. b. Firm A specializes in products for landlords; firm B specializes in products for renters.

Chapter 28 Credit and Inventory Management

7.

8.

9.

10.

BASIC (Questions 1–12)

1.

2.

3.

4.

5.

c. Firm A sells to customers with an inventory turnover of 10 times; firm B sells to customers with an inventory turnover of 20 times. d. Firm A sells fresh fruit; firm B sells canned fruit. e. Firm A sells and installs carpeting; firm Bs ellsr ugs. Inventory Types What are the different inventory types? How do the types differ? Why are some types said to have dependent demand, whereas other types are said to have independent demand? Just-in-Time Inventory If a company moves to a JIT inventory management system, what will happen to inventory turnover? What will happen to total asset turnover? What will happen to return on equity (ROE)? (Hint: Remember the Du Pont equation from Chapter 3.) Inventory Costs If a company’s inventory carrying costs are $5 million per year and its fixed order costs are $8 million per year, do you think the firm keeps too much inventory on hand or too little? Why? Inventory Period At least part of Dell’s corporate profits can be traced to its inventory management. Using just-in-time inventory, Dell typically maintains an inventory of three to four days’ sales. Competitors such as Hewlett-Packard and IBM have attempted to match Dell’s inventory policies, but lag far behind. In an industry where the price of PC components continues to decline, Dell clearly has a competitive advantage. Why would you say that it is to Dell’s advantage to have such a short inventory period? If doing this is valuable, why don’t all other PC manufacturers switcht oDe ll’sa pproach?

Cash Discounts You place an order for 400 units of inventory at a unit price of $125. The supplier offers terms of 1/10, net 30. a. How long do you have to pay before the account is overdue? If you take the full period, how much should you remit? b. What is the discount being offered? How quickly must you pay to get the discount? If you do take the discount, how much should you remit? c. If you don’t take the discount, how much interest are you paying implicitly? How many days’ credit are you receiving? Size of Accounts Receivable The Tate Corporation has annual sales of $47 million. The average collection period is 36 days. What is the average investment in accounts receivable as shown on the balance sheet? ACP and Accounts Receivable Kyoto Joe, Inc., sells earnings forecasts for Japanese securities. Its credit terms are 2/10, net 30. Based on experience, 65 percent of all customers will take the discount. a. What is the average collection period for Kyoto Joe? b. If Kyoto Joe sells 1,300 forecasts every month at a price of $1,700 each, what is its average balance sheet amount in accounts receivable? Size of Accounts Receivable Tidwell, Inc., has weekly credit sales of $19,400, and the average collection period is 34 days. The cost of production is 75 percent of the selling price. What is the average accounts receivable figure? Terms of Sale A firm offers terms of 1/10, net 35. What effective annual interest rate does the firm earn when a customer does not take the discount? Without doing any calculations, explain what will happen to this effective rate if: a. The discount is changed to 2 percent. b. The credit period is increased to 60 days. c. The discount period is increased to 15 days.

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ACP and Receivables Turnover Lipman, Inc., has an average collection period of 39 days. Its average daily investment in receivables is $47,500. What are annual credit sales? What is the receivables turnover? Size of Accounts Receivable Essence of Skunk Fragrances, Ltd., sells 5,600 units of its perfume collection each year at a price per unit of $425. All sales are on credit with terms of 1 10, net 40. The discount is taken by 60 percent of the customers. What is the total amount of the company’s accounts receivable? In reaction to sales by its main competitor, Sewage Spray, Essence of Skunk is considering a change in its credit policy to terms of 2 10, net 30 to preserve its market share. How will this change in policy affect accounts receivable? Size of Accounts Receivable The Arizona Bay Corporation sells on credit terms of net 30. Its accounts are, on average, 8 days past due. If annual credit sales are $8.4 million, what is the company’s balance sheet amount in accounts receivable? Evaluating Credit Policy Air Spares is a wholesaler that stocks engine components and test equipment for the commercial aircraft industry. A new customer has placed an order for eight high-bypass turbine engines, which increase fuel economy. The variable cost is $1.6 million per unit, and the credit price is $1.87 million each. Credit is extended for one period, and based on historical experience, payment for about 1 out of every 200 such orders is never collected. The required return is 2.9 percent per period. a. Assuming that this is a one-time order, should it be filled? The customer will not buy if credit is not extended. b. What is the break-even probability of default in part (a)? c. Suppose that customers who don’t default become repeat customers and place the same order every period forever. Further assume that repeat customers never default. Should the order be filled? What is the break-even probability of default? d. Describe in general terms why credit terms will be more liberal when repeat orders areap ossibility. Credit Policy Evaluation Lealos, Inc., is considering a change in its cash-only sales policy. The new terms of sale would be net one month. Based on the following information, determine if Lealos should proceed or not. Describe the buildup of receivables in this case. The required return is 1.5 percent per month.

Price per unit Cost per unit Unit sales per month

11.

12.

Current Policy

New Policy

$720 $495 1,305

$720 $495 1,380

EOQ Redan Manufacturing uses 2,500 switch assemblies per week and then reorders another 2,500. If the relevant carrying cost per switch assembly is $9 and the fixed order cost is $1,700, is Redan’s inventory policy optimal? Why or why not? EOQ The Trektronics store begins each week with 300 phasers in stock. This stock is depleted each week and reordered. If the carrying cost per phaser is $41 per year and the fixed order cost is $95, what is the total carrying cost? What is the restocking cost? Should Trektronics increase or decrease its order size? Describe an optimal inventory policy for Trektronics in terms of order size and order frequency.

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13.

14.

Credit and Inventory Management

EOQ Derivation Prove that when carrying costs and restocking costs are as described in the chapter, the EOQ must occur at the point where the carrying costs and restocking costs are equal. Credit Policy Evaluation The Harrington Corporation is considering a change in its cash-only policy. The new terms would be net one period. Based on the following information, determine if Harrington should proceed or not. The required return is 2.5 percent per period.

Price per unit Cost per unit Unit sales per month

15.

873

Current Policy

New Policy

$91 $47 3,850

$94 $47 3,940

Credit Policy Evaluation Happy Times currently has an all-cash credit policy. It is considering making a change in the credit policy by going to terms of net 30 days. Based on the following information, what do you recommend? The required return is .95 percent per month.

Price per unit Cost per unit Unit sales per month

16.

CHALLENGE (Questions1 7–20)

17. 18.

19. 20.

$290 $230 1,105

New Policy $295 $234 1,125

Credit Policy The Silver Spokes Bicycle Shop has decided to offer credit to its customers during the spring selling season. Sales are expected to be 500 bicycles. The average cost to the shop of a bicycle is $490. The owner knows that only 96 percent of the customers will be able to make their payments. To identify the remaining 4 percent, the company is considering subscribing to a credit agency. The initial charge for this service is $450, with an additional charge of $5 per individual report. Should she subscribe to the agency? Break-Even Quantity In Problem 14, what is the break-even quantity for the new creditp olicy? Credit Markup In Problem 14, what is the break-even price per unit that should be charged under the new credit policy? Assume that the sales figure under the new policy is 4,100 units and all other values remain the same. Credit Markup In Problem 15, what is the break-even price per unit under the new credit policy? Assume all other values remain the same. Safety Stocks and Order Points Saché, Inc., expects to sell 700 of its designer suits every week. The store is open seven days a week and expects to sell the same number of suits every day. The company has an EOQ of 500 suits and a safety stock of 100 suits. Once an order is placed, it takes three days for Saché to get the suits in. How many orders does the company place per year? Assume that it is Monday morning before the store opens, and a shipment of suits has just arrived. When will Saché place its next order?

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Appendix 28A More about Credit Policy Analysis

Mini Case

To access the appendix for this chapter, please go to www.mhhe.com/rwj.

CREDIT POLICY AT BRAAM INDUSTRIES Tricia Haltiwinger, the president of Braam Industries, has been exploring ways of improving the company’s financial performance. Braam Industries manufactures and sells office equipment to retailers. The company’s growth has been relatively slow in recent years, but with an expansion in the economy, it appears that sales may increase more quickly in the future. Tricia has asked Andrew Preston, the company’s treasurer, to examine Braam’s credit policy to see if a different credit policy can help increase profitability. The company currently has a policy of net 30. As with any credit sales, default rates are always of concern. Because of Braam’s screening and collection process, the default rate on credit is currently only 1.5 percent. Andrew has examined the company’s credit policy in relation to other vendors, and he has determined that three options are available. The first option is to relax the company’s decision on when to grant credit. The second option is to increase the credit period to net 45, and the third option is a combination of the relaxed credit policy and the extension of the credit period to net 45. On the positive side, each of the three policies under consideration would increase sales. The three policies have the drawbacks that default rates would increase, the administrative costs of managing the firm’s receivables would increase, and the receivables period would increase. The credit policy change would impact all four of these variables in different degrees. Andrew has prepared the following table outlining the effect on each of these variables:

Current policy Option 1 Option 2 Option 3

Annual Sales (millions)

Default Rate (% of sales)

Administrative Costs (% of sales)

Receivables Period

$140 158 149 167

1.90% 2.90 2.20 2.50

1.60% 2.70 1.90 2.10

38 days 41 51 49

Braam’s variable costs of production are 45 percent of sales, and the relevant interest rate is a 6 percent effective annual rate. Which credit policy should the company use? Also, notice that in option 3 the default rate and administrative costs are below those in option 2. Ist hisp lausible?W hyo rw hyn ot?

PART VIII

CHAPTER 29

Mergers, Acquisitions, andDi vestitures In a tumultuous period for investment banks, on January 1, 2009, Bank of America (BOA) finalized its acquisition of Merrill Lynch. Merrill Lynch was the largest surviving investment bank after Bear Stearns was acquired, Lehman Brothers filed for bankruptcy, and Goldman Sachs and Morgan Stanley converted into bank holding companies. The acquisition of Merrill Lynch was valued at about $21 billion in stock. In the acquisition, Merrill Lynch shareholders received .8595 shares of BOA stock for each share of Merrill Lynch. So why would BOA purchase Merrill Lynch? Lots of reasons. The new company would become the largest U.S. bank with $2.7 trillion in assets and also be the largest underwriter of global high-yield debt, the third largest underwriter of global equity, and the ninth largest adviser on global mergers and acquisitions. And just as important, BOA estimated that it could achieve $7 billion per year in annual cost reductions. Unfortunately, BOA underestimated the problems at Merrill Lynch. For the fourth quarter of 2008, Merrill Lynch reported a huge loss of $15 billion, leaving BOA shareholders in shock over what had seemed like a great deal strategically for the bank. How do companies like BOA determine whether an acquisition is a good idea? This chapter explores reasons that mergers should take place—and just as important, reasons why they should not.

29.1 The Basic Forms of Acquisitions Acquisitions follow one of three basic forms: (1) Merger or consolidation, (2) acquisition of stock, and (3) acquisition of assets.

Mergero rCo nsolidation A merger refers to the absorption of one firm by another. The acquiring firm retains its name and identity, and it acquires all of the assets and liabilities of the acquired firm. After a merger, the acquired firm ceases to exist as a separate business entity. A consolidation is the same as a merger except that an entirely new firm is created. In a consolidation, both the acquiring firm and the acquired firm terminate their previous legal existence and become part of the new firm.

EXAMPLE29.1

Merger Basics Suppose firm A acquires firm B in a merger. Further, suppose firm B’s shareholders are given one share of firm A’s stock in exchange for two shares of firm B’s stock. From a legal standpoint, firm A’s shareholders are not directly affected by the merger. However, firm B’s shares cease to exist. In a consolidation, the shareholders of firm A and firm B exchange their shares for shares of a new firm (e.g., firm C ).

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Because of the similarities between mergers and consolidations, we shall refer to both types of reorganization as mergers. Here are two important points about mergers and consolidations: 1. A merger is legally straightforward and does not cost as much as other forms of acquisition. It avoids the necessity of transferring title of each individual asset of the acquired firm to the acquiring firm. 2. The stockholders of each firm must approve a merger.1T ypically,tw o-thirdso f share owners must vote in favor for it to be approved. In addition, shareholders of the acquired firm have appraisal rights. This means that they can demand that the acquiring firm purchase their shares at a fair value. Often, the acquiring firm and the dissenting shareholders of the acquired firm cannot agree on a fair value, which results in expensive legal proceedings.

Acquisitiono fSto ck A second way to acquire another firm is to purchase the firm’s voting stock in exchange for cash, shares of stock, or other securities. This process may start as a private offer from the management of one firm to another. At some point the offer is taken directly to the selling firm’s stockholders, often by a tender offer. A tender offer is a public offer to buy shares of a target firm. It is made by one firm directly to the shareholders of another firm. The offer is communicated to the target firm’s shareholders by public announcements such as newspaper advertisements. Sometimes a general mailing is used in a tender offer. However, a general mailing is difficult because the names and addresses of the stockholders of record are not usually available. The following factors are involved in choosing between an acquisition of stock and a merger: 1. In an acquisition of stock, shareholder meetings need not be held and a vote is not required. If the shareholders of the target firm do not like the offer, they are not required to accept it and need not tender their shares. 2. In an acquisition of stock, the bidding firm can deal directly with the shareholders of a target firm via a tender offer. The target firm’s management and board of directors are bypassed. 3. Target managers often resist acquisition. In such cases, acquisition of stock circumvents the target firm’s management. Resistance by the target firm’s management often makes the cost of acquisition of stock higher than the cost by merger. 4. Frequently a minority of shareholders will hold out in a tender offer, and thus, the target firm cannot be completely absorbed. 5. Complete absorption of one firm by another requires a merger. Many acquisitions of stock end with a formal merger.

Acquisitiono fAsse ts One firm can acquire another by buying all of its assets. The selling firm does not necessarily vanish because its “shell” can be retained. A formal vote of the target stockholders is required in an acquisition of assets. An advantage here is that although the acquirer is often left with minority shareholders in an acquisition of stock, this does 1

Mergers between corporations require compliance with state laws. In virtually all states, the shareholders of each corporation must give their assent.

Chapter 29

Mergers, Acquisitions, and Divestitures

Figure 29.1

877

Merger or consolidation

Varieties of Takeovers

Takeovers

Acquisition

Acquisition of stock

Proxy contest

Acquisition of assets

Going private

not happen in an acquisition of assets. Minority shareholders often present problems, such as holdouts. However, asset acquisition involves transferring title to individual assets, which can be costly.

ACl assificationSche me Financial analysts have typically classified acquisitions into three types: 1. Horizontal acquisition: Here, both the acquirer and acquired are in the same industry. Exxon’s acquisition of Mobil in 1998 is an example of a horizontal merger in the oil industry. 2. Vertical acquisition: A vertical acquisition involves firms at different steps of the production process. The acquisition by an airline company of a travel agency would be a vertical acquisition. 3. Conglomerate acquisition: The acquiring firm and the acquired firm are not related to each other. The acquisition of a food products firm by a computer firm would be considered a conglomerate acquisition.

A Note about Takeovers Takeover is a general and imprecise term referring to the transfer of control of a firm from one group of shareholders to another.2 A firm that has decided to take over another firm is usually referred to as the bidder. The bidder offers to pay cash or securities to obtain the stock or assets of another company. If the offer is accepted, the target firm will give up control over its stock or assets to the bidder in exchange for consideration (i.e., its stock, its debt, or cash).3 Takeovers can occur by acquisitions, proxy contests, and going-private transactions. Thus, takeovers encompass a broader set of activities than acquisitions, as depicted in Figure29.1. If a takeover is achieved by acquisition, it will be by merger, tender offer for shares of stock, or purchase of assets. In mergers and tender offers, the acquiring firm buys the voting common stock of the acquired firm. Proxy contests can result in takeovers as well. Proxy contests occur when a group of shareholders attempts to gain seats on the board of directors. A proxy is written authorization for one shareholder to vote the stock of another shareholder. In a proxy contest, an insurgent group of shareholders solicits proxies from other shareholders. In going-private transactions, a small group of investors purchases all the equity shares of a public firm. The group usually includes members of incumbent management 2

Control can usually be defined as having a majority vote on the board of directors. Audra L. Boone and J. Harold Mulherin in “How Are Firms Sold?” Journal of Finance (April 2007), look closely at the takeover process and the chain of negotiations and competitive bidding.

3

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and some outside investors. The shares of the firm are delisted from stock exchanges and can no longer be purchased in the open market.

29.2 Synergy The previous section discussed the basic forms of acquisition. We now examine why firms are acquired. (Although the previous section pointed out that acquisitions and mergers have different definitions, these differences will be unimportant in this, and many of the following, sections. Thus, unless otherwise stated, we will refer to acquisitions and mergers synonymously.) Much of our thinking here can be organized around the following four questions: 1. Is there a rational reason for mergers? Yes—in a word, synergy. Suppose firm A is contemplating acquiring firm B. The value of firm A is VA and the value of firm B is VB. (It is reasonable to assume that for public companies, VA and VB can be determined by observing the market prices of the outstanding securities.) The difference between the value of the combined firm (VAB) and the sum of the values of the firms as separate entities is the synergy from the acquisition: Synergy = VAB − (VA + VB) In words, synergy occurs if the value of the combined firm after the merger is greater than the sum of the value of the acquiring firm and the value of the acquired firm before the merger. 2. Where does this magic force, synergy, come from? Increases in cash flow create value. We define ∆CFt as the difference between the cash flows at date t of the combined firm and the sum of the cash flows of the two separate firms. From the chapters about capital budgeting, we know that the cash flow in any period t can be written as: ∆CFt = ∆Revt − ∆Costst − ∆Taxest − ∆Capital Requirementst where ∆Revt is the incremental revenue of the acquisition; ∆Costst is the incremental costs of the acquisition; ∆Taxest is the incremental acquisition taxes; and ∆Capital Requirementst is the incremental new investment required in working capital and fixed assets. It follows from our classification of incremental cash flows that the possible sources of synergy fall into four basic categories: Revenue enhancement, cost reduction, lower taxes, and lower capital requirements.4 Improvements in at least one of

4

Many reasons are given by firms to justify mergers and acquisitions. When two firms merge, the boards of directors of the two firms adopt an agreement of merger. The agreement of merger of U.S. Steel and Marathon Oil is typical. It lists the economic benefits that shareholders can expect from the merger (key words have been italicized): U.S. Steel believes that the acquisition of Marathon provides U.S. Steel with an attractive opportunity to diversify into the energy business. Reasons for the merger include, but are not limited to, the facts that consummation of the merger will allow U.S. Steel to consolidate Marathon into U.S. Steel’s federal income tax return, will also contribute to greater efficiency, and will enhance the ability to manage capital by permitting the movement of cash between U.S. Steel and Marathon. Additionally, the merger will eliminate the possibility of conflicts of interests between the interests of minority and majority shareholders and will enhance management flexibility. The acquisition will provide Marathon shareholders with a substantial premium over historical market prices for their shares. However, shareholders will no longer continue to share in the future prospects of the company.

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these four categories create synergy. Each of these categories will be discussed in detail in the next section. In addition, reasons are often provided for mergers where improvements are not expected in any of these four categories. These “bad” reasons for mergers will be discussed in Section 29.4. 3. How are these synergistic gains shared? In general, the acquiring firm pays a premium for the acquired, or target, firm. For example, if the stock of the target is selling for $50, the acquirer might need to pay $60 a share, implying a premium of $10, or 20 percent. The gain to the target in this example is $10. Suppose that the synergy from the merger is $30. The gain to the acquiring firm, or bidder, would be $20 (=$30 − $10). The bidder would actually lose if the synergy were less than the premium of $10. A more detailed treatment of these gains or losses will be provided in Section 29.6. 4. Are there other motives for a merger besides synergy? Yes. As we have said, synergy is the source of benefit to stockholders. However, the managers are likely to view a potential merger differently. Even if the synergy from the merger is less than the premium paid to the target, the managers of the acquiring firm may still benefit. For example, the revenues of the combined firm after the merger will almost certainly be greater than the revenues of the bidder before the merger. The managers may receive higher compensation once they are managing a larger firm. Even beyond the increase in compensation, managers generally experience greater prestige and power when managing a larger firm. Conversely, the managers of the target could lose their jobs after the acquisition. They might very well oppose the takeover even if their stockholders would benefit from the premium. These issues will be discussed in more detail in Section 29.9.

29.3 Sourceso f Synergy In this section, we discuss sources of synergy.5

RevenueE nhancement A combined firm may generate greater revenues than two separate firms. Increased revenues can come from marketing gains, strategic benefits, and market power. Marketing Gains It is frequently claimed that, due to improved marketing, mergers and acquisitions can increase operating revenues. Improvements can be made in the following areas: 1. Ineffective media programming and advertising efforts. 2. A weakd istributionn etwork. 3. Anu nbalancedp roductmix. Strategic Benefits Some acquisitions promise a strategic benefit, which is more like an option than a standard investment opportunity. For example, imagine that a sewing

5

Matthew Rhodes-Kropf and David Robinson, in “The Market for Mergers and the Boundaries of the Firm,” Journal of Finance (June 2008), address a related question of who buys whom. Contrary to conventional wisdom, they argue that it does not appear that firms with relatively high market value tend to buy firms with relatively low values. Instead, they show firms tend to pair with other firms having similar ratios.

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Figure29 .2

Special Topics

Cost per unit

Economies of Scale and the Optimal Size oftheF irm

Minimum cost

Economies of scale

Diseconomies of scale Size Optimal size

machine company acquires a computer company. The firm will be well positioned if technological advances allow computer-driven sewing machines in the future. Michael Porter has used the word beachhead to denote the strategic benefits from entering a new industry.6 He uses the example of Procter & Gamble’s acquisition of the Charmin Paper Company as a beachhead that allowed Procter & Gamble to develop a highly interrelated cluster of paper products—disposable diapers, paper towels, feminine hygiene products, and bathroom tissue. Market or Monopoly Power One firm may acquire another to reduce competition. If so, prices can be increased, generating monopoly profits. However, mergers that reduce competition do not benefit society, and the U.S. Department of Justice or the Federal Trade Commission may challenge them.

CostR eduction A combined firm may operate more efficiently than two separate firms. When Bank of America agreed to acquire Security Pacific, lower costs were cited as the primary reason. A merger can increase operating efficiency in the following ways: Economy of Scale Economy of scale means that the average cost of production falls as the level of production increases. Figure 29.2 illustrates the relation between cost per unit and size for a typical firm. As can be seen, average cost first falls and then rises. In other words, the firm experiences economies of scale until optimal firm size is reached. Diseconomies of scale arise after that. Though the precise nature of economies of scale is not known, it is one obvious benefit of horizontal mergers. The phrase spreading overhead is frequently used in connection with economies of scale. This refers to sharing central facilities such as corporate headquarters, top management, and computer systems.

6

M. Porter, Competitive Advantage (New York: Free Press, 1998).

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Economies of Vertical Integration Operating economies can be gained from vertical combinations as well as from horizontal combinations. The main purpose of vertical acquisitions is to make coordination of closely related operating activities easier. This is probably why most forest product firms that cut timber also own sawmills and hauling equipment. Because petroleum is used to make plastics and other chemical products, the DuPont–Conoco merger was motivated by DuPont’s need for a steady supply of oil. Economies of vertical integration probably explain why most airline companies own airplanes. They also may explain why some airline companies have purchased hotels and car rental companies. Technology Transfer Technology transfer is another reason for a merger. An automobile manufacturer might well acquire an aircraft company if aerospace technology can improve automotive quality. This technology transfer was the motivation behind the merger of General Motors and Hughes Aircraft. Complementary Resources Some firms acquire others to improve usage of existing resources. A ski equipment store merging with a tennis equipment store will smooth sales over both the winter and summer seasons, thereby making better use of storec apacity. Elimination of Inefficient Management A change in management can often increase firm value. Some managers overspend on perquisites and pet projects, making them ripe for takeover. For example, the leveraged buyout of RJR Nabisco was instituted primarily to halt the profligate behavior of CEO Ross Johnson. Alternatively, incumbent managers may not understand changing market conditions or new technology, making it difficult for them to abandon old strategies. Although the board of directors should replace these managers, the board is often unable to act independently. Thus, a merger may be needed to make the necessary replacements. Michael C. Jensen cites the oil industry as an example of managerial inefficiency.7 In the late 1970s, changes in the oil industry included expectations of lower oil prices, increased exploration and development costs, and higher real interest rates. As a result of these changes, substantial reductions in exploration and development were called for. However, many oil company managers were unable to downsize their firms. Acquiring companies sought out oil firms in order to reduce their investment levels. For example, T. Boone Pickens of Mesa Petroleum attempted to buy three oil companies—Unocal, Phillips, and Getty—to install more frugal management. Although he was unable to make the acquisitions, his attempts spurred existing management to reduce expenditures on exploration and development, generating huge gains to the shareholders of these firms, including himself. Mergers and acquisitions can be viewed as part of the labor market for top management. Michael Jensen and Richard Ruback have used the phrase “market for corporate control,” in which alternative management teams compete for the right to managec orporateac tivities.8

7 M. C. Jensen, “Agency Costs of Free Cash Flow, Corporate Finance, and Takeovers,” American Economic Review (1986). 8

M. C. Jensen and R. S. Ruback, “The Market for Corporate Control: The Scientific Evidence,” Journal of Financial Economics 11 (1983).

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Table 29.1

Before Merger

Tax Effect of Merger of Firms A and B

Firm A

Taxable income Taxes Net income

After Merger Firm B

Firm AB

If State 1

If State 2

If State 1

If State 2

If State 1

If State 2

$200 68 $132

−$100 0 −$100

−$100 0 −$100

$200 68 $132

$100 34 $ 66

$100 34 $ 66

Neither firm will be able to deduct its losses prior to the merger. The merger allows the losses from A to offset the taxable profits from B—and vice versa.

TaxG ains Tax reduction may be a powerful incentive for some acquisitions. This reduction can come from: 1. The use of tax losses. 2. The use of unused debt capacity. 3. Theu seo f su rplusfu nds. Net Operating Losses A firm with a profitable division and an unprofitable one will have a low tax bill because the loss in one division offsets the income in the other. However, if the two divisions are actually separate companies, the profitable firm will not be able to use the losses of the unprofitable one to offset its income. Thus, in the right circumstances, a merger can lower taxes. Consider Table 29.1, which shows pretax income, taxes, and aftertax income for firms A and B. Firm A earns $200 in state 1 but loses money in state 2. The firm pays taxes in state 1 but is not entitled to a tax rebate in state 2. Conversely, firm B turns a profit in state 2 but not in state 1. This firm pays taxes only in state 2. The table shows that the combined tax bill of the two separate firms is always $68, regardless of which situation occurs. However, the last two columns of the table show that after a merger, the combined firm will pay taxes of only $34. Taxes drop after the merger, because a loss in one division offsets the gain in the other. The message of this example is that firms need taxable profits to take advantage of potential losses. These losses are often referred to as net operating losses, or NOL for short. Mergers can sometimes bring losses and profits together. However, there are two qualifications to the previous example: 1. Federal tax laws permit firms that experience alternating periods of profits and losses to equalize their taxes by carryback and carryforward provisions. The accounting rules are complicated but generally a firm that has been profitable but has a loss in the current year can get refunds of income taxes paid in the two previous years and can carry the loss forward for 20 years. Thus, a merger to exploit unused tax shields must offer tax savings over and above what can be accomplishedb yfir msviac arryovers.9 2. The IRS may disallow an acquisition if the principal purpose of the acquisition is to avoid federal tax. This is one of the catch-22s of the Internal Revenue Code. 9

Under the 1986 Tax Reform Act, a corporation’s ability to carry forward net operating losses (and other tax credits) is limited when more than 50 percent of the stock changes hands over a three-year period.

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Debt Capacity There are at least two cases where mergers allow for increased debt and a larger tax shield. In the first case, the target has too little debt, and the acquirer can infuse the target with the missing debt. In the second case, both the target and acquirer have optimal debt levels. A merger leads to risk reduction, generating greater debt capacity and a larger tax shield. We treat each case in turn. Case 1: Unused Debt Capacity In Chapter 17, we pointed out that every firm has a certain amount of debt capacity. This debt capacity is beneficial because greater debt leads to a greater tax shield. More formally, every firm can borrow a certain amount before the marginal costs of financial distress equal the marginal tax shield. This debt capacity is a function of many factors, perhaps the most important being the risk of the firm. Firms with high risk generally cannot borrow as much as firms with low risk. For example, a utility or a supermarket, both firms with low risk, can have a higher debt-to-value ratio than a technology firm. Some firms, for whatever reason, have less debt than is optimal. Perhaps the managers are risk-averse, or perhaps the managers simply don’t know how to assess debt capacity properly. Is it bad for a firm to have too little debt? The answer is yes. As we have said, the optimal level of debt occurs when the marginal cost of financial distress equals the marginal tax shield. Too little debt reduces firm value. This is where mergers come in. A firm with little or no debt is an inviting target. An acquirer could raise the target’s debt level after the merger to create a bigger tax shield. Case 2: Increased Debt Capacity Let’s move back to the principles of modern portfolio theory, as presented in Chapter 11. Consider two stocks in different industries, where both stocks have the same risk or standard deviation. A portfolio of these two stocks has lower risk than that of either stock separately. In other words, the twostock portfolio is somewhat diversified, whereas each stock by itself is completely undiversified.10 Now, rather than considering an individual buying both stocks, consider a merger between the two underlying firms. Because the risk of the combined firm is less than that of either one separately, banks should be willing to lend more money to the combined firm than the total of what they would lend to the two firms separately. In other words, the risk reduction that the merger generates leads to greater debt capacity. For example, imagine that each firm can borrow $100 on its own before the merger. Perhaps the combined firm after the merger will be able to borrow $250. Debt capacity has increased by $50 (=$250 − $200). Remember that debt generates a tax shield. If debt rises after the merger, taxes will fall. That is, simply because of the greater interest payments after the merger, the tax bill of the combined firm should be less than the sum of the tax bills of the two separate firms before the merger. In other words, the increased debt capacity from a merger can reduce taxes. To summarize, we first considered the case where the target had too little leverage. The acquirer could infuse the target with more debt, generating a greater tax shield. Next, we considered the case where both the target and acquirer began with optimal debt levels. A merger leads to more debt even here. That is, the risk reduction from the merger creates greater debt capacity and thus a greater tax shield. 10

Although diversification is most easily explained by considering stocks in different industries, the key is that the returns on the two stocks are less than perfectly correlated—a relationship that should occur even for stocks in the same industry.

In Their Own Words MICHAEL C. JENSEN ON MERGERS AND ACQUISITIONS Economic analysis and evidence indicate that takeovers, LBOs, and corporate restructurings are playing an important role in helping the economy adjust to major competitive changes in the last two decades. The competition among alternative management teams and organizational structures for control of corporate assets has enabled vast economic resources to move more quickly to their highest-valued use. In the process, substantial benefits for the economy as a whole as well as for shareholders have been created. Overall gains to selling-firm shareholders from mergers, acquisitions, leveraged buyouts, and other corporate restructurings in the 12-year period 1977–1988 totaled over $500 billion in 1988 dollars. I estimate gains to buyingfirm shareholders to be at least $50 billion for the same period. These gains equaled 53 percent of the total cash dividends (valued in 1988 dollars) paid to investors by the entire corporate sector in the same period. Mergers and acquisitions are a response to new technologies or market conditions that require a strategic

change in a company’s direction or use of resources. Compared to current management, a new owner is often better able to accomplish major change in the existing organizational structure. Alternatively, leveraged buyouts bring about organizational change by creating entrepreneurial incentives for management and by eliminating the centralized bureaucratic obstacles to maneuverability that are inherent in large public corporations. When managers have a substantial ownership interest in the organization, the conflicts of interest between shareholders and managers over the payout of the company’s free cash flow are reduced. Management’s incentives are focused on maximizing the value of the enterprise, rather than building empires—often through poorly conceived diversification acquisitions—without regard to shareholder value. Finally, the required repayment of debt replaces management’s discretion in paying dividends and the tendency to overretain cash. Substantial increases in efficiency are thereby created. Michael C. Jensen is Jesse Isidor Straus Professor of Business Administration, Emeritus at Harvard University. An outstanding scholar and researcher, he is famous for his pathbreaking analysis of the modern corporation and its relations with its stockholders.

Surplus Funds Another quirk in the tax law involves surplus funds. Consider a firm that has free cash flow. That is, it has cash flow available after payment of all taxes and after all positive net present value projects have been funded. In this situation, aside from purchasing securities, the firm can either pay dividends or buy back shares. We have already seen in our previous discussion of dividend policy that an extra dividend will increase the income tax paid by some investors. Investors pay lower taxes in a share repurchase.11 However, a share repurchase is not a legal option if the sole purpose is to avoid taxes on dividends. Instead, the firm might make acquisitions with its excess funds. Here, the shareholders of the acquiring firm avoid the taxes they would have paid on a dividend.12 And no taxes are paid on dividends remitted from the acquired firm.

ReducedCa pitalR equirements Earlier in this chapter, we stated that due to economies of scale, mergers can reduce operating costs. It follows that mergers can reduce capital requirements as well. Accountants typically divide capital into two components: Fixed capital and working capital. When two firms merge, the managers will likely find duplicate facilities. For example, if both firms had their own headquarters, all executives in the merged firm could be moved to one headquarters building, allowing the other headquarters to be sold. Some plants might be redundant as well. Or two merging firms in the same industry might consolidate their research and development, permitting some R&D facilities to be sold. 11 A dividend is taxable to all tax-paying recipients. A repurchase creates a tax liability only for those who choose to sell (and do so at a profit). 12 The situation is actually a little more complex: The target’s shareholders must pay taxes on their capital gains. These stockholders will likely demand a premium from the acquirer to offset this tax.

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The same goes for working capital. The inventory-to-sales ratio and the cash-tosales ratio often decrease as firm size increases. A merger permits these economies of scale to be realized, allowing a reduction in working capital.

29.4 Two Financial Side Effects of Acquisitions EarningsG rowth An acquisition can create the appearance of earnings growth, perhaps fooling investors into thinking that the firm is worth more than it really is. Let’s consider two companies, Global Resources, Ltd., and Regional Enterprises, as depicted in the first two columns of Table 29.2. As can be seen, earnings per share are $1 for both companies. However, Global sells for $25 per share, implying a price–earnings (P/E) ratio of 25 (=$25 $1). By contrast, Regional sells for $10, implying a P/E ratio of 10. This means that an investor in Global pays $25 to get $1 in earnings, whereas an investor in Regional receives the same $1 in earnings on only a $10 investment. Are investors getting a better deal with Regional? Not necessarily. Perhaps Global’s earnings are expected to grow faster than are Regional’s earnings. If this is the case, an investor in Global will expect to receive high earnings in later years, making up for low earnings in the short term. In fact, Chapter 9 argues that the primary determinant of a firm’s P/E ratio is the market’s expectation of the firm’s growth rate in earnings. Now let’s imagine that Global acquires Regional, with the merger creating no value. If the market is smart, it will realize that the combined firm is worth the sum of the values of the separate firms. In this case, the market value of the combined firm will be $3,500, which is equal to the sum of the values of the separate firms before the merger. At these values, Global will acquire Regional by exchanging 40 of its shares for 100 shares of Regional, so that Global will have 140 shares outstanding after the merger.13 Global’s stock price remains at $25 (=$3,500 140). With 140 shares outstanding and $200 of earnings after the merger, Global earns $1.43 (=$200 140) per share after the merger. Its P/E ratio becomes 17.5 (=$25 $1.43), a drop from 25 before the merger. This scenario is represented by the third column of Table 29.2.

Table 29.2 Financial Positions of Global Resources, Ltd., and Regional Enterprises

Global Resources before Merger Earnings per share Price per share Price–earnings ratio Number of shares Total earnings Total value

Regional Enterprises before Merger

$ $

1.00 25.00 25 100 $ 100 $2,500

$ $

1.00 10.00 10 100 $ 100 $1,000

Global Resources after Merger The Market Is “Smart” $ $

1.43 25.00 17.5 140 $ 200 $3,500

The Market Is “Fooled” $ $

1.43 35.71 25 140 $ 200 $5,000

Exchange ratio: 1 share in Global for 2.5 shares in Regional.

13

This ratio implies a fair exchange because a share of Regional is selling for 40 percent (=$10 $25) of the price of a share of Global.

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Why has the P/E dropped? The combined firm’s P/E will be an average of Global’s high P/E and Regional’s low P/E before the merger. This is common sense once you think about it. Global’s P/E should drop when it takes on a new division with low growth. Let us now consider the possibility that the market is fooled. As we just said, the acquisition enables Global to increase its earnings per share from $1 to $1.43. If the market is fooled, it might mistake the 43 percent increase in earnings per share for true growth. In this case, the price–earnings ratio of Global may not fall after the merger. Suppose the price–earnings ratio of Global remains at 25. The total value of the combined firm will increase to $5,000 (=$25 × $200), and the stock price per share of Global will increase to $35.71 (=$5,000 140). This is reflected in the last column of the table. This is earnings growth magic. Can we expect this magic to work in the real world? Managers of a previous generation certainly thought so, with firms such as LTV Industries, ITT, and Litton Industries all trying to play the P/E-multiple game in the 1960s. However, in hindsight, it looks as if they played the game without much success. These operators have all dropped out with few, if any, replacements. It appears that the market is too smart to be fooled this easily.

Diversification Diversification is often mentioned as a benefit of one firm acquiring another. Earlier in this chapter, we noted that U.S. Steel included diversification as a benefit in its acquisition of Marathon Oil. At the time of the merger, U.S. Steel was a cash-rich company, with over 20 percent of its assets in cash and marketable securities. It is not uncommon to see firms with surplus cash articulating a need for diversification. However, we argue that diversification, by itself, cannot produce increases in value. To see this, recall that a business’s variability of return can be separated into two parts: (1) What is specific to the business and called unsystematic and (2) what is systematic because it is common to all businesses. Systematic variability cannot be eliminated by diversification, so mergers will not eliminate this risk at all. By contrast, unsystematic risk can be diversified away through mergers. However, the investor does not need widely diversified companies such as General Electric to eliminate unsystematic risk. Shareholders can diversify more easily than corporations by simply purchasing common stock in different corporations. For example, the shareholders of U.S. Steel could have purchased shares in Marathon if they believed there would be diversification gains in doing so. Thus, diversification through conglomerate merger may not benefit shareholders.14 Diversification can produce gains to the acquiring firm only if one of two things is true: 1. Diversification decreases the unsystematic variability at lower costs than by investors’ adjustments to personal portfolios. This seems very unlikely. 2. Diversification reduces risk and thereby increases debt capacity. This possibility wasme ntioned earlierin th ec hapter.

14

In fact, a number of scholars have argued that diversification can reduce firm value by weakening corporate focus, a point to be developed in a later section of this chapter.

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29.5 A Cost to Stockholders from Reduction in Risk We considered two financial side effects of mergers in the previous section. Merging for either of these two reasons will not necessarily destroy value. Rather, it is just unlikely that merging for these two reasons will increase value. In this section, we examine a by-product of acquisitions that should actually destroy value, at least from the stockholders’ point of view. As we will see, mergers increase the safety of bonds, raising the value of these bonds and hurting the stockholders. In Chapter 11, we considered an individual adding one security after another, all of equal risk, to a portfolio. We saw that as long as the securities were less than perfectly positively correlated with each other, the risk of this portfolio fell as the number of securities rose. In a word, this risk reduction reflected diversification. Diversification also happens in a merger. When two firms merge, the volatility of their combined value is usually less than their volatilities as separate entities. However, there is a surprising result here. Whereas an individual benefits from portfolio diversification, diversification from a merger may actually hurt the stockholders. The reason is that the bondholders are likely to gain from the merger because their debt is now “insured” by two firms, not just one. It turns out that this gain to the bondholders is at the stockholders’ expense.

TheB aseCa se Consider an example where firm A acquires firm B. Panel I of Table 29.3 shows the net present values of firm A and firm B prior to the merger in the two possible states of the economy. Because the probability of each state is .50, the market value of each firm is the average of its values in the two states. For example, the market value of firm Ais : .5 × $80 + .5 × $20 =$50 Now imagine that the merger of the two firms generates no synergy. The combined firm AB will have a market value of $75 (=$50 + $25), the sum of the values of firm A and firm B. Further imagine that the stockholders of firm B receive stock in AB equal to firm B’s stand-alone market value of $25. In other words, firm B receives no premium. Because the value of AB is $75, the stockholders of firm A have a value of $50 (=$75 − $25) after the merger—just what they had before the merger. Thus, the stockholders of both firms A and B are indifferent to the merger.

Both Firms Have Debt Alternatively, imagine that firm A has debt with a face value of $30 in its capital structure, as shown in panel II of Table 29.3. Without a merger, firm A will default on its debt in state 2 because the value of firm A in this state is $20, less than the face value of the debt of $30. As a consequence, firm A cannot pay the full value of the debt claim; the bondholders receive only $20 in this state. The creditors take the possibility of default into account, valuing the debt at $25 (=.5 × $30 + .5 × $20). Firm B’s debt has a face value of $15. Firm B will default in state 1 because the value of the firm in this state is $10, less than the face value of the debt of $15. The value of firm B’s debt is $12.50 (=.5 × $10 + .5 × $15). It follows that the sum of the value of firm A’s debt and the value of firm B’s debt is $37.50 (=$25 + $12.50). Now let’s see what happens after the merger. Firm AB is worth $90 in state 1 and $60 in state 2, implying a market value of $75 (=.5 × $90 + .5 × $60). The face value of the debt in the combined firm is $45 (=$30 + $15). Because the value of the firm

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Table 29.3

NPV

Stock-Swap Mergers

State 1 Probability

.5

State 2

Market Value

.5

I. Base case (no debt in either firm’s capital structure) Values before merger: Firm A $80 $20 Firm B 10 40 * Values after merger: Firm AB $90 $60 II. Debt with face value of $30 in firm A’s capital structure Debt with face value of $15 in firm B’s capital structure Values before merger: Firm A $80 $20 Debt 30 20 Equity 50 0 Firm B $10 $40 Debt 10 15 Equity 0 25 Values after merger:† Firm AB $90 $60 Debt 45 45 Equity 45 15

$50 25 $75

$50 25 25 $25 12.50 12.50 $75 45 30

Values of both firm A’s debt and firm B’s debt rise after the merger. Values of both firm A’s stock and firm B’s stock fall after the merger. *Stockholders in firm A receive $50 of stock in firm AB. Stockholders in firm B receive $25 of stock in firm AB. Thus, stockholders in both firms are indifferent to the merger. † Stockholders in firm A receive stock in firm AB worth $20. Stockholders in firm B receive stock in firm AB worth $10. Gains and losses from the merger are:

Loss to stockholders in firm A: $20 − $25 = −$5 Loss to stockholders in firm B: $10 − $12.50 = −$2.50 Combined gain to bondholders in both firms: $45.00 − $37.50 = $7.50

is greater than $45 in either state, the bondholders always get paid in full. Thus, the value of the debt is its face value of $45. This value is $7.50 greater than the sum of the values of the two debts before the merger, which we just found to be $37.50. Therefore, the merger benefits the bondholders. What about the stockholders? Because the equity of firm A was worth $25 and the equity of firm B was worth $12.50 before the merger, let’s assume that firm AB issues two shares to firm A’s stockholders for every share issued to firm B’s stockholders. Firm AB’s equity is $30, so firm A’s shareholders get shares worth $20 and firm B’s shareholders get shares worth $10. Firm A’s stockholders lose $5 (=$20 − $25) from the merger. Similarly, firm B’s stockholders lose $2.50 (=$10 − $12.50). The total loss to the stockholders of both firms is $7.50, exactly the gain to the bondholders from the merger. There are a lot of numbers in this example. The point is that the bondholders gain $7.50 and the stockholders lose $7.50 from the merger. Why does this transfer of value occur? To see what is going on, notice that when the two firms are separate, firm B does not guarantee firm A’s debt. That is, if firm A defaults on its debt, firm B does not help the bondholders of firm A. However, after the merger the bondholders can draw on the cash flows from both A and B. When one of the divisions of the combined firm fails, creditors

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can be paid from the profits of the other division. This mutual guarantee, which is called the coinsurance effect, makes the debt less risky and more valuable than before. There is no net benefit to the firm as a whole. The bondholders gain the coinsurance effect, and the stockholders lose the coinsurance effect. Some general conclusions emerge from the preceding analysis: 1. Mergers usually help bondholders. The size of the gain to bondholders depends on the reduction in the probability of bankruptcy after the combination. That is, the less risky the combined firm is, the greater are the gains to bondholders. 2. Stockholders are hurt by the amount that bondholders gain. 3. Conclusion 2 applies to mergers without synergy. In practice, much depends on thesiz eo f th esyn ergy.

How Can Shareholders Reduce Their Losses from the Coinsurance Effect? The coinsurance effect raises bondholder values and lowers shareholder values. However, there are at least two ways in which shareholders can reduce or eliminate the coinsurance effect. First, the shareholders of firm A could retire its debt before the merger announcement date and reissue an equal amount of debt after the merger. Because debt is retired at the low premerger price, this type of refinancing transaction can neutralize the coinsurance effect to the bondholders. Also, note that the debt capacity of the combined firm is likely to increase because the acquisition reduces the probability of financial distress. Thus, the shareholders’ second alternative is simply to issue more debt after the merger. An increase in debt following the merger will have two effects, even without the prior action of debt retirement. The interest tax shield from new corporate debt raises firm value, as discussed in an earlier section of this chapter. In addition, an increase in debt after the merger raises the probability of financial distress, thereby reducing or eliminating the bondholders’ gain from the coinsurance effect.

29.6 The NPV of a Merger Firms typically use NPV analysis when making acquisitions. The analysis is relatively straightforward when the consideration is cash. The analysis becomes more complex when the consideration is stock.

Cash Suppose firm A and firm B have values as separate entities of $500 and $100, respectively. They are both all-equity firms. If firm A acquires firm B, the merged firm AB will have a combined value of $700 due to synergies of $100. The board of firm B has indicated that it will sell firm B if it is offered $150 in cash. Should firm A acquire firm B? Assuming that firm A finances the acquisition out of its own retained earnings, its value after the acquisition is:15 Valueo f f irm A after the acquisition = Value of combined firm – Cash paid = $700 – $150 =$550 15

The analysis will be essentially the same if new stock is issued. However, the analysis will differ if new debt is issued to fund the acquisition because of the tax shield to debt. An adjusted present value (APV) approach would be necessary here.

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Table 29.4

Special Topics

Cost of Acquisition: Cash versus Common Stock

Before Acquisition

Market value (VA, VB) Number of shares Price per share

After Acquisition: Firm A

(1)

(2)

(3)

Cash*

(4) Common Stock† Exchange Ratio (.75:1)

(5) Common Stock† Exchange Ratio (.6819:1)

Firm A

Firm B

$500 25 $ 20

$100 10 $ 10

$550 25 $ 22

$700 32.5 $ 21.54

$700 31.819 $ 22

*Value of firm A after acquisition: Cash VA = VAB – Cash $550 = $700 – $150 †

Value of firm A after acquisition: Common stock VA = VAB $700 = $700

Because firm A was worth $500 prior to the acquisition, the NPV to firm A’s stockholders is: $50 = $550 –$500

(29.1)

Assuming that there are 25 shares in firm A, each share of the firm is worth $20 (=$500 25) prior to the merger and $22 (=$550 25) after the merger. These calculations are displayed in the first and third columns of Table 29.4. Looking at the rise in stock price, we conclude that firm A should make the acquisition. We spoke earlier of both the synergy and the premium of a merger. We can also value the NPV of a merger to the acquirer: NPV of a merger to acquirer = Synergy −P remium Because the value of the combined firm is $700 and the premerger values of A and B were $500 and $100, respectively, the synergy is $100 [=$700 − ($500 + $100)]. The premium is $50 (=$150 − $100). Thus, the NPV of the merger to the acquirer is: NPV of merger to firm A = $100 − $50 =$50 One caveat is in order. This textbook has consistently argued that the market value of a firm is the best estimate of its true value. However, we must adjust our analysis when discussing mergers. If the true price of firm A without the merger is $500, the market value of firm A may actually be above $500 when merger negotiations take place. This happens because the market price reflects the possibility that the merger will occur. For example, if the probability is 60 percent that the merger will take place, the market price of firm A will be:

$530 =

Market value of firm A with merger $550

× ×

Probability of merger .60

+ +

Market value of firm A without merger $500

× ×

Probability of no merger .40

The managers would underestimate the NPV from the merger in Equation 29.1 if the market price of firm A were used. Thus, managers face the difficult task of valuing their own firm without the acquisition.

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CommonSto ck Of course, firm A could purchase firm B with common stock instead of cash. Unfortunately, the analysis is not as straightforward here. To handle this scenario, we need to know how many shares are outstanding in firm B. We assume that there are 10 shares outstanding, as indicated in column 2 of Table 29.4. Suppose firm A exchanges 7.5 of its shares for the entire 10 shares of firm B. We call this an exchange ratio of .75:1. The value of each share of firm A’s stock before the acquisition is $20. Because 7.5 × $20 = $150, this exchange appears to be the equivalent of purchasing firm B in cash for $150. This is incorrect: The true cost to firm A is greater than $150. To see this, note that firm A has 32.5 (=25 + 7.5) shares outstanding after the merger. Firm B shareholders own 23 percent (=7.5 32.5) of the combined firm. Their holdings are valued at $161 (=23% × $700). Because these stockholders receive stock in firm A worth $161, the cost of the merger to firm A’s stockholders must be $161, not $150. This result is shown in column 4 of Table 29.4. The value of each share of firm A’s stock after a stock-for-stock transaction is only $21.54 (=$700 32.5). We found out earlier that the value of each share is $22 after a cash-for-stock transaction. The difference is that the cost of the stock-for-stock transaction to firm A is higher. This nonintuitive result occurs because the exchange ratio of 7.5 shares of firm A for 10 shares of firm B was based on the premerger prices of the two firms. However, because the stock of firm A rises after the merger, firm B stockholders receive more than $150 in firm Asto ck. What should the exchange ratio be so that firm B stockholders receive only $150 of firm A’s stock? We begin by defining α, the proportion of the shares in the combined firm that firm B’s stockholders own. Because the combined firm’s value is $700, the value of firm B stockholders after the merger is: Value of Firm BS tockholdersafte rM erger α × $700 Setting α × $700 = $150, we find that α = 21.43%. In other words, firm B’s stockholders will receive stock worth $150 if they receive 21.43 percent of the firm after the merger. Now we determine the number of shares issued to firm B’s shareholders. The proportion, α, that firm B’s shareholders have in the combined firm can be expressed as follows: New shares issued New shares issued α = ____________________________ = _____________________ Old shares + New shares issued 25 + New shares issued Plugging our value of α into the equation yields: New shares issued .2143 = _____________________ 25 + New shares issued Solving for the unknown, we have: News hares = 6.819 shares Total shares outstanding after the merger are 31.819 (=25 + 6.819). Because 6.819 shares of firm A are exchanged for 10 shares of firm B, the exchange ratio is .6819:1. Results at the exchange ratio of .6819:1 are displayed in column 5 of Table 29.4. Because there are now 31.819 shares, each share of common stock is worth $22 (=$700 31.819), exactly what it is worth in the cash-for-stock transaction. Thus,

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given that the board of firm B will sell its firm for $150, this is the fair exchange ratio, not the ratio of .75:1 mentioned earlier.

Cash versus Common Stock In this section, we have examined both cash deals and stock-for-stock deals. Our analysis leads to the following question: When do bidders want to pay with cash and when do they want to pay with stock? There is no easy formula: The decision hinges on a few variables, with perhaps the most important being the price of the bidder’s stock. In the example of Table 29.4, firm A’s market price per share prior to the merger was $20. Let’s now assume that at the time firm A’s managers believed the “true” price was $15. In other words, the managers believed that their stock was overvalued. Is it likely for managers to have a different view than that of the market? Yes—managers often have more information than does the market. After all, managers deal with customers, suppliers, and employees daily and are likely to obtain private information. Now imagine that firm A’s managers are considering acquiring firm B with either cash or stock. The overvaluation would have no impact on the merger terms in a cash deal; firm B would still receive $150 in cash. However, the overvaluation would have a big impact on a stock-for-stock deal. Although firm B receives $150 worth of A’s stock as calculated at market prices, firm A’s managers know that the true value of the stock is less than $150. How should firm A pay for the acquisition? Clearly, firm A has an incentive to pay with stock because it would end up giving away less than $150 of value. This conclusion might seem rather cynical because firm A is, in some sense, trying to cheat firm B’s stockholders. However, both theory and empirical evidence suggest that firms are more likely to acquire with stock when their own stocks are overvalued.16 The story is not quite this simple. Just as the managers of firm A think strategically, firm B’s managers will likely think this way as well. Suppose that in the merger negotiations, firm A’s managers push for a stock-for-stock deal. This might tip off firm B’s managers that firm A is overpriced. Perhaps firm B’s managers will ask for better terms than firm A is currently offering. Alternatively, firm B may resolve to accept cash or not to sell at all. And just as firm B learns from the negotiations, the market learns also. Empirical evidence shows that the acquirer’s stock price generally falls upon the announcement of asto ck-for-stockd eal.17 However, this discussion does not imply that mistakes are never made. For example, consider the stock-for-stock merger in January 2001 between AOL, an Internet service provider, and Time Warner (TW), a media firm. Although the deal was presented as a merger of equals and the combined company is now called Time Warner, AOL appears, in retrospect, to have been the acquirer. The merger was one of the biggest of all time, with a combined market capitalization between the two firms of about $350 billion at the time of the announcement in January 2000. (The delay of about a year between merger announcement and merger completion was due to regulatory review.) It is also considered one of the worst deals of all time, with Time Warner having a market value of about $35 billion in early 2009. 16 The basic theoretical ideas are presented in S. Myers and N. Majluf, “Corporate Financing and Investment Decisions When Firms Have Information That Investors Do Not Have,” Journal of Financial Economics(1984). 17 For example, see G. Andrade, M. Mitchell, and E. Stafford, “New Evidence and Perspectives on Mergers,” Journal of Economic Perspectives (Spring 2001); and R. Heron and E. Lie, “Operating Performance and the Method of Payment in Takeovers,” Journal of Financial and Quantitative Analysis(2 002).

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AOL was in a precarious position at the time of the merger, providing narrowband Internet service when consumers were hungering for broadband. Also, at least in retrospect, Internet stocks were greatly overpriced. The deal allowed AOL to offer its inflated stock as currency for a company not in the technology industry and, therefore, not nearly as overpriced, if overpriced at all. Had TW looked at the deal in this way, it might have simply called it off. (Alternatively, it could have demanded cash, though it is unlikely that AOL had the financial resources to pay in this way.) Just as TW’s managers did not understand all the implications of the merger right away, it appears that the market did not either. TW’s stock price rose over 25 percent relative to the market in the week following the merger announcement.

29.7 Friendly versus Hostile Takeovers Mergers are generally initiated by the acquiring, not the acquired, firm. Thus, the acquirer must decide to purchase another firm, select the tactics to effectuate the merger, determine the highest price it is willing to pay, set an initial bid price, and make contact with the target firm. Often the CEO of the acquiring firm simply calls the CEO of the target and proposes a merger. Should the target be receptive, a merger eventually occurs. Of course there may be many meetings, with negotiations over price, terms of payment, and other parameters. The target’s board of directors generally has to approve the acquisition. Sometimes the bidder’s board must also give its approval. Finally, an affirmative vote by the stockholders is needed. But when all is said and done, an acquisition that proceeds in this way is viewed as friendly. Of course, not all acquisitions are friendly. The target’s management may resist the merger, in which case the acquirer must decide whether to pursue the merger and, if so, what tactics to use. Facing resistance, the acquirer may begin by purchasing some of the target’s stock in secret. This position is often called a toehold. The Williams Act, passed in 1968 and one of the landmark pieces of legislation of the era, requires that the acquirer file a Schedule 13D with the Securities and Exchange Commission (SEC) within 10 days of obtaining a 5 percent holding in the target’s stock. The acquirer must provide detailed information, including its intentions and its position in the target, on this schedule. Secrecy ends at this point because the acquirer must state that it plans to acquire the target. The price of the target’s shares will probably rise after the filing, with the new stock price reflecting the possibility that the target will be bought out at a premium. Acquirers will, however, often make the most of this 10-day delay, buying as much stock as possible at the low prefiling price during this period. Although the acquirer may continue to purchase shares in the open market, an acquisition is unlikely to be effectuated in this manner. Rather, the acquirer is more likely at some point to make a tender offer (an offer made directly to the stockholders to buy shares at a premium above the current market price). The tender offer may specify that the acquirer will purchase all shares that are tendered—that is, turned in to the acquirer. Alternatively, the offer may state that the acquirer will purchase all shares up to, say, 50 percent of the number of shares outstanding. If more shares are tendered, prorating will occur. For example, if, in the extreme case, all of the shares are tendered, each stockholder will be allowed to sell one share for every two shares tendered. The acquirer may also say that it will accept the tendered shares only if a minimum number of shares have been tendered. Under the Williams Act, a tender offer must be held open for at least 20 days. This delay gives the target time to respond. For example, the target may want to notify its

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stockholders not to tender their shares. It may release statements to the press criticizing the offer. The target may also encourage other firms to enter the bidding process. At some point, the tender offer ends, at which time the acquirer finds out how many shares have been tendered. The acquirer does not necessarily need 100 percent of the shares to obtain control of the target. In some companies, a holding of 20 percent or so may be enough for control. In others the percentage needed for control is much higher. Control is a vague term, but you might think of it operationally as control over the board of directors. Stockholders elect members of the board, who, in turn, appoint managers. If the acquirer receives enough stock to elect a majority of the board members, these members can appoint the managers whom the acquirer wants. And effective control can often be achieved with less than a majority. As long as some of the original board members vote with the acquirer, a few new board members can gain the acquirer a working majority. Sometimes, once the acquirer gets working control, it proposes a merger to obtain the few remaining shares that it does not already own. The transaction is now friendly because the board of directors will approve it. Mergers of this type are often called cleanupme rgers. A tender offer is not the only way to gain control of a hostile target. Alternatively, the acquirer may continue to buy more shares in the open market until control is achieved. This strategy, often called a street sweep, is infrequently used, perhaps because of the difficulty of buying enough shares to obtain control. Also, as mentioned, tender offers often allow the acquirer to return the tendered shares if fewer shares than the desired number are tendered. By contrast, shares purchased in the open market cannot be returned. Another means to obtain control is a proxy fight—a procedure involving corporate voting. Elections for seats on the board of directors are generally held at the annual stockholders’ meeting, perhaps four to five months after the end of the firm’s fiscal year. After purchasing shares in the target company, the acquirer nominates a slate of candidates to run against the current directors. The acquirer generally hires a proxy solicitor, who contacts shareholders prior to the stockholders’ meeting, making a pitch for the insurgent slate. Should the acquirer’s candidates win a majority of seats on the board, the acquirer will control the firm. And as with tender offers, effective control can often be achieved with less than a majority. The acquirer may just want to change a few specific policies of the firm, such as the firm’s capital budgeting program or its diversification plan. Or it may simply want to replace management. If some of the original board members are sympathetic to the acquirer’s plans, a few new board members can give the acquirer a working majority. For example, consider Carl Icahn’s proxy fight with Blockbuster. Carl Icahn’s group was Blockbuster’s biggest stockholder in early 2005, owning 9.7 percent of the firm’s Class A stock and 7.7 percent of the firm’s Class B shares. With the company losing over $1 billion in 2004, Mr. Icahn publicly criticized Blockbuster, calling for a number of changes involving spending cuts. He, along with two of his associates, won seats on the Blockbuster board in 2005. Though his group did not win a majority on the seven-member board, pundits argued that he would be able to move the company in his direction. Whereas mergers end up with the acquirer owning all of the target’s stock, the victor in a proxy fight does not gain additional shares. The reward to the proxy victor is simply share price appreciation if the victor’s policies prove effective. In fact, just the threat of a proxy fight may raise share prices because management may improve operations to head off the fight. For example, Mr. Icahn had threatened a proxy fight with

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Kerr-McGee (KM), withdrawing in April 2005 when the stock price rose in response to KM’s new policies.

29.8 Defensive Tactics Target firm managers frequently resist takeover attempts. Actions to defeat a takeover may benefit the target shareholders if the bidding firm raises its offer price or another firm makes a bid. Alternatively, resistance may simply reflect self-interest at the shareholders’ expense. That is, the target managers might fight a takeover to preserve their jobs. Sometimes management resists while simultaneously improving corporate policies. Stockholders can benefit in this case, even if the takeover fails. In this section, we describe various ways in which target managers resist takeovers. A company is said to be “in play” if one or more suitors are currently interested in acquiring it. It is useful to separate defensive tactics before a company is in play from tactics after the company is in play.

Deterring Takeovers before Being in Play Corporate Charters The corporate charter refers to the articles of incorporation and corporate bylaws governing a firm.18 Among other provisions, the charter establishes conditions allowing a takeover. Firms frequently amend charters to make acquisitions more difficult. As examples, consider the following two amendments: 1. Classified board: In an unclassified board of directors, stockholders elect all of the directors each year. In a classified, or staggered, board, only a fraction of the board is elected each year, with terms running for multiple years. For example, one-third of the board might stand for election each year, with terms running for three years. Classified boards increase the time an acquirer needs to obtain a majority of seats on the board. In the previous example, the acquirer can gain control of only one-third of the seats in the first year after acquisition. Another year must pass before the acquirer is able to control two-thirds of the seats. Therefore, the acquirer may not be able to change management as quickly as it would like. However, some argue that classified boards are not necessarily effective because the old directors often choose to vote with the acquirer. 2. Supermajority provisions: Corporate charters determine the percentage of voting shares needed to approve important transactions such as mergers. A supermajority provision in the charter means that this percentage is above 50 percent. Two-thirds majorities are common, though the number can be much higher. A supermajority provision clearly increases the difficulty of acquisition in the face of hostile management. Many charters with supermajority provisions have what is known as a board out clause as well. Here supermajority does not apply if the board of directors approves the merger. This clause makes sure that the provision hinderso nlyh ostiletak eovers. Golden Parachutes This colorful term refers to generous severance packages provided to management in the event of a takeover. The argument is that golden parachutes 18

Ronald Masulis, Cong Wang, and Fei Xie in “Corporate Governance and Acquirer Returns,” Journal of Finance (August 2007), find that acquirer firms with more antitakeover provisions receive lower stock market returns than otherwise.

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will deter takeovers by raising the cost of acquisition. However, some authorities point out that the deterrence effect is likely to be unimportant because a severance package, even a generous one, is probably a small part of the cost of acquiring a firm. In addition, some argue that golden parachutes actually increase the probability of a takeover. The reasoning here is that management has a natural tendency to resist any takeover because of the possibility of job loss. A large severance package softens the blow of a takeover, reducing management’s inclination to resist. Although we are now discussing measures to deter a future hostile takeover, golden parachutes can also be invoked once a bid has been received. For example, when the Scotville board endorsed a $523 million tender offer from First City Properties, it arranged for 13 top executives to receive termination payments of $5 million each. Poison Pills The poison pill is a sophisticated defensive tactic that Martin Lipton, a well-known New York attorney, developed in the early 1980s. Since then a number of variants have surfaced, so there is no single definition of a poison pill. Perhaps the example of PeopleSoft (PS) will illustrate the general idea. At one point in 2005, PS’s poison pill provision stated that once a bidder acquired 20 percent or more of PeopleSoft’s shares, all stockholders except the acquirer could buy new shares from the corporation at half price. At the time, PS had about 400 million shares outstanding. Should some bidder acquire 20 percent of the company (80 million shares), every shareholder except the bidder would be able to buy 16 new shares for every one previously held. If all shareholders exercised this option, PeopleSoft would have to issue 5.12 billion (=.8 × 400 million × 16) new shares, bringing its total to 5.52 billion. The stock price would drop because the company would be selling shares at half price. The bidder’s percentage of the firm would drop from 20 percent to 1.45 percent (=80 million 5.52 billion). Dilution of this magnitude causes some critics to argue that poison pills are insurmountable.

Deterring a Takeover after the Company Is in Play Greenmail and Standstill Agreements Managers may arrange a targeted repurchase to forestall a takeover attempt. In a targeted repurchase, a firm buys back its own stock from a potential bidder, usually at a substantial premium, with the proviso that the seller promises not to acquire the company for a specified period. Critics of such payments label them greenmail. A standstill agreement occurs when the acquirer, for a fee, agrees to limit its holdings in the target. As part of the agreement, the acquirer often promises to offer the target a right of first refusal in the event that the acquirer sells its shares. This promise prevents the block of shares from falling into the hands of another would-be acquirer.

EXAMPLE29.2

Takeover Defenses Suppose on April 2, 2008, Torrance Oil, Inc., a large independent oil refinery, had 28 million shares outstanding, and the company’s stock price closed the day before at $49.25 per share on the New York Stock Exchange. Further suppose that on April 2, Torrance’s board of directors made two decisions: 1. The board approved management’s agreement with the Strauss family of Canada to buy, for $51 a share, the Strauss’ 2.6 million shares in Torrance. This was part of a greenmail agreement ending the Strauss family’s attempt to control Torrance.

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2. The board authorized the company to repurchase 7.5 million shares (27 percent of the outstanding shares) of its stock. The board simultaneously established an employee stock ownership plan to be funded with 4.9 million shares of Torrance stock. These two actions made Torrance invulnerable to unfriendly takeover attempts. In effect, the company was selling about 20 percent of its stock to the employee stock ownership plan. Earlier, Torrance had put in place a provision that said 80 percent of the stockholders have to approve a takeover. Torrance’s stock price fell by $.25 over the next two days. Because this move can probably be explained by random error, there is no evidence that Torrance’s actions reduced shareholder value.

Greenmail has been a colorful part of the financial lexicon since its first application in the late 1970s. Since then, pundits have commented numerous times on either its ethical or unethical nature. Greenmail has declined in recent years, perhaps for two reasons. First, Congress has imposed a tax on the profits from greenmail. Second, the law on greenmail is currently unsettled, causing recipients to worry about potential lawsuits. White Knight and White Squire A firm facing an unfriendly merger offer might arrange to be acquired by a friendly suitor, commonly referred to as a white knight. The white knight might be favored simply because it is willing to pay a higher purchase price. Alternatively, it might promise not to lay off employees, fire managers, or sell off divisions. Management instead may wish to avoid any acquisition at all. A third party, termed a white squire, might be invited to make a significant investment in the firm, under the condition that it vote with management and not purchase additional shares. White squires are generally offered shares at favorable prices. Billionaire investor Warren Buffett has acted as a white squire to many firms, including Champion International andGille tte. Recapitalizations and Repurchases Target management will often issue debt to pay out a dividend—a transaction called a leveraged recapitalization. A share repurchase, where debt is issued to buy back shares, is a similar transaction. The two transactions fend off takeovers in a number of ways. First, the stock price may rise, perhaps because of the increased tax shield from greater debt. A rise in stock price makes the acquisition less attractive to the bidder. However, the price will rise only if the firm’s debt level before the recapitalization was below the optimum, so a levered recapitalization is not recommended for every target. Consultants point out that firms with low debt but with stable cash flows are ideal candidates for “recaps.” Second, as part of the recapitalization, management may issue new securities that give management greater voting control than it had before the recap. The increase in control makes a hostile takeover more difficult. Third, firms with a lot of cash on their balance sheets are often seen as attractive targets. As part of the recap, the target may use this cash to pay a dividend or buy back stock, reducing the firm’s appeal as a takeover candidate. Exclusionary Self-Tenders An exclusionary self-tender is the opposite of a targeted repurchase. Here, the firm makes a tender offer for a given amount of its own stock while excluding targeted stockholders. In a particularly celebrated case, Unocal, a large integrated oil firm, made a tender offer for 29 percent of its shares while excluding its largest shareholder, Mesa Partners II (led by T. Boone Pickens). Unocal’s self-tender was for $72 per share, which was $16 over

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the prevailing market price. It was designed to defeat Mesa’s attempted takeover of Unocal by transferring wealth, in effect, from Mesa to Unocal’s other stockholders. Asset Restructurings In addition to altering capital structure, firms may sell off existing assets or buy new ones to avoid takeover. Targets generally sell, or divest, assets for two reasons. First, a target firm may have assembled a hodgepodge of assets in different lines of business, with the various segments fitting together poorly. Value might be increased by placing these divisions into separate firms. Academics often emphasize the concept of corporate focus. The idea here is that firms function best by focusing on those few businesses that they really know. A rise in stock price following a divestiture will reduce the target’s appeal to a bidder. The second reason is that a bidder might be interested in a specific division of the target. The target can reduce the bidder’s interest by selling off this division. Although the strategy may fend off a merger, it can hurt the target’s stockholders if the division is worth more to the target than to the division’s buyer. Authorities frequently talk of selling off the crown jewels or pursuing a scorched earth policy. While some targets divest existing assets, others buy new ones. Two reasons are generally given here. First, the bidder may like the target as is. The addition of an unrelated business makes the target less appealing to the acquirer. However, a bidder can always sell off the new business, so the purchase is likely not a strong defense. Second, antitrust legislation is designed to prohibit mergers that reduce competition. Antitrust law is enforced by both the Department of Justice (DOJ) and the Federal Trade Commission (FTC). A target may purchase a company, knowing that this new division will pose antitrust problems for the bidder. However, this strategy might not be effective because, in its filings with the DOJ and the FTC, the bidder can state its intention to sell off the unrelated business.

29.9 Do Mergers Add Value? In Section 29.2, we stated that synergy occurs if the value of the combined firm after the merger is greater than the sum of the value of the acquiring firm and the value of the acquired firm before the merger. Section 29.3 provided a number of sources of synergy in mergers, implying that mergers can create value. We now want to know whether mergers actually create value in practice. This is an empirical question and must be answered by empirical evidence. There are a number of ways to measure value creation, but many academics favor event studies. These studies estimate abnormal stock returns on, and around, the merger announcement date. An abnormal return is usually defined as the difference between an actual stock return and the return on a market index or control group of stocks. This control group is used to net out the effect of marketwide or industrywide influences. Consider Table 29.5, where returns around the announcement days of mergers are reported. The average abnormal percentage return across all mergers from 1980 to 2001 is 1.35%. This number combines the returns on both the acquiring company and the acquired company. Because 1.35% is positive, the market believes that mergers on average create value. The other three returns in the first column are positive as well, implying value creation in the different subperiods. Many other academic studies have provided similar results. Thus, it appears from this column that the synergies we mentioned in Section 29.3 show up in the real world. However, the next column tells us something different. Across all mergers from 1980 to 2001, the aggregate dollar change around the day of merger announcement is −$79 billion. This means that the market is, on average, reducing the combined stock

Chapter 29

Table 29.5

Mergers, Acquisitions, and Divestitures

899

Percentage and Dollar Returns for Mergers

Gain or Loss to Merger (Both Acquired and Acquiring Firms)

Gain or Loss to Acquiring Firms

Time Period

Abnormal Percentage Return

Aggregate Dollar Gain or Loss

Abnormal Percentage Return

Aggregate Dollar Gain or Loss

1980–2001 1980–1990 1991–2001 1998–2001

1.35% 2.41 1.04 .29

−$79 billion $12 billion −$90 billion –$134 billion

1.10% .64 1.20 .69

−$220 billion −$4 billion −$216 billion –$240 billion

SOURCE:: Modified from Sara Moeller, Frederik Schlingemann, and René Stulz, “Wealth Destruction on a Massive Scale? A Study of Acquiring-Firm Returns in the Recent Merger Wave,” Journal of Finance (April 2005), Table 1.

value of the acquiring and acquired companies around the merger announcement date. Though the difference between the two columns may seem confusing, there is an explanation. Although most mergers have created value, mergers involving the very largest firms have lost value. The abnormal percentage return is an unweighted average in which the returns on all mergers are treated equally. A positive return here reflects all those small mergers that created value. However, losses in a few large mergers cause the aggregate dollar change to be negative. But there is more. The rest of the second column indicates that the aggregate dollar losses occurred only in the 1998 to 2001 period. While there were losses of −$134 billion in this period, there were gains of $12 billion from 1980 to 1990. And interpolation of the table indicates that there were gains of $44 billion (=$134 − $90) from 1991 through 1997. Thus, it appears that some large mergers lost a great deal of value from 1998 to 2001. The results in a table such as Table 29.5 should have important implications for public policy because Congress is always wondering whether mergers are to be encouraged or discouraged. However, the results in that table are, unfortunately, ambiguous. On the one hand, you could focus on the first column, saying that mergers create value on average. Proponents of this view might argue that the great losses in the few large mergers were flukes, not likely to occur again. On the other hand, we cannot easily ignore the fact that over the entire period, mergers destroyed more value than they created. A proponent of this position might quote the old adage, “Except for World War I and World War II, the 20th century was quite peaceful.” Before we move on, some final thoughts are in order. Readers may be bothered that abnormal returns are taken only around the time of the acquisition, well before all of the acquisition’s impact is revealed. Academics look at long-term returns but they have a special fondness for short-term returns. If markets are efficient, the shortterm return provides an unbiased estimate of the total effect of the merger. Long-term returns, while capturing more information about a merger, also reflect the impact of many unrelated events.

Returns to Bidders The preceding results combined returns on both bidders and targets. Investors want to separate the bidders from the targets. Columns 3 and 4 of Table 29.5 provide returns for acquiring companies alone. The third column shows that abnormal percentage returns for bidders have been positive for the entire sample period and for each of the individual subperiods—a result similar to that for bidders and targets combined. The fourth column indicates aggregate dollar losses, suggesting that large mergers did

Part VIII

Figure 29.3

Special Topics

Billion dollars

Yearly Aggregate Dollar Gain or Loss for the Shareholders of Acquiring Firms

40 20 0 ⴚ20 ⴚ40 ⴚ60 ⴚ80 ⴚ100 ⴚ120

2001

2000

1999

1998

1997

1996

1995

1994

1993

1992

1991

1990

1989

1988

1987

1986

1985

1984

1983

1982

ⴚ160

1981

ⴚ140 1980

900

Years The graph shows the aggregate dollar gain or loss across all acquiring firms each year from 1980 to 2001. SOURCE: Taken from Figure 1, Sara Moeller, Frederik Schlingemann, and René Stulz, “Wealth Destruction on a Massive Scale? A Study of Acquiring-Firm Returns in the Recent Merger Wave,” Journal of Finance (April 2005).

worse than small ones. The time pattern for these aggregate dollar losses to bidders is presented in Figure 29.3. Again, the large losses occurred from 1998 to 2001, with the greatest loss in 2000. Let’s fast-forward a few decades and imagine that you are the CEO of a company. In that position you will certainly be faced with potential acquisitions. Does the evidence in Table 29.5 and Figure 29.3 encourage you to make acquisitions or not? Again, the evidence is ambiguous. On the one hand, you could focus on the averages in column 3 of the table, likely increasing your appetite for acquisitions. On the other hand, column 4 of the table, as well as the figure, might give you pause.

TargetCo mpanies Although the evidence just presented for both the combined entity and the bidder alone is ambiguous, the evidence for targets is crystal clear. Acquisitions benefit the target’s stockholders. Consider the following chart, which shows the median merger premium over different periods in the United States:19 Time Period Premium

19

1973–1998

1973–1979

1980–1989

1990–1998

42.1%

47.2%

37.7%

34.5%

Taken from Gregor Andrade, Mark Mitchell, and Erik Stafford, “New Evidence and Perspectives on Mergers,” Journal of Economic Perspectives (Spring 2001), Table 1.

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The premium is the difference between the acquisition price per share and the target’s pre-acquisition share price, divided by the target’s pre-acquisition share price. The average premium is quite high for the entire sample period and for the various subsamples. For example, a target stock selling at $100 per share before the acquisition that is later acquired for $142.1 per share generates a premium of 42.1 percent. Clearly, stockholders of any firm trading at $100 would love to be able to sell their holdings for $142.1 per share. Though other studies may provide different estimates of the average premium, all studies show positive premiums. Thus, we can conclude that mergers benefit the target stockholders. This conclusion leads to at least two implications. First, we should be somewhat skeptical of target managers who resist takeovers. These managers may claim that the target’s stock price does not reflect the true value of the company. Or they may say that resistance will induce the bidder to raise its offer. These arguments could be true in certain situations, but they may also provide cover for managers who are simply scared of losing their jobs after acquisition. Second, the premium creates a hurdle for the acquiring company. Even in a merger with true synergies, the acquiring stockholders will lose if the premium exceeds the dollar value of these synergies.

The Managers versus the Stockholders Managers of Bidding Firms The preceding discussion was presented from the stockholders’ point of view. Because, in theory, stockholders pay the salaries of managers, we might think that managers would look at things from the stockholders’ point of view. However, it is important to realize that individual stockholders have little clout with managers. For example, the typical stockholder is simply not in a position to pick up the phone and give the managers a piece of her mind. It is true that the stockholders elect the board of directors, which monitors the managers. However, an elected director has little contact with individual stockholders. Thus, it is fair to ask whether managers are held fully accountable for their actions. This question is at the heart of what economists call agency theory. Researchers in this area often argue that managers work less hard, get paid more, and make worse business decisions than they would if stockholders had more control over them. And there is a special place in agency theory for mergers. Managers frequently receive bonuses for acquiring other companies. In addition, their pay is often positively related to the size of their firm. Finally, managers’ prestige is also tied to firm size. Because firm size increases with acquisitions, managers are disposed to look favorably on acquisitions, perhaps even ones with a negative NPV. A fascinating study20 compared companies where managers received a lot of options on their own company’s stock as part of their compensation package with companies where the managers did not. Because option values rise and fall in tandem with the firm’s stock price, managers receiving options have an incentive to forgo mergers with negative NPVs. The paper reported that the acquisitions by firms where managers receive lots of options (termed equity-based compensation in the paper) create more value than the acquisitions by firms where managers receive few or no options. Agency theory may also explain why the biggest merger failures have involved large firms. Managers owning a small fraction of their firm’s stock have less incentive to behave responsibly because the great majority of any losses are borne by other stockholders. Managers of large firms likely have a smaller percentage interest in their 20

Sudip Datta, Mai Iskandar-Datta, and Kartik Raman, “Executive Compensation and Corporate Acquisition Decisions,” Journal of Finance (December 2001).

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firm’s stock than do managers of small firms (a large percentage of a large firm is too costly to acquire). Thus, the merger failures of large acquirers may be due to the small percentage ownership of the managers. An earlier chapter of this text discussed the free cash flow hypothesis. The idea here is that managers can spend only what they have. Managers of firms with low cash flow are likely to run out of cash before they run out of good (positive NPV) investments. Conversely, managers of firms with high cash flow are likely to have cash on hand even after all the good investments are taken. Managers are rewarded for growth, so managers with cash flow above that needed for good projects have an incentive to spend the remainder on bad (negative NPV) projects. A paper tested this conjecture, finding that “cash-rich firms are more likely than other firms to attempt acquisitions. . . . cash-rich bidders destroy seven cents in value for every dollar of cash reserves held. . . . consistent with the stock return evidence, mergers in which the bidder is cash-rich are followed by abnormal declines in operating performance.”21 The previous discussion has considered the possibility that some managers are knaves—more interested in their own welfare than in the welfare of their stockholders. However, a recent paper entertained the idea that other managers were more fools than knaves. Malmendier and Tate22 classified certain CEOs as overconfident, either because they refused to exercise stock options on their own company’s stock when it was rational to do so or because the press portrayed them as confident or optimistic. The authors find that these overconfident managers are more likely to make acquisitions than are other managers. In addition, the stock market reacts more negatively to announcements of acquisitions when the acquiring CEO is overconfident. Managers of Target Firms Our discussion has just focused on the managers of acquiring firms, finding that these managers sometimes make more acquisitions than they should. However, that is only half of the story. Stockholders of target firms may have just as hard a time controlling their managers. While there are many ways that managers of target firms can put themselves ahead of their stockholders, two seem to stand out. First, we said earlier that because premiums are positive, takeovers are beneficial to the target’s stockholders. However, if managers may be fired after their firms are acquired, they may resist these takeovers.23 Tactics employed to resist takeover, generally called defensive tactics, were discussed in an earlier section of this chapter. Second, managers who cannot avoid takeover may bargain with the bidder, getting a good deal for themselves at the expense of their shareholders. Consider Wulf’s fascinating work on mergers of equals (MOEs).24 Some deals are announced as MOEs, primarily because both firms have equal ownership in and equal representation on the board of directors of the merged entity. AOL and Time Warner, Daimler-Benz and Chrysler, Morgan Stanley and Dean Witter, and Fleet Financial Group and BankBoston are generally held out as examples of MOEs. Nevertheless, authorities point out that in any deal one firm is typically “more equal” than the other. That is, the target and the bidder can usually be distinguished in practice. For example, Daimler-Benz is commonly classified as the bidder and Chrysler as the target in their merger. 21

From Jarrad Harford, “Corporate Cash Reserves and Acquisitions,” Journal of Finance (December 1999), p. 1969.

22

Ulrike Malmendier and Geoffrey Tate, “Who Makes Acquisitions? CEO Overconfidence and the Market’s Reaction,” unpublished paper, Stanford University (December 2003). 23 24

However, as stated earlier, managers may resist takeovers to raise the offer price, not to prevent the merger.

Julie Wulf, “Do CEOs in Mergers Trade Power for Premium? Evidence From ‘Mergers of Equals,’ ” Journal of Law, Economics, and Organization (Spring2004).

Chapter 29

Mergers, Acquisitions, and Divestitures

903

Wulf finds that targets get a lower percentage of the merger gains, as measured by abnormal returns around the announcement date, in MOEs than in other mergers. And the percentage of the gains going to the target is negatively related to the representation of the target’s officers and directors on the postmerger board. These and other findings lead Wulf to conclude, “They [the findings of the paper] suggest that CEOs trade power for premium in merger of equals transactions.”

29.10 The Tax Forms of Acquisitions If one firm buys another, the transaction may be taxable or tax-free. In a taxable acquisition, the shareholders of the acquired firm are considered to have sold their shares, and their realized capital gains or losses will be taxed. In a taxable transaction, the appraised value of the assets of the selling firm may be revalued, as we explain next. In a tax-free acquisition, the selling shareholders are considered to have exchanged their old shares for new ones of equal value, and they have experienced no capital gains or losses. In a tax-free acquisition, the assets are not revalued.

EXAMPLE29.3

Taxes Suppose that 15 years ago Bill Evans started the Samurai Machinery (SM) Corp., which purchased plant and equipment costing $80,000. These have been the only assets of SM, and the company has no debts. Bill is the sole proprietor of SM and owns all the shares. For tax purposes the assets of SM have been depreciated using the straight-line method over 10 years and have no salvage value. The annual depreciation expense has been $8,000 (=$80,000 10). The machinery has no accounting value today (i.e., it has been written off the books). However, because of inflation, the fair market value of the machinery is $200,000. As a consequence, the S. A. Steel Company has bid $200,000 for all of the outstanding stock of Samurai.

Tax-Free Transaction If Bill Evans receives shares of S. A. Steel worth $200,000, the IRS will treat the sale as a tax-free transaction. Thus, Bill will not have to pay taxes on any gain received from the stock. In addition, S. A. Steel will be allowed the same depreciation deduction that Samurai Machinery was allowed. Because the asset has already been fully depreciated, S. A. Steel will receive no depreciation deduction. Taxable Transaction If S. A. Steel pays $200,000 in cash for Samurai Machinery, the transaction will be taxable with the following consequences: 1. In the year of the merger, Bill Evans must pay taxes on the difference between the merger price of $200,000 and his initial contribution to the firm of $80,000. Thus, his taxable income is $120,000 (=$200,000 −$80,000). 2. S. A. Steel may elect to write up the value of the machinery. In this case, S. A. Steel will be able to depreciate the machinery from an initial tax basis of $200,000. If S. A. Steel depreciates straight-line over 10 years, depreciation will be $20,000 (=$200,000 10) per year. If S. A. Steel elects to write up the machinery, S. A. Steel must treat the $200,000 write-up as taxable income immediately.25

25

Technically, Samurai Machinery pays this tax. However, because Samurai is now a subsidiary of S. A. Steel, S. A. Steel is the effective taxpayer.

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Table 29.6

Special Topics

The Tax Consequences of S. A. Steel Company’s Acquisition of Samurai Machinery

Type of Acquisition Buyer or Seller

Taxable Acquisition

Tax-Free Acquisition

Bill Evans (Seller)

Immediate tax on $120,000 ($200,000 − $80,000)

S. A. Steel (Buyer)

S. A. Steel may elect to write up assets: 1. Assets of Samurai are written up to $200,000 (with useful life of 10 years). Annual depreciation expense is $20,000. 2. Immediate tax on $200,000 write-up of assets. Alternatively, S. A. Steel may elect not to write up assets. Here there is neither additional depreciation nor immediate tax. Typically acquirers elect not to write up assets.

Capital gains tax not paid until Evans sells shares of S. A. Steel No additional depreciation

S. A. Steel acquires Samurai Machinery for $200,000, which is the market value of Samurai’s equipment. The book value of the equipment is $0. Bill Evans started Samurai Steel 15 years ago with a contribution of $80,000. The tax consequences of a tax-free acquisition are better than the tax consequences of a taxable acquisition because the seller pays no immediate tax on a tax-free acquisition.

3. Should S. A. Steel not elect the write-up, there is no increase in depreciation. Thus, depreciation remains zero in this example. In addition, because there is no write-up, S. A. Steel does not need to recognize any additional taxable income. Because the tax benefits from depreciation occur slowly over time and the taxable income is recognized immediately, the acquirer generally elects not to write up the value of the machinery in a taxable transaction. Because the write-up is not allowed for tax-free transactions and is generally not chosen for taxable ones, the only real tax difference between the two types of transactions concerns the taxation of the selling shareholders. These individuals can defer taxes under a tax-free situation but must pay taxes immediately under a taxable situation, so the tax-free transaction has better tax consequences. The tax implications for both types of transactions are displayed in Table 29.6.

29.11 Accounting for Acquisitions Earlier in this text we mentioned that firms keep two distinct sets of books: The stockholders’ books and the tax books. The previous section concerned the effects of acquisitions on the tax books. We now consider the stockholders’ books. When one firm acquires another, the buyer uses the purchase method to account for the acquisition. The purchase method requires that the assets of the acquired firm be reported at their fair market value on the books of the acquiring firm. This allows the acquiring firm to establish a new cost basis for the acquired assets. In a purchase, an accounting term called goodwill is created. Goodwill is the excess of the purchase price over the sum of the fair market values of the individual assets acquired.

Chapter 29

EXAMPLE 29.4

Mergers, Acquisitions, and Divestitures

905

Acquisitions and Accounting Suppose firm A acquires firm B, creating a new firm, AB. Firm A’s and firm B’s financial positions at the date of the acquisition are shown in Table 29.7. The book value of firm B on the date of the acquisition is $10 million. This is the sum of $8 million in buildings and $2 million in cash. However, an appraiser states that the sum of the fair market values of the individual buildings is $14 million. With $2 million in cash, the sum of the market values of the individual assets in firm B is $16 million. This represents the value to be received if the firm is liquidated by selling off the individual assets separately. However, the whole is often worth more than the sum of the parts in business. Firm A pays $19 million in cash for firm B. This difference of $3 million (=$19 million − $16 million) is goodwill. It represents the increase in value from keeping the firm as an ongoing business. Firm A issued $19 million in new debt to finance the acquisition. The total assets of firm AB increase to $39 million. The buildings of firm B appear in the new balance sheet at their current market value. That is, the market value of the assets of the acquired firm becomes part of the book value of the new firm. However, the assets of the acquiring firm (firm A) remain at their old book value. They are not revalued upward when the new firm is created. The excess of the purchase price over the sum of the fair market values of the individual assets acquired is $3 million. This amount is reported as goodwill. Financial analysts generally ignore goodwill because it has no cash flow consequences. Each year the firm must assess the value of its goodwill. If the value goes down (this is called impairment in accounting speak), the amount of goodwill on the balance sheet must be decreased accordingly. Otherwise no amortization is required.

Table 29.7

Accounting for Acquisitions: Purchase ($ in millions)

Firm A

Firm B

Firm AB

Cash $ 4 Equity $20 Land 16 Buildings 0

Cash $ 2 Equity $10 Land 0 Buildings 8

Cash $ 6 Debt $19 Land 16 Equity 20 Buildings 14 Goodwill 3

Total

Total

Total

$20

$20

$10

$10

$39

$39

When the purchase method is used, the assets of the acquired firm (firm B) appear in the combined firm’s books at their fair market value.

29.12 Going Private and Leveraged Buyouts Going-private transactions and leveraged buyouts have much in common with mergers, and it is worthwhile to discuss them in this chapter. A publicly traded firm goes private when a private group, usually composed of existing management, purchases its stock. As a consequence, the firm’s stock is taken off the market (if it is an exchangetraded stock, it is delisted) and is no longer traded. Thus, in going-private transactions, shareholders of publicly held firms are forced to accept cash for their shares. Going-private transactions are frequently leveraged buyouts (LBOs). In a leveraged buyout the cash offer price is financed with large amounts of debt. Part of the appeal of LBOs is that the arrangement calls for little equity capital. This equity capital is generally supplied by a small group of investors, some of whom are likely to be managers of the firm being purchased. The selling stockholders are invariably paid a premium above market price in an LBO, just as in a merger. As with a merger, the acquirer profits only if the synergy

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created is greater than the premium. Synergy is quite plausible in a merger of two firms, and we delineated a number of types of synergy earlier in the chapter. However, it is more difficult to explain synergy in an LBO because only one firm is involved. Two reasons are generally given for value creation in an LBO. First, the extra debt provides a tax deduction, which, as earlier chapters suggested, leads to an increase in firm value. Most LBOs center around firms with stable earnings and with low to moderate debt. The LBO may simply increase the firm’s debt to its optimum level. The second source of value comes from increased efficiency and is often explained in terms of “the carrot and the stick.” Managers become owners under an LBO, giving them an incentive to work hard. This incentive is commonly referred to as the carrot, and the carrots in some LBOs have been huge. For example, consider the LBO of Gibson Greeting Cards (GGC), previously a division of RCA, for which the management buyout group paid about $80 million. Because of the leveraged nature of the transaction, the group invested only about $1 million of its own capital. The division was taken private in 1982, but only for a brief period; GGC went public as its own company in 1984. The value of the initial public offering (IPO) was almost $300 million. One of the principals in the buyout group, William Simon, who was a former secretary of the U.S. Treasury, received $66 million from the IPO on an investment of somewhat under $350,000. Interest payments from the high level of debt constitute the stick. Large interest payments can easily turn a profitable firm before an LBO into an unprofitable one after the LBO. Management must make changes, either through revenue increases or cost reductions, to keep the firm in the black. Agency theory, a topic mentioned earlier in this chapter, suggests that managers can be wasteful with a large free cash flow. Interest payments reduce this cash flow, forcing managers to curb the waste. Though it is easy to measure the additional tax shields from an LBO, it is difficult to measure the gains from increased efficiency. Nevertheless, this increased efficiency is considered at least as important as the tax shield in explaining the LBO phenomenon. Academic research suggests that LBOs have, on average, created value. First, premiums are positive, as they are with mergers, implying that selling stockholders benefit. Second, studies indicate that LBOs that eventually go public generate high returns for the management group. Finally, other studies show that operating performance increases after the LBO. However, we cannot be completely confident of value creation because researchers have difficulty obtaining data about LBOs that do not go public. If these LBOs generally destroy value, the sample of firms going public would be a biased one. Regardless of the average performance of firms undertaking an LBO, we can be sure of one thing: Because of the great leverage involved, the risk is huge.

29.13 Divestitures This chapter has primarily been concerned with acquisitions, but it is also worthwhile to consider their opposite—divestitures. Divestitures come in a number of different varieties, the most important of which we discuss next.

Sale The most basic type of divestiture is the sale of a division, business unit, segment, or set of assets to another company. The buyer generally, but not always, pays in cash. A number of reasons are provided for sales. First, in an earlier section of this chapter we

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considered asset sales as a defense against hostile takeovers. It was pointed out in that section that sales often improve corporate focus, leading to greater overall value for the seller. This same rationale applies when the selling company is not in play. Second, asset sales provide needed cash to liquidity-poor firms. Third, it is often argued that the paucity of data about individual business segments makes large, diversified firms hard to value. Investors may discount the firm’s overall value because of this lack of transparency. Sell-offs streamline a firm, making it easier to value. However, this argument is inconsistent with market efficiency because it implies that large, diversified firms sell below their true value. Fourth, firms may simply want to sell unprofitable divisions. However, unprofitable divisions are likely to have low values to anyone. A division should be sold only if its value is greater to the buyer than to the seller. There has been a fair amount of research on sell-offs, with academics reaching two conclusions. First, event studies show that returns on the seller’s stock are positive around the time of the announcement of sale, suggesting that sell-offs create value to the seller. Second, acquisitions are often sold off down the road. For example, Kaplan and Weisbach26 found that over 40 percent of acquisitions were later divested, a result that does not reflect well on mergers. The average time between acquisition and divestiture was about seven years.

Spin-Off In a spin-off, a parent firm turns a division into a separate entity and distributes shares in this entity to the parent’s stockholders. Spin-offs differ from sales in at least two ways. First, the parent firm receives no cash from a spin-off: Shares are sent for free to the stockholders. Second, the initial stockholders of the spun-off division are the same as the parent’s stockholders. By contrast, the buyer in a sell-off is most likely another firm. However, because the shares of the division are publicly traded after the spin-off, the identities of the stockholders will change over time. At least four reasons are generally given for a spin-off. First, as with a sell-off, the spinoff may increase corporate focus. Second, because the spun-off division is now publicly traded, the Securities and Exchange Commission requires additional information to be disseminated—so investors may find it easier to value the parent and subsidiary after the spin-off. Third, corporations often compensate executives with shares of stock in addition to cash. The stock acts as an incentive: Good performance from managers leads to stock price increases. However, prior to the spin-off, executives can receive stock only in the parent company. If the division is small relative to the entire firm, price movement in the parent’s stock will be less related to the performance of the manager’s division than to the performance of the rest of the firm. Thus, divisional managers may see little relation between their effort and stock appreciation. However, after the spin-off, the manager can be given stock in the subsidiary. The manager’s effort should directly impact price movement in the subsidiary’s stock. Fourth, the tax consequences from a spin-off are generally better than from a sale because the parent receives no cash from a spin-off.

Carve-Out In a carve-out, the firm turns a division into a separate entity and then sells shares in the division to the public. Generally the parent retains a large interest in the division. This transaction is similar to a spin-off, and the first three benefits listed for a spin-off 26

Steven Kaplan and Michael Weisbach, “The Success of Acquisitions: Evidence from Divestitures,” Journal of Finance (March 1992).

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apply to a carve-out as well. However, the big difference is that the firm receives cash from a carve-out, but not from a spin-off. The receipt of cash can be both good and bad. On the one hand, many firms need cash. Michaely and Shaw27 find that large, profitable firms are more likely to use carve-outs, whereas small, unprofitable firms are more likely to use spin-offs. One interpretation is that firms generally prefer the cash that comes with a carve-out. However, small and unprofitable firms have trouble issuing stock. They must resort to a spin-off, where stock in the subsidiary is merely given to their own stockholders. Unfortunately, there is also a dark side to cash, as developed in the free cash flow hypothesis. That is, firms with cash exceeding that needed for profitable capital budgeting projects may spend it on unprofitable ones. Allen and McConnell28 find that the stock market reacts positively to announcements of carve-outs if the cash is used to reduce debt. The market reacts neutrally if the cash is used for investment projects.

TrackingSto cks A parent corporation issues tracking stock to “track” the performance of a specific division of the corporation. For example, if the tracking stock pays dividends, the size of the dividend depends on the division’s performance. However, although “trackers” trade separately from the parent’s stock, the division stays with the parent. By contrast, the subsidiary separates from the parent in a spin-off. The first tracking stock was tied to the performance of EDS, a subsidiary of General Motors. Later, large firms such as Walt Disney and Sony issued trackers. However, few companies have issued tracking stocks in recent years, and parents have pulled most of those issued in earlier times. Perhaps the biggest problem with tracking stocks is their lack of clearly defined property rights. An optimistic accountant can increase the earnings of a particular division, leading to a larger dividend. A pessimistic accountant will have the reverse effect. Although accountants affect the earnings of regular companies, a change in earnings will not directly impact dividends. 27 Roni Michaely and Wayne Shaw, “The Choice of Going Public: Spin-offs vs. Carve-outs,” Financial Management (Autumn 1995). 28 Jeffrey Allen and John McConnell, “Equity Carve-outs and Managerial Discretion,” Journal of Finance (February 1998).

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Summary and Conclusions

1. One firm can acquire another in several different ways. The three legal forms of acquisition are merger and consolidation, acquisition of stock, and acquisition of assets. Mergers and consolidations are the least costly from a legal standpoint, but they require a vote of approval by the shareholders. Acquisition of stock does not require a shareholder vote and is usually done via a tender offer. However, it is difficult to obtain 100 percent control with a tender offer. Acquisition of assets is comparatively costly because it requires more difficult transfer of asset ownership. 2. The synergy from an acquisition is defined as the value of the combined firm (VAB ) less the value of the two firms as separate entities (VA and VB ): Synergy = VAB – (VA + VB ) The shareholders of the acquiring firm will gain if the synergy from the merger is greater than the premium.

Chapter 29 Mergers, Acquisitions, and Divestitures

909

Concept Questions

1.

2.

3.

Merger Accounting Explain the difference between purchase and pooling of interests accounting for mergers. What is the effect on cash flows of the choice of accounting method? On EPS? Merger Concepts Indicate whether you think the following claims regarding takeovers are true or false. In each case, provide a brief explanation for your answer. a. By merging competitors, takeovers have created monopolies that will raise product prices, reduce production, and harm consumers. b. Managers act in their own interests at times and in reality may not be answerable to shareholders. Takeovers may reflect runaway management. c. In an efficient market, takeovers would not occur because market price would reflect the true value of corporations. Thus, bidding firms would not be justified in paying premiums above market prices for target firms. d. Traders and institutional investors, having extremely short time horizons, are influenced by their perceptions of what other market traders will be thinking of stock prospects and do not value takeovers based on fundamental factors. Thus, they will sell shares in target firms despite the true value of the firms. e. Mergers are a way of avoiding taxes because they allow the acquiring firm to write up the value of the assets of the acquired firm. f. Acquisitions analysis frequently focuses on the total value of the firms involved. An acquisition, however, will usually affect relative values of stocks and bonds, as wellas t heirt otalv alue. Merger Rationale Explain why diversification per se is probably not a good reason for a merger.

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3. The possible benefits of an acquisition come from the following: a. Revenuee nhancement. b. Costr eduction. c. Lowert axes. d. Reducedc apitalr equirements. 4. Stockholders may not benefit from a merger that is done only to achieve diversification or earnings growth. And the reduction in risk from a merger may actually help bondholders and hurt stockholders. 5. A merger is said to be friendly when the managers of the target support it. A merger is said to be hostile when the target managers do not support it. Some of the most colorful language of finance stems from defensive tactics in hostile takeover battles. Poison pills, golden parachutes, crown jewels, and greenmail are terms that describe various antitakeovert actics. 6. The empirical research on mergers and acquisitions is extensive. On average, the shareholders of acquired firms fare very well. The effect of mergers on acquiring stockholders is less clear. 7. Mergers and acquisitions involve complicated tax and accounting rules. Mergers and acquisitions can be taxable or tax-free transactions. In a taxable transaction each selling shareholder must pay taxes on the stock’s capital appreciation. Should the acquiring firm elect to write up the assets, additional tax implications arise. However, acquiring firms do not generally elect to write up the assets for tax purposes. The selling stockholders do not pay taxes at the time of a tax-free acquisition. The purchase method is used to account for mergers and acquisitions. 8. In a going-private transaction, a buyout group, usually including the firm’s management, buys all the shares of the other stockholders. The stock is no longer publicly traded. A leveraged buyout is a going-private transaction financed by extensive leverage.

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4.

5. 6.

7.

8.

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9.

10.

Questions and Problems

1.

2. BASIC (Questions 1–10)

Special Topics

Corporate Split In May 2005, high-end retailer Nieman Marcus announced plans to sell off its private label credit card business. Unlike other credit cards, private label credit cards can be used only in a particular merchant’s store. Why might a company split off a division? Is there a possibility of reverse synergy? Poison Pills Are poison pills good or bad for stockholders? How do you think acquiring firms are able to get around poison pills? Merger and Taxes Describe the advantages and disadvantages of a taxable merger as opposed to a tax-free exchange. What is the basic determinant of tax status in a merger? Would an LBO be taxable or nontaxable? Explain. Economies of Scale What does it mean to say that a proposed merger will take advantage of available economies of scale? Suppose Eastern Power Co. and Western Power Co. are located in different time zones. Both operate at 60 percent of capacity except for peak periods, when they operate at 100 percent of capacity. The peak periods begin at 9:00 a.m. and 5:00 p.m. local time and last about 45 minutes. Explain why a merger between Eastern and Western might make sense. Hostile Takeovers What types of actions might the management of a firm take to fight a hostile acquisition bid from an unwanted suitor? How do the target firm shareholders benefit from the defensive tactics of their management team? How are the target firm shareholders harmed by such actions? Explain. Merger Offers Suppose a company in which you own stock has attracted two takeover offers. Would it ever make sense for your company’s management to favor the lower offer? Does the form of payment affect your answer at all? Merger Profit Acquiring firm stockholders seem to benefit little from takeovers. Why is this finding a puzzle? What are some of the reasons offered for it?

Calculating Synergy Evan, Inc., has offered $620 million cash for all of the common stock in Tanner Corporation. Based on recent market information, Tanner is worth $585 million as an independent operation. If the merger makes economic sense for Evan, what is the minimum estimated value of the synergistic benefits from theme rger? Balance Sheets for Mergers Consider the following premerger information about firm X and firm Y:

Total earnings Shares outstanding Per-share values: Market Book

3.

Firm X

Firm Y

$50,000 26,000

$29,000 20,000

$ $

$ $

53 21

19 9

Assume that firm X acquires firm Y by paying cash for all the shares outstanding at a merger premium of $5 per share. Assuming that neither firm has any debt before or after the merger, construct the postmerger balance sheet for firm X assuming the use of (a) pooling of interests accounting methods and (b) purchase accounting methods. Balance Sheets for Mergers Assume that the following balance sheets are stated at book value. Construct a postmerger balance sheet assuming that Jurion Co. purchases James, Inc., and the pooling of interests method of accounting is used.

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Mergers, Acquisitions, and Divestitures

911

Jurion Co. Current assets Net fixed assets Total

$ 8,000 23,000 $31,000

Current liabilities Long-term debt Equity Total

$ 4,500 8,500 18,000 $31,000

James, Inc. Current assets Net fixed assets Total

4.

$9,700

Current liabilities Long-term debt Equity Total

$1,900 1,200 6,600 $9,700

Incorporating Goodwill In the previous problem, suppose the fair market value of James’s fixed assets is $12,000 versus the $7,100 book value shown. Jurion pays $17,000 for James and raises the needed funds through an issue of long-term debt. Construct the postmerger balance sheet now, assuming that the purchase method of accounting is used. Balance Sheets for Mergers Silver Enterprises has acquired All Gold Mining in a merger transaction. Construct the balance sheet for the new corporation if the merger is treated as a pooling of interests for accounting purposes. The following balance sheets represent the premerger book values for both firms: Silver Enterprises Current assets Other assets Net fixed assets Total

$ 4,300 900 7,900 $13,100

Current liabilities Long-term debt Equity Total

$ 2,600 1,800 8,700 $13,100

All Gold Mining Current assets Other assets Net fixed assets Total

6.

7.

$1,300 450 3,900 $5,650

Current liabilities Long-term debt Equity Total

$ 1,200 0 4,450 $ 5,650

Incorporating Goodwill In the previous problem, construct the balance sheet for the new corporation assuming that the transaction is treated as a purchase for accounting purposes. The market value of All Gold Mining’s fixed assets is $3,900; the market values for current and other assets are the same as the book values. Assume that Silver Enterprises issues $9,100 in new long-term debt to finance the acquisition. Cash versus Stock Payment Penn Corp. is analyzing the possible acquisition of Teller Company. Both firms have no debt. Penn believes the acquisition will increase its total aftertax annual cash flow by $1.6 million indefinitely. The current market value of Teller is $65 million, and that of Penn is $98 million. The appropriate discount rate for the incremental cash flows is 12 percent. Penn is trying to decide

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5.

$2,600 7,100

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Special Topics

whether it should offer 40 percent of its stock or $70 million in cash to Teller’s shareholders. a. What is the cost of each alternative? b. What is the NPV of each alternative? c. Whichalt ernatives houldP ennc hoose? EPS, PE, and Mergers The shareholders of Flannery Company have voted in favor of a buyout offer from Stultz Corporation. Information about each firm is given here:

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Price–earnings ratio Shares outstanding Earnings

9.

Stultz

5.25 90,000 $450,000

21 180,000 $675,000

Flannery’s shareholders will receive one share of Stultz stock for every three shares they hold in Flannery. a. What will the EPS of Stultz be after the merger? What will the PE ratio be if the NPV of the acquisition is zero? b. What must Stultz feel is the value of the synergy between these two firms? Explain how your answer can be reconciled with the decision to go ahead with the takeover. Merger Rationale Cholern Electric Company (CEC) is a public utility that provides electricity to the central Colorado area. Recent events at its Mile-High Nuclear Station have been discouraging. Several shareholders have expressed concern over last year’s financial statements. Income Statement Last Year ($ in millions) Revenue Fuel Other expenses Interest Net income

10.

Flannery

$110 50 30 30 $ 0

Balance Sheet End of Year ($ in millions) Assets Debt Equity

$400 300 100

Recently, a wealthy group of individuals has offered to purchase half of CEC’s assets at fair market price. Management recommends that this offer be accepted because “We believe our expertise in the energy industry can be better exploited by CEC if we sell our electricity generating and transmission assets and enter the telecommunications business. Although telecommunications is a riskier business than providing electricity as a public utility, it is also potentially very profitable.” Should the management approve this transaction? Why or why not? Cash versus Stock as Payment Consider the following premerger information about a bidding firm (firm B) and a target firm (firm T ). Assume that both firms have no debt outstanding.

Shares outstanding Price per share

Firm B

Firm T

2,900 $39

1,400 $26

Chapter 29

INTERMEDIATE (Questions 11–16)

11.

12.

Mergers, Acquisitions, and Divestitures

Firm B has estimated that the value of the synergistic benefits from acquiring firm T is $5,500. a. If firm T is willing to be acquired for $29 per share in cash, what is the NPV of them erger? b. What will the price per share of the merged firm be assuming the conditions in( a)? c. In part (a), what is the merger premium? d. Suppose firm T is agreeable to a merger by an exchange of stock. If B offers three of its shares for every five of T ’s shares, what will the price per share of the merged firm be? e. What is the NPV of the merger assuming the conditions in (d)? Cash versus Stock as Payment In Problem 10, are the shareholders of firm T better off with the cash offer or the stock offer? At what exchange ratio of B shares to T shares would the shareholders in T be indifferent between the two offers? Effects of a Stock Exchange Consider the following premerger information about firm A and firm B:

14.

15.

Firm A

Firm B

$1,600 600 $ 50

$700 250 $ 20

Assume that firm A acquires firm B via an exchange of stock at a price of $22 for each share of B’s stock. Both A and B have no debt outstanding. a. What will the earnings per share, EPS, of firm A be after the merger? b. What will firm A’s price per share be after the merger if the market incorrectly analyzes this reported earnings growth (that is, the price–earnings ratio does not change)? c. What will the price–earnings ratio of the postmerger firm be if the market correctly analyzes the transaction? d. If there are no synergy gains, what will the share price of A be after the merger? What will the price–earnings ratio be? What does your answer for the share price tell you about the amount A bid for B? Was it too high? Too low? Explain. Merger NPV Show that the NPV of a merger can be expressed as the value of the synergistic benefits, ∆V, less the merger premium. Merger NPV Fly-By-Night Couriers is analyzing the possible acquisition of Flashin-the-Pan Restaurants. Neither firm has debt. The forecasts of Fly-By-Night show that the purchase would increase its annual aftertax cash flow by $500,000 indefinitely. The current market value of Flash-in-the-Pan is $10 million. The current market value of Fly-By-Night is $26 million. The appropriate discount rate for the incremental cash flows is 8 percent. Fly-By-Night is trying to decide whether it will offer 30 percent of its stock or $13 million in cash to Flash-in-the-Pan. a. What is the synergy from the merger? b. What is the value of Flash-in-the-Pan to Fly-By-Night? c. What is the cost to Fly-By-Night of each alternative? d. What is the NPV to Fly-By-Night of each alternative? e. Whatalt ernatives houldF ly-By-Nightu se? Merger NPV Harrods PLC has a market value of £500 million and 30 million shares outstanding. Selfridge Department Store has a market value of £180 million and 20 million shares outstanding. Harrods is contemplating acquiring Selfridge.

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Total earnings Shares outstanding Price per share

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Special Topics

Harrods’s CFO concludes that the combined firm with synergy will be worth £720 million, and Selfridge can be acquired at a premium of £25 million. a. If Harrods offers 12 million shares of its stock in exchange for the 20 million shares of Selfridge, what will the stock price of Harrods be after the acquisition? b. What exchange ratio between the two stocks would make the value of the stock offer equivalent to a cash offer of £205 million? Mergers and Shareholder Value Bentley Corp. and Rolls Manufacturing are considering a merger. The possible states of the economy and each company’s value in that state are shown here: State

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Boom Recession

CHALLENGE (Questions 17–18)

17.

Probability

Bentley

Rolls

.70 .30

$280,000 $100,000

$250,000 $ 70,000

Bentley currently has a bond issue outstanding with a face value of $125,000. Rolls is an all-equity company. a. What is the value of each company before the merger? b. What are the values of each company’s debt and equity before the merger? c. If the companies continue to operate separately, what are the total value of the companies, the total value of the equity, and the total value of the debt? d. What would be the value of the merged company? What would be the value of the merged company’s debt and equity? e. Is there a transfer of wealth in this case? Why? f. Suppose that the face value of Bentley’s debt was $90,000. Would this affect the transfero f w ealth? Calculating NPV Plant, Inc., is considering making an offer to purchase Palmer Corp. Plant’s vice president of finance has collected the following information:

Price–earnings ratio Shares outstanding Earnings Dividends

Plant

Palmer

14.5 1,000,000 $2,800,000 700,000

10 500,000 $640,000 380,000

Plant also knows that securities analysts expect the earnings and dividends of Palmer to grow at a constant rate of 4 percent each year. Plant management believes that the acquisition of Palmer will provide the firm with some economies of scale that will increase this growth rate to 6 percent per year. a. What is the value of Palmer to Plant? b. What would Plant’s gain be from this acquisition? c. If Plant were to offer $13 in cash for each share of Palmer, what would the NPV of the acquisition be? d. What is the most Plant should be willing to pay in cash per share for the stock of Palmer? e. If Plant were to offer 150,000 of its shares in exchange for the outstanding stock of Palmer, what would the NPV be? f. Should the acquisition be attempted? If so, should it be as in (c) or as in (e)? g. Plant’s outside financial consultants think that the 6 percent growth rate is too optimistic and a 5 percent rate is more realistic. How does this change your previousan swers?

Chapter 29

18.

Mergers, Acquisitions, and Divestitures

915

State

Probability

Value

Rainy Warm Hot

.1 .4 .5

$200,000 350,000 800,000

Mini Case

The weather conditions in each town are independent of those in the other. Furthermore, each company has an outstanding debt claim of $350,000. Assume that no premiums are paid in the merger. a. What are the possible values of the combined company? b. What are the possible values of end-of-period debt and stock after the merger? c. Show that the bondholders are better off and the stockholders are worse off in the combined firm than they would have been if the firms had remained separate.

THE BIRDIE GOLF–HYBRID GOLF MERGER Birdie Golf, Inc., has been in merger talks with Hybrid Golf Company for the past six months. After several rounds of negotiations, the offer under discussion is a cash offer of $440 million for Hybrid Golf. Both companies have niche markets in the golf club industry, and the companies believe a merger will result in significant synergies due to economies of scale in manufacturing and marketing, as well as significant savings in general and administrative expenses. Bryce Bichon, the financial officer for Birdie, has been instrumental in the merger negotiations. Bryce has prepared the following pro forma financial statements for Hybrid Golf assuming the merger takes place. The financial statements include all synergistic benefits from the merger:

2010

2011

2012

2013

2014

Sales Production costs Depreciation Other expenses

$640,000,000 $720,000,000 $800,000,000 $900,000,000 449,000,000 504,000,000 560,000,000 632,000,000 60,000,000 64,000,000 66,000,000 66,400,000 64,000,000 72,000,000 80,000,000 90,400,000

$1,000,000,000 705,000,000 67,000,000 97,000,000

EBIT Interest

$ 67,000,000 $ 80,000,000 $ 94,000,000 $111,200,000 15,200,000 17,600,000 19,200,000 20,000,000

$ 131,000,000 21,600,000

Taxable income Taxes (40%)

$ 51,800,000 $ 62,400,000 $ 74,800,000 $ 91,200,000 20,720,000 24,960,000 29,920,000 36,480,000

$ 109,400,000 43,760,000

Net income

$ 31,080,000 $ 37,440,000 $ 44,880,000 $ 54,720,000

$

65,640,000

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Mergers and Shareholder Value The Chocolate Ice Cream Company and the Vanilla Ice Cream Company have agreed to merge and form Fudge Swirl Consolidated. Both companies are exactly alike except that they are located in different towns. The endof-period value of each firm is determined by the weather, as shown below. There will be no synergy to the merger.

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Bryce is also aware that the Hybrid Golf division will require investments each year for continuing operations, along with sources of financing. The following table outlines the required investments and sources of financing: 2010

2011

2012

2013

2014

Investments: Net working capital Fixed assets Total

$16,000,000 $20,000,000 $20,000,000 $ 24,000,000 12,000,000 20,000,000 14,400,000 96,000,000 $28,000,000 $40,000,000 $34,400,000 $120,000,000

$24,000,000 5,600,000 $29,600,000

Sources of financing: New debt Profit retention Total

$28,000,000 $12,800,000 $12,800,000 $ 12,000,000 0 27,200,000 21,600,000 21,600,000 $28,000,000 $40,000,000 $34,400,000 $ 33,600,000

$ 9,600,000 20,000,000 $29,600,000

The management of Birdie Golf feels that the capital structure at Hybrid Golf is not optimal. If the merger takes place, Hybrid Golf will immediately increase its leverage with an $88 million debt issue, which would be followed by a $120 million dividend payment to Birdie Golf. This will increase Hybrid’s debt-to-equity ratio from .50 to 1.00. Birdie Golf will also be able to use a $20 million tax loss carryforward in 2011 and 2012 from Hybrid Golf’s previous operations. The total value of Hybrid Golf is expected to be $720 million in five years, and the company will have $240 million in debt at that time. Stock in Birdie Golf currently sells for $94 per share, and the company has 14.4 million shares of stock outstanding. Hybrid Golf has 6.4 million shares of stock outstanding. Both companies can borrow at an 8 percent interest rate. The risk-free rate is 6 percent, and the expected return on the market is 13 percent. Bryce believes the current cost of capital for Birdie Golf is 11 percent. The beta for Hybrid Golf stock at its current capital structure is 1.30. Bryce has asked you to analyze the financial aspects of the potential merger. Specifically, he has asked you to answer the following questions: 1. Suppose Hybrid shareholders will agree to a merger price of $68.75 per share. Should Birdie proceed with the merger? 2. What is the highest price per share that Birdie should be willing to pay for Hybrid? 3. Suppose Birdie is unwilling to pay cash for the merger but will consider a stock exchange. What exchange ratio would make the merger terms equivalent to the original merger price of $68.75 per share? 4. What is the highest exchange ratio Birdie would be willing to pay and still undertake theme rger?

CHAPTER 30

FinancialDi stress In late 2008, financial problems at General Motors (GM) and Ford were much in the news. Both automakers were saddled with large debt loads and legacy costs such as retiree health care benefits. The overall economy also presented problems for both companies. In September, Ford announced that its sales from the previous year had dropped about 34 percent. Because of aggressive pricing such as “employee discount” promotions, GM’s sales dropped only about 16 percent. Both companies fought against filing for bankruptcy, even going to the U.S. Congress to request a bailout. In testimony before Congress, Rick Wagoner, the CEO of GM, stated that independent research showed that 80 percent of customers would not consider buying a car from GM if the company was in bankruptcy. GM and Ford are examples of companies experiencing significant financial distress, the subject of this chapter. A firm with insufficient cash flow to make contractually required financial obligations, such as interest payments, is in financial distress. A firm that defaults on a required payment may be forced to liquidate its assets, but, more often, a defaulting firm will reorganize its financial structure. Financial restructuring involves replacing old financial claims with new ones and takes place with private workouts or legal bankruptcy. Private workouts are voluntary arrangements to restructure a company’s debt, such as postponing a payment or reducing the size of the payment. If a private workout is not possible, formal bankruptcy is usually required.

30.1 What Is Financial Distress? Financial distress is surprisingly hard to define precisely. This is true partly because of the variety of events befalling firms under financial distress. The list of events is almost endless, but here are some examples: Dividend reductions Plantc losings Losses Layoffs CEOr esignations Plummetingsto ckp rices Financial distress is a situation where a firm’s operating cash flows are not sufficient to satisfy current obligations (such as trade credits or interest expenses) and the firm is forced to take corrective action.1 Financial distress may lead a firm to default on a contract, and it may involve financial restructuring between the firm, its creditors, 1

This definition is close to the one used by Karen Wruck, “Financial Distress: Reorganization and Organizational Efficiency,” Journal of Financial Economics 27 (1990), p. 425. 917

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Table30.1 The Largest U.S. Bankruptcies

Firm 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Lehman Brothers Holdings, Inc. General Motors Corp. Conseco, Inc. Chrysler, LLC WorldCom, Inc. Refco, Inc. Enron Corp. Delta Air Lines, Inc. General Growth Properties, Inc. Pacific Gas & Electric Co. Thornburg Mortgage, Inc. Charter Communications, Inc. Calpine Corp. New Century Financial Corp. UAL Corp. Texaco, Inc. (incl. subsidiaries) Delphi Corp. Conseco Finance Corp. Olympia & York Realty Corp. Lyondell Chemical Co.

Liabilities ($ in millions)

Bankruptcy Date

$613,000.00 172,810.00 56,639.30 55,200.00 45,984.00 33,300.00 31,237.00 28,546.00 27,293.00 25,717.00 24,700.00 24,185.67 23,358.00 23,000.00 22,164.00 21,603.00 20,903.00 20,278.50 19,800.00 19,337.00

15-Sep-08 1-Jun-09 2-Dec-02 30-Apr-09 21-Jul-02 5-Oct-05 2-Dec-01 5-Dec-05 22-Apr-09 6-Apr-01 1-May-09 27-Mar-09 5-Dec-05 2-Apr-07 2-Dec-02 1-Apr-87 5-Oct-05 2-Dec-02 15-May-92 6-Jan-09

SOURCE: Supplied by Edward I. Altman, NYU Salomon Center, Stern School of Business.

and its equity investors. Usually the firm is forced to take actions that it would not havetak enif it hads ufficientc ashf low. Our definition of financial distress can be expanded somewhat by linking it to insolvency. Insolvency is defined in Black’s Law Dictionaryas: 2 Inability to pay one’s debts; lack of means of paying one’s debts. Such a condition of a woman’s (or man’s) assets and liabilities that the former made immediately available would be insufficient to discharge the latter.

This definition has two general themes: stocks and flows.3 These two ways of thinking about insolvency are depicted in Figure 30.1. Stock-based insolvency occurs when a firm has negative net worth, so the value of assets is less than the value of its debts. Flow-based insolvency occurs when operating cash flow is insufficient to meet current obligations. Flow-based insolvency refers to the inability to pay one’s debts. Insolvency may lead to bankruptcy. Some of the largest U.S. bankruptcies are in Table 30.1.

30.2 WhatHap pensi nF inancialD istress? In June 2008, General Motors (GM) reported second quarter net income of negative $15 million. It also lost money in 2005 and 2007 and steadily lost its market share to rivals such as Toyota, BMW, and Honda. Its accounting shareholder equity turned 2 3

Taken from Black’s Law Dictionary, 5th ed. (St. Paul, MN: West Publishing Company), p. 716.

Edward Altman was one of the first to distinguish between stock-based insolvency and flow-based insolvency. See Edward Altman, Corporate Financial Distress: A Complete Guide to Predicting, Avoiding, and Dealing with Bankruptcy, 2nd ed. (New York: John Wiley & Sons, 1993).

Chapter 30

Figure 30.1

Financial Distress

919

A. Stock-based insolvency

Insolvency

Solvent firm A s s e t s

Insolvent firm A s s e t s

Debt Equity

D e b t

Negative equity

B. Flow-based insolvency $ Cash flow shortfall

Contractual obligations

Firm cash flow

Insolvency

Stock-based insolvency occurs when the value of the assets of a firm is less than the value of the debts. This implies negative equity. Flow-based insolvency occurs when firm cash flows are insufficient to cover contractually required payments.

negative in 2006 and its stock price decreased from $50 in late 2003 to about $1 in 2009. Automobile customers had good reason to worry about buying cars from GM. GM struggled to increase sales, cut costs, attempted to sell assets (e.g., the Hummer line), drew down bank debt, and arranged for more long-term financing. GM was clearly a firm experiencing financial distress. GM filed for bankruptcy on June 1, 2009. Firms deal with financial distress in several ways, such as these: 1. 2. 3. 4. 5. 6. 7.

Sellingmajo rasse ts. Mergingw ithan otherf irm. Reducing capital spending and research and development. Issuingn ewse curities. Negotiating with banks and other creditors. Exchangingd ebtf ore quity. Filingf orb ankruptcy.

Items (1), (2), and (3) concern the firm’s assets. Items (4), (5), (6), and (7) involve the right side of the firm’s balance sheet and are examples of financial restructuring. Financial distress may involve both asset restructuring and financial restructuring (i.e., changes on both sides of the balance sheet).

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Figure30 .2 What Happens in FinancialD istress

No financial restructuring %

49

Private workout

Financial distress 51 %

%

47

Financial restructuring

83%

Reorganize and emerge

7%

Merge with another firm

53

%

Legal bankruptcy Chapter 11

10%

Liquidation

SOURCE: Karen H. Wruck, “Financial Distress: Reorganization and Organizational Efficiency,” Journal of Financial Economics 27 (1990), Figure 2. See also Stuart C. Gilson, Kose John, and Larry H. P. Lang, “Troubled Debt Restructurings: An Empirical Study of Private Reorganization of Firms in Default,” Journal of Financial Economics 27 (1990); and Lawrence A. Weiss, “Bankruptcy Resolution: Direct Costs and Violation of Priority of Claims,” Journal of Financial Economics 27 (1990).

Some firms may actually benefit from financial distress by restructuring their assets. For example, a levered recapitalization can change a firm’s behavior and force a firm to dispose of unrelated businesses. A firm going through a levered recapitalization will add a great deal of debt and, as a consequence, its cash flow may not be sufficient to cover required payments, and it may be forced to sell its noncore businesses. For some firms, financial distress may bring about new organizational forms and new operating strategies. However, in this chapter we focus on financial restructuring. Financial restructuring may occur in a private workout or a bankruptcy reorganization under Chapter 11 of the U.S. bankruptcy code. Figure 30.2 shows how large public firms move through financial distress. Approximately half of the financial restructurings have been done via private workouts. Most large public firms (approximately 83 percent) that file for Chapter 11 bankruptcy are able to reorganize and continue to do business.4 Financial distress can serve as a firm’s “early warning” system for trouble. Firms with more debt will experience financial distress earlier than firms with less debt. However, firms that experience financial distress earlier will have more time for private workouts and reorganization. Firms with low leverage will experience financial distress later and, in many instances, be forced to liquidate.

4

However, less than 20 percent of all firms (public or private) going through a Chapter 11 bankruptcy are successfully reorganized.

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30.3 Bankruptcy Liquidation and Reorganization Firms that cannot or choose not to make contractually required payments to creditors have two basic options: Liquidation or reorganization. This section discusses bankruptcyliq uidationa ndr eorganization.5 Liquidation means termination of the firm as a going concern; it involves selling the assets of the firm for salvage value. The proceeds, net of transactions costs, are distributed to creditors in order of established priority. Reorganization is the option of keeping the firm a going concern; it sometimes involves issuing new securities to replace old securities. Liquidation and formal reorganization may be done by bankruptcy. Bankruptcy is a legal proceeding and can be done voluntarily with the corporation filing the petition or involuntarily with the creditors filing the petition.

BankruptcyL iquidation Chapter 7 of the Bankruptcy Reform Act of 1978 deals with “straight” liquidation. The following sequence of events is typical: 1. A petition is filed in a federal court. A corporation may file a voluntary petition, or involuntary petitions may be filed against the corporation. 2. A bankruptcy trustee is elected by the creditors to take over the assets of the debtor corporation. The trustee will attempt to liquidate the assets. 3. When the assets are liquidated, after payment of the costs of administration, proceeds are distributed among the creditors. 4. If any assets remain after expenses and payments to creditors, they are distributed toth esh areholders. Conditions Leading to Involuntary Bankruptcy An involuntary bankruptcy petition may be filed by creditors if both the following conditions are met: 1. The corporation is not paying debts as they become due. 2. If there are more than 12 creditors, at least three with claims totaling $13,475 or more must join in the filing. If there are fewer than 12 creditors, then only one with a claim of $13,475 is required to file. Priority of Claims Once a corporation is determined to be bankrupt, liquidation takes place. The distribution of the proceeds of the liquidation occurs according to the following priority: 1. Administration expenses associated with liquidating the bankrupt company’s assets. 2. Unsecured claims arising after the filing of an involuntary bankruptcy petition. 5

One of the most important choices a bankrupt firm must make is whether to liquidate or reorganize. Arturo Bris, Ivo Welch, and Ning Zhu have looked closely at this choice in “The Costs of Bankruptcy: Chapter 7 Liquidation versus Chapter 11 Reorganization,” Journal of Finance (June 2006). They find: • Very small firms (i.e., with assets less than $100,000), are more likely to liquidate than reorganize compared to large firms. • Firms with a large number of secured creditors are more likely to try to reorganize. • Firms with an unsecured creditor, especially a bank, are more likely to choose liquidation. • Firms that have large negative equity are more likely to try to reorganize.

In Their Own Words EDWARD I. ALTMAN* ON CORPORATE FINANCIAL DISTRESS AND BANKRUPTCY As we entered the new millennium, corporate distress and bankruptcy were no longer a niche area of corporate evolution. Indeed, the bankruptcy rate of U.S. corporations reached record proportions in 2001∕2002, with as many as 77 large corporations filing for protection under Chapter 11 of the bankruptcy code with liabilities greater than $1 billion—an unprecedented number. While telecommunication firms “lead” the way, airlines, steel companies, retailers, and, in general, a broad cross-section of industrial sectors have succumbed to a combination of excessive debt and poor operating results. The average American company is far riskier today than it was just two decades ago, and the roles of the bankruptcy courts and restructuring specialists have never been more important. Financial distress of private and public entities throughout the world is a frequent occurrence with important implications for their many stakeholders. While the role of corporate bankruptcy laws is clear— either to provide a legal procedure that permits firms which have temporary liquidity problems to restructure and successfully emerge as continuing entities or to provide an orderly process to liquidate assets for the benefit of creditors before asset values are dissipated—bankruptcy laws differ markedly from country to country. It is generally agreed upon that the U.S. Chapter 11 provisions under the Bankruptcy Reform Act of 1978 provide the most protection for bankrupt firms’ assets and result in a greater likelihood of successful reorganization than is found in other countries where liquidation and sale of the assets for the benefit of creditors is more likely the result. But the U.S. code’s process is usually lengthy (averaging close to two years, except where a sufficient number of creditors agree in advance via a prepackaged Chapter 11)

3. 4. 5. 6. 7. 8. 9. 922

and expensive, and the reorganized entity is not always successful in avoiding subsequent distress. If the reorganization is not successful, then liquidation under Chapter 7 will usually ensue. Bankruptcy processes in the industrialized world outside the United States strongly favor senior creditors who obtain control of the firm and seek to enforce greater adherence to debt contracts. The U.K. process, for example, is speedy and less costly, but the reduced costs can result in undesirable liquidations, unemployment, and underinvestment. The new bankruptcy code in Germany attempts to reduce the considerable power of secured creditors but it is still closer to the U.K. system. In the United States, creditors and owners can negotiate “violations” to the “absolute priority rule”—this “rule” holds that more senior creditors must be paid in full, prior to any payments to more junior creditors or to owners. (However, the so-called “violations” to absolute priority have empirically been shown to be relatively small—such as under 10 percent of firm value.) Finally, the U.S. system gives the court the right to sanction postpetition debt financing, usually with superpriority status over existing claims, thereby facilitating the continuing operation of the firm. Recently, France had a similar successful experience. A measure of performance of the U.S. bankruptcy system is the proportion of firms that emerge successfully. The results in the United States of late are somewhat mixed, with close to 83 percent of large firms emerging but probably less than 20 percent of smaller entities. And a not insignificant number of firms suffer subsequent distress and may file again (Chapter 22). Regardless of the location, one of the objectives of bankruptcy and other distressed workout arrangements is that creditors and other suppliers of capital clearly know their rights and expected recoveries in the event of a distressed situation. When these are

Wages,salarie s,an dc ommissions. Contributions to employee benefit plans arising within 180 days before the filing date. Consumerc laims. Taxc laims. Secured and unsecured creditors’ claims. Preferredsto ckholders’c laims. Commonsto ckholders’c laims.

not transparent and ∕or are based on outdated processes with arbitrary and possibly corrupt outcomes, then the entire economic system suffers and growth is inhibited. Such is the case in several emerging market countries. Revision of these outdated systems should be a priority. In addition to the comparative benefits of different national restructuring systems, a number of intriguing theoretical and empirical issues are related to the distressed firm. Among these are corporate debt capacity, manager–creditor–owner incentives, ability to predict distress, data and computations for default rate estimation, investment in securities of distressed firms, and postreorganization performance assessment. Corporate distress has a major impact on creditor– debtor relationships and, combined with business risk and tax considerations, affects the capital structure of companies. One key question is how costly are the expected distress costs compared to the expected tax benefits of using leverage—the so-called trade-off theory. Most analysts agree that the sum of direct (e.g., legal fees) and indirect costs is in the range of 10–20 percent of firm value. Whether the taking of excess risk and overinvestment are examples of agency conflicts between managers and creditors rests upon one’s view as to who are the true residual owners of a distressed firm—the existing equityholders or creditors who will more than likely be the new owners of a reorganized entity. Existing management has the exclusive right to file the first plan of reorganization within 120 days of filing, with exclusivity extensions possible. Their incentives and influence can be biased, however, and not always in accord with other stakeholders, primarily creditors. Limiting this exclusivity would appear to be desirable to speed up the process and restrict managerial abuse. Distress prediction models have intrigued researchers and practitioners for more than 50 years. Models have evolved from univariate financial statement ratios

to multivariate statistical classification models, to contingent claim and market value–based approaches, and finally to using artificial intelligence techniques. Most large financial institutions have one or more of these types of models in place as more sophisticated credit risk management frameworks are being introduced, sometimes combined with aggressive credit asset portfolio strategies. Increasingly, private credit assets are being treated as securities with estimates of default and recovery given default the critical inputs to their valuation. Perhaps the most intriguing by-product of corporate distress is the development of a relatively new class of investors known as vultures. These money managers specialize in securities of distressed and defaulted companies. Defaulted bonds have had a small following ever since the Great Depression of the 1930s, but this has grown to more than 70 institutional “vulture” specialists, actively managing over $60 billion in 2003. The size of the distressed and defaulted market grew dramatically in recent years, and by year-end 2002, estimates by this author were over $940 billion (face value) and $510 billion (market value) for the public and private markets combined (mainly public defaulted and distressed bonds and private bank loans). Distressed debt investors have target annual rates of return of 15 to 25 percent. Although these annual returns are sometimes earned, the overall annual rate of return from 1987 through 2002 has been less than 10 percent—similar to high-yield bonds and considerably below returns in the stock market. Yet, the incredible supply of potential investment opportunities has created unprecedented interest in this alternative asset class. *

Edward I. Altman is Max L. Heine Professor of Finance, NYU Stern School of Business. He is widely recognized as one of the world’s experts on bankruptcy and credit analysis, as well as the distressed debt and high-yield bond markets.

The priority rule in liquidation is the absolute priority rule(AP R). One qualification to this list concerns secured creditors. Liens on property are outside APR ordering. However, if the secured property is liquidated and provides cash insufficient to cover the amount owed them, the secured creditors join with unsecured creditors in dividing the remaining liquidating value. In contrast, if the secured property is liquidated for proceeds greater than the secured claim, the net proceeds are used to pay unsecured creditors and others. 923

924

EXAMPLE30.1

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APR The B. O. Drug Company is to be liquidated. Its liquidating value is $2.7 million. Bonds worth $1.5 million are secured by a mortgage on the B.O. Drug Company corporate headquarters building, which is sold for $1 million; $200,000 is used to cover administrative costs and other claims (including unpaid wages, pension benefits, consumer claims, and taxes). After paying $200,000 to the administrative priority claims, the amount available to pay secured and unsecured creditors is $2.5 million. This is less than the amount of unpaid debt of $4 million. Under APR, all creditors must be paid before shareholders, and the mortgage bondholders have first claim on the $1 million obtained from the sale of the headquarters building. The trustee has proposed the following distribution:

Type of Claim

Prior Claim

Bonds (secured by mortgage) Subordinated debentures Common stockholders Total

$ 1,500,000 2,500,000 10,000,000 $14,000,000

Cash Received under Liquidation $1,500,000 1,000,000 0 $2,500,000

Calculation of the Distribution Cash received from sale of assets available for distribution Cash paid to secured bondholders on sale of mortgaged property Available to bond and debenture holders Total claims remaining ($4,000,000 less payment of $1,000,000 on secured bonds) Distribution of remaining $1,500,000 to cover total remaining claims of $3,000,000 Type of Claim Remaining Bonds Debentures Total

Claim on Liquidation Proceeds $ 500,000 2,500,000 $3,000,000

$2,500,000 1,000,000 $1,500,000 $3,000,000

Cash Received $ 500,000 1,000,000 $1,500,000

BankruptcyR eorganization Corporate reorganization takes place under Chapter 11 of the Federal Bankruptcy Reform Act of 1978, as amended by the Bankruptcy Abuse Prevention and Consumer Protection Act of 2005.6 The general objective of a proceeding under Chapter 11 is

6

Do bankruptcy codes matter? The answer is yes for Sergei A. Davydenko and Julian R. Franks in “Do Bankruptcy Codes Matter? A Study of Defaults in France, Germany, and the U.K.,” Journal of Finance (April 2008). They find that the different bankruptcy codes of France, Germany, and the U.K. produce different outcomes of financial distress situations even though banks make significant adjustments in response to creditors’ friendly or unfriendly codes, respectively.

Chapter 30

Financial Distress

925

to plan to restructure the corporation with some provision for repayment of creditors. A typical sequence of events follows: 1. A voluntary petition can be filed by the corporation, or an involuntary petition can be filed by three or more creditors (or one creditor if the total creditors are fewer than 12—see the previous section). The involuntary petition must allege that the corporation is not paying its debts. 2. Usually, a federal judge approves the petition, and a time for filing proofs of claims of creditors and of shareholders is set. 3. In most cases, the corporation (the “debtor in possession”) continues to run the business.7 4. For 120 days only the corporation can file a reorganization plan. If it does, the corporation is given 180 days from the filing date to gain acceptance of the plan. 5. Creditors and shareholders are divided into classes. A class of creditors accepts the plan if two-thirds of the class (in dollar amount) and one-half of the class (in number)h avein dicateda pproval.8 6. After acceptance by creditors, the plan is confirmed by the court. 7. Payments in cash, property, and securities are made to creditors and shareholders. The plan may provide for the issuance of new securities.

EXAMPLE 30.2

Chapter 11 Suppose B.O. Drug Co. decides to reorganize under Chapter 11. Generally senior claims are honored in full before various other claims receive anything. Assume that the “going concern” value of B.O. Drug Co. is $3 million and that its balance sheet is as shown: Assets Liabilities Mortgage bonds Subordinated debentures Stockholders’ equity

$3,000,000 1,500,000 2,500,000 −1,000,000

The firm has proposed the following reorganization plan:

Old Security

Old Claim

New Claim with Reorganization Plan

Mortgage bonds Subordinated debentures

$1,500,000 2,500,000

$1,500,000 1,500,000 (continued )

7

In Chapter 11 bankruptcies, the firm (now called “debtor in possession”) continues to operate. In many cases, the firm will seek to borrow new money and use the proceeds to pay off secured creditors and to continue to operate until a reorganization plan is approved. 8 We are describing the standard events in a bankruptcy reorganization. Petitions are almost always accepted, and the general rule is that a reorganization plan will be accepted by the court if all of the creditor classes accept it and it will be rejected if all of the creditor classes reject it. However, if one or more (but not all) of the classes accept it, the plan may be eligible for a “cram down” procedure. A cram down takes place if the bankruptcy court finds a plan fair and equitable and accepts the plan for all creditors.

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The firm has also proposed a distribution of new securities under a new claim with this reorganization plan:

Old Security

Received under Proposed Reorganization Plan

Mortgage bonds

$1,000,000 in 9% senior debentures $500,000 in 11% subordinated debentures

Debentures

$1,000,000 in 8% preferred stock $500,000 in common stock

However, it will be difficult for the firm to convince secured creditors (mortgage bonds) to accept unsecured debentures of equal face value. In addition, the corporation may wish to allow the old stockholders to retain some participation in the firm. Needless to say, this would be a violation of the absolute priority rule, and the holders of the debentures would not be happy.

30.4 Private Workout or Bankruptcy: Which Is Best? A firm that defaults on its debt payments will need to restructure its financial claims. The firm will have two choices: Formal bankruptcy or private workout. The previous section described two types of formal bankruptcies: Bankruptcy liquidation and bankruptcy reorganization. This section compares private workouts with bankruptcy reorganizations. Both types of financial restructuring involve exchanging new financial claims for old financial claims. Usually, senior debt is replaced with junior debt

Absolute Priority Rule (APR) The absolute priority rule states that senior claims are fully satisfied before junior claims receive anything. Deviationf romR ule Equityholders Unsecured creditors Secured creditors

Expectation: No payout Reality: Payout in 81 percent of cases Expectation: Full payout after secured creditors Reality: Violation in 78 percent of cases Expectation: Full payout Reality: Full payout in 92 percent of cases

Reasonsf orV iolations Creditors want to avoid the expense of litigation. Debtors are given a 120-day opportunity to cause delay and harm value. Managers often own equity and demand to be compensated. Bankruptcy judges like consensual plans and pressure parties to compromise. SOURCE: Lawrence A. Weiss, “Bankruptcy Resolution: Direct Costs and Violation of Priority of Claims,” Journal of FinancialEconom ics 27 (1990).

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and junior debt is replaced with equity. Much recent academic research has described what happens in private workouts and formal bankruptcies.9 • Historically, half of financial restructurings have been private, but recently, formal bankruptcies have dominated. • Firms that emerge from private workouts experience stock price increases that are much greater than those for firms emerging from formal bankruptcies. • The direct costs of private workouts are much less than the costs of formal bankruptcies. • Top management usually loses pay and sometimes jobs in both private workouts andf ormalb ankruptcies. These facts, when taken together, seem to suggest that a private workout is much better than a formal bankruptcy. We then ask: Why do firms ever use formal bankruptcies to restructure?

TheMa rginalF irm For the average firm, a formal bankruptcy is more costly than a private workout, but for other firms formal bankruptcy is better. Formal bankruptcy allows firms to issue debt that is senior to all previously incurred debt. This new debt is “debtor in possession” (DIP) debt. For firms that need a temporary injection of cash, DIP debt makes bankruptcy reorganization an attractive alternative to a private workout. There are some tax advantages to bankruptcy. Firms do not lose tax carryforwards in bankruptcy, and the tax treatment of the cancellation of indebtedness is better in bankruptcy. Also, interest on prebankruptcy unsecured debt stops accruing in formal bankruptcy.

Holdouts Bankruptcy is usually better for the equity investors than it is for the creditors. Using DIP debt and stopping prebankruptcy interest from accruing on unsecured debt helps the stockholders and hurts the creditors. As a consequence, equity investors can usually hold out for a better deal in bankruptcy. The absolute priority rule, which favors creditors over equity investors, is usually violated in formal bankruptcies. One recent study found that in 81 percent of recent bankruptcies the equity investor obtained some compensation.10 Under Chapter 11, the creditors are often forced to give up some of their seniority rights to get management and the equity investors to agree to a deal.

Complexity A firm with a complicated capital structure will have more trouble putting together a private workout. Firms with secured creditors and trade creditors such as Macy’s 9 For example, see Stuart Gilson, “Managing Default: Some Evidence on How Firms Choose between Workouts and Bankruptcy,” Journal of Applied Corporate Finance (Summer 1991); and Stuart C. Gilson, Kose John, and Larry H. P. Lang, “Troubled Debt Restructurings: An Empirical Study of Private Reorganization of Firms in Default,” Journal of Financial Economics 27 (1990). 10

Lawrence A. Weiss, “Bankruptcy Resolution: Direct Costs and Violation of Priority of Claims,” Journal of Financial Economics 27 (1990). However, W. Beranek, R. Boehmer, and B. Smith, in “Much Ado about Nothing: Absolute Priority Deviations in Chapter 11,” Financial Management (Autumn 1996), find that 33.8 percent of bankruptcy reorganizations leave the stockholders with nothing. They also point out that deviations from the absolute priority rule are to be expected because the bankruptcy code allows creditors to waive their rights if they perceive a waiver to be in their best interests. A rejoinder can be found in Allan C. Eberhart and Lawrence A. Weiss, “The Importance of Deviations from the Absolute Priority Rule in Chapter 11 Bankruptcy Proceedings,” Financial Management 27 (1998).

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and Carter Hale will usually use formal bankruptcy because it is too hard to reach an agreement with many different types of creditors.

Lacko fI nformation There is an inherent conflict of interest between equity investors and creditors, and the conflict is accentuated when both have incomplete information about the circumstances of financial distress. When a firm initially experiences a cash flow shortfall, it may not know whether the shortfall is permanent or temporary. If the shortfall is permanent, creditors will push for a formal reorganization or liquidation. However, if the cash flow shortfall is temporary, formal reorganization or liquidation may not be necessary. Equity investors will push for this viewpoint. This conflict of interest cannot easily be resolved. These last two points are especially important. They suggest that financial distress will be more expensive (cheaper) if complexity is high (low) and information is incomplete (complete). Complexity and lack of information make cheap workouts less likely.

30.5 Prepackaged Bankruptcy11 On October 5, 2004, Choice One Communications, a broadband data, Internet services, and phone company, filed for Chapter 11 reorganization under the U.S. bankruptcy code. At the time of the filing, the company had about $1 billion in debt. A firm in this situation could reasonably be expected to spend a year or longer in bankruptcy. Not so with Choice One. Its reorganization plan was confirmed by the U.S Bankruptcy Court on November 10, 2004, six weeks after the date of filing! Firms typically file bankruptcy to seek protection from their creditors, essentially admitting that they cannot meet their financial obligations as they are presently structured. Once in bankruptcy, the firm attempts to reorganize its financial picture so that it can survive. A key to this process is that the creditors must ultimately give their approval to the restructuring plan. The time a firm spends in Chapter 11 depends on many things, but it usually depends most on the time it takes to get creditors to agree to a plan of reorganization. Prepackaged bankruptcy is a combination of a private workout and legal bankruptcy. Prior to filing bankruptcy, the firm approaches its creditors with a plan for reorganization. The two sides negotiate a settlement and agree on the details of how the firm’s finances will be restructured in bankruptcy. Then, the firm puts together the necessary paperwork for the bankruptcy court before filing for bankruptcy. A filing is a prepack if the firm walks into court and, at the same time, files a reorganization plan complete with the documentation of the approval of its creditors, which is exactly what Choice One did. The key to the prepackaged reorganization process is that both sides have something to gain and something to lose. If bankruptcy is imminent, it may make sense for the creditors to expedite the process even though they are likely to take a financial loss in the restructuring. Choice One’s bankruptcy was relatively painless for most creditors. Interest payments were made on its debt while in bankruptcy, and all vendors were paid. The prepack for Choice One was approved by 100 percent of creditors. Two sets of bondholders were involved. The senior bondholders exchanged $404 million worth of long-term debt for $175 million in new notes and 90 percent of the new stock in the company. The 11 John McConnell and Henri Servaes, “The Economics of Prepackaged Bankruptcy,” Journal of Applied Corporate Finance (Summer 1991), describe prepackaged bankruptcy.

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929

subordinated bondholders had their $252 million worth of bonds converted to 10 percent of the new stock and the ability to purchase more common stock in the future. Of course, stockholders received nothing and, in fact, had their shares canceled. Prepackaged bankruptcy arrangements require that most creditors reach agreement privately. Prepackaged bankruptcy doesn’t seem to work when there are thousands of reluctant trade creditors, such as in the case of a retail firm like Macy’s or Revco D. S.12 The main benefit of prepackaged bankruptcy is that it forces holdouts to accept a bankruptcy reorganization. If a large fraction of a firm’s creditors can agree privately to a reorganization plan, the holdout problem may be avoided. It makes a reorganization plan in formal bankruptcy easier to put together.13 A study by McConnell, Lease, and Tashjian reports that prepackaged bankruptcies offer many of the advantages of a formal bankruptcy, but they are also more efficient. Their results suggest that the time spent and the direct costs of resolving financial distress are less in a prepackaged bankruptcy than in a formal bankruptcy.14

30.6 Predicting Corporate Bankruptcy: The Z-Score Model Many potential lenders use credit scoring models to assess the creditworthiness of prospective borrowers. The general idea is to find factors that enable the lenders to discriminate between good and bad credit risks. To put it more precisely, lenders want to identify attributes of the borrower that can be used to predict default or bankruptcy. Edward Altman, a professor at New York University, has developed a model using financial statement ratios and multiple discriminant analyses to predict bankruptcy for publicly traded manufacturing firms. The resultant model is of the form: Net working capital EBIT Z = 3.3 __________ + 1.2 _________________ Total assets Total assets Market value of equity Sales + 1.0 __________ + .6 ____________________ Total assets Book value of debt Accumulated retained earnings + 1.4 ___________________________ Total assets where Z is an index of bankruptcy. A score of Z less than 2.675 indicates that a firm has a 95 percent chance of becoming bankrupt within one year. However, Altman’s results show that in practice scores between 1.81 and 2.99 should be thought of as a gray area. In actual use, bankruptcy would be predicted if Z ≤ 1.81 and nonbankruptcy if Z ≥ 2.99. Altman shows that bankrupt firms and nonbankrupt firms have very different financial profiles one year

12

S. Chatterjee, U. S. Dhillon, and G. G. Ramirez, in “Prepackaged Bankruptcies and Workouts,” Financial Management (Spring 1996), find that firms using prepackaged bankruptcy arrangements are smaller and in better financial shape and have greater short-term liquidity problems than firms using private workouts or Chapter 11. 13 During bankruptcy, a proposed plan can be “crammed down” on a class of creditors. A bankruptcy court can force creditors to participate in a reorganization if it can be shown that the plan is “fair and equitable.” 14

John J. McConnell, Ronald Lease, and Elizabeth Tashjian, “Prepacks as a Mechanism for Resolving Financial Distress: The Evidence,” Journal of Applied Corporate Finance 8 (1996).

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Table30.2 Financial Statement Ratios One Year before Bankruptcy: ManufacturingF irms

Average Ratios One Year before Bankruptcy of : Bankrupt Firms Net working capital _________________

Total assets Accumulated retained earnings __________________________ Total assets EBIT __________ Total assets Market value of equity ___________________ Total liabilities Sales ______ Assets

Nonbankrupt Firms

−6.1%

41.4%

−62.6%

35.5%

−31.8%

15.4%

40.1%

247.7%

150 %

190 %

SOURCE: Edward I. Altman, Corporate Financial Distress and Bankruptcy (New York: John Wiley & Sons, 1993),Table 3.1, p. 109.

before bankruptcy. These different financial ratios are the key intuition behind the Z-scoremo delan dar ed epictedin T able30.2. Altman’s original Z-score model requires a firm to have publicly traded equity and be a manufacturer. He uses a revised model to make it applicable for private firms and nonmanufacturers. The resulting model is this: Net working capital Accumulated retained earnings Z = 6.56 _________________ + 3.26 ___________________________ Total assets Total assets Book value of equity EBIT + 1.05 __________ + 6.72 __________________ Total assets Total liabilities where Z < 1.23 indicates a bankruptcy prediction, 1.23 ≥ Z ≤ 2.90 indicates a gray area, andZ > 2.90 indicates no bankruptcy.

EXAMPLE30.3

U.S. Composite Corporation is attempting to increase its line of credit with First National State Bank. The director of credit management of First National State Bank uses the Z-score model to determine creditworthiness. U.S. Composite Corporation is not a publicly traded firm, so the revised Z-score model must be used. The balance sheet and income statement of U.S. Composite Corporation are in Tables 2.1 and 2.2 (Chapter 2). The first step is to determine the value of each of the financial statement variables and apply them in the revised Z-score model: ($ in millions) Net working capital _________________ Total assets Accumulated retained earnings __________________________ Total assets EBIT __________

Total assets Book value of equity _________________ Total liabilities

=

275 _____

=

390 _____

=

219 _____

=

805 ____

1,879 1,879 1,879 588

=

.146

=

.208

=

.117

= 1.369

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The next step is to calculate the revised Z-score: Z = 6.56 × .146 + 3.26 × .208 + 1.05 × .117 + 6.72 × 1.369 = 10.96 Finally, we determine that the Z-score is above 2.9, and we conclude that U.S. Composite is a good credit risk.

Summary and Conclusions

1. 2. 3. 4. 5. 6. 7. 8.

9.

10.

Financial Distress Define financial distress using the stock-based and flow-based approaches. Financial Distress What are some benefits of financial distress? Prepackaged Bankruptcy What is prepackaged bankruptcy? What is the main benefit of prepackaged bankruptcy? Financial Distress Why doesn’t financial distress always cause firms to die? Liquidation versus Reorganization What is the difference between liquidation and reorganization? APR What is the absolute priority rule? DIP Loans What are DIP loans? Where do DIP loans fall in the APR? Bankruptcy Ethics Firms sometimes use the threat of a bankruptcy filing to force creditors to renegotiate terms. Critics argue that in such cases the firm is using bankruptcy laws “as a sword rather than a shield.” Is this an ethical tactic? Bankruptcy Ethics Several firms have entered bankruptcy, or threatened to enter bankruptcy, at least in part as a means of reducing labor costs. Whether this move is ethical, or proper, is hotly debated. Is this an ethical use of bankruptcy? Bankruptcy versus Private Workouts Why do so many firms file for legal bankruptcy when private workouts are so much less expensive?

www.mhhe.com/rwj

Concept Questions

This chapter examined what happens when firms experience financial distress. 1. Financial distress is a situation where a firm’s operating cash flow is not sufficient to cover contractual obligations. Financially distressed firms are often forced to take corrective action and undergo financial restructuring. Financial restructuring involves exchanging new financial claims for old ones. 2. Financial restructuring can be accomplished with a private workout or formal bankruptcy. Financial restructuring can involve liquidation or reorganization. However, liquidation is not as common. 3. Corporate bankruptcy involves Chapter 7 liquidation or Chapter 11 reorganization. An essential feature of the U.S. bankruptcy code is the absolute priority rule. The absolute priority rule states that senior creditors are paid in full before junior creditors receive anything. However, in practice the absolute priority rule is often violated. 4. A new form of financial restructuring is prepackaged bankruptcy. It is a hybrid of a private workout and formal bankruptcy. 5. Firms experiencing financial distress can be identified by different-looking financial statements. The Z-score model captures some of these differences.

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Chapter 7 When the Beacon Computer Company filed for bankruptcy under Chapter 7 of the U.S. bankruptcy code, it had the following balance sheet information: Liquidating Value

BASIC (Questions 1–2)

Total assets

2.

$28,500

Claims Trade credit Secured mortgage notes Senior debentures Junior debentures Equity

Assuming there are no legal fees associated with the bankruptcy, as a trustee, what distribution of liquidating value do you propose? Chapter 11 When the Master Printing Company filed for bankruptcy, it filed under Chapter 11 of the U.S. bankruptcy code. Key information is shown here:

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Assets

Going concern value

3.

Claims

$27,000

Mortgage bonds Senior debentures Junior debentures Book equity

$19,000 9,500 7,500 −9,000

As a trustee, what reorganization plan would you accept? Z-Score Fair-to-Midland Manufacturing, Inc., (FMM) has applied for a loan at True Credit Bank. Jon Fulkerson, the credit analyst at the bank, has gathered the following information from the company’s financial statements: Total assets EBIT Net working capital Book value of equity Accumulated retained earnings Sales

4.

$4,800 8,000 10,000 15,000 −9,300

$ 42,000 6,500 3,100 19,000 13,500 61,000

The stock price of FMM is $18 per share and there are 5,000 shares outstanding. What is the Z-score for this company? Z-Score Jon Fulkerson has also received a credit application from Seether, LLC, a private company. An abbreviated portion of the financial information provided by the company is shown below: Total assets EBIT Net working capital Book value of equity Accumulated retained earnings Total liabilities

Whatis t heZ -scoref ort hisc ompany?

$75,000 8,300 6,800 26,000 19,000 49,000

CHAPTER 31

InternationalCo rporate Finance In fall 2007, Canadians cheered as the Canadian dollar, popularly known as the “loonie,” reached parity with the U.S. dollar for the first time in 31 years, meaning that one loonie could be exchanged for one greenback. As recently as five years before, one loonie was worth only $.62. By November 2007, the loonie reached $1.10, a level not seen since the 1870s, though it fell back to about $.79 by January 2009. The dollar took a dive Down Under as well. In June 2008, the Australian dollar reached a high of Australian $.96 per U.S. dollar, its highest level in more than 23 years, although it fell back to about $.65 in January 2009. So what were the effects of these exchange rate shifts? Using Canada as an example, the higher value of the loonie meant that Canadian exports were more expensive in the United States, so exports declined. The increased value of the loonie was also blamed for the loss of more than 268,000 manufacturing jobs in Canada, primarily in areas near the U.S.–Canadian border. Since traveling in Canada became more expensive for U.S. visitors, tourism dropped as well, reaching its lowest level in 35 years. In this chapter, we explore the important role played by currencies and exchange rates in international finance, along with a number of other key topics.

Corporations with significant foreign operations are often called international corporations or multinationals. Such corporations must consider many financial factors that do not directly affect purely domestic firms. These include foreign exchange rates, differing interest rates from country to country, complex accounting methods for foreign operations, foreign tax rates, and foreign government intervention. The basic principles of corporate finance still apply to international corporations; like domestic companies, these firms seek to invest in projects that create more value for the shareholders than they cost and to arrange financing that raises cash at the lowest possible cost. In other words, the net present value principle holds for both foreign and domestic operations, although it is usually more complicated to apply the NPV rule to foreign investments. One of the most significant complications of international finance is foreign exchange. The foreign exchange markets provide important information and opportunities for an international corporation when it undertakes capital budgeting and financing decisions. As we will discuss, international exchange rates, interest rates, and inflation rates are closely related. We will spend much of this chapter exploring the connection between these financial variables. We won’t have much to say here about the role of cultural and social differences in international business. Neither will we be discussing the implications of differing political and economic systems. These factors are of great importance to international businesses, but it would take another book to do them justice. Consequently, we will 933

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focus only on some purely financial considerations in international finance and some key aspects of foreign exchange markets.

31.1 Terminology A common buzzword for the student of business finance is globalization. The first step in learning about the globalization of financial markets is to conquer the new vocabulary. As with any specialty, international finance is rich in jargon. Accordingly, we get started on the subject with a highly eclectic vocabulary exercise. The terms that follow are presented alphabetically, and they are not all of equal importance. We choose these in particular because they appear frequently in the financial press or because they illustrate the colorful nature of the language of international finance. See www.adr.com for more.

1. An American depositary receipt (ADR) is a security issued in the United States that represents shares of a foreign stock, allowing that stock to be traded in the United States. Foreign companies use ADRs, which are issued in U.S. dollars, to expand the pool of potential U.S. investors. ADRs are available in two forms for a large and growing number of foreign companies: Company sponsored, which are listed on an exchange, and unsponsored, which usually are held by the investment bank that makes a market in the ADR. Both forms are available to individual investors, but only company-sponsored issues are quoted daily in newspapers. 2. The cross-rate is the implicit exchange rate between two currencies (usually non-U.S.) when both are quoted in some third currency, usually the U.S. dollar. 3. Eurocurrency is money deposited in a financial center outside of the country whose currency is involved. For instance, Eurodollars—the most widely used Eurocurrency—are U.S. dollars deposited in banks outside the U.S. banking system. 4. Gilts, technically, are British and Irish government securities, although the term also includes issues of local British authorities and some overseas public-sector offerings.

For current LIBOR rates, see www.bloomberg.com.

5. The London Interbank Offer Rate (LIBOR) is the rate that most international banks charge one another for overnight loans of Eurodollars in the London market. LIBOR is a cornerstone in the pricing of money market issues and other short-term debt issues by both government and corporate borrowers. Interest rates are frequently quoted as some spread over LIBOR, and they then float with the LIBOR rate.

31.2 ForeignEx changeMark ets and Exchange Rates The foreign exchange market is undoubtedly the world’s largest financial market. It is the market where one country’s currency is traded for another’s. Most of the trading takes place in a few currencies: The U.S. dollar ($), the British pound sterling (£), the Japanese yen (¥), and the euro ( ). Table 31.1 lists some of the more common currencies and their symbols. The foreign exchange market is an over-the-counter market, so there is no single location where traders get together. Instead, market participants are located in the major commercial and investment banks around the world. They communicate using computers, telephones, and other telecommunication devices. For example, one

Chapter 31

Table 31.1 International Currency Symbols

International Corporate Finance

Country Australia Canada Denmark EMU India Iran Japan Kuwait Mexico Norway Saudi Arabia Singapore South Africa Sweden Switzerland United Kingdom United States

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Currency

Symbol

Dollar Dollar Krone Euro Rupee Rial Yen Dinar Peso Krone Riyal Dollar Rand Krona Franc Pound Dollar

A$ Can$ DKr € Rs Rl ¥ KD Ps NKr SR S$ R SKr SF £ $

communication network for foreign transactions is maintained by the Society for Worldwide Interbank Financial Telecommunication (SWIFT), a Belgian not-forprofit cooperative. Using data transmission lines, a bank in New York can send messages to a bank in London via SWIFT regional processing centers. The many different types of participants in the foreign exchange market include the following: Visit SWIFT at www.swift.com.

1. Importers who pay for goods using foreign currencies. 2. Exporters who receive foreign currency and may want to convert to the domestic currency. 3. Portfolio managers who buy or sell foreign stocks and bonds. 4. Foreign exchange brokers who match buy and sell orders. 5. Traders who “make a market” in foreign currencies. 6. Speculators who try to profit from changes in exchange rates.

ExchangeR ates An exchange rate is simply the price of one country’s currency expressed in terms of another country’s currency. In practice, almost all trading of currencies takes place in terms of the U.S. dollar. For example, both the Swiss franc and the Japanese yen are traded with their prices quoted in U.S. dollars. Exchange rates are constantly changing. Exchange Rate Quotations Figure 31.1 reproduces exchange rate quotations as they appeared in The Wall Street Journal in 2008. The first column (labeled “in US$”) gives the number of dollars it takes to buy one unit of foreign currency. Because this is the price in dollars of a foreign currency, it is called a direct or

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Figure 31.1 Exchange Rate Quotations

SOURCE: Reprinted by permission of The Wall Street Journal, © 2008 Dow Jones & Company, Inc., September 29, 2008. All rights reserved worldwide.

Get up-to-the-minute exchange rates at www.xe.com and www.exchangerate .com.

American quote (remember that “Americans are direct”). For example, the Australian dollar is quoted at .8009, which means that you can buy one Australian dollar with U.S. $.8009. The second column shows the indirect, or European, exchange rate (even though the currency may not be European). This is the amount of foreign currency per U.S. dollar. The Australian dollar is quoted here at 1.2486, so you can get 1.2486 Australian dollars for one U.S. dollar. Naturally this second exchange rate is just the reciprocal of the first one (possibly with a little rounding error): 1/.8009 = 1.2486. The third column shows the year-to-date (YTD) percentage change in the dollar’s value versus another currency. You can also find exchange rates on a number of Web sites. Suppose you have just returned from your dream vacation to Jamaica and feel rich because you have 10,000 Jamaican dollars left over. You now need to convert these to U.S. dollars. How much will you have? We went to www.xe.com and used the currency converter on the site to find out. This is what we found:

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Looks like you left Jamaica just before you ran out of money.

EXAMPLE31 .1

A Yen for Euros Suppose you have $1,000. Based on the rates in Figure 31.1, how many Japanese yen can you get? Alternatively, if a Porsche costs €100,000 (recall that € is the symbol for the euro), how many dollars will you need to buy it? The exchange rate in terms of yen per dollar (second column) is 104.29. Your $1,000 will thus get you: $1,000 × 104.29 yen per $1 = 104,290 yen Because the exchange rate in terms of dollars per euro (first column) is 1.4441, you will need: €100,000 × $1.4441 per € = $144,410

Cross-Rates and Triangle Arbitrage Using the U.S. dollar as the common denominator in quoting exchange rates greatly reduces the number of possible cross-currency quotes. For example, with five major currencies, there would potentially be 10 exchange rates instead of just 4.1 Also, the fact that the dollar is used throughout cuts down on inconsistencies in the exchange rate quotations. Earlier, we defined the cross-rate as the exchange rate for a non-U.S. currency expressed in terms of another non-U.S. currency. For example, suppose we observe the following for the euro ( ) and the Swiss franc (SF): per $1 = 1.00 SF per $1 =2.00 Suppose the cross-rate is quoted as: per SF =.40 What do you think? The cross-rate here is inconsistent with the exchange rates. To see this, suppose you have $100. If you convert this to Swiss francs, you will receive: $100 × SF 2 per $1 =S F200 If you convert this to euros at the cross-rate, you will have: SF200 × .4 per SF 1 = 80 1

There are four exchange rates instead of five because one exchange rate would involve the exchange of a currency for itself. More generally, it might seem that there should be 25 exchange rates with five currencies. There are 25 different combinations, but, of these, 5 involve the exchange of a currency for itself. Of the remaining 20, half are redundant because they are just the reciprocals of another exchange rate. Of the remaining 10, 6 can be eliminated by using a common denominator.

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However, if you just convert your dollars to euros without going through Swiss francs, you will have: $100 × 1 per $1 = 100 What we see is that the euro has two prices, 1 per $1 and .80 per $1, with the price we pay depending on how we get the euros. To make money, we want to buy low and sell high. The important thing to note is that euros are cheaper if you buy them with dollars because you get 1 euro instead of just .8. You should proceed as follows: 1. Buy100e urosf or$100. 2. Use the 100 euros to buy Swiss francs at the cross-rate. Because it takes .4 euros to buy a Swiss franc, you will receive 100 .4 = SF 250. 3. Use the SF 250 to buy dollars. Because the exchange rate is SF 2 per dollar, you receive SF 250/2 = $125, for a round-trip profit of $25. 4. Repeatste ps1th rough3. This particular activity is called triangle arbitrage because the arbitrage involves moving through three different exchange rates: € 1/$1

SF 2/$1 ⫽ $.50/SF 1

€ .4/SF 1 ⫽ SF 2.5/€ 1

To prevent such opportunities, it is not difficult to see that because a dollar will buy you either one euro or two Swiss francs, the cross-rate must be: ( 1 $1) (SF 2 $1) = 1 SF2 That is, the cross-rate must be one euro per two Swiss francs. If it were anything else, there would be a triangle arbitrage opportunity.

EXAMPLE31 .2

Shedding Some Pounds Suppose the exchange rates for the British pound and Swiss franc are: Pounds per $1 = .60 SF per $1 = 2.00 The cross-rate is three francs per pound. Is this consistent? Explain how to go about making some money. The cross-rate should be SF 2.00/£.60 = SF 3.33 per pound. You can buy a pound for SF 3 in one market, and you can sell a pound for SF 3.33 in another. So we want to first get some francs, then use the francs to buy some pounds, and then sell the pounds. Assuming you have $100, you could: 1. Exchange dollars for francs: $100 × 2 = SF 200. 2. Exchange francs for pounds: SF 200/3 = £66.67. 3. Exchange pounds for dollars: £66.67/.60 = $111.12. This would result in an $11.12 round-trip profit.

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Types of Transactions There are two basic types of trades in the foreign exchange market: Spot trades and forward trades. A spot trade is an agreement to exchange currency “on the spot,” which actually means that the transaction will be completed or settled within two business days. The exchange rate on a spot trade is called the spot exchange rate. Implicitly, all of the exchange rates and transactions we have discussed so far have referred to the spot market. A forward trade is an agreement to exchange currency at some time in the future. The exchange rate that will be used is agreed upon today and is called the forward exchange rate. A forward trade will normally be settled sometime in the next 12 months. If you look back at Figure 31.1, you will see forward exchange rates quoted for some of the major currencies. For example, the spot exchange rate for the Swiss franc is SF 1 = $.9188. The 180-day (6-month) forward exchange rate is SF 1 = $.9257. This means that you can buy a Swiss franc today for $.9188, or you can agree to take delivery of a Swiss franc in 180 days and pay $.9257 at that time. Notice that the Swiss franc is more expensive in the forward market ($.9257 versus $.9188). Because the Swiss franc is more expensive in the future than it is today, it is said to be selling at a premium relative to the dollar. For the same reason, the dollar is said to be selling at a discount relative to the Swiss franc. Why does the forward market exist? One answer is that it allows businesses and individuals to lock in a future exchange rate today, thereby eliminating any risk from unfavorable shifts in the exchange rate.

EXAMPLE31 .3

Looking Forward Suppose you are expecting to receive a million British pounds in six months, and you agree to a forward trade to exchange your pounds for dollars. Based on Figure 31.1, how many dollars will you get in six months? Is the pound selling at a discount or a premium relative to the dollar? In Figure 31.1, the spot exchange rate and the 180-day forward rate in terms of dollars per pound are $1.8091 = £1 and $1.7974 = £1, respectively. If you expect £1 million in 180 days, then you will get £1 million × $1.7974 per pound = $1.7974 million. Because it is less expensive to buy a pound in the forward market than in the spot market ($1.7974 versus $1.8091), the pound is said to be selling at a discount relative to the dollar.

As we mentioned earlier, it is standard practice around the world (with a few exceptions) to quote exchange rates in terms of the U.S. dollar. This means that rates are quoted as the amount of currency per U.S. dollar. For the remainder of this chapter, we will stick with this form. Things can get extremely confusing if you forget this. Thus, when we say things like “the exchange rate is expected to rise,” it is important to remember that we are talking about the exchange rate quoted as units of foreign currency per dollar.

31.3 PurchasingP ower Parity Now that we have discussed what exchange rate quotations mean, we can address an obvious question: What determines the level of the spot exchange rate? In addition, because we know that exchange rates change through time, we can ask the related

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question, what determines the rate of change in exchange rates? At least part of the answer in both cases goes by the name of purchasing power parity (PPP), the idea that the exchange rate adjusts to keep purchasing power constant among currencies. As we discuss next, there are two forms of PPP, absolute and relative.

AbsoluteP urchasingP owerP arity The basic idea behind absolute purchasing power parity is that a commodity costs the same regardless of what currency is used to purchase it or where it is selling. This is a very straightforward concept. If a beer costs £2 in London, and the exchange rate is £.60 per dollar, then a beer costs £2 .60 = $3.33 in New York. In other words, absolute PPP says that $1 will buy you the same number of, say, cheeseburgers anywhere in the world. (This concept is sometimes referred to as the “law of one price.”) More formally, let S0 be the spot exchange rate between the British pound and the U.S. dollar today (time 0), and remember that we are quoting exchange rates as the amount of foreign currency per dollar. Let PUS and PUK be the current U.S. and British prices, respectively, on a particular commodity, say, apples. Absolute PPP simply says that: PUK = S0 × PUS This tells us that the British price for something is equal to the U.S. price for that same something multiplied by the exchange rate. The rationale behind absolute PPP is similar to that behind triangle arbitrage. If PPP did not hold, arbitrage would be possible (in principle) if apples were moved from one country to another. For example, suppose apples are selling in New York for $4 per bushel, whereas in London the price is £2.40 per bushel. Absolute PPP implies that: PUK = S0 × PUS £2.40 = S0 × $4 S0 = £ 2.40 $4 = £ .60 That is, the implied spot exchange rate is £.60 per dollar. Equivalently, a pound is worth $1 £.60 = $1.67. Suppose instead that the actual exchange rate is £.50. Starting with $4, a trader could buy a bushel of apples in New York, ship it to London, and sell it there for £2.40. Our trader could then convert the £2.40 into dollars at the prevailing exchange rate, S0 = £.50, yielding a total of £2.40 .50 = $4.80. The round-trip gain would be 80 cents. Because of this profit potential, forces are set in motion to change the exchange rate and/or the price of apples. In our example, apples would begin moving from New York to London. The reduced supply of apples in New York would raise the price of apples there, and the increased supply in Britain would lower the price of apples in London. In addition to moving apples around, apple traders would be busily converting pounds back into dollars to buy more apples. This activity would increase the supply of pounds and simultaneously increase the demand for dollars. We would expect the value of a pound to fall. This means that the dollar would be getting more valuable, so it would take more pounds to buy one dollar. Because the exchange rate is quoted as pounds per dollar, we would expect the exchange rate to rise from £.50. For absolute PPP to hold absolutely, several things must be true: 1. The transaction costs of trading apples—shipping, insurance, spoilage, and so on—must be zero.

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2. There must be no barriers to trading apples—no tariffs, taxes, or other political barriers. 3. Finally, an apple in New York must be identical to an apple in London. It won’t do any good for you to send red apples to London if the English eat only green apples. Given the fact that the transaction costs are not zero and that the other conditions are rarely met exactly, it is not surprising that absolute PPP is really applicable only to traded goods, and then only to very uniform ones. For this reason, absolute PPP does not imply that a Mercedes costs the same as a Ford or that a nuclear power plant in France costs the same as one in New York. In the case of the cars, they are not identical. In the case of the power plants, even if they were identical, they are expensive and would be very difficult to ship. On the other hand, we would be very surprised to see a significant violation of absolute PPP for gold. As an example of a violation of absolute PPP, in late 2003, the euro was going for about $1.30. Porsche’s new (and very desirable) Carrera GT sold for about $440,000 in the United States. This converted to a euro price of 338,462 before tax and 392,615 after tax. The price of the car in Germany was 452,690, which meant that if German residents could ship the car for less than 60,000, they would be better off buying it in the United States. Violations of PPP are actually sought out by corporations. For example, in mid-2004, Alcoa announced that it would build a $1 billion aluminum smelter plant on the Caribbean island of Trinidad. At the same time, the company was breaking ground on another $1 billion plant in Iceland and looking into other locations including China, Brunei, Bahrain, Brazil, and Canada. In all cases, low energy costs were the attraction (aluminum smelting is very energy-intensive). Meanwhile, the company had several plants in the Pacific Northwest that were closed because higher electricity prices in this region made the plants unprofitable. One of the more famous violations of absolute PPP is the Big Mac Index constructed by The Economist. To construct the index, prices for a Big Mac in different countries are gathered from McDonald’s. Nearby you will find a recent Big Mac index from www.economist.com. (We will leave it to you to find the most recent index.) As you can see from the index, absolute PPP does not seem to hold, at least for the Big Mac. In fact, in only 5 of the 29 currencies surveyed by The Economist is the exchange rate within 10 percent of that predicted by absolute PPP. The largest disparity is in Switzerland, where the currency is apparently overvalued by about 60 percent. And 11 of the 29 currencies are “incorrectly” priced by more than 40 percent. Why? There are several reasons. First, a Big Mac is not really transportable. Yes, you can load a ship with Big Macs and send it to Denmark where the currency is supposedly overvalued by more than 40 percent. But do you really think people would buy your Big Macs? Probably not. Even though it is relatively easy to transport a Big Mac, it would be relatively expensive, and the hamburger would suffer in quality along the way. Also, if you look, the price of the Big Mac is the average price from New York, Chicago, San Francisco, and Atlanta. The reason is that Big Macs do not sell for the same price in the United States, where presumably they are all purchased with the dollar. The cost of living and competition are only a couple of the factors that affect the price of a Big Mac in the United States. If Big Macs are not

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priced the same in the same currency, would we expect absolute PPP to hold across currencies? Finally, differing tastes can account for the apparent discrepancy. In the United States, hamburgers and fast food have become a staple of the American diet. In other countries, hamburgers have not become as entrenched. We would expect the price of the Big Mac to be lower in the United States because there is much more competition.

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Having examined the Big Mac, we should say that absolute PPP should hold more closely for more easily transportable items. For instance, there are many companies with stock listed on both the NYSE and the stock exchange of another country. If you examine the share prices on the two exchanges you will find that the price of the stock is almost exactly what absolute PPP would predict. The reason is that a share of stock in a particular company is (usually) the same wherever you buy it and whatever currency you use.

RelativeP urchasingP owerP arity As a practical matter, a relative version of purchasing power parity has evolved. Relative purchasing power parity does not tell us what determines the absolute level of the exchange rate. Instead, it tells us what determines the change in the exchange rate over time. The Basic Idea Suppose the British pound–U.S. dollar exchange rate is currently S0 = £.50. Further suppose that the inflation rate in Britain is predicted to be 10 percent over the coming year, and (for the moment) the inflation rate in the United States is predicted to be zero. What do you think the exchange rate will be in a year? If you think about it, you see that a dollar currently costs .50 pounds in Britain. With 10 percent inflation, we expect prices in Britain to generally rise by 10 percent. So we expect that the price of a dollar will go up by 10 percent, and the exchange rate should rise to £.50 × 1.1 = £.55. If the inflation rate in the United States is not zero, then we need to worry about the relative inflation rates in the two countries. For example, suppose the U.S. inflation rate is predicted to be 4 percent. Relative to prices in the United States, prices in Britain are rising at a rate of 10 percent − 4 percent = 6 percent per year. So we expect the price of the dollar to rise by 6 percent, and the predicted exchange rate is £.50 × 1.06 = £.53. The Result In general, relative PPP says that the change in the exchange rate is determined by the difference in the inflation rates of the two countries. To be more specific, we will use the following notation: S0 = Current (Time 0) spot exchange rate (foreign currency per dollar). E(St) = Expected exchange rate in tp eriods. hUS = Inflation rate in the United States. hFC = Foreign country inflation rate. Based on our preceding discussion, relative PPP says that the expected percentage change in the exchange rate over the next year, [E(S1) − S0] S0, is: [E(S1) − S0] S0 ≅ hFC − hUS

(31.1)

In words, relative PPP simply says that the expected percentage change in the exchange rate is equal to the difference in inflation rates.2 If we rearrange this slightly, we get: E(S1) ≅ S0 × [1 + (hFC − hUS)] 2

(31.2)

Equation 31.1 is actually an approximation; the relative PPP predicts that: 1 + hFC E(S1) − S0 _____ E(S1) _______ __________ = S −1 S0 = 1 + hFC and S0 0

E(S1) _____

will hold precisely. So, in our example, the change in the value of a UK pound per dollar would be: 1 + .10 1.058 = _______ 1 + .04 or 5.8 percent instead of 6 percent. This is a widely used approximation, and we use it from time to time for ease of exposition.

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This result makes a certain amount of sense, but care must be used in quoting the exchange rate. In our example involving Britain and the United States, relative PPP tells us that the exchange rate will rise by hFC − hUS = 10 percent − 4 percent = 6 percent per year. Assuming the difference in inflation rates doesn’t change, the expected exchange rate in two years, E(S2), will therefore be: E(S2) = E(S1) × (1 + .06) = .53 × 1.06 =.562 Notice that we could have written this as: E(S2) = .53 × 1.06 = .50 × (1.06 × 1.06) = .50 × 1.062 In general, relative PPP says that the expected exchange rate at some time in the future, E(St ), is: E(St) ≅ S0 × [1 + (hFC − hUS)]t

(31.3)

As we will see, this is a very useful relationship. Because we don’t really expect absolute PPP to hold for most goods, we will focus on relative PPP in our following discussion. Henceforth, when we refer to PPP without further qualification, we mean relative PPP.

EXAMPLE31 .4

It’s All Relative Suppose the Japanese exchange rate is currently 105 yen per dollar. The inflation rate in Japan over the next three years will run, say, 2 percent per year, whereas the U.S. inflation rate will be 6 percent. Based on relative PPP, what will the exchange rate be in three years? Because the U.S. inflation rate is higher, we expect that a dollar will become less valuable. The exchange rate change will be 2 percent − 6 percent = −4 percent per year. Over three years the exchange rate will fall to: E(S3) ≅ S0 × [1 + (hFC − hUS)]3 ≅ 105 × [1 + (−.04)]3 ≅ 92.90

Currency Appreciation and Depreciation We frequently hear things like “the dollar strengthened (or weakened) in financial markets today” or “the dollar is expected to appreciate (or depreciate) relative to the pound.” When we say that the dollar strengthens or appreciates, we mean that the value of a dollar rises, so it takes more foreign currency to buy a dollar. What happens to the exchange rates as currencies fluctuate in value depends on how exchange rates are quoted. Because we are quoting them as units of foreign currency per dollar, the exchange rate moves in the same direction as the value of the dollar: It rises as the dollar strengthens, and it falls as the dollar weakens. Relative PPP tells us that the exchange rate will rise if the U.S. inflation rate is lower than the foreign country’s. This happens because the foreign currency depreciates in value and therefore weakens relative to the dollar.

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31.4 Interest Rate Parity, Unbiased Forward Rates, and the International Fisher Effect The next issue we need to address is the relationship between spot exchange rates, forward exchange rates, and interest rates. To get started, we need some additional notation: Ft = Forward exchange rate for settlement at time t. RUS = U.S. nominal risk-free interest rate. RFC = Foreign country nominal risk-free interest rate. As before, we will use S0 to stand for the spot exchange rate. You can take the U.S. nominal risk-free rate, RUS , to be the T-bill rate.

CoveredI nterestAr bitrage Suppose we observe the following information about U.S. and Swiss currencies in the market: S0 = SF 2.00 F1 = SF 1.90 RUS = 10% RS = 5% where RS is the nominal risk-free rate in Switzerland. The period is one year, so F1 is the 360-day forward rate. Do you see an arbitrage opportunity here? There is one. Suppose you have $1 to invest, and you want a riskless investment. One option you have is to invest the $1 in a riskless U.S. investment such as a 360-day T-bill. If you do this, then in one period your $1 will be worth: $ value in 1 period = $1 × (1 + RUS) =$1.10 Alternatively, you can invest in the Swiss risk-free investment. To do this, you need to convert your $1 to Swiss francs and simultaneously execute a forward trade to convert francs back to dollars in one year. The necessary steps would be as follows: 1. Convert your $1 to $1 × S0 = SF 2.00. 2. At the same time, enter into a forward agreement to convert Swiss francs back to dollars in one year. Because the forward rate is SF 1.90, you will get $1 for every SF 1.90 that you have in one year. 3. Invest your SF 2.00 in Switzerland at RS. In one year you will have: SF value in 1 year = SF 2.00 × (1 + RS) = SF 2.00 × 1.05 =S F2.10 4. Convert your SF 2.10 back to dollars at the agreed-upon rate of SF 1.90 = $1. You end up with: $ value in 1 year = SF 2.10 1.90 =$1.1053

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Notice that the value in one year resulting from this strategy can be written as: $ value in 1 year = $1 × S0 × (1 + RS) F1 = $1 × 2 × 1.05 1.90 =$1.1053 The return on this investment is apparently 10.53 percent. This is higher than the 10 percent we get from investing in the United States. Because both investments are risk-free, there is an arbitrage opportunity. To exploit the difference in interest rates, you need to borrow, say, $5 million at the lower U.S. rate and invest it at the higher Swiss rate. What is the round-trip profit from doing this? To find out, we can work through the steps outlined previously: 1. Convert the $5 million at SF 2 = $1 to get SF 10 million. 2. Agree to exchange Swiss francs for dollars in one year at SF 1.90 to the dollar. 3. Invest the SF 10 million for one year at RS = 5 percent. You end up with SF 10.5 million. 4. Convert the SF 10.5 million back to dollars to fulfill the forward contract. You receive SF 10.5 million/1.90 =$5,526,316. 5. Repay the loan with interest. You owe $5 million plus 10 percent interest for a total of $5.5 million. You have $5,526,316, so your round-trip profit is a risk-free $26,316. The activity that we have illustrated here goes by the name of covered interest arbitrage. The term covered refers to the fact that we are covered in the event of a change in the exchange rate because we lock in the forward exchange rate today.

InterestR ateP arity If we assume that significant covered interest arbitrage opportunities do not exist, then there must be some relationship between spot exchange rates, forward exchange rates, and relative interest rates. To see what this relationship is, note that in general strategy 1 from the preceding discussion, investing in a riskless U.S. investment, gives us 1 + RUS for every dollar we invest. Strategy 2, investing in a foreign risk-free investment, gives us S0 × (1 + RFC)/F1 for every dollar we invest. Because these have to be equal to prevent arbitrage, it must be the case that: 1 + RUS = S0 × (1 + RFC) F1 Rearranging this a bit gets us the famous interest rate parity (IRP)c ondition: F1 S0 = (1 + RFC) (1 + RUS)

(31.4)

There is a very useful approximation for IRP that illustrates clearly what is going on and is not difficult to remember.3 If we define the percentage forward premium or discount as (F1 − S0)/S0, then IRP says that this percentage premium or discount is approximately equal to the difference in interest rates: (F1 − S0) S0 ≅ RFC − RUS

(31.5)

Here we note that F1 S0 − 1 = (F1 − S0) S0 and (1 + RFC) (1 + RUS) is approximately equal to RFC − RUS.

3

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Loosely, IRP says that any difference in interest rates between two countries for some period is just offset by the change in the relative value of the currencies, thereby eliminating any arbitrage possibilities. Notice that we could also write: F1 ≅ S0 × [1 + (RFC − RUS)]

(31.6)

In general, if we have t periods instead of just one, the IRP approximation is written like this: Ft ≅ S0 × [1 + (RFC − RUS)]t

(31.7)

EXAMPLE31 .5 Parity Check Suppose the exchange rate for Japanese yen, S0, is currently ¥120 = $1. If the interest rate in the United States is RUS = 10 percent and the interest rate in Japan is RJ = 5 percent, then what must the forward rate be to prevent covered interest arbitrage? From IRP, we have: F1 ≅ S0 × [1 + (RJ − RUS)] ≅ ¥120 × [1 + (.05 − .10)] ≅ ¥120 × .95 ≅ ¥114 Notice that the yen will sell at a premium relative to the dollar. (Why?)

Forward Rates and Future Spot Rates In addition to PPP and IRP, there is one more basic relationship we need to discuss. What is the connection between the forward rate and the expected future spot rate? The unbiased forward rates (UFR) condition says that the forward rate, F1, is equal to the expected future spot rate, E(S1): F1 = E(S1) With t periods, UFR would be written as: Ft = E(St) Loosely, the UFR condition says that, on average, the forward exchange rate is equal to the future spot exchange rate. If we ignore risk, then the UFR condition should hold. Suppose the forward rate for the Japanese yen is consistently lower than the future spot rate by, say, 10 yen. This means that anyone who wanted to convert dollars to yen in the future would consistently get more yen by not agreeing to a forward exchange. The forward rate would have to rise to get anyone interested in a forward exchange. Similarly, if the forward rate were consistently higher than the future spot rate, then anyone who wanted to convert yen to dollars would get more dollars per yen by not agreeing to a forward trade. The forward exchange rate would have to fall to attract such traders. For these reasons, the forward and actual future spot rates should be equal to each other on average. What the future spot rate will actually be is uncertain, of course. The UFR condition may not hold if traders are willing to pay a premium to avoid this uncertainty. If the condition does hold, then the 180-day forward rate that we see today should be an unbiased predictor of what the exchange rate will actually be in 180 days.

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PuttingI tAl lT ogether We have developed three relationships—PPP, IRP, and UFR—that describe the interactions between key financial variables such as interest rates, exchange rates, and inflation rates. We now explore the implications of these relationships as a group. Uncovered Interest Parity To start, it is useful to collect our international financial market relationships in one place: PPP: E(S1) ≅ S0 × [1 + (hFC − hUS)] IRP: F1 ≅ S0 × [1 + (RFC − RUS)] UFR: F1 = E(S1) We begin by combining UFR and IRP. Because we know that F1 = E(S1) from the UFR condition, we can substitute E(S1) for F1 in IRP.4T her esultis: UIP:E (S1) ≅ S0 × [1 + (RFC − RUS)]

(31.8)

This important relationship is called uncovered interest parity (UIP), and it will play a key role in our international capital budgeting discussion that follows. With tp eriods, UIP becomes: E(St) ≅ S0 × [1 + (RFC − RUS)]t

(31.9)

The International Fisher Effect Next we compare PPP and UIP. Both of them have E(S1) on the left side, so their right sides must be equal. We thus have: S0 × [1 + (hFC − hUS)] = S0 × [1 + (RFC − RUS)] hFC − hUS = RFC − RUS This tells us that the difference in returns between the United States and a foreign country is just equal to the difference in inflation rates. Rearranging this slightly gives us the international Fisher effect (IFE): IFE: RUS − hUS = RFC − hFC

(31.10)

The IFE says that real rates are equal across countries.5 The conclusion that real returns are equal across countries is really basic economics. If real returns were higher in, say, Brazil than in the United States, money would flow out of U.S. financial markets and into Brazilian markets. Asset prices in Brazil would rise and their returns would fall. At the same time, asset prices in the United States would fall and their returns would rise. This process acts to equalize real returns. Having said all this, we need to note a couple of things. First, we really haven’t explicitly dealt with risk in our discussion. We might reach a different conclusion about real returns once we do, particularly if people in different countries have different tastes and attitudes toward risk. Second, there are many barriers to the movement of money 4

Here again, we are dealing in an approximation for ease of exposition. The exact equations are: (1 + hFC) PPP:E (S1) = S0 × ________ (1 + hUS)

[ [

] ]

(1 + RFC) IRP: F1 = S0 × _________ (1 + RUS) 5

Notice that our result here is in terms of the approximate real rate, R – h (see Chapter 6), because we used approximations for PPP and IRP. For the exact result, see Problem 18 at the end of the chapter.

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and capital around the world. Real returns might be different in two different countries for long periods if money can’t move freely between them. Despite these problems, we expect that capital markets will become increasingly internationalized. As this occurs, any differences in real rates will probably diminish. The laws of economics have little respect for national boundaries.

31.5 InternationalCap italBudg eting Kihlstrom Equipment, a U.S.-based international company, is evaluating an overseas investment. Kihlstrom’s exports of drill bits have increased to such a degree that it is considering building a distribution center in France. The project will cost 2 million to launch. The cash flows are expected to be .9 million a year for the next three years. The current spot exchange rate for euros is .5. Recall that this is euros per dollar, so a euro is worth $1 .5 = $2. The risk-free rate in the United States is 5 percent, and the risk-free rate in France is 7 percent. Note that the exchange rate and the two interest rates are observed in financial markets, not estimated.6 Kihlstrom’s WACC on dollar investments of this sort is 10 percent.7 Should Kihlstrom take this investment? As always, the answer depends on the NPV; but how do we calculate the net present value of this project in U.S. dollars? There are two basic methods: 1. The home currency approach: Convert all the euro cash flows into dollars, and then discount at 10 percent to find the NPV in dollars. Notice that for this approach we have to come up with the future exchange rates to convert the future projected euro cash flows into dollars. 2. The foreign currency approach: Determine the required return on euro investments, and then discount the euro cash flows to find the NPV in euros. Then convert this euro NPV to a dollar NPV. This approach requires us to somehow convert the 10 percent dollar required return to the equivalent euro required return. The difference between these two approaches is primarily a matter of when we convert from euros to dollars. In the first case, we convert before estimating the NPV. In the second case, we convert after estimating NPV. It might appear that the second approach is superior because for it we have to come up with only one number, the euro discount rate. Furthermore, because the first approach requires us to forecast future exchange rates, it probably seems that there is greater room for error with this approach. As we illustrate next, however, based on our previous results, the two approaches are really the same. 6

For example, the interest rates might be the short-term Eurodollar and euro deposit rates offered by large banks. 7 Kihlstrom’s WACC is determined in the usual way. Suppose that the market values of debt and equity and associated capital costs are: Debt Equity

$500 $500 $1,000

5% 16%

with the corporate tax rate equal to 20 percent. It follows that: S B ______ WACC = ______ B + S R0(1 − TC) + B + S RB 1 1 = __ (5%)(1 − .20) + __ 16% 2 2 = 10%

( )

( )

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Method 1: The Home Currency Approach To convert the project’s future cash flows into dollars, we will invoke the uncovered interest parity, or UIP, relation to come up with the projected exchange rates. Based on our earlier discussion, the expected exchange rate at time t,E (St ),is: E(St) = S0 × [1 + (R − RUS)]t where R stands for the nominal risk-free rate in France. Because R is 7 percent, RUS is 5 percent, and the current exchange rate (S0) is .5: E(St) = .5 × [1 + (.07 − .05)]t = .5 × 1.02t The projected exchange rates for the drill bit project are shown here: Year

Expected Exchange Rate .5 × 1.021 = .5100 .5 × 1.022 = .5202 .5 × 1.023 = .5306

1 2 3

Using these exchange rates, along with the current exchange rate, we can convert all of the euro cash flows to dollars (note that all of the cash flows in this example are in millions):

Year 0 1 2 3

(1)

(2)

Cash Flow in mil

Expected Exchange Rate

− 2.0

.5000 .5100 .5202 .5306

.9 .9 .9

(3) Cash Flow in $mil (1) (2)

−$4.00 1.76 1.73 1.70

To finish off, we calculate the NPV in the ordinary way: NPV$ = −$4 + $1.76 1.10 + $1.73 1.102 + $1.70 1.103 =$.3millio n So, the project appears to be profitable.

Method 2: The Foreign Currency Approach Kihlstrom requires a nominal return of 10 percent on the dollar-denominated cash flows. We need to convert this to a rate suitable for euro-denominated cash flows. Based on the international Fisher effect, we know that the difference in the nominal rates is: R − RUS = h − hUS = 7% − 5% =2% The appropriate discount rate for estimating the euro cash flows from the drill bit project is approximately equal to 10 percent plus an extra 2 percent to compensate for the greater euro inflation rate.

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If we calculate the NPV of the euro cash flows at this rate, we get: NPV = − 2 + .9 1.12 + .9 1.122 + .9 1.123 = .16millio n The NPV of this project is .16 million. Taking this project makes us .16 million richer today. What is this in dollars? Because the exchange rate today is .5, the dollar NPV of the project is: NPV$ = NPV S0 = .16 .5 =$.3millio n This is the same dollar NPV that we previously calculated. The important thing to recognize from our example is that the two capital budgeting procedures are actually the same and will always give the same answer.8 In this second approach, the fact that we are implicitly forecasting exchange rates is simply hidden. Even so, the foreign currency approach is computationally a little easier.

UnremittedCa shF lows The previous example assumed that all aftertax cash flows from the foreign investment could be remitted to (paid out to) the parent firm. Actually, substantial differences can exist between the cash flows generated by a foreign project and the amount that can be remitted, or “repatriated,” to the parent firm. A foreign subsidiary can remit funds to a parent in many forms, including the following: 1. Dividends. 2. Managementf eesf orc entrals ervices. 3. Royalties on the use of trade names and patents. However cash flows are repatriated, international firms must pay special attention to remittances because there may be current and future controls on remittances. Many governments are sensitive to the charge of being exploited by foreign national firms. In such cases, governments are tempted to limit the ability of international firms to remit cash flows. Funds that cannot currently be remitted are sometimes said to be blocked.

The Cost of Capital for International Firms In the previous chapter, we expressed some skepticism concerning the benefits of diversification. We can make a stronger case for diversification in international firms than for purely domestic firms. Suppose barriers prevented shareholders in the United States from holding foreign securities; the financial markets of different countries would be segmented. Further suppose that firms in the United States were not subject to the same barriers. In such a case, a firm engaging in international investing could provide indirect diversification for U.S. shareholders that they could not achieve by investing within the United States. This could lead to the lowering of the risk premium on international projects. In general, if the costs of investing abroad are lower for a firm than for its shareholders, there is an advantage to international diversification by firms, and this advantage will be reflected in a lower riskadjusted discount rate. 8

Actually, there will be a slight difference because we are using the approximate relationships. If we calculate the required return as 1.10 × (1 + .02) − 1 = .122 (12.2%), then we get exactly the same NPV. See Problem 18 for more detail.

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Alternatively, if there were no barriers to international investing for shareholders, shareholders could obtain the benefit of international diversification for themselves by buying foreign securities. In this case, the project cost of capital for a firm in the United States would not depend on whether the project was in the United States or in a foreign country. In practice, holding foreign securities involves substantial expenses. These expenses include taxes, the costs of obtaining information, and trading costs. This implies that although U.S. investors are free to hold foreign securities, they will not be perfectly internationally diversified. Firms may determine that international investments inherently involve more political risk than domestic investments. This extra risk may offset the gains from international diversification. Firms may increase the discount rate to allow for the risk of expropriation and foreign exchange remittance controls.

31.6 Exchange RateR isk Exchange rate risk is the natural consequence of international operations in a world where relative currency values move up and down. Managing exchange rate risk is an important part of international finance. As we discuss next, there are three different types of exchange rate risk or exposure: Short-term exposure, long-term exposure, and translation exposure.

Short-TermE xposure The day-to-day fluctuations in exchange rates create short-term risks for international firms. Most such firms have contractual agreements to buy and sell goods in the near future at set prices. When different currencies are involved, such transactions have an extra element of risk. For example, imagine that you are importing imitation pasta from Italy and reselling it in the United States under the Impasta brand name. Your largest customer has ordered 10,000 cases of Impasta. You place the order with your supplier today, but you won’t pay until the goods arrive in 60 days. Your selling price is $6 per case. Your cost is 8.4 euros per case, and the exchange rate is currently 1.50, so it takes 1.50 euros to buy $1. At the current exchange rate, your cost in dollars of filling the order is 8.4 1.5 = $5.60 per case, so your pretax profit on the order is 10,000 × ($6 − 5.60) = $4,000. However, the exchange rate in 60 days will probably be different, so your profit will depend on what the future exchange rate turns out to be. For example, if the rate goes to 1.6, your cost is 8.4 1.6 = $5.25 per case. Your profit goes to $7,500. If the exchange rate goes to, say, 1.4, then your cost is 8.4 1.4 = $6, and your profit is zero. The short-term exposure in our example can be reduced or eliminated in several ways. The most obvious way is by entering into a forward exchange agreement to lock in an exchange rate. For example, suppose the 60-day forward rate is 1.58. What will be your profit if you hedge? What profit should you expect if you don’t? If you hedge, you lock in an exchange rate of 1.58. Your cost in dollars will thus be 8.4 1.58 = $5.32 per case, so your profit will be 10,000 × ($6 − 5.32) = $6,800. If you don’t hedge, then, assuming that the forward rate is an unbiased predictor (in other words, assuming the UFR condition holds), you should expect that the exchange rate will actually be 1.58 in 60 days. You should expect to make $6,800. Alternatively, if this strategy is not feasible, you could simply borrow the dollars today, convert them into euros, and invest the euros for 60 days to earn some interest. Based on IRP, this amounts to entering into a forward contract.

In Their Own Words RICHARD M. LEVICH ON FORWARD EXCHANGE RATES What is the relationship between today’s three-month forward exchange rate, which can be observed in the market, and the spot exchange rate of three months from today, which cannot be observed until the future? One popular answer is that there is no relationship. As every bank trader knows, the possibility of covered interest arbitrage between domestic and foreign securities establishes a close link between the forward premium and the interest rate differential. At any moment, a trader can check a screen and observe that the forward premium and the interest rate differentials are nearly identical, especially when Eurocurrency interest rates are used. Thus, the trader might say, “The forward rate reflects today’s interest differential. It has nothing to do with expectations.” To check the second popular belief, that the forward rate reflects exchange rate expectations, takes a bit more work. Take today’s three-month forward rate as of January 15 and compare it to the spot exchange rate that actually exists three months later on April 15. This produces one observation of the forward rate as a forecaster—not enough to accept or reject a theory. The idea that the forward rate might be an unbiased predictor of the future spot rate suggests that, on average and looking at many observations, the prediction error is small. So collect more data using the forward rate of

April 15 and match it with the spot rate of July 15, and then the forward rate of July 15 matched to the spot rate of October 15, and so on. Look at the data for 8–10 years to have a large sample of observations. The data suggest that in the early 1980s when the dollar was very strong, the forward rate significantly underestimated the strength of the dollar, and the forward rate was a biased predictor. But from 1985 to 1987 when the dollar depreciated sharply, the forward rate tended to overestimate the strength of the dollar, and the forward rate was again a biased predictor, but with the opposite sign as the earlier period. Looking at all of the 1980s—you guessed it—the forward rate was on average very close to the future spot exchange rate. There are two messages here. First, even if there were “no relationship” between the forward rate and the future spot rate, the treasurer of General Motors would want to know exactly what that “nonrelationship” was. Because if the forward rate were consistently 3 percent higher than, or consistently 5 percent lower than, the future spot rate, the treasurer would be facing a tantalizing profit opportunity. A watch that is three minutes fast or five minutes slow is a very useful watch as long as the bias is known and consistent. Richard M. Levich is Professor of Finance and International Business at New York University. He has written extensively on exchange rates and other issues in international economics and finance.

Long-TermE xposure In the long term, the value of a foreign operation can fluctuate because of unanticipated changes in relative economic conditions. For example, imagine that we own a labor-intensive assembly operation located in another country to take advantage of lower wages. Through time, unexpected changes in economic conditions can raise the foreign wage levels to the point where the cost advantage is eliminated or even becomes negative. The impact of changes in exchange rate levels can be substantial. For example, during 2005, the U.S. dollar continued to weaken against other currencies. This meant domestic manufacturers took home more for each dollar’s worth of sales they made, which can lead to big profit swings. For example, during 2005, PepsiCo estimated that it gained about $251 million due to currency swings. The dramatic effect of exchange rate movements on profitability is also shown by the analysis done by Iluka Resources, Ltd., an Australian mining company, which stated that a one-cent movement in the Australian dollar–U.S. dollar exchange rate would change its net income by $5 million. Hedging long-term exposure is more difficult than hedging short-term risks. For one thing, organized forward markets don’t exist for such long-term needs. Instead, the primary option that firms have is to try to match up foreign currency inflows and 953

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outflows. The same thing goes for matching foreign currency–denominated assets and liabilities. For example, a firm that sells in a foreign country might try to concentrate its raw material purchases and labor expenses in that country. That way, the dollar values of its revenues and costs will move up and down together. Probably the best examples of this type of hedging are the so-called transplant auto manufacturers such as BMW, Honda, Mercedes, and Toyota, which now build a substantial portion of the cars they sell in the United States at plants located in the United States, thereby obtaining some degree of immunization against exchange rate movements. For example, BMW produces 160,000 cars in South Carolina and exports about 100,000 of them. The costs of manufacturing the cars are paid mostly in dollars, and, when BMW exports the cars to Europe, it receives euros. When the dollar weakens, these vehicles become more profitable for BMW. At the same time, BMW exports about 217,000 cars to the United States each year. The costs of manufacturing these imported cars are mostly in euros, so they become less profitable when the dollar weakens. Taken together, these gains and losses tend to offset each other and give BMW a natural hedge. Similarly, a firm can reduce its long-term exchange rate risk by borrowing in the foreign country. Fluctuations in the value of the foreign subsidiary’s assets will then be at least partially offset by changes in the value of the liabilities.

TranslationE xposure When a U.S. company calculates its accounting net income and EPS for some period, it must translate everything into dollars. This can create some problems for the accountants when there are significant foreign operations. In particular, two issues arise: 1. What is the appropriate exchange rate to use for translating each balance sheet account? 2. How should balance sheet accounting gains and losses from foreign currency translationb eh andled? To illustrate the accounting problem, suppose we started a small foreign subsidiary in Lilliputia a year ago. The local currency is the gulliver, abbreviated GL. At the beginning of the year, the exchange rate was GL 2 = $1, and the balance sheet in gullivers looked like this: Assets

GL 1,000

Liabilities Equity

GL 500 500

At 2 gullivers to the dollar, the beginning balance sheet in dollars was as follows: Assets

$500

Liabilities Equity

$250 250

Lilliputia is a quiet place, and nothing at all actually happened during the year. As a result, net income was zero (before consideration of exchange rate changes). However, the exchange rate did change to 4 gullivers = $1 purely because the Lilliputian inflation rate is much higher than the U.S. inflation rate. Because nothing happened, the accounting ending balance sheet in gullivers is the same as the beginning one. However, if we convert it to dollars at the new exchange rate, we get these figures: Assets

$250

Liabilities Equity

$125 125

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Notice that the value of the equity has gone down by $125, even though net income was exactly zero. Despite the fact that absolutely nothing happened, there is a $125 accounting loss. How to handle this $125 loss has been a controversial accounting question. One obvious and consistent way to handle this loss is simply to report the loss on the parent’s income statement. During periods of volatile exchange rates, this kind of treatment can dramatically impact an international company’s reported EPS. This is purely an accounting phenomenon, but even so, such fluctuations are disliked by some financial managers. The current approach to handling translation gains and losses is based on rules set out in the Financial Accounting Standards Board (FASB) Statement of Financial Accounting Standards No. 52 (FASB 52), issued in December 1981. For the most part, FASB 52 requires that all assets and liabilities be translated from the subsidiary’s currency into the parent’s currency using the exchange rate that currently prevails. Any translation gains and losses that occur are accumulated in a special account within the shareholders’ equity section of the balance sheet. This account might be labeled something like “unrealized foreign exchange gains (losses).” The amounts involved can be substantial, at least from an accounting standpoint. These gains and losses are not reported on the income statement. As a result, the impact of translation gains and losses will not be recognized explicitly in net income until the underlying assets and liabilities are sold or otherwise liquidated.

ManagingE xchangeR ateR isk For a large multinational firm, the management of exchange rate risk is complicated by the fact that there can be many different currencies involved in many different subsidiaries. It is likely that a change in some exchange rate will benefit some subsidiaries and hurt others. The net effect on the overall firm depends on its net exposure. For example, suppose a firm has two divisions. Division A buys goods in the United States for dollars and sells them in Britain for pounds. Division B buys goods in Britain for pounds and sells them in the United States for dollars. If these two divisions are of roughly equal size in terms of their inflows and outflows, then the overall firm obviously has little exchange rate risk. In our example, if the firm’s net position in pounds (the amount coming in less the amount going out) is small, the exchange rate risk is small. However, if one division, acting on its own, were to start hedging its exchange rate risk, then the overall firm’s exchange rate risk would go up. The moral of the story is that multinational firms have to be conscious of the overall position that the firm has in a foreign currency. For this reason, management of exchange rate risk is probably best handled on a centralized basis.

31.7 Political Risk One final element of risk in international investing is political risk: Changes in value that arise as a consequence of political actions. This is not a problem faced exclusively by international firms. For example, changes in U.S. tax laws and regulations may benefit some U.S. firms and hurt others, so political risk exists nationally as well as internationally.

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Some countries have more political risk than others, however. When firms have operations in these riskier countries, the extra political risk may lead the firms to require higher returns on overseas investments to compensate for the possibility that funds may be blocked, critical operations interrupted, and contracts abrogated. In the most extreme case, the possibility of outright confiscation may be a concern in countries with relatively unstable political environments. Political risk also depends on the nature of the business: Some businesses are less likely to be confiscated because they are not particularly valuable in the hands of a different owner. An assembly operation supplying subcomponents that only the parent company uses would not be an attractive takeover target, for example. Similarly, a manufacturing operation that requires the use of specialized components from the parent is of little value without the parent company’s cooperation. Natural resource developments, such as copper mining and oil drilling, are just the opposite. Once the operation is in place, much of the value is in the commodity. The political risk for such investments is much higher for this reason. Also, the issue of exploitation is more pronounced with such investments, again increasing the political risk. Political risk can be hedged in several ways, particularly when confiscation or nationalization is a concern. The use of local financing, perhaps from the government of the foreign country in question, reduces the possible loss because the company can refuse to pay the debt in the event of unfavorable political activities. Based on our discussion in this section, structuring the operation in such a way that it requires significant parent company involvement to function is another way to reduce political risk.

www.mhhe.com/rwj

Summary and Conclusions

The international firm has a more complicated life than the purely domestic firm. Management must understand the connection between interest rates, foreign currency exchange rates, and inflation, and it must become aware of many different financial market regulations and tax systems. This chapter is intended to be a concise introduction to some of the financial issues that come up in international finance. Our coverage has been necessarily brief. The main topics we discussed are the following: 1. Some basic vocabulary: We briefly defined some exotic terms such as LIBOR and Eurocurrency. 2. The basic mechanics of exchange rate quotations: We discussed the spot and forward markets and how exchange rates are interpreted. 3. The fundamental relationships between international financial variables: a. Absolute and relative purchasing power parity, PPP. b. Interestr atep arity,I RP. c. Unbiasedf orwardr ates,UF R. Absolute purchasing power parity states that $1 should have the same purchasing power in each country. This means that an orange costs the same whether you buy it in New York or in Tokyo. Relative purchasing power parity means that the expected percentage change in exchange rates between the currencies of two countries is equal to the difference in their inflation rates. Interest rate parity implies that the percentage difference between the forward exchange rate and the spot exchange rate is equal to the interest rate differential. We showed how covered interest arbitrage forces this relationship to hold.

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The unbiased forward rates condition indicates that the current forward rate is a good predictor of the future spot exchange rate. 4. International capital budgeting: We showed that the basic foreign exchange relationships imply two other conditions: a. Uncoveredin terestp arity. b. Thein ternationalF ishere ffect. By invoking these two conditions, we learned how to estimate NPVs in foreign currencies and how to convert foreign currencies into dollars to estimate NPV in the usual way. 5. Exchange rate and political risk: We described the various types of exchange rate risk and discussed some common approaches to managing the effect of fluctuating exchange rates on the cash flows and value of the international firm. We also discussed political risk and some ways of managing exposure to it.

Concept Questions

1.

3.

4. 5.

6.

7.

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2.

Spot and Forward Rates Suppose the exchange rate for the Swiss franc is quoted as SF 1.50 in the spot market and SF 1.53 in the 90-day forward market. a. Is the dollar selling at a premium or a discount relative to the franc? b. Does the financial market expect the franc to strengthen relative to the dollar? Explain. c. What do you suspect is true about relative economic conditions in the United Statesan dS witzerland? Purchasing Power Parity Suppose the rate of inflation in Mexico will run about 3 percent higher than the U.S. inflation rate over the next several years. All other things being the same, what will happen to the Mexican peso versus dollar exchange rate? What relationship are you relying on in answering? Exchange Rates The exchange rate for the Australian dollar is currently A$1.40. This exchange rate is expected to rise by 10 percent over the next year. a. Is the Australian dollar expected to get stronger or weaker? b. What do you think about the relative inflation rates in the United States and Australia? c. What do you think about the relative nominal interest rates in the United States andA ustralia?R elativer ealr ates? Exchange Rates Are exchange rate changes necessarily good or bad for a particular company? International Risks At one point, Duracell International confirmed that it was planning to open battery manufacturing plants in China and India. Manufacturing in these countries allows Duracell to avoid import duties of between 30 and 35 percent that have made alkaline batteries prohibitively expensive for some consumers. What additional advantages might Duracell see in this proposal? What are some of the risks to Duracell? Multinational Corporations Given that many multinationals based in many countries have much greater sales outside their domestic markets than within them, what is the particular relevance of their domestic currency? Exchange Rate Movements Are the following statements true or false? Explain why. a. If the general price index in Great Britain rises faster than that in the United States, we would expect the pound to appreciate relative to the dollar. b. Suppose you are a German machine tool exporter, and you invoice all of your sales in foreign currency. Further suppose that the euro monetary authorities begin to undertake an expansionary monetary policy. If it is certain that the easy money policy will result in higher inflation rates in Germany relative to those in other countries, then you should use the forward markets to protect yourself against future losses resulting from the deterioration in the value of the euro.

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Part VIII

8.

9.

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10.

11.

12.

13. 14.

Questions and Problems BASIC (Questions1–1 3)

1.

Special Topics

c. If you could accurately estimate differences in the relative inflation rates of two countries over a long period while other market participants were unable to do so, you could successfully speculate in spot currency markets. Exchange Rate Movements Some countries encourage movements in their exchange rate relative to those of some other country as a short-term means of addressing foreign trade imbalances. For each of the following scenarios, evaluate the impact the announcement would have on an American importer and an American exporter doing business with the foreign country: a. Officials in the administration of the U.S. government announce that they are comfortable with a rising euro relative to the dollar. b. British monetary authorities announce that they feel the pound has been driven too low by currency speculators relative to the dollar. c. The Brazilian government announces that it will print billions of new reais and inject them into the economy in an effort to reduce the country’s unemployment rate. International Capital Market Relationships We discussed five international capital market relationships: Relative PPP, IRP, UFR, UIP, and the international Fisher effect. Which of these would you expect to hold most closely? Which do you think would be most likely to be violated? Exchange Rate Risk If you are an exporter who must make payments in foreign currency three months after receiving each shipment and you predict that the domestic currency will appreciate in value over this period, is there any value in hedging your currency exposure? International Capital Budgeting Suppose it is your task to evaluate two different investments in new subsidiaries for your company, one in your own country and the other in a foreign country. You calculate the cash flows of both projects to be identical after exchange rate differences. Under what circumstances might you choose to invest in the foreign subsidiary? Give an example of a country where certain factors might influence you to alter this decision and invest at home. International Capital Budgeting An investment in a foreign subsidiary is estimated to have a positive NPV after the discount rate used in the calculations is adjusted for political risk and any advantages from diversification. Does this mean the project is acceptable? Why or why not? International Borrowing If a U.S. firm raises funds for a foreign subsidiary, what are the disadvantages to borrowing in the United States? How would you overcome them? International Investment If financial markets are perfectly competitive and the Eurodollar rate is above that offered in the U.S. loan market, you would immediately want to borrow money in the United States and invest it in Eurodollars. True or false? Explain.

Using Exchange Rates Take a look back at Figure 31.1 to answer the following questions: a. If you have $100, how many euros can you get? b. How much is one euro worth? c. If you have 5 million euros, how many dollars do you have? d. Which is worth more, a New Zealand dollar or a Singapore dollar? e. Which is worth more, a Mexican peso or a Chilean peso? f. How many Mexican pesos can you get for a euro? What do you call this rate? g. Per unit, what is the most valuable currency of those listed? The least valuable?

Chapter 31 International Corporate Finance

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3.

959

Using the Cross-Rate Use the information in Figure 31.1 to answer the following questions: a. Which would you rather have, $100 or £100? Why? b. Which would you rather have, 100 Swiss francs (SF) or £100? Why? c. What is the cross-rate for Swiss francs in terms of British pounds? For British pounds in terms of Swiss francs? Forward Exchange Rates Use the information in Figure 31.1 to answer the followingq uestions: a. What is the six-month forward rate for the Japanese yen in yen per U.S. dollar? Is the yen selling at a premium or a discount? Explain. b. What is the three-month forward rate for British pounds in U.S. dollars per pound? Is the dollar selling at a premium or a discount? Explain. c. What do you think will happen to the value of the dollar relative to the yen and the pound, based on the information in the figure? Explain. Using Spot and Forward Exchange Rates Suppose the spot exchange rate for the Canadian dollar is Can$1.18 and the six-month forward rate is Can$1.13. a. Which is worth more, a U.S. dollar or a Canadian dollar? b. Assuming absolute PPP holds, what is the cost in the United States of an Elkhead beer if the price in Canada is Can$2.19? Why might the beer actually sell at a different price in the United States? c. Is the U.S. dollar selling at a premium or a discount relative to the Canadian dollar? d. Which currency is expected to appreciate in value? e. Which country do you think has higher interest rates—the United States or Canada?E xplain.

5.

Cross-Rates and Arbitrage Suppose the Japanese yen exchange rate is ¥110 = $1, and the British pound exchange rate is £1 =$1.65. a. What is the cross-rate in terms of yen per pound? b. Suppose the cross-rate is ¥183 = £1. Is there an arbitrage opportunity here? If there is, explain how to take advantage of the mispricing.

6.

Interest Rate Parity Use Figure 31.1 to answer the following questions. Suppose interest rate parity holds, and the current six-month risk-free rate in the United States is 2.6 percent. What must the six-month risk-free rate be in Great Britain? In Japan? In Switzerland?

7.

Interest Rates and Arbitrage The treasurer of a major U.S. firm has $30 million to invest for three months. The annual interest rate in the United States is .25 percent per month. The interest rate in Great Britain is .41 percent per month. The spot exchange rate is £.54, and the three-month forward rate is £.53. Ignoring transaction costs, in which country would the treasurer want to invest the company’s funds? Why?

8.

Inflation and Exchange Rates Suppose the current exchange rate for the Polish zloty is Z 4.27. The expected exchange rate in three years is Z 4.51. What is the difference in the annual inflation rates for the United States and Poland over this period? Assume that the anticipated rate is constant for both countries. What relationship are you relying on in answering?

9.

Exchange Rate Risk Suppose your company imports computer motherboards from Singapore. The exchange rate is given in Figure 31.1. You have just placed an order for 30,000 motherboards at a cost to you of 168.5 Singapore dollars each. You will pay for the shipment when it arrives in 90 days. You can sell the motherboards for $125 each. Calculate your profit if the exchange rate goes up or down by 10 percent over the next 90 days. What is the break-even exchange rate? What percentage rise or fall does this represent in terms of the Singapore dollar versus the U.S. dollar?

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4.

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Part VIII

10.

11.

12.

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13.

INTERMEDIATE (Questions1 4–16)

14.

15.

16.

CHALLENGE (Questions1 7–18)

17.

Special Topics

Exchange Rates and Arbitrage Suppose the spot and six-month forward rates on the Norwegian krone are Kr 6.84 and Kr 6.96, respectively. The annual risk-free rate in the United States is 4 percent, and the annual risk-free rate in Norway is 7 percent. a. Is there an arbitrage opportunity here? If so, how would you exploit it? b. What must the six-month forward rate be to prevent arbitrage? The International Fisher Effect You observe that the inflation rate in the United States is 2.5 percent per year and that T-bills currently yield 4.1 percent annually. What do you estimate the inflation rate to be in: a. Australia if short-term Australian government securities yield 4 percent per year? b. Canada if short-term Canadian government securities yield 6 percent per year? c. Taiwan if short-term Taiwanese government securities yield 9 percent per year? Spot versus Forward Rates Suppose the spot and three-month forward rates for the yen are ¥118.15 and ¥116.32, respectively. a. Is the yen expected to get stronger or weaker? b. What would you estimate is the difference between the inflation rates of the UnitedS tatesan dJ apan? Expected Spot Rates Suppose the spot exchange rate for the Hungarian forint is HUF 209. The inflation rate in the United States is 3.5 percent per year and is 5.7 percent in Hungary. What do you predict the exchange rate will be in one year? In two years? In five years? What relationship are you using? Capital Budgeting Lakonishok Equipment has an investment opportunity in Europe. The project costs 18 million and is expected to produce cash flows of 3.6 million in year 1, 4.1 million in year 2, and 5.1 million in year 3. The current spot exchange rate is $1.22/ and the current risk-free rate in the United States is 4.8 percent, compared to that in Europe of 4.1 percent. The appropriate discount rate for the project is estimated to be 13 percent, the U.S. cost of capital for the company. In addition, the subsidiary can be sold at the end of three years for an estimated 12.2 million. What is the NPV of the project? Capital Budgeting You are evaluating a proposed expansion of an existing subsidiary located in Switzerland. The cost of the expansion would be SF 25 million. The cash flows from the project would be SF 7.2 million per year for the next five years. The dollar required return is 13 percent per year, and the current exchange rate is SF 1.72. The going rate on Eurodollars is 8 percent per year. It is 7 percent per year on Swiss francs. a. What do you project will happen to exchange rates over the next four years? b. Based on your answer in (a), convert the projected franc flows into dollar flows and calculate the NPV. c. What is the required return on franc flows? Based on your answer, calculate the NPV in francs and then convert to dollars. Translation Exposure Atreides International has operations in Arrakis. The balance sheet for this division in Arrakeen solaris shows assets of 23,000 solaris, debt in the amount of 9,000 solaris, and equity of 14,000 solaris. a. If the current exchange ratio is 1.20 solaris per dollar, what does the balance sheet look like in dollars? b. Assume that one year from now the balance sheet in solaris is exactly the same as at the beginning of the year. If the exchange rate is 1.40 solaris per dollar, what does the balance sheet look like in dollars now? c. Rework part (b) assuming the exchange rate is 1.12 solaris per dollar. Translation Exposure In the previous problem, assume the equity increases by 1,250 solaris due to retained earnings. If the exchange rate at the end of the year is 1.24 solaris per dollar, what does the balance sheet look like?

Chapter 31 International Corporate Finance

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Using the Exact International Fisher Effect From our discussion of the Fisher effect in Chapter 6, we know that the actual relationship between a nominal rate, R, a real rate, r, and an inflation rate, h, can be written as follows:

1 + r = (1 + R) (1 + h)

S&P Problem

www.mhhe.com/edumarketinsight 1. American Depositary Receipts Nestlé S. A. has American depositary receipts listed on the over-the-counter market. Many ADRs listed on U.S. exchanges are for fractional shares. In the case of Nestlé, four ADRs are equal to one registered share of stock. Find the information for Nestlé using the ticker symbol “3NSRGY.” a. Click on the “Mthly. Adj. Prices” link and find Nestlé’s closing price for December 2008. Assume the exchange rate on that day was $/SF = 1.216 and Nestlé shares traded for SF 43.53. Is there an arbitrage opportunity available? If so, how would you take advantage of it? b. What exchange rate is necessary to eliminate the arbitrage opportunity available in( a)? c. Dividend payments made to ADR shareholders are in U.S. dollars. Suppose you own 90 Nestlé ADRs. Assume the current exchange rate is the rate you calculated in (b). Nestlé declares a dividend of SF 1.15. What U.S. dollar dividend payment willy our eceive?

Mini Case

EAST COAST YACHTS GOES INTERNATIONAL Larissa Warren, the owner of East Coast Yachts, has been in discussions with a yacht dealer in Monaco about selling the company’s yachts in Europe. Jarek Jachowicz, the dealer, wants to add East Coast Yachts to his current retail line. Jarek has told Larissa that he feels the retail sales will be approximately 8 million per month. All sales will be made in euros, and Jarek will retain 5 percent of the retail sales as commission, which will be paid in euros. Because the yachts will be customized to order, the first sales will take place in one month. Jarek will pay East Coast Yachts for the order 90 days after it is filled. This payment schedule will continue for the length of the contract between the two companies. Larissa is confident the company can handle the extra volume with its existing facilities, but she is unsure about any potential financial risks of selling yachts in Europe. In her discussion with Jarek she found that the current exchange rate is $1.45/ . At this exchange rate the company would spend 80 percent of the sales income on production costs. This number does not reflect the sales commission to be paid to Jarek. Larissa has decided to ask Dan Ervin, the company’s financial analyst, to prepare an analysis of the proposed international sales. Specifically, she asks Dan to answer the followingq uestions: 1. What are the pros and cons of the international sales plan? What additional risks will the company face? 2. What will happen to the company’s profits if the dollar strengthens? What if the dollar weakens?

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This is the domesticF ishere ffect. a. What is the nonapproximate form of the international Fisher effect? b. Based on your answer in (a), what is the exact form for UIP? (Hint: Recall the exact form of IRP and use UFR.) c. What is the exact form for relative PPP? (Hint: Combine your previous two answers.) d. Recalculate the NPV for the Kihlstrom drill bit project (discussed in Section 31.5) using the exact forms for the UIP and the international Fisher effect. Verify that you getp reciselyt hes amean swere itherw ay.

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Special Topics

3. Ignoring taxes, what are East Coast Yacht’s projected gains or losses from this proposed arrangement at the current exchange rate of $1.45/ ? What will happen to profits if the exchange rate changes to $1.30/ ? At what exchange rate will the company breake ven? 4. How can the company hedge its exchange rate risk? What are the implications for this approach? 5. Taking all factors into account, should the company pursue international sales further?W hyo rw hyn ot?

Appendix A Mathematical Tables

Table A.1 Present Value of $1 to Be Received after T Periods = 1 (1 + r)T Table A.2 Present Value of an Annuity of $1 per Period for T Periods = [1 − 1 (1 + r)T ] r Table A.3 Future Value of $1 at the End of T Periods = (1 + r)T Table A.4 Future Value of an Annuity of $1 per Period for T Periods = [(1 + r)T −1] r Table A.5 Future Value of $1 with a Continuously Compounded Rate r for T Periods: Values of e rT Table A.6 Present Value of $1 with a Continuous Discount Rate r for T Periods: Values of e−rT

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Table A.1

Present Value of $1 to Be Received after T Periods = 1 (1 + r )T Interest Rate

Period

1%

2%

3%

4%

5%

6%

7%

8%

9%

1 2 3 4 5

.9901 .9803 .9706 .9610 .9515

.9804 .9612 .9423 .9238 .9057

.9709 .9426 .9151 .8885 .8626

.9615 .9246 .8890 .8548 .8219

.9524 .9070 .8638 .8227 .7835

.9434 .8900 .8396 .7921 .7473

.9346 .8734 .8163 .7629 .7130

.9259 .8573 .7938 .7350 .6806

.9174 .8417 .7722 .7084 .6499

6 7 8 9 10

.9420 .9327 .9235 .9143 .9053

.8880 .8706 .8535 .8368 .8203

.8375 .8131 .7894 .7664 .7441

.7903 .7599 .7307 .7026 .6756

.7462 .7107 .6768 .6446 .6139

.7050 .6651 .6274 .5919 .5584

.6663 .6227 .5820 .5439 .5083

.6302 .5835 .5403 .5002 .4632

.5963 .5470 .5019 .4604 .4224

11 12 13 14 15

.8963 .8874 .8787 .8700 .8613

.8043 .7885 .7730 .7579 .7430

.7224 .7014 .6810 .6611 .6419

.6496 .6246 .6006 .5775 .5553

.5847 .5568 .5303 .5051 .4810

.5268 .4970 .4688 .4423 .4173

.4751 .4440 .4150 .3878 .3624

.4289 .3971 .3677 .3405 .3152

.3875 .3555 .3262 .2992 .2745

16 17 18 19 20

.8528 .8444 .8360 .8277 .8195

.7284 .7142 .7002 .6864 .6730

.6232 .6050 .5874 .5703 .5537

.5339 .5134 .4936 .4746 .4564

.4581 .4363 .4155 .3957 .3769

.3936 .3714 .3503 .3305 .3118

.3387 .3166 .2959 .2765 .2584

.2919 .2703 .2502 .2317 .2145

.2519 .2311 .2120 .1945 .1784

21 22 23 24 25

.8114 .8034 .7954 .7876 .7798

.6598 .6468 .6342 .6217 .6095

.5375 .5219 .5067 .4919 .4776

.4388 .4220 .4057 .3901 .3751

.3589 .3418 .3256 .3101 .2953

.2942 .2775 .2618 .2470 .2330

.2415 .2257 .2109 .1971 .1842

.1987 .1839 .1703 .1577 .1460

.1637 .1502 .1378 .1264 .1160

30 40 50

.7419 .6717 .6080

.5521 .4529 .3715

.4120 .3066 .2281

.3083 .2083 .1407

.2314 .1420 .0872

.1741 .0972 .0543

.1314 .0668 .0339

.0994 .0460 .0213

.0754 .0318 .0134

Period

10%

12%

14%

15%

16%

18%

20%

24%

28%

32%

36%

1 2 3 4 5

.9091 .8264 .7513 .6830 .6209

.8929 .7972 .7118 .6355 .5674

.8772 .7695 .6750 .5921 .5194

.8696 .7561 .6575 .5718 .4972

.8621 .7432 .6407 .5523 .4761

.8475 .7182 .6086 .5158 .4371

.8333 .6944 .5787 .4823 .4019

.8065 .6504 .5245 .4230 .3411

.7813 .6104 .4768 .3725 .2910

.7576 .5739 .4348 .3294 .2495

.7353 .5407 .3975 .2923 .2149

6 7 8 9 10

.5645 .5132 .4665 .4241 .3855

.5066 .4523 .4039 .3606 .3220

.4556 .3996 .3506 .3075 .2697

.4323 .3759 .3269 .2843 .2472

.4104 .3538 .3050 .2630 .2267

.3704 .3139 .2660 .2255 .1911

.3349 .2791 .2326 .1938 .1615

.2751 .2218 .1789 .1443 .1164

.2274 .1776 .1388 .1084 .0847

.1890 .1432 .1085 .0822 .0623

.1580 .1162 .0854 .0628 .0462

11 12 13 14 15

.3505 .3186 .2897 .2633 .2394

.2875 .2567 .2292 .2046 .1827

.2366 .2076 .1821 .1597 .1401

.2149 .1869 .1625 .1413 .1229

.1954 .1685 .1452 .1252 .1079

.1619 .1372 .1163 .0985 .0835

.1346 .1122 .0935 .0779 .0649

.0938 .0757 .0610 .0492 .0397

.0662 .0517 .0404 .0316 .0247

.0472 .0357 .0271 .0205 .0155

.0340 .0250 .0184 .0135 .0099

16 17 18 19 20

.2176 .1978 .1799 .1635 .1486

.1631 .1456 .1300 .1161 .1037

.1229 .1078 .0946 .0829 .0728

.1069 .0929 .0808 .0703 .0611

.0930 .0802 .0691 .0596 .0514

.0708 .0600 .0508 .0431 .0365

.0541 .0451 .0376 .0313 .0261

.0320 .0258 .0208 .0168 .0135

.0193 .0150 .0118 .0092 .0072

.0118 .0089 .0068 .0051 .0039

.0073 .0054 .0039 .0029 .0021

21 22 23 24 25

.1351 .1228 .1117 .1015 .0923

.0926 .0826 .0738 .0659 .0588

.0638 .0560 .0491 .0431 .0378

.0531 .0462 .0402 .0349 .0304

.0443 .0382 .0329 .0284 .0245

.0309 .0262 .0222 .0188 .0160

.0217 .0181 .0151 .0126 .0105

.0109 .0088 .0071 .0057 .0046

.0056 .0044 .0034 .0027 .0021

.0029 .0022 .0017 .0013 .0010

.0016 .0012 .0008 .0006 .0005

30 40 50

.0573 .0221 .0085

.0334 .0107 .0035

.0196 .0053 .0014

.0151 .0037 .0009

.0116 .0026 .0006

.0070 .0013 .0003

.0042 .0007 .0001

.0016 .0002 *

.0006 .0001 *

.0002 * *

.0001 * *

* The factor is zero to four decimal places.

Table A.2

Present Value of an Annuity of $1 per Period for T Periods = [1 − 1 (1 + r)T ] r Interest Rate

Number of Periods

1%

2%

3%

4%

5%

6%

7%

8%

9%

1 2 3 4 5

.9901 1.9704 2.9410 3.9020 4.8534

.9804 1.9416 2.8839 3.8077 4.7135

.9709 1.9135 2.8286 3.7171 4.5797

.9615 1.8861 2.7751 3.6299 4.4518

.9524 1.8594 2.7232 3.5460 4.3295

.9434 1.8334 2.6730 3.4651 4.2124

.9346 1.8080 2.6243 3.3872 4.1002

.9259 1.7833 2.5771 3.3121 3.9927

.9174 1.7591 2.5313 3.2397 3.8897

6 7 8 9 10

5.7955 6.7282 7.6517 8.5660 9.4713

5.6014 6.4720 7.3255 8.1622 8.9826

5.4172 6.2303 7.0197 7.7861 8.5302

5.2421 6.0021 6.7327 7.4353 8.1109

5.0757 5.7864 6.4632 7.1078 7.7217

4.9173 5.5824 6.2098 6.8017 7.3601

4.7665 5.3893 5.9713 6.5152 7.0236

4.6229 5.2064 5.7466 6.2469 6.7101

4.4859 5.0330 5.5348 5.9952 6.4177

11 12 13 14 15

10.3676 11.2551 12.1337 13.0037 13.8651

9.7868 10.5753 11.3484 12.1062 12.8493

9.2526 9.9540 10.6350 11.2961 11.9379

8.7605 9.3851 9.9856 10.5631 11.1184

8.3064 8.8633 9.3936 9.8986 10.3797

7.8869 8.3838 8.8527 9.2950 9.7122

7.4987 7.9427 8.3577 8.7455 9.1079

7.1390 7.5361 7.9038 8.2442 8.5595

6.8052 7.1607 7.4869 7.7862 8.0607

16 17 18 19 20

14.7179 15.5623 16.3983 17.2260 18.0456

13.5777 14.2919 14.9920 15.6785 16.3514

12.5611 13.1661 13.7535 14.3238 14.8775

11.6523 12.1657 12.6593 13.1339 13.5903

10.8378 11.2741 11.6896 12.0853 12.4622

10.1059 10.4773 10.8276 11.1581 11.4699

9.4466 9.7632 10.0591 10.3356 10.5940

8.8514 9.1216 9.3719 9.6036 9.8181

8.3126 8.5436 8.7556 8.9501 9.1285

21 22 23 24 25

18.8570 19.6604 20.4558 21.2434 22.0232

17.0112 17.6580 18.2922 18.9139 19.5235

15.4150 15.9369 16.4436 16.9355 17.4131

14.0292 14.4511 14.8568 15.2470 15.6221

12.8212 13.1630 13.4886 13.7986 14.0939

11.7641 12.0416 12.3034 12.5504 12.7834

10.8355 11.0612 11.2722 11.4693 11.6536

10.0168 10.2007 10.3741 10.5288 10.6748

9.2922 9.4424 9.5802 9.7066 9.8226

30 40 50

25.8077 32.8347 39.1961

22.3965 27.3555 31.4236

19.6004 23.1148 25.7298

17.2920 19.7928 21.4822

15.3725 17.1591 18.2559

13.7648 15.0463 15.7619

12.4090 13.3317 13.8007

11.2578 11.9246 12.2335

10.2737 10.7574 10.9617

Number of Periods

10%

12%

14%

15%

16%

18%

20%

24%

28%

32%

1 2 3 4 5

.9091 1.7355 2.4869 3.1699 3.7908

.8929 1.6901 2.4018 3.0373 3.6048

.8772 1.6467 2.3216 2.9137 3.4331

.8696 1.6257 2.2832 2.8550 3.3522

.8621 1.6052 2.2459 2.7982 3.2743

.8475 1.5656 2.1743 2.6901 3.1272

.8333 1.5278 2.1065 2.5887 2.9906

.8065 1.4568 1.9813 2.4043 2.7454

.7813 1.3916 1.8684 2.2410 2.5320

.7576 1.3315 1.7663 2.0957 2.3452

6 7 8 9 10

4.3553 4.8684 5.3349 5.7590 6.1446

4.1114 4.5638 4.9676 5.3282 5.6502

3.8887 4.2883 4.6389 4.9464 5.2161

3.7845 4.1604 4.4873 4.7716 5.0188

3.6847 4.0386 4.3436 4.6065 4.8332

3.4976 3.8115 4.0776 4.3030 4.4941

3.3255 3.6046 3.8372 4.0310 4.1925

3.0205 3.2423 3.4212 3.5655 3.6819

2.7594 2.9370 3.0758 3.1842 3.2689

2.5342 2.6775 2.7860 2.8681 2.9304

11 12 13 14 15

6.4951 6.8137 7.1034 7.3667 7.6061

5.9377 6.1944 6.4235 6.6282 6.8109

5.4527 5.6603 5.8424 6.0021 6.1422

5.2337 5.4206 5.5831 5.7245 5.8474

5.0286 5.1971 5.3423 5.4675 5.5755

4.6560 4.7932 4.9095 5.0081 5.0916

4.3271 4.4392 4.5327 4.6106 4.6755

3.7757 3.8514 3.9124 3.9616 4.0013

3.3351 3.3868 3.4272 3.4587 3.4834

2.9776 3.0133 3.0404 3.0609 3.0764

16 17 18 19 20

7.8237 8.0216 8.2014 8.3649 8.5136

6.9740 7.1196 7.2497 7.3658 7.4694

6.2651 6.3729 6.4674 6.5504 6.6231

5.9542 6.0472 6.1280 6.1982 6.2593

5.6685 5.7487 5.8178 5.8775 5.9288

5.1624 5.2223 5.2732 5.3162 5.3527

4.7296 4.7746 4.8122 4.8435 4.8696

4.0333 4.0591 4.0799 4.0967 4.1103

3.5026 3.5177 3.5294 3.5386 3.5458

3.0882 3.0971 3.1039 3.1090 3.1129

21 22 23 24 25

8.6487 8.7715 8.8832 8.9847 9.0770

7.5620 7.6446 7.7184 7.7843 7.8431

6.6870 6.7429 6.7921 6.8351 6.8729

6.3125 6.3587 6.3988 6.4338 6.4641

5.9731 6.0113 6.0442 6.0726 6.0971

5.3837 5.4099 5.4321 5.4509 5.4669

4.8913 4.9094 4.9245 4.9371 4.9476

4.1212 4.1300 4.1371 4.1428 4.1474

3.5514 3.5558 3.5592 3.5619 3.5640

3.1158 3.1180 3.1197 3.1210 3.1220

30 40 50

9.4269 9.7791 9.9148

8.0552 8.2438 8.3045

7.0027 7.1050 7.1327

6.5660 6.6418 6.6605

6.1772 6.2335 6.2463

5.5168 5.5482 5.5541

4.9789 4.9966 4.9995

4.1601 4.1659 4.1666

3.5693 3.5712 3.5714

3.1242 3.1250 3.1250

Table A.3

Future Value of $1 at the End of T Periods = (1 + r )T Interest Rate

Period

1%

2%

3%

4%

5%

6%

7%

8%

9%

1 2 3 4 5

1.0100 1.0201 1.0303 1.0406 1.0510

1.0200 1.0404 1.0612 1.0824 1.1041

1.0300 1.0609 1.0927 1.1255 1.1593

1.0400 1.0816 1.1249 1.1699 1.2167

1.0500 1.1025 1.1576 1.2155 1.2763

1.0600 1.1236 1.1910 1.2625 1.3382

1.0700 1.1449 1.2250 1.3108 1.4026

1.0800 1.1664 1.2597 1.3605 1.4693

1.0900 1.1881 1.2950 1.4116 1.5386

6 7 8 9 10

1.0615 1.0721 1.0829 1.0937 1.1046

1.1262 1.1487 1.1717 1.1951 1.2190

1.1941 1.2299 1.2668 1.3048 1.3439

1.2653 1.3159 1.3686 1.4233 1.4802

1.3401 1.4071 1.4775 1.5513 1.6289

1.4185 1.5036 1.5938 1.6895 1.7908

1.5007 1.6058 1.7182 1.8385 1.9672

1.5869 1.7138 1.8509 1.9990 2.1589

1.6771 1.8280 1.9926 2.1719 2.3674

11 12 13 14 15

1.1157 1.1268 1.1381 1.1495 1.1610

1.2434 1.2682 1.2936 1.3195 1.3459

1.3842 1.4258 1.4685 1.5126 1.5580

1.5395 1.6010 1.6651 1.7317 1.8009

1.7103 1.7959 1.8856 1.9799 2.0789

1.8983 2.0122 2.1329 2.2609 2.3966

2.1049 2.2522 2.4098 2.5785 2.7590

2.3316 2.5182 2.7196 2.9372 3.1722

2.5804 2.8127 3.0658 3.3417 3.6425

16 17 18 19 20

1.1726 1.1843 1.1961 1.2081 1.2202

1.3728 1.4002 1.4282 1.4568 1.4859

1.6047 1.6528 1.7024 1.7535 1.8061

1.8730 1.9479 2.0258 2.1068 2.1911

2.1829 2.2920 2.4066 2.5270 2.6533

2.5404 2.6928 2.8543 3.0256 3.2071

2.9522 3.1588 3.3799 3.6165 3.8697

3.4259 3.7000 3.9960 4.3157 4.6610

3.9703 4.3276 4.7171 5.1417 5.6044

21 22 23 24 25

1.2324 1.2447 1.2572 1.2697 1.2824

1.5157 1.5460 1.5769 1.6084 1.6406

1.8603 1.9161 1.9736 2.0328 2.0938

2.2788 2.3699 2.4647 2.5633 2.6658

2.7860 2.9253 3.0715 3.2251 3.3864

3.3996 3.6035 3.8197 4.0489 4.2919

4.1406 4.4304 4.7405 5.0724 5.4274

5.0338 5.4365 5.8715 6.3412 6.8485

6.1088 6.6586 7.2579 7.9111 8.6231

30 40 50 60

1.3478 1.4889 1.6446 1.8167

1.8114 2.2080 2.6916 3.2810

2.4273 3.2620 4.3839 5.8916

3.2434 4.8010 7.1067 10.520

4.3219 7.0400 11.467 18.679

5.7435 10.286 18.420 32.988

7.6123 14.974 29.457 57.946

Period

10.063 21.725 46.902 101.26

13.268 31.409 74.358 176.03

10%

12%

14%

15%

16%

18%

20%

24%

28%

32%

36%

1 2 3 4 5

1.1000 1.2100 1.3310 1.4641 1.6105

1.1200 1.2544 1.4049 1.5735 1.7623

1.1400 1.2996 1.4815 1.6890 1.9254

1.1500 1.3225 1.5209 1.7490 2.0114

1.1600 1.3456 1.5609 1.8106 2.1003

1.1800 1.3924 1.6430 1.9388 2.2878

1.2000 1.4400 1.7280 2.0736 2.4883

1.2400 1.5376 1.9066 2.3642 2.9316

1.2800 1.6384 2.0972 2.6844 3.4360

1.3200 1.7424 2.3000 3.0360 4.0075

1.3600 1.8496 2.5155 3.4210 4.6526

6 7 8 9 10

1.7716 1.9487 2.1436 2.3579 2.5937

1.9738 2.2107 2.4760 2.7731 3.1058

2.1950 2.5023 2.8526 3.2519 3.7072

2.3131 2.6600 3.0590 3.5179 4.0456

2.4364 2.8262 3.2784 3.8030 4.4114

2.6996 3.1855 3.7589 4.4355 5.2338

2.9860 3.5832 4.2998 5.1598 6.1917

3.6352 4.5077 5.5895 6.9310 8.5944

4.3980 5.6295 7.2058 9.2234 11.806

5.2899 6.9826 9.2170 12.166 16.060

6.3275 8.6054 11.703 15.917 21.647

11 12 13 14 15

2.8531 3.1384 3.4523 3.7975 4.1772

3.4785 3.8960 4.3635 4.8871 5.4736

4.2262 4.8179 5.4924 6.2613 7.1379

4.6524 5.3503 6.1528 7.0757 8.1371

5.1173 5.9360 6.8858 7.9875 9.2655

6.1759 7.2876 8.5994 10.147 11.974

7.4301 8.9161 10.699 12.839 15.407

10.657 13.215 16.386 20.319 25.196

15.112 19.343 24.759 31.691 40.565

21.199 27.983 36.937 48.757 64.359

29.439 40.037 54.451 74.053 100.71

16 17 18 19 20

4.5950 5.0545 5.5599 6.1159 6.7275

6.1304 6.8660 7.6900 8.6128 9.6463

8.1372 9.2765 10.575 12.056 13.743

9.3576 10.761 12.375 14.232 16.367

10.748 12.468 14.463 16.777 19.461

14.129 16.672 19.673 23.214 27.393

18.488 22.186 26.623 31.948 38.338

31.243 38.741 48.039 59.568 73.864

51.923 66.461 86.071 108.89 139.38

84.954 112.14 148.02 195.39 257.92

136.97 186.28 253.34 344.54 468.57

21 22 23 24 25

7.4002 8.1403 8.9543 9.8497 10.835

10.804 12.100 13.552 15.179 17.000

15.668 17.861 20.362 23.212 26.462

18.822 21.645 24.891 28.625 32.919

22.574 26.186 30.376 35.236 40.874

32.324 38.142 45.008 53.109 62.669

46.005 55.206 66.247 79.497 95.396

91.592 113.57 140.83 174.63 216.54

178.41 228.36 292.30 374.14 478.90

29.960 93.051 289.00 897.60

50.950 188.88 700.23 2595.9

66.212 267.86 1083.7 4384.0

85.850 378.72 1670.7 7370.2

30 40 50 60

17.449 45.259 117.39 304.48

*FVIV > 99,999.

143.37 750.38 3927.4 20555.

237.38 1469.8 9100.4 56348.

634.82 5455.9 46890. *

1645.5 19427. * *

340.45 449.39 593.20 783.02 1033.6 4142.1 66521. * *

637.26 866.67 1178.7 1603.0 2180.1 10143. * * *

Table A.4

Future Value of an Annuity of $1 per Period for T Periods = [(1 + r)T − 1] r Interest Rate

Number of Periods

1%

2%

3%

4%

5%

6%

7%

8%

9%

1 2 3 4 5

1.0000 2.0100 3.0301 4.0604 5.1010

1.0000 2.0200 3.0604 4.1216 5.2040

1.0000 2.0300 3.0909 4.1836 5.3091

1.0000 2.0400 3.1216 4.2465 5.4163

1.0000 2.0500 3.1525 4.3101 5.5256

1.0000 2.0600 3.1836 4.3746 5.6371

1.0000 2.0700 3.2149 4.4399 5.7507

1.0000 2.0800 3.2464 4.5061 5.8666

1.0000 2.0900 3.2781 4.5731 5.9847

6 7 8 9 10

6.1520 7.2135 8.2857 9.3685 10.462

6.3081 7.4343 8.5830 9.7546 10.950

6.4684 7.6625 8.8932 10.159 11.464

6.6330 7.8983 9.2142 10.583 12.006

6.8019 8.1420 9.5491 11.027 12.578

6.9753 8.3938 9.8975 11.491 13.181

7.1533 8.6540 10.260 11.978 13.816

7.3359 8.9228 10.637 12.488 14.487

7.5233 9.2004 11.028 13.021 15.193

11 12 13 14 15

11.567 12.683 13.809 14.947 16.097

12.169 13.412 14.680 15.974 17.293

12.808 14.192 15.618 17.086 18.599

13.486 15.026 16.627 18.292 20.024

14.207 15.917 17.713 19.599 21.579

14.972 16.870 18.882 21.015 23.276

15.784 17.888 20.141 22.550 25.129

16.645 18.977 21.495 24.215 27.152

17.560 20.141 22.953 26.019 29.361

16 17 18 19 20

17.258 18.430 19.615 20.811 22.019

18.639 20.012 21.412 22.841 24.297

20.157 21.762 23.414 25.117 26.870

21.825 23.698 25.645 27.671 29.778

23.657 25.840 28.132 30.539 33.066

25.673 28.213 30.906 33.760 36.786

27.888 30.840 33.999 37.379 40.995

30.324 33.750 37.450 41.446 45.762

33.003 36.974 41.301 46.018 51.160

21 22 23 24 25

23.239 24.472 25.716 26.973 28.243

25.783 27.299 28.845 30.422 32.030

28.676 30.537 32.453 34.426 36.459

31.969 34.248 36.618 39.083 41.646

35.719 38.505 41.430 44.502 47.727

39.993 43.392 46.996 50.816 54.865

44.865 49.006 53.436 58.177 63.249

50.423 55.457 60.893 66.765 73.106

56.765 62.873 69.532 76.790 84.701

30 40 50 60

34.785 48.886 64.463 81.670

40.568 60.402 84.579 114.05

47.575 75.401 112.80 163.05

56.085 95.026 152.67 237.99

66.439 120.80 209.35 353.58

79.058 154.76 290.34 533.13

94.461 199.64 406.53 813.52

Number of Periods

113.28 259.06 573.77 1253.2

136.31 337.88 815.08 1944.8

10%

12%

14%

15%

16%

18%

20%

24%

28%

32%

36%

1 2 3 4 5

1.0000 2.1000 3.3100 3.6410 6.1051

1.0000 2.1200 3.3744 4.7793 6.3528

1.0000 2.1400 3.4396 4.9211 6.6101

1.0000 2.1500 3.4725 4.9934 6.7424

1.0000 2.1600 3.5056 5.0665 6.8771

1.0000 2.1800 3.5724 5.2154 7.1542

1.0000 2.2000 3.6400 5.3680 7.4416

1.0000 2.2400 3.7776 5.6842 8.0484

1.0000 2.2800 3.9184 6.0156 8.6999

1.0000 2.3200 4.0624 6.3624 9.3983

1.0000 2.3600 4.2096 6.7251 10.146

6 7 8 9 10

7.7156 9.4872 11.436 13.579 15.937

8.1152 10.089 12.300 14.776 17.549

8.5355 10.730 13.233 16.085 19.337

8.7537 11.067 13.727 16.786 20.304

8.9775 11.414 14.240 17.519 21.321

9.4420 12.142 15.327 19.086 23.521

9.9299 12.916 16.499 20.799 25.959

10.980 14.615 19.123 24.712 31.643

12.136 16.534 22.163 29.369 38.593

13.406 18.696 25.678 34.895 47.062

14.799 21.126 29.732 41.435 57.352

11 12 13 14 15

18.531 21.384 24.523 27.975 31.772

20.655 24.133 28.029 32.393 37.280

23.045 27.271 32.089 37.581 43.842

24.349 29.002 34.352 40.505 47.580

25.733 30.850 36.786 43.672 51.660

28.755 34.931 42.219 50.818 60.965

32.150 39.581 48.497 59.196 72.035

40.238 50.895 64.110 80.496 100.82

50.398 65.510 84.853 109.61 141.30

63.122 84.320 112.30 149.24 198.00

78.998 108.44 148.47 202.93 276.98

16 17 18 19 20

35.950 40.545 45.599 51.159 57.275

42.753 48.884 55.750 64.440 72.052

50.980 59.118 68.394 78.969 91.025

55.717 65.075 75.836 88.212 102.44

60.925 71.673 84.141 98.603 115.38

72.939 87.068 103.74 123.41 146.63

87.442 105.93 128.12 154.74 186.69

126.01 157.25 195.99 244.03 303.60

181.87 233.79 300.25 385.32 494.21

262.36 347.31 459.45 607.47 802.86

21 22 23 24 25

64.002 71.403 79.543 88.497 98.347

81.699 92.503 104.60 118.16 133.33

104.77 120.44 138.30 158.66 181.87

118.81 137.63 159.28 184.17 212.79

134.84 157.41 183.60 213.98 249.21

174.02 206.34 244.49 289.49 342.60

225.03 271.03 326.24 392.48 471.98

377.46 469.06 582.63 723.46 898.09

633.59 812.00 1040.4 1332.7 1706.8

356.79 1342.0 4994.5 18535.

434.75 1779.1 7217.7 29220.

530.31 2360.8 10436. 46058.

790.95 4163.2 21813. *

30 164.49 40 442.59 50 1163.9 60 3034.8 *FVIFA > 99,999.

241.33 767.09 2400.0 7471.6

1181.9 7343.9 45497. *

2640.9 22729. * *

5873.2 69377. * *

1060.8 1401.2 1850.6 2443.8 3226.8 12941. * * *

377.69 514.66 700.94 954.28 1298.8 1767.4 2404.7 3271.3 4450.0 6053.0 28172.3 * * *

968

1%

1.0101 1.0202 1.0305 1.0408 1.0513

1.0618 1.0725 1.0833 1.0942 1.1052

1.1163 1.1275 1.1388 1.1503 1.1618

1.1735 1.1853 1.1972 1.2092 1.2214

1.2337 1.2461 1.2586 1.2712 1.2840

1.3499 1.4191 1.4918 1.5683 1.6487

1.7333 1.8221

1 2 3 4 5

6 7 8 9 10

11 12 13 14 15

16 17 18 19 20

21 22 23 24 25

30 35 40 45 50

55 60

3.0042 3.3201

1.8221 2.0138 2.2255 2.4596 2.7183

1.5220 1.5527 1.5841 1.6161 1.6487

1.3771 1.4049 1.4333 1.4623 1.4918

1.2461 1.2712 1.2969 1.3231 1.3499

1.1275 1.1503 1.1735 1.1972 1.2214

1.0202 1.0408 1.0618 1.0833 1.1052

2%

5.2070 6.0496

2.4596 2.8577 3.3201 3.8574 4.4817

1.8776 1.9348 1.9937 2.0544 2.1170

1.6161 1.6653 1.7160 1.7683 1.8221

1.3910 1.4333 1.4770 1.5220 1.5683

1.1972 1.2337 1.2712 1.3100 1.3499

1.0305 1.0618 1.0942 1.1275 1.1618

3%

9.0250 11.0232

3.3204 4.0552 4.9530 6.0496 7.3891

2.3164 2.4109 2.5093 2.6117 2.7183

1.8965 1.9739 2.0544 2.1383 2.2255

1.5527 1.6161 1.6820 1.7507 1.8221

1.2712 1.3231 1.3771 1.4333 1.4918

1.0408 1.0833 1.1275 1.1735 1.2214

4%

15.6426 20.0855

4.4817 5.7546 7.3891 9.4877 12.1825

2.8577 3.0042 3.1582 3.3201 3.4903

2.2255 2.3396 2.4596 2.5857 2.7183

1.7333 1.8221 1.9155 2.0138 2.1170

1.3499 1.4191 1.4918 1.5683 1.6487

1.0513 1.1052 1.1618 1.2214 1.2840

5%

27.1126 36.5982

6.0496 8.1662 11.0232 14.8797 20.0855

3.5254 3.7434 3.9749 4.2207 4.4817

2.6117 2.7732 2.9447 3.1268 3.3201

1.9348 2.0544 2.1815 2.3164 2.4596

1.4333 1.5220 1.6161 1.7160 1.8221

1.0618 1.1275 1.1972 1.2712 1.3499

6%

46.9931 66.6863

8.1662 11.5883 16.4446 23.3361 33.1155

4.3492 4.6646 5.0028 5.3656 5.7546

3.0649 3.2871 3.5254 3.7810 4.0552

2.1598 2.3164 2.4843 2.6645 2.8577

1.5220 1.6323 1.7507 1.8776 2.0138

1.0725 1.1503 1.2337 1.3231 1.4191

7%

81.4509 121.5104

11.0232 16.4446 24.5235 36.5982 54.5982

5.3656 5.8124 6.2965 6.8210 7.3891

3.5966 3.8962 4.2207 4.5722 4.9530

2.4109 2.6117 2.8292 3.0649 3.3201

1.6161 1.7507 1.8965 2.0544 2.2255

1.0833 1.1735 1.2712 1.3771 1.4918

8%

14.8797 23.3361 36.5982 57.3975 90.0171

6.6194 7.2427 7.9248 8.6711 9.4877

4.2207 4.6182 5.0531 5.5290 6.0496

2.6912 2.9447 3.2220 3.5254 3.8574

1.7160 1.8776 2.0544 2.2479 2.4596

1.0942 1.1972 1.3100 1.4333 1.5683

9%

141.1750 221.4064

Continuously Compounded Rate (r)

Future Value of $1 with a Continuously Compounded Rate r for T Periods: Values of e rT

Period (T )

Table A.5

244.6919 403.4288

20.0855 33.1155 54.5982 90.0171 148.4132

8.1662 9.0250 9.9742 11.0232 12.1825

4.9530 5.4739 6.0496 6.6859 7.3891

3.0042 3.3201 3.6693 4.0552 4.4817

1.8221 2.0138 2.2255 2.4596 2.7183

1.1052 1.2214 1.3499 1.4918 1.6487

10%

424.1130 735.0952

27.1126 46.9931 81.4509 141.1750 244.6919

10.0744 11.2459 12.5535 14.0132 15.6426

5.8124 6.4883 7.2427 8.0849 9.0250

3.3535 3.7434 4.1787 4.6646 5.2070

1.9348 2.1598 2.4109 2.6912 3.0042

1.1163 1.2461 1.3910 1.5527 1.7333

11%

735.0952 1339.431

36.5982 66.6863 121.5104 221.4064 403.4288

12.4286 14.0132 15.7998 17.8143 20.0855

6.8210 7.6906 8.6711 9.7767 11.0232

3.7434 4.2207 4.7588 5.3656 6.0496

2.0544 2.3164 2.6117 2.9447 3.3201

1.1275 1.2712 1.4333 1.6161 1.8221

12%

1274.106 2440.602

49.4024 94.6324 181.2722 347.2344 665.1416

15.3329 17.4615 19.8857 22.6464 25.7903

8.0045 9.1157 10.3812 11.8224 13.4637

4.1787 4.7588 5.4195 6.1719 7.0287

2.1815 2.4843 2.8292 3.2220 3.6693

1.1388 1.2969 1.4770 1.6820 1.9155

13%

2208.348 4447.067

66.6863 134.2898 270.4264 544.5719 1096.633

18.9158 21.7584 25.0281 28.7892 33.1155

9.3933 10.8049 12.4286 14.2963 16.4446

4.6646 5.3656 6.1719 7.0993 8.1662

2.3164 2.6645 3.0649 3.5254 4.0552

1.1503 1.3231 1.5220 1.7507 2.0138

14%

969

15%

1.1618 1.3499 1.5683 1.8221 2.1170

2.4596 2.8577 3.3201 3.8574 4.4817

5.2070 6.0496 7.0287 8.1662 9.4877

11.0232 12.8071 14.8797 17.2878 20.0855

23.3361 27.1126 31.5004 36.5982 42.5211

90.0171 190.5663 403.4288 854.0588 1808.042

3827.626 8103.084

Period (T )

1 2 3 4 5

6 7 8 9 10

11 12 13 14 15

16 17 18 19 20

21 22 23 24 25

30 35 40 45 50

55 60

6634.244 14764.78

121.5104 270.4264 601.8450 1339.431 2980.958

28.7892 33.7844 39.6464 46.5255 54.5982

12.9358 15.1803 17.8143 20.9052 24.5325

5.8124 6.8210 8.0045 9.3933 11.0232

2.6117 3.0649 3.5966 4.2207 4.9530

1.1735 1.3771 1.6161 1.8965 2.2255

16%

11498.82 26903.19

164.0219 383.7533 897.8473 2100.646 4914.769

35.5166 42.0980 49.8990 59.1455 70.1054

15.1803 17.9933 21.3276 25.2797 29.9641

6.4883 7.6906 9.1157 10.8049 12.0871

2.7732 3.2871 3.8962 4.6182 5.4739

1.1853 1.4049 1.6653 1.9739 2.3396

17%

54.0549 65.3659 79.0436 95.5835 115.5843

20.9052 25.2797 30.5694 36.9661 44.7012

8.0849 9.7767 11.8224 14.2963 17.2878

3.1268 3.7810 4.5722 5.5290 6.6859

1.2092 1.4623 1.7683 2.1383 2.5857

19%

66.6863 81.4509 99.4843 121.5104 148.4132

24.5325 29.9641 36.5982 44.7012 54.5982

9.0250 11.0232 13.4637 16.4446 20.0855

3.3201 4.0552 4.9530 6.0496 7.3891

1.2214 1.4918 1.8221 2.2255 2.7183

20%

82.2695 101.4940 125.2110 154.4700 190.5663

28.7892 35.5166 43.8160 54.0549 66.6863

10.0744 12.4286 15.3329 18.9158 23.3361

3.5254 4.3492 5.3656 6.6194 8.1662

1.2337 1.5220 1.8776 2.3164 2.8577

21%

101.4940 126.4694 157.5905 196.3699 244.6919

33.7844 42.0980 52.4573 65.3659 81.4509

11.2459 14.0132 17.4615 21.7584 27.1126

3.7434 4.6646 5.8124 7.2427 9.0250

1.2461 1.5527 1.9348 2.4109 3.0042

22%

125.2110 157.5905 198.3434 249.6350 314.1907

39.6464 49.8990 62.8028 79.0436 99.4843

12.5535 15.7998 19.8857 25.0281 31.5004

3.9749 5.0028 6.2965 7.9248 9.9742

1.2586 1.5841 1.9937 2.5093 3.1582

23%

154.4700 196.3699 249.6350 317.3483 403.4288

46.5255 59.1455 75.1886 95.5835 121.5104

14.0132 17.8143 22.6464 28.7892 36.5982

4.2207 5.3656 6.8210 8.6711 11.0232

1.2712 1.6161 2.0544 2.6117 3.3201

24%

190.5663 244.6919 314.1907 403.4288 518.0128

54.5982 70.1054 90.0171 115.5843 148.4132

15.6426 20.0855 25.7903 33.1155 42.5211

4.4817 5.7546 7.3891 9.4877 12.1825

1.2840 1.6487 2.1170 2.7183 3.4903

25%

19930.37 49020.80

34544.37 89321.72

59874.14 162754.8

103777.0 296558.6

179871.9 540364.9

311763.4 984609.1

540364.9 1794075.

936589.2 3269017.

221.4064 298.8674 403.4288 544.5719 735.0952 992.2747 1339.431 1808.042 544.5719 772.7843 1096.633 1556.197 2208.348 3133.795 4447.067 6310.688 1339.431 1998.196 2980.958 4447.067 6634.244 9897.129 14764.78 22026.47 3294.468 5166.754 8103.084 12708.17 19930.37 31257.04 49020.80 76879.92 8103.084 13359.73 22026.47 36315.50 59874.14 98715.77 162754.8 268337.3

43.8160 52.4573 62.8028 75.1886 90.0171

17.8143 21.3276 25.5337 30.5694 36.5982

7.2427 8.6711 10.3812 12.4286 14.8797

2.9447 3.5254 4.2207 5.0531 6.0496

1.1972 1.4333 1.7160 2.0544 2.4596

18%

Continuously Compounded Rate (r)

290.0345 379.9349 497.7013 651.9709 854.0588

75.1886 98.4944 129.0242 169.0171 221.4064

19.4919 25.5337 33.4483 43.8160 57.3975

5.0351 6.6194 8.6711 11.3589 14.8797

1.3100 1.7160 2.2479 2.9447 3.8574

27%

1623346. 5956538.

2813669. 10853520.

2440.602 3294.468 8955.293 12708.17 32859.63 49020.80 120571.7 189094.1 442413.4 729416.4

235.0974 304.9049 395.4404 512.8585 665.1416

64.0715 83.0963 107.7701 139.7702 181.2722

17.4615 22.6464 29.3708 38.0918 49.4024

4.7588 6.1719 8.0045 10.3812 13.4637

1.2969 1.6820 2.1815 2.8292 3.6693

26%

4876801. 19776403.

4447.067 18033.74 73130.44 296558.6 1202604.

357.8092 473.4281 626.4068 828.8175 1096.633

88.2347 116.7459 154.4700 204.3839 270.4264

21.7584 28.7892 38.0918 50.4004 66.6863

5.3656 7.0993 9.3933 12.4286 16.4446

1.3231 1.7507 2.3164 3.0649 4.0552

28%

970

1%

.9900 .9802 .9704 .9608 .9512

.9418 .9324 .9231 .9139 .9048

.8958 .8869 .8781 .8694 .8607

.8521 .8437 .8353 .8270 .8187

.8106 .8025 .7945 .7866 .7788

.7408 .7047 .6703 .6376 .6065

.5769 .5488

Period (T )

1 2 3 4 5

6 7 8 9 10

11 12 13 14 15

16 17 18 19 20

21 22 23 24 25

30 35 40 45 50

55 60

Table A.6

2%

.3329 .3012

.5488 .4966 .4493 .4066 .3679

.6570 .6440 .6313 .6188 .6065

.7261 .7118 .6977 .6839 .6703

.8025 .7866 .7711 .7558 .7408

.8869 .8694 .8521 .8353 .8187

.9802 .9608 .9418 .9231 .9048

3%

.1920 .1653

.4066 .3499 .3012 .2592 .2231

.5326 .5169 .5016 .4868 .4724

.6188 .6005 .5827 .5655 .5488

.7189 .6977 .6771 .6570 .6376

.8353 .8106 .7866 .7634 .7408

.9704 .9418 .9139 .8869 .8607

4%

.1108 .0907

.3012 .2466 .2019 .1653 .1353

.4317 .4148 .3985 .3829 .3679

.5273 .5066 .4868 .4677 .4493

.6440 .6188 .5945 .5712 .5488

.7866 .7558 .7261 .6977 .6703

.9608 .9231 .8869 .8521 .8187

5%

.0639 .0498

.2231 .1738 .1353 .1054 .0821

.3499 .3329 .3166 .3012 .2865

.4493 .4274 .4066 .3867 .3679

.5769 .5488 .5220 .4966 .4724

.7408 .7047 .6703 .6376 .6065

.9512 .9048 .8607 .8187 .7788

6%

.0369 .0273

.1653 .1225 .0907 .0672 .0498

.2837 .2671 .2516 .2369 .2231

.3829 .3606 .3396 .3198 .3012

.5169 .4868 .4584 .4317 .4066

.6977 .6570 .6188 .5827 .5488

.9418 .8869 .8353 .7866 .7408

.0213 .0150

.1225 .0863 .0608 .0429 .0302

.2299 .2144 .1999 .1864 .1738

.3263 .3042 .2837 .2645 .2466

.4630 .4317 .4025 .3753 .3499

.6570 .6126 .5712 .5326 .4966

.9324 .8694 .8106 .7558 .7047

7%

.0123 .0082

.0907 .0608 .0408 .0273 .0183

.1864 .1720 .1588 .1466 .1353

.2780 .2567 .2369 .2187 .2019

.4148 .3829 .3535 .3263 .3012

.6188 .5712 .5273 .4868 .4493

.9231 .8521 .7866 .7261 .6703

8%

.0071 .0045

.0672 .0429 .0273 .0174 .0111

.1511 .1381 .1262 .1153 .1054

.2369 .2165 .1979 .1809 .1653

.3716 .3396 .3104 .2837 .2592

.5827 .5326 .4868 .4449 .4066

.9139 .8353 .7634 .6977 .6376

9%

.0041 .0025

.0498 .0302 .0183 .0111 .0067

.1225 .1108 .1003 .0907 .0821

.2019 .1827 .1653 .1496 .1353

.3329 .3012 .2725 .2466 .2231

.5488 .4966 .4493 .4066 .3679

.9048 .8187 .7408 .6703 .6065

10%

Continuous Discount Rate (r)

.0024 .0014

.0369 .0213 .0123 .0071 .0041

.0993 .0889 .0797 .0714 .0639

.1720 .1541 .1381 .1237 .1108

.2982 .2671 .2393 .2144 .1920

.5169 .4630 .4148 .3716 .3329

.8958 .8025 .7189 .6440 .5769

11%

Present Value of $1 with a Continuous Discount Rate r for T Periods: Values of e− rT

12%

.0014 .0007

.0273 .0150 .0082 .0045 .0025

.0805 .0714 .0633 .0561 .0498

.1466 .1300 .1153 .1023 .0907

.2671 .2369 .2101 .1864 .1653

.4868 .4317 .3829 .3396 .3012

.8869 .7866 .6977 .6188 .5488

13%

.0008 .0004

.0202 .0106 .0055 .0029 .0015

.0652 .0573 .0503 .0442 .0388

.1249 .1097 .0963 .0846 .0743

.2393 .2101 .1845 .1620 .1423

.4584 .4025 .3535 .3104 .2725

.8781 .7711 .6771 .5945 .5220

14%

.0005 .0002

.0150 .0074 .0037 .0018 .0009

.0529 .0460 .0400 .0347 .0302

.1065 .0926 .0805 .0699 .0608

.2144 .1864 .1620 .1409 .1225

.4317 .3753 .3263 .2837 .2466

.8694 .7558 .6570 .5712 .4966

15%

.0003 .0001

.0111 .0052 .0025 .0012 .0006

.0429 .0369 .0317 .0273 .0235

.0907 .0781 .0672 .0578 .0498

.1920 .1653 .1423 .1225 .1054

.4066 .3499 .3012 .2592 .2231

.8607 .7408 .6376 .5488 .4724

16%

.0002 .0001

.0082 .0037 .0017 .0007 .0003

.0347 .0296 .0252 .0215 .0183

.0773 .0659 .0561 .0478 .0408

.1720 .1466 .1249 .1065 .0907

.3829 .3263 .2780 .2369 .2019

.8521 .7261 .6188 .5273 .4493

17%

.0001 .0000

.0061 .0026 .0011 .0005 .0002

.0282 .0238 .0200 .0169 .0143

.0659 .0556 .0469 .0396 .0334

.1541 .1300 .1097 .0926 .0781

.3606 .3042 .2576 .2165 .1827

.8437 .7118 .6005 .5066 .4274

971

18%

.8353 .6977 .5827 .4868 .4066

.3396 .2837 .2369 .1979 .1653

.1381 .1154 .0963 .0805 .0672

.0561 .0469 .0392 .0327 .0273

.0228 .0191 .0159 .0133 .0111

.0045 .0018 .0007 .0003 .0001

.0001 .0000

Period (T )

1 2 3 4 5

6 7 8 9 10

11 12 13 14 15

16 17 18 19 20

21 22 23 24 25

30 35 40 45 50

55 60

.0000 .0000

.0033 .0013 .0005 .0002 .0001

.0185 .0153 .0127 .0105 .0087

.0478 .0396 .0327 .0271 .0224

.1237 .1023 .0846 .0699 .0578

.3198 .2645 .2187 .1809 .1496

.8270 .6839 .5655 .4677 .3867

19%

.0000 .0000

.0025 .0009 .0003 .0001 .0000

.0150 .0123 .0101 .0082 .0067

.0408 .0334 .0273 .0224 .0183

.1108 .0907 .0743 .0608 .0498

.3012 .2466 .2019 .1653 .1353

.8187 .6703 .5488 .4493 .3679

20%

.0000 .0000

.0018 .0006 .0002 .0001 .0000

.0122 .0099 .0080 .0065 .0052

.0347 .0282 .0228 .0185 .0150

.0993 .0805 .0652 .0529 .0429

.2837 .2299 .1864 .1511 .1225

.8106 .6570 .5326 .4317 .3499

21%

.0000 .0000

.0014 .0005 .0002 .0001 .0000

.0099 .0079 .0063 .0051 .0041

.0296 .0238 .0191 .0153 .0123

.0889 .0714 .0573 .0460 .0369

.2671 .2144 .1720 .1381 .1108

.8025 .6440 .5169 .4148 .3329

22%

.0000 .0000

.0010 .0003 .0001 .0000 .0000

.0080 .0063 .0050 .0040 .0032

.0252 .0200 .0159 .0127 .0101

.0797 .0633 .0503 .0400 .0317

.2516 .1999 .1588 .1262 .1003

.7945 .6313 .5016 .3985 .3166

23%

.0000 .0000

.0007 .0002 .0001 .0000 .0000

.0065 .0051 .0040 .0032 .0025

.0215 .0169 .0133 .0105 .0082

.0714 .0561 .0442 .0347 .0273

.2369 .1864 .1466 .1153 .0907

.7866 .6188 .4868 .3829 .3012

24%

.0000 .0000

.0006 .0002 .0000 .0000 .0000

.0052 .0041 .0032 .0025 .0019

.0183 .0143 .0111 .0087 .0067

.0639 .0498 .0388 .0302 .0235

.2231 .1738 .1353 .1054 .0821

.7788 .6065 .4724 .3679 .2865

25%

.0000 .0000

.0004 .0001 .0000 .0000 .0000

.0043 .0033 .0025 .0019 .0015

.0156 .0120 .0093 .0072 .0055

.0573 .0442 .0340 .0263 .0202

.2101 .1620 .1249 .0963 .0743

.7711 .5945 .4584 .3535 .2725

26%

.0000 .0000

.0003 .0001 .0000 .0000 .0000

.0034 .0026 .0020 .0015 .0012

.0133 .0102 .0078 .0059 .0045

.0513 .0392 .0299 .0228 .0174

.1979 .1511 .1153 .0880 .0672

.7634 .5827 .4449 .3396 .2592

27%

Continuous Discount Rate (r)

.0000 .0000

.0002 .0001 .0000 .0000 .0000

.0028 .0021 .0016 .0012 .0009

.0113 .0086 .0065 .0049 .0037

.0460 .0347 .0263 .0198 .0150

.1864 .1409 .1065 .0805 .0608

.7558 .5712 .4317 .3263 .2466

28%

.0000 .0000

.0002 .0000 .0000 .0000 .0000

.0023 .0017 .0013 .0009 .0007

.0097 .0072 .0054 .0040 .0030

.0412 .0308 .0231 .0172 .0129

.1755 .1313 .0983 .0735 .0550

.7483 .5599 .4190 .3135 .2346

29%

.0000 .0000

.0001 .0000 .0000 .0000 .0000

.0018 .0014 .0010 .0007 .0006

.0082 .0061 .0045 .0033 .0025

.0369 .0273 .0202 .0150 .0111

.1653 .1225 .0907 .0672 .0498

.7408 .5488 .4066 .3012 .2231

30%

.0000 .0000

.0001 .0000 .0000 .0000 .0000

.0015 .0011 .0008 .0006 .0004

.0070 .0051 .0038 .0028 .0020

.0330 .0242 .0178 .0130 .0096

.1557 .1142 .0837 .0614 .0450

.7334 .5379 .3946 .2894 .2122

31%

.0000 .0000

.0001 .0000 .0000 .0000 .0000

.0012 .0009 .0006 .0005 .0003

.0060 .0043 .0032 .0023 .0017

.0296 .0215 .0156 .0113 .0082

.1466 .1065 .0773 .0561 .0408

.7261 .5273 .3829 .2780 .2019

32%

.0000 .0000

.0001 .0000 .0000 .0000 .0000

.0010 .0007 .0005 .0004 .0003

.0051 .0037 .0026 .0019 .0014

.0265 .0191 .0137 .0099 .0071

.1381 .0993 .0714 .0513 .0369

.7189 .5169 .3716 .2671 .1920

33%

.0000 .0000

.0000 .0000 .0000 .0000 .0000

.0008 .0006 .0004 .0003 .0002

.0043 .0031 .0022 .0016 .0011

.0238 .0169 .0120 .0086 .0061

.1300 .0926 .0659 .0469 .0334

.7118 .5066 .3606 .2567 .1827

34%

.0000 .0000

.0000 .0000 .0000 .0000 .0000

.0006 .0005 .0003 .0002 .0002

.0037 .0026 .0018 .0013 .0009

.0213 .0150 .0106 .0074 .0052

.1225 .0863 .0608 .0429 .0302

.7047 .4966 .3499 .2466 .1738

35%

Appendix B Solutions to Selected End-of-Chapter Problems CHAPTER 2

2 6 10 14

16

$148,850; $98,850 $364,000 $789,000 a. $52,540 b. $18,100 c. $2,250 d. $1,790 $393,000

CHAPTER 3

2 6 10 14 16

1.90 times; 19.19%; $123,775.50 15.61% 6.72% 33.63 days 8.54t imes

18

22

c. 42.43%; 25.03% d. 18.78% a. 1.63 years; 1.60 years b. $605,259.20; $386,476.33 c. 34.45%; 41.87% d. 27.49% 25.00%; 33.33%; 42.86%; 66.67%

CHAPTER 6

2 6 10 16 18 22 28 32

$1,154.53 22.01% −$106,311.69; −$105,895.27 $22,522,500 $968,750 $43,748.88 $1,395,938; 20.72% $264.41

CHAPTER 4

2

4 10

14 18 22 26 30 34 38 42 44 52 56 60 64

a. $1,790.85 b. $2,367.36 c. $3,207.14 8.04 years; 16.09 years a. $3,462.03 b. $2,564.73 c. $3,132.57 d. $3,326.28 $307,692.31; 5.88% EAR = 176.68% 4.81% $3,257,576 $325,001.73 $1,660,364 $504,129.05 −$2,438.23; 12.04% $123,869.69 $8,148.66 $15,456.89 EAR = 16.28% APR = 31.65%; EAR =36.67%

CHAPTER 5

2 6 10 14

972

4.23 years; 6.39 years; Never 33.37%; 29.32% a. 14.81% d. −$683.42; $635.42 a. .86 years; 1.56 years b. $235.46; $417.05

CHAPTER 7

2 6 10 14

20

NPVBest = $2,528,859 NPVWorst = −$1,379,598 Go to market NPV = $15,500,000 Test market NPV = $15,977,477 6,366 units Payback = 3.19 years NPV = $7,507,381 IRR = 25.15% a. 1,067 b. 2,379

CHAPTER 8

2

6 10 16

18

a. $1,000 b. $802.38 c. $1,283.62 6.56% 6.84% Current yield = 7.71% YTM = 8.03% Effective annual yield = 8.19% $1,062

CHAPTER 9

2 6 8 13

10.91% $3.91 6.21% $38.57

Appendix B

18 23 29

$92.41 14.13% a. $63.61 b. $91.53

CHAPTER 10

2 6 10 14 20

1.58%; 13.04% 2.91%; 3.01% a. 6.72% b. 6.10% 7.30% Arithmetic average = 7.17% Geometric average =2.45%

Solutions to Selected End-of-Chapter Problems

6

10 14

$6.67; $8.18; $5.22 $5,750 $5,750 $4.00; $4.93; $3.13 Breakeven = $5,750 $4,730,000 VU = $535,294.12 V =$585,544.12 a. b. c. d.

CHAPTER 17

4 8

$750,000 a. $85,000,000 b. 27.66% c. 12.77%

CHAPTER 11

2 6

10 14 18

12.74% E(RA) = 7.65% σA = 1.71% E(RB) = 12.05% σB = 15.57% a. 6.98% b. σ2 = .03312; σ = 18.20% 1.46 Market risk premium =6.77%

CHAPTER 12

2 5

a. 2.81% b. 11.01% F1 = 6.49% F2 =5.64%

CHAPTER 18

2 6 10 13

CHAPTER 19

2 6 10

14

CHAPTER 13

2 6

10 14 18 22

10.37% Book value = $140,000,000 Market value = $123,200,000 RD = 3.57% a. .2143; .7857 b. .7793; .2207 a. .3196; .6084 b. 10.27% $42,385,321 $9,719,777

CHAPTER 15

2 6 10 14

1,151 $1,112.79 7.42% $119.73

$102,373.23 a. $1,148,766 b. $1,099,840 $2,584,826 $4,837,789

a. New shares issued = 2,000 b. New shares issued = 5,000 7,731; $47.50 a. $115 b. $120 c. 25,000 a. $1,054,821 b. $72.99; $1,504,821.43 c. 665.34

CHAPTER 20

2

6 12 15

a. $34 b. 1,333,333; 2.55 c. $32.87; $1.13 d. 34,000; 34,000 1,258,766 19.18% $28.15

CHAPTER 21

2 6 10 14

−$13,074.25 −$22,969.80 $1,514,203 a. −$40,065.81 b. $1,483,252

CHAPTER 22 CHAPTER 16

2

a. $.99; $2.47; $3.21 b. $.09; $2.56; $3.79

4 6

a. $13.40 b. $2.17 $1.51

973

974

10 14 18 22 26

34

Appendix B

Solutions to Selected End-of-Chapter Problems

Call = $3.65; Put = $6.90 $246,505.71 $75.00 Project A: Equity = $4,919.05; Debt = $12,080.95 Project B: Equity = $4,052.51; Debt = $13,347.59 a. $5.44 b. .46; Borrow $31.71 c. $5.44 $10.80

CHAPTER 23

2 6 10

$1,213,088 $107,101.33 $6,161,619

6

10

a. $28,620 b. 2.49 days c. $28,620 d. $5.31 e. $17,225 $3,900,000;$195,000

CHAPTER 28

2 6 10 14 18

$4,635,616 9.3590 times; $444,551.28 $148,275 $276,200 $90.53

CHAPTER 29 CHAPTER 24

2 5 10 14

14.23 $18 a. $563.75 b. 13.95 years $895.03

CHAPTER 25

2 6 9 14

−$11,500; $22,000 2.783 years $22,400 a. $410.78 b. $494.10

CHAPTER 26

2 6 10

Cash = $2,035 Current assets = $5,590 Operating cycle = 85.95 days Cash cycle = 38.50 days Ending cash balance = $398,160; $508,544; $754,464

2 6 10

14

CHAPTER 30

4

a. Disbursement float = $56,000 Collection float = −$52,000 Net float = $4,000 b. Disbursement float = $56,000 Collection float = −$26,000 Net float = $30,000

5.103

CHAPTER 31

2

6

CHAPTER 27

2

a. Assets = $726,000 b. Assets = $1,026,000 Goodwill = $3,450 a. $1,300 b. $39.45 c. $4,200; $41.44 d. $7,087.17 a. $6,250,000 b. $16,250,000 c. $13,000,000; $12,675,000 d. NPVCash = $3,250,000 NPVStock =$3,575,000

10 14

£ = $55.276 SF/£ = 1.9690 £/SF = .5079 Great Britain = 3.25% Japan = .90% Switzerland = 1.86% Kr/$ = 6.9418 $847,605.21

Name Index Note: Page numbers followed by n indicate material in footnotes or source notes.

A Adkerson,R., 720,721 Agrawal, Anup, 545,545n Allen,F ranklin, 594n Allen,J effrey, 908,908n Allen,P aul, 408 Altman,E dwardI., 480,480n ,523–524, 524n, 918n, 929, 930n Andrade,Gr egor, 524,524n ,892n ,900n Ang,J ., 597,597n ,670,670n Asquith,P aul, 592,592n ,628,628n ,758n

B Banz,R.W ., 385,448n Bar-Or,Y uval, 524,524n Barber,B rad, 444n Barberis,Nic holas, 452n Barnea,A., 757n Baum,J amesC ., 627n,628n Benioff,M ark, 622 Beranek,W., 927n Berens,J .L ., 540,540n ,542n ,548 Bernardo,An tonio, 594n Berra,Y ogi, 76,76n Bethal,J enniferE ., 643n Bhagat,S ., 623n,642,642n Bhattacharya,S ., 594n Biddle,G .C ., 453,453n Black,F ischer, 691,693 Blankfein,L loydM ., 14,720,721 Boehmer,R., 927n Boone,A udraL ., 877n Booth,J ., 639,639n Bowie,Da vid, 479 Boyle,B arbara, 159 Brav,A ., 601n Brigham,E .F ., 755n Briloff,Ab raham, 60n Brin,S ergy, 622 Bris,A rturo, 524,524n ,921n Brown,J ames, 479 Bruno,A.V ., 644,644n Buffett,W arren, 607,897

C Caesar,J ulius, 94–95 Campbell,Cyn thiaJ ., 758n Carlson,M urray, 629n Caton,GaryL ., 758n Chabraja,Nic holasD ., 14–15 Chatterjee,S ., 929n Chen,N ., 382n

Chenault,K., 720,721 Cornelli,F rancesca, 627n Cowan,A.R., 758n Cox,J ohnC ., 768n Crutchley,Clair e, 629n Cuny,C .L ., 540,540n ,542n ,548 Cutler,Da vidM ., 524,524n ,525

D Dabora,E milM ., 446,446n David,G ., 720,721 Davydenko,S ergeiA., 924n DeAngelo,Harry , 592,592n ,599, 599n,604n DeAngelo,L inda, 592,592n ,599, 599n,604n Dhillon,U .S ., 929n Dimson,E lroy, 318,319n ,320n , 321n,358n Doidge,Cr aig, 17n

E Easterday,K athryn, 449n Ebbers,B ernie, 17 Eberhart,Allan C ., 927n Ederington,L ouisH., 758n ElizabethI,Qu eeno f E ngland, 531 Ellison,L arry, 15,720,721 Essner,R., 720,721 Ezzel,J .R., 507n

F Fairbank,R., 720, 721 Fama, Eugene F., 385, 397n, 449, 449n, 450n, 452, 452n, 598, 598n Fawcett,S tanleyE ., 627n,628n Fernando,Ch itruS ., 622n Fields,W.C ., 769 Fisher,Ad lai, 629n Fisher,Irvin g, 256 Flath,D ., 669,669n Flynn,E rroll, 528 Franks,J ollanR., 924n French, Kenneth R., 385, 397n, 449, 449n, 450n, 452, 452n, 598, 598n Froot,K ennethA., 446,446n

G Gates,B ill, 408 Gaye,M arvin, 479 Giammarino,R onald, 629n Gilson,S tuartC ., 920n,927n

Goldreich,Da vid, 627n Graham, John R., 157n, 158n, 209, 209n, 218n, 394n, 406n, 545n, 546, 546n, 547n, 596, 596n, 601n Grullon,Gu stavo, 589,589n Gutchers,Vlad imirA., 622n

H Hall,B rianJ ., 458–459,459n Hansen,R obertS ., 592n,623,623n Harford,J arrad, 826n,902n Harris,M ., 757n Harvey,Camp bellR., 157n,158n ,209, 209n, 218n, 394n, 406n, 546, 546n, 547n,601n Haugen,R.A., 757n Haugen,R obertS ., 629n Heron,R., 892n Higgins,R obertC ., 76 Hirsch,E mile, 206 Hoberg,Ge rard, 627n Hong,H., 453,453n Hull,J ohnC ., 693n,732n Hunt,Ne lsonB unker, 769 Hunt,W illiamHe rbert, 769

I Ibbotson, Roger G., 94, 305n, 306n, 307n, 308n, 310n, 312n, 382 Icahn,Car l, 15,894–895 Ikenberry,Da vid, 455,455n ,598,598n Ingersoll,J ohnE ., 757,757n ,768n Inselbag,I., 558n

J Jaffe,S tanley, 150–151 Jagannathan,R., 397n Jamail,J oe, 525 Jarrow,R., 623n Jensen,M ichaelC ., 13n,537n ,881, 881n,884 John,K ose, 594n,920n ,927n Johnson,R oss, 881 Julio,B randon, 598,598n

K Kaplan,R.S ., 453,453n Kaplan,S tevenN ., 524,524n ,907,907n Karolyi,An drew, 17n Kaufold,H., 283n,558n Keim,Do naldB ., 449,449n Keynes,J ohnM aynard, 446,531,824 975

976

Name Index

Khanna,Na veen, 623n Kolasinski,Ad am, 448,448n Korwar,A.N ., 628,628n Kothari,S .P ., 450n Kumar,Alo k, 596,596n Kumar,R aman, 592n

Moeller,S ara, 899n,900n Monks,R obert, 13n Moore,W.T ., 758n Mulherin,J .Har old, 877n Mullins,D .,J r., 592,592n ,628,628n Myers,S .C ., 537n,538n ,892n

L

N

Lai,K amW ah, 637n Lakonishok,J ., 455,455n Lamont,Ow en, 446,446n Lang,L arryN .P ., 537n,920n ,927n Lansing,S herry, 150–151 LaP orta,R afael, 13n Lease,R onald, 929,929n Lee,In moo, 630n–632n,631 Levich,Ric hardM ., 953 Lewis,Cr aig M., 757,757n Li,Xu , 448,448n Lie,E ., 892n Liebman,J effreyB ., 458–459,459n Lindahl,F .W., 453,453n Lintner,J ohn, 359n,599,599n ,600 Lipton,M artin, 896 Litwak,M ark, 159n Ljungqvist,Ale xander, 627n Lockhead,S cott, 630n–632n,631 Logue,D ., 623n Lopez-De-Silanes,F lorencio, 13n Loughran,T im, 449n Lubben,S tephenJ ., 524,524n

Nagarajan,Nan du, 545,545n Nayan,N ., 758n Nichols,Nan cyA., 218n Niven,Da vid, 528

M Majluf,N ., 892n Malkiel,B .G ., 436n Malmendier,Ulrik e, 902,902n Mandelker,G ., 453,453n Mansi,S attarA., 826n Markowitz,Harry , 345n Marr,M .W., 642,642n Marsh,P aul, 318,319n ,320n ,321n ,358n Masulis,R onald, 628,628n ,895n Maxwell,W illiamF ., 826n Mazzeo,M .A ., 758n McConnell,J ohnJ ., 908,908n ,928n , 929,929n McGrattan,E .R., 397n Michaely,R oni, 589,589n ,592,592n , 601n,908,908n Mikkelson,W.H., 628,628n ,755n Miles,J .A., 507n Miller, Merton, 430, 430n, 493, 493n, 502, 502n, 503, 512, 513, 530, 532, 538, 540n, 544n, 580, 581–582, 594n Minuit,P eter, 95 Mitchell,M ark, 892n,900n Modigliani,F ranco, 493,493n ,502,502n , 503, 512, 513, 530, 532, 538, 580, 581–582

O Odean,T errance, 444n Opler,T im, 806,806n

P Page,L arry, 622 Partch,M .M ., 628,628n Pastor,L ubos, 442n Peterson,D ., 597,597n Peterson,P ., 597,597n Peterson,P .P ., 670,670n Pickens,T .B oone, 881,897 Pinkowitz,L ee, 13n,806,806n Porter,M ichael, 880,880n Procrustes, 76,76n

R Ragolski,Ric hardJ ., 757,757n Ramirez,G .G ., 929n Raviv,A., 757n Reinganum,M .R., 448n Rhodes-Kropf,M atthew, 879n Ricci,Ch ristina, 206 Ritter, Jay R., 397n, 454, 454n, 455, 456n, 624, 624n, 625n, 626, 626n, 627n, 630n–632n,631 Roberts,B rian, 469 Robinson,Da vid, 879n Rock,K., 594n,625n Roll,Ric hard, 382n,383n ,453,453n Ross,S tevenA., 382n,385,594n ,768n Rowling, J.K., 15 Rozeff,M ichael, 592n Ruback,Ric hardS ., 881,881n

S Sabathia,C .C ., 87 Scherbina,A., 397n Schlingemann,F rederik, 899n,900n Scholes,M yron, 691,693 Schultz,Ho ward, 720 Seigel,J eremyJ ., 318n Senbet,L ., 757n Servaes,He nri, 928n Seward,J amesK., 757,757n Shah,K., 534n

Shanken,J ., 450n Sharpe,W illiamF ., 359n Shaw,W ayne, 908,908n Shefrin,He rshM ., 591,591n Shleifer,An drei, 13n,432,432n ,443,452n Shome,Dilip K., 592n Siegel,J eremyJ ., 257n Simon,W illiam, 906 Simpson,R on, 159 Singal,V ijay, 444n Singh,A.K., 758n Sinquefield, Rex A., 94, 305n, 306n, 307n, 308n, 310n, 312n, 382 Sirri,E rikR., 643n Skinner,Do uglas, 582n,599,599n Sloan,R.G ., 450n Slovis,M yron, 637n Smith,Ad am, 534n,534–535 Smith,B ., 927n Smith, C. W., Jr., 529, 529n, 637, 637n, 638n, 639, 670, 670n Smith,F rederick, 526 Smith,R., 639,639n Spindt,P aulA., 622n Stafford,E rik, 892n,900n Stambaugh,R obertF ., 442n Statman,M eir, 591,591n Staunton,M ichael, 318,319n ,320n , 321n,358n Stein,J ., 757n Stulz, René, 13n, 17n, 537n, 806, 806n, 899n,900n Suggitt,He atherJ ., 480,480n Summers,L awrenceH., 524,524n ,525 Sushka,M arie, 637n Szewczyk,S amuelH., 440,440n ,441n

T Tashjian,E lizabeth, 929,929n Tate,Ge offrey, 902,902n Teixeira,M ark, 87,101 Thain,J ., 720,721 Thaler,Ric hardH., 446,446n ,452n , 592,592n Thompson,G .R., 642,642n ,720,721 Tsetsekos,Ge orgeP ., 440,440n ,441n Tufano,P eter, 430n Tyebjee,T .T ., 644,644n

V Varitek,J ason, 87 Vermaelen,T ., 455,455n Victoria,Qu eeno f E ngland, 531 Vishny,R obert, 13n

W Wagoner,Ric k, 917 Wakeman,L .M ., 670,670n Waksal,S amuel, 17

Name Index

Walkling,R alph, 13n,537n Wang,Co ng, 895n Warner, Jerold B., 458, 458n, 524, 524n, 529,529n Watts,R ossL ., 458,458n Weisbach,M ichael, 907,907n Weiss,L awrenceA., 523–524,524n ,920n , 926n,927n Welch, Ivo, 320, 320n, 524, 524n, 594n, 627n,921n

977

White,M .J ., 523–524,524n Williams,J oseph, 594n Williams,R., 720,721 Williamson,R ohan, 13n,806,806n Winfrey,Op rah, 15 Womack,K., 592,592n Wruck,K arenH., 458,458n ,917n ,920n Wulf,J ulie, 902n,902–903

X Xie,F ei, 895n

Z Zantout,Z aherZ ., 440,440n ,441n Zhao,Qu anshui, 630n–632n,631 Zhu,Nin g, 524,524n ,921n

Subject Index Note: Page numbers followed by n indicate material in footnotes.

A Abandonmento ption, 220–222,724,725 ABCa pproach, 863 Abercrombie&F itch, 286 ABNAM RO, 240 Abnormalr eturns(ARs), 630,898 calculationo f, 439–440,440n cumulative(CARs), 440n,440–441 Absolutep riorityru le(AP R), 922,923, 924, 926, 927, 927n Absolutep urchasingp owerp arity, 940–943,956 Acceleratedc ollections, 835–837 Acceleratedd epreciation, 286,656 AccentureL td., 401 Accounting fraudulent, 454 generally accepted principles of, 9, 22, 22n,24 leasingan d, 654–656 Accountingd ilution, 640–641 Accountingfe es, 523 Accountingin come, 669 Accountingme thods choice of, market efficiency and, 453n, 453–454 choiceo f,P Er atioan d, 286–287 financialsta tementan alysisan d, 60 LIFOan dF IFO, 286–287,453 Accountingsta tements, 75 balancesh eet( SeeB alancesh eet(s)) cash flows statement (See Statement of cashf lows) common-size( SeeCo mmon-size statements) incomesta tement( SeeIn come statement) Accountsiz e, 850 Accountsp ayable, 811 Accountsp ayablep eriod, 798 Accountsr eceivable, 813,847–848 days’ sales in receivables ratio, 53, 801, 801n,84 8 liquidityo f, 21 monitoring, 859–860,860n receivables turnover ratio, 53, 53n, 801, 801n,80 2 Accountsr eceivablep eriod, 798,801,803, 848,849 ACH(au tomatedc learinghouse) transfers, 835 Acid-test(q uick)r atio, 50 ACP. SeeA veragec ollectionp eriod 978

Acquisitions, 908,909 accountingf or, 904–905 acquisitiono f asse ts, 876–877 acquisitiono f sto ck, 876,909 classificationo f, 877 costfr omrisk r eduction, 887–889 diversificationan d, 886,886n earningsgr owthan d, 885n,885–886 economicb enefitso f, 884 executivec ompensationan d, 901,901n goingp rivate, 905 horizontalo rv ertical, 877,881 LBOs( SeeL everagedb uyouts) byme rger( SeeM erger(s)) top ayd ividends, 587 speculationin , 457 synergyan d( SeeS ynergy(ies)) takeovers( See Takeover(s); Takeover defenses) taxf ormso f, 903–904 taxgain sfr om, 882–884 See alsoDi vestitures;M erger(s) AdelphiaCo mmunications, 17,34 Adjustedp resentv alue(AP V)a pproach to capital budgeting in levered firm, 553–555,554n ,555n exampleo f, 554n,562–565 guidelinef oru se, 558–559 summaryo f, 560 Administrativefe es, 523 AdobeS ystems, 268,286 AdolphCo ors, 469 ADR(Ame ricand epositaryr eceipt), 934 Advancec ommitments, 777n,777–778 Aeropostale, 44 AetnaIn c., 720,721 Aflac, 1 Aftermarket, 621 Aftertaxc osto f d ebt, 411–412 Aftertaxin terestr ate, 662–663,663n Agencyc osts convertibleb ondsan d, 756–757,757n debt–equityfin ancingan d, 536 directan din direct, 14 of e quity, 534n,534–537,536n exampleo f, 535,535n freec ashf lowan d, 536–537,537n high-dividendp olicyan d, 591–592,592n selfishin vestmentstr ategiesan d, 525–528 Agencyp roblem, 13,13n ,18 Agencyr elationship, 13 Agencyth eory, 901–902,906

Agingsc hedule, 860,860n Agreemento f me rger, 878n AIG (American International Group), 300 AIM(Alte rnativeIn vestmentM arket), 18 Alcoa, 281,941 All-debtfir ms, 413,413n All-equityfir ms averagec osto f c apital, 412 capitalstru ctureo f, 545n,545–5 46 cost of capital for, 497, 561, 561n, 563 estimatingc osto f c apitalf or, 394–395 NPVo f me rgerto , 889n,889–890 stockfin ancingf or, 499–500 unleveredb etasf or, 567 Allocatedc osts, 173–174 AlternativeIn vestmentM arket(AI M), 18 Alternativesto ckissu eme thods, 617, 617n,619,619n Altria, 399 Amazon.com, 284,339,399,676,799,803 Amcor, 846 AmericanAir lines, 399–400 Americand epositaryr eceipt(ADR), 934 AmericanE xpressCo mpany, 720,721 American International Group (AIG), 300 American options, 676, 685n, 687–689, 690 Americanq uote, 935–936 AmeriCashAd vance, 103 AmeriServeF oodD istribution,In c., 248,477 AmgenIn c., 750 Amortization EBITDA, 47,52,54n ,54–55,57 of le ases, 652–653 of lo an, 116–120 Amortizationsc hedule, 116,117 AMRCo rporation, 399–400 AnadarkoP etroleum, 286 “Angels,” 644 Annualp ercentager ate(AP R[S AIR]), 102,103–104 Annuity(ies) delayed, 112 growing, 115–116,122 infrequent, 113 multiple, 113–115 ordinary, 113,122 simplifyingf ormulaf or, 109n,10 9–115 spreadsheeta pplications, 111 Annuityd ue, 113,122 Annuityfac tor, 110–111 Anomalieso f mar kete fficiency, 445,452 Antitrustle gislation, 898 AOL, 892–893,902

Subject Index

Apple,In c., 5,401,644,652,804 Appraisalrigh ts, 876 Appraisedv alue, 903 APR(a bsolutep riorityru le), 922,923, 924, 926, 927, 927n APR(an nualp ercentager ate), 102, 103–104 APT. See Arbitrage pricing theory (APT) APT(asse tp ricingth eory), 380 APV. See Adjusted present value (APV) approach Arbitrage behavioralfin ancean d, 445 conversionv aluean d, 751 coveredin terestarb itrage, 945–946,953 expectedr eturnsan d, 380 limitsto , 445–447,446n markete fficiencyan d, 433 profitfr om, 686 trianglearb itrage, 938 Arbitragep ricingth eory(AP T), 371–386 betas, arbitrage, and expected returns, 379–381 CAPMc ompared, 381–383 empiricala pproachesto , 383–385 Fama–Frenchth ree-factormo del and, 385 mutualfu ndr eturnsc ase, 391 portfoliosan dfac tormo dels, 374–378 systematicrisk an db etas, 371–374,374n Arbitrageurs, 380 Arithmetica verager eturn, 315,317,317n Arrearage, 471 ARs. SeeAb normalr eturns ArthurR ock&Co ., 644 Articleso f in corporation, 5 ArtT echnologyGr oup(A TG), 859–860 AskJ eeves, 642 Askp rice, 250,288,681,682 Asset(s) acquisition of, to acquire company, 876–877 bookv alueo f, 22,22n current( SeeCu rrentasse ts) debt–assetr atio, 544–545,545n efficientse tf ortw oasse ts, 339–344 fixed, 1,21–22,29 impairmento f, 905 leased,r esidualv alueo f, 668 matchingwith lia bilities, 782–784,784n restructuring, 898,906–907,920,931 risky,e xcessr eturno n, 311 shownin b alancesh eet, 20,21 typeso f,d ebt–equityr atioan d, 547 valuationo f, 733–734 varianceo f, 688–689 Assetb eta, 405 Assetman agementr atios, 52–54 charto f, 57

979

days’sale sin in ventory, 52–53, 801,801n days’ sales in receivables, 53, 801, 801n,848 inventorytu rnover, 52,801,801n ,802 payablestu rnover, 802 receivablestu rnover, 53,53n ,801, 801n,802 totalasse ttu rnover, 54,73,803 Assetp ricing, 383–385 CAPM( See Capital asset pricing model) empiricalmo dels, 383–384,386 stylep ortfolios, 384–385 Assetp ricingth eory(AP T), 380 Assetr estructuring, 898,906–907, 920,931 Assignmento f r eceivables, 813 Associationo f Ame ricanM edical Colleges, 120 ATG(ArtT echnologyGr oup), 859–860 AtlantisCasin o, 524 AT&T, 352,616 Automatedc learinghouse(A CH) transfers, 835 AutomaticDa taP rocessing,In c., 401 Automobilein dustry, 917,954 Automobilele ases, 479 Availabilityd elay, 828,829 Availableb alance, 826 AVANIRP harmaceuticals, 607 Averagec ollectionp eriod(A CP), 53,801 cashd iscountsan d, 851 monitoring, 859 forr eceivables, 847,848 Averagec osto f c apital, 412,413,413n Averaged ailyf loat, 828–829 Averagema turity, 780–782,781n Averager eturns, 315–317 arithmeticvs .ge ometrica verages, 315, 317,317n calculating, 310–311 geometrica verages,c alculating, 316–317 risk-freer eturnsan d, 311,312 sizefac torin , 448n,448–449,449n Averagetaxr ates, 26–28 AvisB udgetGr oup, 34 Avitar,In c., 607

B Backdoore quity, 757,757n Balancesh eet(s), 20–23 common-size, 45–46 debtvs .e quity, 22,22n liquidity, 21–22 marketv alue, 499–501,509n ,511,512 percentageo f sale sa pproach, 65–67

prof orma, 62–63,65 valuevs .c ost, 22n,22–23 Balancesh eetmo delo f c orporation, 1–3 BaldwinCo mpanyc ase, 174–181,193 analysiso f p roject, 176–179 depreciation, 176,178,180–181 determinationo f c ashf lows, 175,178 determination of income for taxes, 175, 176,178 financiald ata, 175–177 intereste xpense, 181 investmento utlays, 177–178 netw orkingc apital, 175,179–180 NPVc alculation, 178–179 proposedin vestment, 174–176 salvagev aluean d, 175,1 78 taxb ooksvs .sto ckholders’b ooks, 179 Balloonp ayments, 118,656 Bank(s), 813,859 loansb y( SeeL oan(s)) See alsoIn vestmentb anks BankBoston, 902 Banker’sac ceptances, 813,851 Bank of America (BOA), 471, 478, 616, 875,880 Bankruptcy, 488 absolute priority rule, 922, 923, 924, 926, 927, 927n avoiding, 11 classeso f c reditors, 924,925,925n asglo balissu e, 922,924n of go vernmentale ntity, 523,523n involuntary, 921 “junk”b ondsan d, 522 predicting, 923,929–931 prepackaged, 928n,928– 929,929n ,931 priorityo f c laimsin , 921–923 privatew orkoutc ompared, 297n, 926–928 assh areholderrigh t, 705 of smallc ompanies, 921n,929n U.S.syste m, 922–923 See alsoF inanciald istress BankruptcyAb useP reventionan d Consumer Protection Act of 2005, 924,924n Bankruptcyc osts, 520–522,523,529, 530–531 borneb ysh areholders, 522 lawyers, 522,523n ,523–5 24,524n ,525 riskn eutralityan d, 521n,521–522 Bankruptcyliq uidation(Ch apter7), 921n, 921–924,931 BankruptcyR eformAc to f 1978, 921, 922,924,924n Bankruptcyr eorganization(Ch apter11), 920, 922, 924n, 924–926, 925n, 931 BANs(b ondan ticipationn otes), 841 Bargainp urchasep riceo ption, 655,656 Barnes&No ble, 799

980

Subject Index

BASF, 392 BasicIRRru le, 142–143,148 BayerischeM otorenwerke(B MW)A G, 7,918,954 Beachhead, 880,880n Bearerb onds, 475 BearS tearnsCo mpanies, 618,875 Bed,B ath&B eyond, 356,399 Behavioralfin ance, 443–445,460 academicvie wpoints, 452,452n high-dividendp olicyan d, 590–591, 591n,608 independent deviations from rationality, 432–433, 444, 444n, 451 irrationalityo f in vestors, 432–433 mispricing,arb itragean d, 445 rationalityin , 432,443–444,444n , 590–591,634,637 BellSouth, 240 “Bellwether”b onds, 251,252 Benchmark, 384 Berkshire-Hathaway, 607 Beste ffortsc asho ffer, 619,620 Beta(s), 280n,361,398–405,420 basicme thodo f me asuring, 398 correlationan d, 402–403,420 covariancean d, 402,420 cyclicalityo f r evenuesan d, 404 estimationo f, 398–401 expected return related to, 358, 359, 361,419 financialle veragean d, 404–405,405n formulasf or, 356–357,566n industry betas, use of, 400n, 400–401, 401n, 415n, 420 inflationri skan d, 372 leveragean d, 565–568,566n of mar ketp ortfolio, 380–381 operatingl everagean d, 404,420 of p ortfolio, 360,375–376 projecte valuationan d, 394–395 asp roperme asureo f risk , 357 real-world, 398–399 stabilityo f, 399n,399–400 systematicrisk an d, 350,354–356, 356n, 371–374, 374n unlevered, 567–568 Betac oefficient, 329,372,374 BethesdaM iningCo mpanyc ase, 203–204 Bid-asksp read, 250 Bidders, 877 returnsto ,in me rgers, 899–900 shareholdersan d, 901n,901–902,902n Bidp rice, 250,288,681,682 BigM acIn dex, 941–943 Binomialmo del. SeeT wo-state optionmo del BirdieGo lf–HybridGo lf c ase, 915–916 BJ’sW holesaleClu b, 371

Black–Scholeso ptionp ricingmo del described, 693n,693–698,697n determininge quityv alues, 704 duplicatingstr ategyin , 693–694 example, 694–697,697n notame nableto sim ulation, 739–740 two-statemo delc ompared, 732,733 valuation of executive stock options, 721–723 valuation of start-up company, 725–726 warrantp ricingan d, 748n,748–749 Black’s Law Dictionary, 918,918n Blanketin ventorylie n, 813 Blanketmo rtgage, 475,475n Blockbuster, 894 BMW(B ayerischeM otorenwerke)A G, 7, 918,954 BOA (Bank of America), 471, 478, 616, 875,880 Boardo f d irectors, 5–6,469,616,894,895 Boardo utc lause, 895 BoardwalkP ipelineP artners, 268 Boeing, 281,438 Bond(s), 234–261,477–479 corporate( SeeCo rporateb onds) default-free,p ured iscountb onds, 258 determinantso f yie ldso n, 257–261 EastCo astY achtsc ase, 266–267 featuresan dp rices, 234–235 floating-rate, 477–478 governmentb onds( SeeGo vernment bonds) holdingp eriodr eturnso n, 304 implicito ptionsin , 698–703 internationalb onds, 480 “junk”b onds, 248,260–261,522 maturityo f ( See Maturity of bonds) spreadsheeta pplications, 243–244 Treasuryb onds( See U.S. Treasury bonds) unusualfe atureso f, 478–479 warrantso n, 478 yieldc urveo n, 260–261 YTMo f ( See Yield to maturity) zeroc oupon( SeeZ eroc ouponb onds) Bondan ticipationn otes(B ANs), 841 Bondholders, 22,22n callo ptionsan d, 699–700,757–758 conflictswith sh areholders, 591–592, 592n,608 equitysh iftedto ,in me rger, 704–705 exchangeo ffers, 534 gainfr omme rger, 887–889,909 loangu aranteesan d, 703 personaltax esan d, 544 puto ptionsan d, 701,702 selfishin vestmentstr ategiesan d, 525–528 Bondin terestr ates, 261 accrued,c alculationo f, 252,252n

Fishere ffect, 255–257 inflationrisk an d, 254–255,255n interestr atein dexesan d, 478 interestr aterisk , 238–240 realvs .n ominalr ates, 253–254 termstru ctureo f, 257–260,258n Bondmar kets, 248–252 Bondr atings, 247n,247–248 Bondv aluation conversionv alue, 750–751 facev alue, 235–236,474 optionv alue, 751n,751–752 parv alue, 235,474 principalv alue, 474 realvs .n ominalv alue, 253–255 valuationsu mmary, 241 yieldsan d, 235–238 Bookb alance, 826 Bookbuilding, 619n Bookd ebtr atio, 482–483 Book-to-pricer atios, 449,449n ,450 Bookv alue, 556 of asse ts, 22,22n marketv aluec ompared, 23,483, 640–641 usedb yr atingse rvices, 483 Bopan alysis, 206–209,207n Borrowing inc apitalmar kets, 785 costs of, financial leverage and, 495,495n determiningamo unto f, 692 financialp olicyan d, 809–810 in“ju nk”b onds, 248 riskless, 350–353 intw o-stateo ptionmo del, 692 BostonR edS ox, 87 BostonS cientific, 248,477 Bottom-upa pproach, 187–188 Boundingv alueso f c all, 685–686 BraamIn dustriesc ase, 874 Break-evenan alysis, 210–214 Break-evenle asep ayment, 665,665n Break-evenp oint, 492,493,854 Bridgefin ancing, 479,645 Bristol-MyersS quibb, 861 Brokeragec osts, 806 Brokers, 287–288,495,495n Bubbleth eory, 450–451 BullockGo ldM iningc ase, 169–170 BunyanL umberc ase, 232–233 BurgerKin g, 248,477 Businessmo dels, 804 Businesso rganization, 4–7,18 corporations( SeeCo rporation(s)) partnerships, 4–5,6,643,644 solep roprietorships, 4 Businesssp ending, 480–481 “Buy-a-call”str ategy, 691 “Buysto ckan db orrow”str ategy, 691

Subject Index

C CA,In c., 356,401 Cablevision, 25 Calculators. See Financial calculators/ computers Callablep referredsto ck, 471 Callo ptions, 709 bondholdersan d, 699–700,757–758 boundingv alueo f c all, 685–686 “buy-a-call”str ategy, 691 complexc ontracts, 683 onc onvertibleb onds, 757n, 757–758,758n coveredc allstr ategy, 684 factorsin o ptionv alues, 687–689 gainfr ome xercising, 748 put-callp arity, 683–685,702,709 puto ptionsc ompared, 701–702 quotes, 681,682 “safety margin” theory of, 758, 758n, 759 selling, 680–681,681n stockholdersan d, 699,702,757–758 straightvs .c onvertibled ebt, 755 upperan dlo werb oundso f, 685–686 valuationo f, 727–729,728n valuea te xpiration, 676,677–678, 687,687n warrantsc ompared, 744,745–748,758 Callp remium, 476 Callp rotectedb onds, 476 Callp rovisions, 476–477 Calphalon, 846 CalpineCo rp., 918 Cancellationo ption, 653 Capitalasse tp ricingmo del(CAP M), 280n, 357–361, 362, 371, 386 arbitragep ricingth eoryc ompared, 381–383 cost of capital for projects and divisions, 408–410,409n DDMc omparedto , 406n, 406–407,407n estimating cost of capital with, 393–397,394n expected return on individual securities, 358–361,359n ,379 expected return on market and, 357–358 marketrisk p remiuman d, 396–397 risk-freer atean d, 394,396,407n securitymar ketlin e(S ML)in , 358–361 Capitalb udgeting, 2,18,171–193 APVa pproach( See Adjusted present value (APV) approach) BethesdaM iningCo mpanyc ase, 203–204 BullockGo ldM iningc ase, 169–170 comparisono f a pproaches, 557–560

981

decisionmak ing, 171–193 discountedp aybackp eriod method, 141 discountr ateo f p roject, 392–393 equivalentan nualc ostme thod, 189–193 estimatedd iscountr atean d, 560–562 exampleo f ( SeeB aldwin Companyc ase) flexibilityign oredin , 709 FTEa pproach( See Flow to equity approach) GoodweekT iresc ase, 204–205 incrementalc ashf lowsan d, 171–174,193 inflationan d, 181–186 international( See International capital budgeting) investmentru les( SeeIn vestmentru les) IRR( See Internal rate of return (IRR)) forle veredfir ms, 553–568 McKenzieCo rporationc ase, 552 operatingc ashf lowd efined, 186n, 186–189,187n optionsan d, 705–707 paybackp eriodme thod, 138–141 practiceo f, 157–159 profitabilityin dex, 155–157 riskan alysisin , 206–225 usingNP V( See Net present value (NPV)) WACCa pproach, 556–557 Capitale xpenditures, 811 Capitalgain s, 300–302,303 costo f c apitalan d, 408 dilutedb yn ewsh areholders, 393–394 dividends and, in stock valuation, 268–269,269n effectivetaxr ateo n, 543 yieldo n, 275,303–304 Capitalin tensityr atio, 65 Capitalle ases, 655 Capitallo sses. SeeNe gativec apitalgain s Capitalmar ket(s) borrowingin , 785 efficient( SeeE fficientc apitalmar kets) Capitalmar ketlin e(CM L), 352,361 CapitalOn eF inancialCo rporation, 720, 721–722 Capitalr ationing, 156–157,160 Capitalsp ending, 29–30 Capitalstru cture, 2,18,488–513 of all-e quityfir ms, 545n,545–546 changein ,E BITan d, 505–506, 506n,508 complex,fin anciald istressan d, 927–928 effect of personal taxes on, 543–544,544n establishmento f, 544–547

financial leverage and firm value, 491–495 firm value vs. stockholder interests, 489–490,490n free cash flow hypothesis and, 536–537,537n limitsto u seo f d ebt, 520–548 MMP ropositionIIan d, 495–504, 513,538 piemo delo f, 488–489,531–532 recenttr endsin , 482–483 StephensonR ealE statec ase, 519 taxesan d( SeeCo rporatetax es) trade-off th eoryo f, 530–531 See alsoF inancial distress CAPM. See Capital asset pricing model “Capped”c ouponr ate, 478 Caps, 788 Captivefin ancec ompany, 856 Carryingc osts, 805,806,80 7,813 of gr antingc redit, 855–856 of in ventory, 862,863,86 4,866 Carryingv alue. SeeB ookv alue CARs(c umulativea bnormalr eturns), 440n,440–441 Carve-out, 907–908,908n Casestu dies BaldwinCo mpany, 174–181,193 BethesdaM iningCo mpany, 203–204 BirdieGo lf–HybridGo lf me rger, 915–916 BraamIn dustries, 874 BullockGo ldM ining, 169–170 BunyanL umber, 232–233 CheekP roducts,In c., 573–574 ClissoldIn dustries, 718 East Coast Yachts (See East Coast Yachts case studies) ElectronicT iming,In c., 614–615 ExoticCu isines, 742–743 Goff Co mputer,In c., 426–427 GoodweekT ires, 204–205 KeaferM anufacturing, 822–823 MBAd ecision, 134 McKenzieCo rporation, 552 mutualfu ndr eturns, 391 RaganE ngines, 298–299 RichmondCo rporation, 845 S&SAir , 762 StephensonR ealE state, 519 Warf Co mputers,In c., 41–43,675 WilliamsonM ortgage,In c., 794 Cash componentso f, 796–797 holding, 824–825,826n ,838,842 forp lannede xpenditures, 840 public issue of stock for (See Cash offer) fromsale o f w arrants, 746n,758 short-termfin ancialp lanning, 796–797 sourcesan du seso f, 797

982

Subject Index

Cashb alance, 812 Cashb udgeting, 810–812,814 Cashc ollection, 828,833,842–843 Cashc oncentration, 834–835 Cashc overager atio, 51–52 Cashc ow, 278,280,283 Cashc ycle calculating, 800,802–803 defined, 798–799 inv ariousin dustries, 803–804 See alsoOp eratingc ycle Cashd isbursements, 826–827,829, 837–838,842–843 Cashd iscount(s), 850–851,852 Cashd iscountp eriod, 848 Cashd ividends aggregate,le gacye ffectin , 604 firmswith c ashf or, 587–589, 587n–589n firmswith outc ashf or, 586–587 paymento f, 575–578 Cashe quivalents, 825 Cash flow(s), 7–10, 35, 175, 178, 180, 811 corporatet axesan d, 505–506,506n distributiono f, 217,218 dividendsse te qualto , 578 financial cash flow, 21, 28–31, 30n, 34 from financial statements (See Financialsta tement(s)) fromfin ancingac tivities, 29,33–34 flotationc osts( SeeF lotationc osts) flow-basedin solvency, 918,918n fromgr antingc redit, 847 incremental( SeeIn cremental cashf lows) inflationan d, 183–184 initiald ividendgr eaterth an, 578–579 internallyg enerated, 480,482,484 fromin vestingac tivities, 32 fromle asing, 656–658,657n linkto d ividends, 277n,277–278,278n managemento f, 34 matching,c onvertibleb ondsan d, 756 netin comec ontrasted, 31 from operating activities (SeeOp erating cash flow) optimald ebtle vela nd, 662n, 662–664,663n realo rn ominal, 183,184 riskless, 658–660,671 fromsh ort-runac tivities, 797–798,813 stockv aluationlin kedto , 277n, 277–278,278n timingo f, 9–10,139,768 unremitted, 951 usedin NP V, 138 Warf Co mputersc ase, 41–43 Cashf lowtime lin e, 799 Cashf lowv aluation, 98–100 Cashin vestment, 839–841

Cashman agement, 824–842 acceleratedc ollections, 835–837 cashc ollection, 828,833,842–843 cashc oncentration, 834–835 cashd isbursements, 837–838 collectiontime , 832–833 float( SeeF loat) investingid lec ash, 839–841 lockboxes, 833–834 motivesf orh oldingc ash, 824–826 RichmondCo rporationc ase, 845 Cashme rger, 889n,889–890,892n , 892–893 Casho ffer, 619–627,621n beste fforts, 619,620 Dutchau ctionu nderwriting, 619, 620–621 firmc ommitment, 619,620,623 general, 617,619 GreenS hoep rovision, 621 investmentb anksan d, 622n, 622–623,623n nontraditional, 619 offeringp rice, 623–624 underpricing, 624–627,625n ,627n Cash-out, 806 Casho utflows, 811 Cashr atio, 50 Cashr eserves, 809–810 Cashsu rpluses, 839–840,842 Cashtr ansactions, 765 Caterpillar, 281 CBT(Ch icagoB oardo f T rade), 765,773 CDs(c ertificateso f d eposit), 840,841 CDS(c reditd efaults wap), 784,786–787 CentexCo rp., 20 Certificateso f d eposit(CDs), 840,841 Certificationb yu nderwriter, 623,639 CFOma gazine, 803 CFOs(c hief fin ancialo fficers), 627–628 ChampionIn ternational, 897 Changein n etw orkingc apital, 28 Chapter7b ankruptcyliq uidation, 921n, 921–924,931 Chapter11b ankruptcyr eorganization, 920, 922, 924n, 924–926, 925n, 931 Characteristiclin e, 355,398,402–403 CharminP aperCo mpany, 880 CharterCo mmunications,In c., 918 Check(s), 826,833,834–835 Check Clearing for the 21st Century Act of 2004(Ch eck21) , 832 CheekP roducts,In c.,c ase, 573–574 Chemicalin dustry, 415n Chevron, 44 ChevronTexaco, 158 Chicagoan dE asternR ailroad, 240 ChicagoB oardo f T rade(CB T), 765,773 ChicagoB oardOp tionsE xchange, 676, 677,744

ChicagoCu bs, 488 ChicagoM ercantileE xchange (CME), 765 Chief fin ancialo fficers(CF Os), 627–628 ChipotleM exicanGrill, 624 ChiquitaB randsIn ternational, 744 ChoiceOn eCo mmunications, 928 ChryslerCo rporation, 524,703,90 2,918 CircuitCity , 520 CiscoS ystems, 832 Citigroup, 347,438,479 Claims, 532,921–923 Classifiedb oardo f d irectors, 895 Cleanp rice, 252 Cleanupme rgers, 894 Clearinghouse, 765,767 Clientele(s), 595 Clientelee ffect, 595–596,596n ClissoldIn dustriesc ase, 718 CME (Chicago Mercantile Exchange), 765 CML(c apitalmar ketlin e), 352,361 Coca-ColaCo mpany, 44,240,280,280n , 438,769 CoCob onds, 478 Coinsurancee ffect, 705,887–889 Collar, 478 Collateral, 475,849 Collectedb alance, 826 Collectiona gents, 774 Collectionf loat, 827–828,829 Collectionp olicy, 847,859–861,870 Collectionp rocedures, 860–861 Collectiontime , 832–833 ColumbiaP ictures, 410 ComcastCo rporation, 249,469 Commerciald raft, 851 Commercialp aper, 813,840,841 Commissionb rokers, 288,289 Commitment(s), 479 advance,in h edging, 777n,777– 778 firmc ommitmento ffer, 619,620 ,623 Common-sizesta tements, 45,77 balancesh eets, 45–46 incomesta tements, 46–48 Commonsto ck(s) acquisition of, to acquire company, 876,909 average returns on (SeeA verage returns) classeso f, 469–470 conversionto , 752 convertibled ebtc ompared, 753–754 effectso f righ tso fferingso n, 635–636 featureso f, 467–470,484 histogramo f r eturnso n, 310 holdingp eriodr eturnso n, 304 implicito ptionsin , 698–703 issuingto p ayd ividends, 586–587 large-companysto cks, 304,306, 310, 312,317

Subject Index

low- and no-dividend, cost of capital and, 407–408 mergersf or, 891–892 proxyv oting, 469 rankedb yd ividendyie ld, 596,596n shareholder rights in, 467–469, 468n, 484 small-company stocks, 304, 306, 310, 312 stock-basedin solvency, 918,918n valuationo f ( SeeS tockv aluation) Compaq, 15 Compensatingb alances, 812,825 Competition, 850 Competitiveo ffer, 619,622 Complementaryr esources, 881 Completedc ontractsme thod, 286 Compoundgr owth, 93 Compounding, 91,192 continuous, 104–105 futurev aluean d, 91–94 powero f, 94n,94–95 quarterly, 102–103 semiannual, 101–102, 105, 237–238, 243 Compoundingp eriods, 98,101–105,242 Compoundin terest, 91,92,94 Compoundv alue. SeeF uturev alue(F V) Computerin dustry, 804 Computers. See Financial calculators/ computers ComputerS ciences, 401 Concentrationb anks, 834–835 Conditionalsale sc ontract, 852 Conglomerate(s), 60 Conglomerateac quisition, 877 Conoco, 881 Conseco,In c., 918 ConsecoF inanceCo rp., 918 Conservatism, 286–287, 444, 444n, 448, 452 Consideration, 877 Consolidation(s), 875,908 Consolidationo f d ebt, 529–530,530n Consols, 106–107 Constantgr owthsto cks, 270–272,272n Consumerc redit, 846 Consumerc reditin formation, 858 Consumerd emand, 849 ContinentalAir lines, 339 Contingentc onvertiblec lause, 478 Continuation, 437–438 Continuousc ompounding, 104–105 Contracts complex, in put and call options, 682–683 conditionalsale sc ontract, 852 fixed-an df loating-rate, 785–786 loana greements, 2,474n inv aluationo f c allo ption, 728–729 See also Derivatives; specific kinds of derivatives Contributionmar gin, 211–212 Controlledd isbursementac counts, 838

983

Controlo f fir m, 13n,13–16,877,877n agencyr elationships, 13 managementgo alsan d, 14 shareholderin terestsan d, 14–15,15n takeoversan d, 894 Conversion, 752 Conversionp olicy, 757n,757–758,758n Conversionp remium, 750 Conversionp rice, 749,750 Conversionr atio, 749,750 Conversionv alue, 750–751 Convertibleb onds, 478,749–752,758 agencyc ostsan d, 756–757,757n asb ackdoore quity, 757,757n callo ptionso n, 757n,757–758,758n conversionp olicy, 757n,757–758,758n conversionv alue, 750–751 matchingc ashf lows, 756 optionv alue, 751n,751–752 reasonsf orissu ing, 753–757,755n , 758–759 risksyn ergyan d, 756 S&SAirc ase, 762 straightb ondv alue, 750,751 straightd ebtc ompared, 753 See alsoCo nvertibled ebt;W arrants Convertibled ebt, 753–755 Corporateb onds, 245–247,472–477 basicso f, 472–473,473n equityse curitiesc ompared, 472 holdingp eriodr eturnso n, 304 indenture( SeeIn denture) long-term,r eturnso n, 304,307,312 typeso f, 477–479 yieldso n, 246 Corporatec harter, 895,895n Corporated ecisions, 703–707 Corporated iscountr ate, 409 Corporatefin ance, 1–18 controlo f c orporationan d, 13n,13–16 corporatef ormo f b usiness, 4–7,18 goalo f fin ancialm anagement, 10–12 implications of market efficiency theory, 453–459 importanceo f c ashf lows, 7–10 international( SeeIn ternational corporatefin ance) natureo f, 1–3 optionsan d( SeeOp tion(s)) regulationo f, 16n,16–18 Corporatef ocus, 898 Corporatelo ng-termd ebt. SeeCo rporate bonds Corporater esources, 537 Corporatetax es, 504–512 basicin sight, 504–506,505n ,506n betaan dle veragewith , 566,566n cashf lowan d, 505–506,506n cost of capital and, 497, 497n, 504, 504n

discountingan dd ebtc apacity, 658–660 dividende xclusion, 588, 588n doubletaxa tion, 6 expected return and leverage under, 508–510,509n integration with financial distress costs, 530–532 leasevs .b uyd ecisionan d, 661 MM Proposition I and, 507n, 507–508, 512 MMP ropositionIIan d, 508–510, 509n,512 presentv alueo f tax sh ield, 506 stockp ricean dle verageu nder, 511–512 value of levered firm and, 506–508, 507n WACCan d, 510 See alsoP ersonaltax es;T ax(es) Corporatetaxr ates, 26 Corporation(s), 1–3,5–7 agencyp robleman d, 13,13n ,18 boards of directors (See Board of directors) cashh oldingso f, 826n controlo f, 13n,13–16 dualb ooksk eptb y, 179,904 international, 7,933 private, venture capital supplied by, 643,644 venturec apitalsu ppliedb y, 644 Correlation betac omparedto , 402–403,420 diversificatione ffectan d, 340 negative, 334,335,3 43,343n perfectn egative, 334,342–343,343n positive, 334,335 of se curities’r eturn, 329,332n ,332–335 serialc orrelation, 437–438 zeroc orrelation, 334,335 Correlationc oefficients, 329,355,372, 374,437–438 Cost(s) of b ankruptcy( SeeB ankruptcy) of b orrowing, 495, 495n inb reak-evenan alysis, 211,211n creditp eriodan d, 849–850 of d ecisions, 89 directo rin direct, 629,630 of financial distress (See Financial distressc osts) fixedo rv ariable, 208,209 of f loat, 829–831,830n of h oldingc ash, 825 of h oldingf oreignse curities, 952 incomesta tementan d, 25–26 of new public issue of stock, 629–633, 631n inse nsitivityan alysis, 208–209,209n valuean d, 22n,22–23 See also specific kinds of costs

984

Subject Index

Costco, 291–292 Coste ffectso f c reditp olicy, 852 Cost-minimizingq uantity, 866 Costo f c apital, 392–393,420 for all-equity firm (SeeAll-e quity firms) average, 412,413,413n corporate taxes and, 497, 497n, 504, 504n ford ivisionsan dp rojects, 408–410, 409n EastmanCh emicalCo .e xample, 415–416 Goff Co mputer,In c.c ase, 426–427 inin ternationalc apitalb udgeting, 951–952 forin ternationalfir ms, 951–952 low-dividendsto ckan d, 407–408 WACC( See Weighted average cost of capital) See also Discount rates; Required return Costo f c apital,e stimating forall-e quityfir ms, 394–395 withCAP M, 393–397,394n costo f e quityan d, 415,415n exampleo f, 561n,561–562 Costo f c redit, 850–851,855–856 Costo f d ebt, 410–412,528–530 consolidationo f d ebt, 529–530,530n creditp olicyan d, 852,852n embeddedc ost, 411 estimating,e xampleo f, 415–416 protectivec ovenantsan d, 528–529, 529n,548 Costo f e quity agencyc osts, 534n,534–537,536n debt–equityr atiosan d, 497–498 estimating cost of capital and, 415, 415n leveragean d, 496n,496–502,497n ,513 Costr eduction costso f d ebt, 528–530 financingd ecisionsan d, 429 operatingc osts, 884–885 asso urceo f syn ergy, 880–881 transactionc osts, 666,669,669n Counterparties, 786–787 CountrywideF inancial, 471 Coupon(s)o nb onds corporateb onds, 475 effecto nd urationh edging, 779n, 779–780 fractionalc ouponp eriod, 252n levelc ouponb ond, 234–235 NCAA (“No Coupon At All”), 248, 477 semiannual, 237–238,771 See alsoZ eroc ouponb onds Couponr ate, 235,236,239,478

Covariance betac omparedto , 402,420 formulaf or, 338,338n inp ortfolio, 336–337 of se curities’r eturn, 329,332n , 332–335 CoventryHe althCar e, 248 Coveredc allstr ategy, 684 Coveredin terestarb itrage, 945–946,953 “Cramd own”p rocedure, 925n,929n Credit, 846–848 costso f, 850–851,855–856 fiveC’ so f, 859 Creditan alysis, 847,856–859,870 Creditc ostc urve, 855–856 Creditd efaults wap(CDS ), 784,786–787 Creditin formation, 858–859 Creditin struments, 851–852 Creditman agement, 846–861 collectionp olicy, 847,859–861,870 creditan alysis, 847,856–859,870 creditp olicy( SeeCr editp olicy) nature of credit (SeeCr edit) termso f sale , 846,8 48–852 Creditors(le nders), 472 bondholders( SeeB ondholders) classeso f,b ankruptcyan d, 924, 925,925n Creditp eriod, 848–850 Creditp olicy, 852–854,870 BraamIn dustriesc ase, 874 componentso f, 846–847 effectso f, 852,852n NPVo f s witching, 853–854 optimal, 854–856,870 organizingc reditfu nction, 856 totalc reditc ostc urve, 855–856 Creditr atings, 471,477 Creditr eports, 858 Creditrisk , 850 Creditsc oring, 859 CreditS uisseF irstB oston, 618,632 Creditworthiness, 247–248 Crossoverr ate, 153 Cross-rates, 934,937n ,937–938 “Crownje wels,” 898 Cumd ividend, 576 Cumulativea bnormalr eturns(CARs), 440n,440–441 Cumulatived ividends, 471 Cumulativep robability, 695–696 Cumulativev oting, 468,468n Currency, 934,944 Currencys waps, 784,786 Currentasse ts, 1–2,796 alternativep olicyf or, 808,809 financing, 805,808 liquidityo f, 21 size of investment in, 804–806, 805n, 806n,807

Currentlia bilities, 2,796 Currentr atio, 49–50 Currentyie ldo nb onds, 241 Customertyp e, 850 Cyclicalac tivities, 839

D D.R.Ho rton,In c., 20 Daimler-Benz, 902 “Dartth rowing,” 436n,436–437 Datamin ing, 383–384 Datesc onventions, 108n,108–109 Days’sale sin in ventoryr atio, 52–53, 801,801n Days’ sales in receivables ratio, 53, 801, 801n,848 DDM. SeeDi videndd iscountmo del Dealersin sto cks, 287,288 DeanW itter, 902 Debenture, 475 Debt, 2,473,473n ,507n associationwith le asing, 670,670n consolidationo f, 529–530,530n costo f ( See Cost of debt) effectso f le asingo n, 661–662,6 62n equityan d, 22,22n ,474 issuedf orsh arer epurchases, 467, 482,484 levelo f,p rofitabilityan d, 533–534 limitsto u seo f, 520–548 new,sale o f, 30,30n optimal level of (SeeOp timal debtle vel) possibilityo f d efault, 539 asp roportiono f to talv alue, 412 withp rotectivec ovenants, 528–529, 529n risklessc ashf lowsan d, 660,660 n seniorvs .ju nior, 926–927 taxsh ieldfr om, 506,511–512 taxsu bsidyto , 553,554 Debt–assetr atio, 544–545,545n Debtc apacity announcemento f n ewe quityan d, 629 discountingan d, 658–660,671 mergersan d, 883,883n of p rofitablefir ms, 539–540 Debtd isplacement, 661–664,669 basicc oncept, 661–662,662n debt–equityr atiosan d, 660 optimald ebtle vel, 662n,662–664,663n Debt–equitye xchange, 511–512 Debt–equityfin ancing, 536 Debt–equityr atios, 51,548 bookd ebtr atio, 482–483 costo f e quityan d, 497–498 debtd isplacementan d, 660 growthan d, 540n,540–542 growthr atesan d, 69,70

Subject Index

industryd ifferencesin , 504 shareholderin terestsan d, 489 target, 546n,546–547,547n WACCan d, 414 Debtfin ancing, 500–502,553–554,557 Debtor(b orrower), 472 “Debtorin p ossession,” 925,925n ,927 Debtse rvice, 22,30,654,661 Debtsign aling, 533–534,548 Debt-to-total-valuer atio, 544–545,545n , 555n,556 Decisiontr ees, 219–220,222 binomialtr ee, 735–736 marketingte sts, 223–224 usein risk an alysis, 223–225 Declarationd ate, 576 Declining-balanced epreciation, 180,181 Deedo f tru st, 474,474n Deere&Co mpany, 249,250 Default, 490n,751n ,857–858 Default-freeb onds, 258,260 Defaultrisk bonds, 244,245–246 tob rokers, 495,495n short-termse curities, 840,841 Defaultrisk p remium, 260,261 Defensivetac tics. SeeT akeoverd efenses Deferredc allp remium, 476 Deferredtax es, 25,25n Delayedan nuity, 112 Delistingsh ares, 16n,16–17 Deliverablein strument, 764 DellCo mputer, 356,606,804 DelphiCo rp., 918 Delta, 329,692 DeltaAirL ines,In c., 918 Dependentd emand, 862 Depositorytr ansferc heck(DT C), 834–835 Depreciablep roperty, 180–181 Depreciation, 25 accelerated, 286,656 added back in bottom-up approach, 188 BaldwinCo mpanye xample, 176,178, 180–181 break-evenp ointan d, 213–214 changesin me thod, 453 of c urrency, 944 declining-balance, 180,181 EBITDA, 47,52,54n ,54–55,57 ignoredin to p-downa pproach, 187 asn ominalq uantity, 184 straight-line, 181,286,657 taxb enefitsfr om, 904 totalin vestmente qualto , 274 Depreciationtaxsh ield, 189 Derivatives, 763–764 actualu seo f, 789 durationh edging, 778–784

985

forwardc ontracts, 764–765 futuresc ontracts, 765–769,768n hedgingan d, 769–771 interestr atefu turesc ontracts, 771–778 negativec orrelationswith , 343,343n swapsc ontracts, 763,784–788 WilliamsonM ortgagec ase, 794 Derivedd emand, 862 Derived-demandin ventories, 869 DesignatedOr derT urnaround(DO T), 289 Deviationsfr omr ationality. See Irrationality Differentialgr owthsto cks, 272–273 Dilution, 639–641 of c apitalgain s, 393–394 exerciseo f w arrantsan d, 745–747,758 byp oisonp ills, 896 of p roportionateo wnership, 639 repurchaseso ffsetting, 585 of v alue, 640–641 Directc osts, 14 of fin anciald istress, 523n,523–524, 524n,548 forn ewsto ckissu es, 629,630 Directle ases, 652 Directp lacement, 619 Directq uote, 935–936 Directrigh tso ffer, 619 Dirtyp rice, 252 Disbursementf loat, 826–827,829, 837–838 Discountb onds, 236–237,241,242n ,258 Discountedc ashf lowv aluation, 87–122 annuity, 109n,109–115 compoundingp eriods, 101–105 growingan nuity, 115–116,122 growingp erpetuity, 107–109,108n incrementalc ashf lows, 171–172 loanamo rtization, 116–120 multiperiodc ase, 91–101 one-periodc ase, 87–90 perpetuity, 106–107,122 risklessc ashf lows, 659,659n spreadsheeta pplications, 99,111, 119,121 valuationo f fir m, 120–121 Discountedp aybackp eriodme thod, 141 Discounting atafte rtaxin terestr ate, 662–663,663n debtc apacityan d, 658–660,671 dividendsvs .e arnings, 284 incrementalc ashf lows, 171–172 multiperiod, 96–97 nominalvs .r eal, 184–186 presentv aluean d, 95–98 inp ublicissu eo f st ock, 620 Discountr ates, 88,280n calculationo f, 556,567 corporater ate, 409

estimated,c apitalb udgetingan d, 560–562 ingr owingp erpetuityf ormula, 108 IRRan d, 142,151,153 leasevs .b uyd ecisionan d, 661 PEr atioan d, 286 of p roject, 392–393 risk-adjusted, 395 selectiono f,risk an d, 90 insto ckv aluation, 271,2 75–276 See also Cost of capital; Required return Disney, 281 Dispersiono f r eturns, 339 Distressedd ebtin vestors, 923 Distribution, 575 Diversification, 347–350 acquisitionsan d, 886,886n effective, 377,377n essenceo f, 348–350 informationan d, 347 inin ternationalfir ms, 951 optionsan d, 703–705 of p ortfolios, 376–378,377n ,378n ,386 powero f, 314,347 riskan d, 347–348,349,378 Diversificatione ffect, 338n,338–339,340, 341–342 Divestitures, 906–908 carve-out, 907–908,908n sale, 906–907,907n spin-off, 907 trackingsto cksan d, 908 See alsoAc quisitions;M erger(s) Dividend(s), 292,575–608 capitalgain san d, 268–269,269n inc ash( SeeCash d ividends) choosingo verr epurchases, 602–604 onc ommonsto ck, 470,470n compoundgr owtho f, 93 contento f in formationo n, 592n, 592–593 asc ostto fir m, 393–394 discountingvs .e arnings, 284 earningsc ompared, 281–282 effectso f tax eso n, 586–590 fewerc ompaniesp aying, 598n, 598–599,599n homemade, 580,581 asin comec omponento f r eturns, 300 investmentp olicyan d, 582 no-dividendfir ms, 284n,284–285 NPVc omparedto , 281–282 personaltax esan d, 588,608 policies regarding (See Dividend policy) onp referredsto ck, 412,471 prosan dc onso f p aying, 600 relevanceo f, 581–582 share repurchases as substitutes (See Sharer epurchases)

986

Subject Index

Dividend(s)—Cont. standardp aymentme thod, 575–578 stockd ividends( SeeS tockd ividends) stocksp lits( SeeS tocksp lits) insto ckv aluation, 268–269,269n substantial, 597,597n ,602 taxd isadvantageo f, 586–589 typeso f p ayouts, 575 Dividendd iscountmo del(DDM ), 273–278, 282, 292, 406–408 applicationin n o-dividendfir ms, 285 comparisonwith CAP M, 406n, 406–407,407n in estimating market risk premium, 396–397,397n growthr atean d, 273–275,274n link to cash flows, 277n, 277–278, 278n low-o rn o-dividendsto cks, 407–408 retentionr atiob enefits, 282–284 short-termh orizonsan d, 269 skepticismr egarding, 276–277 totalr eturnin , 275–276 Dividendp ayout, 575 Dividendp ayoutr atio, 64 Dividendp ersh are, 575 Dividendp olicy, 578–582,608 agencyc ostsan d, 591–592,592n behavioralfin ancean d, 590–591, 591n,608 clientelee ffecto n, 595–596,596n desiref orc urrentin comean d, 590 asd eterminanto f gr owth, 73 dividende qualto c ashf low, 578 dividend greater than cash flow, 578–579 effecto nc urrentsto ckp rice, 594 ElectronicT imingc ase, 614–615 fewerc ompaniesp ayingd ividends, 598n,598–599,599n high-dividendp olicy, 590–594 homemaded ividends, 580,581 indifferencep roposition, 579–580 informationc ontentan d, 592n, 592–593 irrelevanceo f, 578–582 signalingan d, 593n,593–594,594n substantiald ividends, 597,597n ,602 surveye videncea bout, 600–602 theoriesa bout, 602n,602–604 Dividendsmo othing, 599n,599–600,602 Dividends-to-earningsr atio, 600 Dividendyie ld, 275,302–304,575 averageyie lds, 397 commonsto cksr ankedb y, 596,596n estimatingwith DDM , 406 onp referredsto ck, 841 Divisionso f fir m, 408–410,409n DJIA (Dow Jones Industrial Average), 347 DOJ(U .S.De partmento f J ustice), 880,898

Dollarr eturns, 300–302 DornierGmB H, 7 DOT(De signatedOr der Turnaround), 289 Doubletaxa tion, 6 DowJ onesIn dustrialA verage (DJIA), 347 DowJ onesIn dustrialsIn dex, 281,402 Downsta tep rices, 729–730 Dribbleme thodo f e quityissu ance, 642 DTC(d epositorytr ansferc heck), 834–835 Dun&B radstreet, 858 Duplicatingstr ategy, 693–694 DuP ontCo rporation, 59,881 DuP ontid entity, 59–61 Durationc oncept, 780–782,781n ,790 Durationh edging, 778–784 durationc onceptan d, 780–782,781n effecto f d ifferentc oupons, 779n, 779–780 liability-assetma tching, 782–784,784n zeroc ouponb onds, 778,778n ,779 Dutchau ction, 583 Dutchau ctionu nderwriting, 619,620–621 Dynegy, 34

E EAC(e quivalentan nualc ost), 191–192, 212–213 EAR(e ffectivean nualr ate), 102,103–104, 850 Earnings dividendsan d, 281–282,284 dividends-to-earningsr atio, 600 falling, 629,629n growthin ,ac quisitionsan d, 885n, 885–886 measureso f, 47 Earningsb eforein terest(E BI), 491–492, 496 Earnings before interest, taxes, depreciation, and amortization (EBITDA), 47, 52, 54n, 54–55, 57 Earnings before interest and taxes (EBIT), 23 change in capital structure and, 505–506,506n ,508 ingr owingfir m, 541n,541–542,542n asme asureo f e arnings, 47 inn o-growthfir m, 540–541 Earningsb eforetax es(E BT), 187 Earningsp ersh are(E PS), 55 effect of leverage on, 491–493, 496, 506, 506n asme asureo f e arnings, 47 inP Er atio, 285,285n inr epurchasea greement, 584 Earningsr etention, 541n Earningssu rprise, 447–448,448n

EastCo astY achtsc asestu dies bonds, 266–267 financialp lanning, 84–86 internationalfin ance, 961–962 markete fficiency, 465n,465–466 publicissu eo f sto ck, 651 riskan dr eturn, 327–328,369–370 EastmanCh emicalCo ., 392,406,4 15–416 EastmanK odak, 415 EAY(e ffectivean nualyie ld), 102,2 42 eBay, 284,356 EBI(e arningsb eforein terest), 491–492, 496 EBIT. See Earnings before interest and taxes EBITDA (earnings before interest, taxes, depreciation, and amortization), 47, 52, 54n, 54–55, 57 EBITDAmar ginr atio, 54n,54–55 EBT(e arningsb eforetax es), 187 ECNs(e lectronicc ommunications networks), 291 Economico rderq uantity(E OQ)mo del, 863–869 carryingc osts, 864 inventoryd epletion, 864 reorderp ointsin , 867–869 safetysto cksin , 867,868 storagec osts, 864–865 totalc osts, 865–867 Economieso f sc ale, 631,631n ,880,884 The Economist, 941 Economy, 808,813–814,884 EDI(e lectronicd atain terchange), 831–832 EDS, 908 Effectivean nualr ate(E AR), 102, 103–104,850 Effectivean nualyie ld(E AY), 102, 242 Effectived iversification, 377,377n Effectivema turity, 781 Effectivetaxr ate, 543 Effectivetime to ma turity, 776,776 n Effectiveyie ldo nb onds, 238 Efficientc apitalmar kets, 287,428– 460, 431 behavioralc hallengeto , 443–445 EastCo astY achtsc ase, 465n,46 5–466 effectso f me rgerso n, 899 eventstu dieso f, 437–443 exampleo f, 430–431 futuresto ckp ricesin , 753 value-creatingd ecisionsin , 428–430 Efficientmar keth ypothesis(E MH), 764 controversyo ver, 451–452 described, 430–433,432n efficacyo f d artth rowing, 436n, 436–437 empiricalc hallengesto , 445–451 foundationso f, 432n,432–433

Subject Index

implicationsf orc orporatefin ance, 453–459 logico f, 432n pricef luctuationsan d, 437 semistrongf orme fficiency, 435–436, 439–443,656 stockholderd isinterestan d, 437 strongf orme fficiency, 435,436,443 summaryo f, 459,460 weakf orme fficiency, 433–434,434n , 435,436,437–439 Efficientse t(fr ontier), 342 for multiplese curities, 344n,344–347, 345n,361 for twoasse ts, 339–344 eFinance.com, 8 EFN(e xternalfin ancingn eeded), 66–75 Electronicc ommunicationsn etworks (ECNs), 291 Electronicd atain terchange(E DI), 831–832 ElectronicDa taS ystems, 401 Electronicfu ndstr ansfers, 825 “Electroniclo ckboxes,” 833–834 ElectronicT iming,In c.,c ase, 614–615 Embeddedc osto f d ebt, 411 Embeddedo ptions, 725–726,740 EmergentB ioSolutions,In c., 300 Empiricalmo dels, 383–384,386 Employeesto cko ptions. SeeE xecutive stocko ptions Endo f mo nth(E OM)d ating, 849,851 End-of-the-yearc onvention, 108n,108–109 EnronCo rp., 17,454,523,918 Enterprisev aluem ultiples, 57 Enterprisev aluer atio, 56–57 EOM(e ndo f mo nth)d ating, 849,851 EPS. SeeE arningsp ersh are Equifax, 858 Equity, 20,21,22 backdoore quity, 757,757n costo f ( See Cost of equity) debtan d, 22,22n ,474 dribbleme thodo f issu ance, 642 maximizationo f o wners’e quity, 12,18 newsto ckissu esan d, 628n, 628–629,629n asp roportiono f to talv alue, 412 seasonede quityo ffering, 454–455, 456,457 shiftedto b ondholders, 704–705 Equity-basedc ompensation, 901,901n Equityb eta, 405 Equityfin ancing, 71 Equityk ickers, 744,744n Equitym ultiplier, 51 Equityrisk p remium, 311,358 globalp erspective, 318–319,320,321n

987

historicalp erspective, 318,318n , 319–321,320n Equitysh ares(se curities), 2,472 Equity–valuer atio, 414 Equivalentan nualc ost(E AC), 191–192, 212–213 Equivalentan nualc ostme thod, 189–193 Erosion, 173 Ethicalissu es insidertr ading, 16–17 useo f f loat, 831,837–838 eToys, 627 Eurobonds, 480 Eurocurrency, 934 EuroDisn ey, 221–222 Europeane xchanger ate, 936 Europeano ptions, 676,685n ,687n ,690n Eventstu dies of e fficientc apitalmar kets, 437–443 measuringv aluec reation, 898 of se mistrongf orme fficiency, 439–441, 440n Exactd atec onvention, 108 Excessr eturn, 311,436–437 Exchangeo ffers, 534 Exchanger ate(s), 935–939 cross-rates, 937n,937–938 expectedr ate, 943n,943–944,953 forwardr ates, 939,953 indirectr ate, 936 profitp otentialin , 940 trianglearb itrage, 938 typeso f tr ansactions, 939 Exchanger ateq uotations, 935–937,956 Exchanger aterisk , 933,952–955,957 forwarde xchanger ates, 953 long-terme xposure, 953–954 managing, 955 short-terme xposure, 952 translatione xposure, 954–955 Exclusionaryse lf-tenders, 897–898 Ex-dividendd ate, 576,577–578 Executivec ompensation, 1 forac quisitions, 901,901n goldenp arachutes, 895–896 asman agerialin centive, 14–15,15n Executivesto cko ptions, 585,719–723 ExoticCu isinesc ase, 742–743 reasonsf or, 719–720 valuationo f, 720–723,722n Exercisep rice, 676,681,682 call option value and, 687, 689, 699–700 goldmin ee xample, 734,735 puto ptionv aluean d, 690,700–701 onw arrant, 745 Exercisingo ptions, 585,676 ExoticCu isinesc ase, 742–743 Exotics wapsc ontracts, 787–788 Expansiono ption, 219–220,724–725

Expectede xchanger ate, 943n,943–944, 953 Expectedma turity, 776 Expectedr eturn(s) onb onds, 245–246 callp ricean d, 698 CAPMan d, 393 underc orporatetax es, 508–510,509n costo f c apitalan d, 408,419 dividendd iscountmo delo f, 406–408 empiricala pproachto , 383–384 on equity, with leverage, 496n, 496–502, 497n,509–510 estimatingwith DDM , 406 onin dividualse curities, 358–361, 359n,379 onmar ket, 357–358 onp ortfolio, 335–336,36 0,361 related to betas, 358, 359, 361, 419 risklessle ndingan d, 351 onse curities, 329 securitymar ketlin ef or, 379–380 tosh areholders, 393–394 variancean d, 330n,330– 332 Expenses, 811 “Expensivelu nch”sto ry, 755 Experian, 858 Expirationd ate of call option, 676, 677–678, 687, 687n of p uto ption, 678–679,690 Ex-rightsd ate, 636 Externalfin ancingn eeded(E FN), 66–75 Extrac ashd ividends, 575 Exxon, 877 ExxonMobil, 13n,158,371,827

F Facev alueo f b onds, 235–236,474 Factor(s), 813 Factoring, 813,855 Factormo dels, 386 Fama–Frenchth ree-factormo del, 385 multifactormo delo f AP T, 382 portfoliosan d, 374–378,385 single-factormo dels, 374–378,380n , 380–381 of syste maticrisk , 371–374 Faire xchanger atio, 891–892 Fairmar ketr ateo f r eturn, 656 Fairv alue, 431 Fama–Frenchth ree-factormo del, 385 FannieM ae, 300 FASB. See Financial Accounting StandardsB oard Feasiblese t, 341,344,344n FederalE xpress, 526 FederalR eserveB oard, 16n FederalT radeCo mmission, 880,898 FEDI(fin ancialE DI), 831–832

988

Subject Index

FiatS pA, 7 FidelityM agellanF und, 313–314 Fieldw arehousefin ancing, 813 FIFO(first-in ,first-o ut)ac counting, 286–287,453 FinancialAc countingS tandardsB oard (FASB), 179 Statement of Financial Accounting Standards No. 13, 654,655 Statement of Financial Accounting Standards No. 52, 955 Financialasse ts, 587–589 Financialc alculators/computers errorsin c alculations, 137,138 geometrica verager eturns, 316 NASDAQ, 290–291 simulationf orfin anciald ecisions, 736–738 softwarep ackages, 345 See alsoS preadsheeta pplications Financialc ashf low, 21,28–31,30n ,34 Financialc risiso f 2008, 300,321–322 Financiald ecisionmak ing, 89 capitalstru cturean d, 488–513 dividendsan do therp ayouts, 575–608 ine fficientc apitalmar kets, 428–460 financialsta tementsu sedin , 44 investmentd ecisionsan d, 68 inle veredfir ms, 553–568 long-termfin ancing, 467–484 marginaltaxr atesan d, 28 optionfr ameworkf or, 707–709,709n See also specific kinds of decisions Financiald eficit, 480–481 Financiald istress, 917n,917–918, 918n,931 academicvie wo f, 922–923 bankruptcyliq uidation(Ch apter7), 921n,921–924,931 bankruptcyr eorganization(Ch apter 11), 920, 922, 924n, 924–926, 925n,931 complexc apitalstru cturean d, 927–928 holdouts, 927,927n lacko f in formationan d, 928 of mar ginalfir ms, 927 processo f, 918–920,920n See alsoB ankruptcy Financiald istressc osts, 520–548 agencyc osts( SeeAge ncyc osts) APVa pproachan d, 553 directc osts, 523n,523–524,524n indirectc osts, 524n,524–525 integrationwith taxe ffects, 530–532 pecking-orderth eory, 537n,537–540, 538n reducingc ostso f d ebt, 528–530 signaling, 533–534,548 useo f d erivativesan d, 789 See alsoB ankruptcy

FinancialE DI(F EDI), 831–832 Financialga p, 480 FinancialIn dustryR egulatoryA uthority (FINRA), 249 Financialin novation, 430,430n Financialle ases, 653–654 Financialle verage, 491–495,506–508,513 betaan d, 404–405,405n cost of equity and, 496n, 496–502, 497n,513 debt vs. equity choice, 492, 493n, 493–495 expectedR OEwith , 496n,496–502, 497n,509–510 keyassu mptionr egarding, 495,495n returnsto sh areholdersan d, 491–493, 496, 506, 506n See alsoL everedfir ms Financialle verager atios. SeeL everage ratios Financialman agers, 3,10–12,800 Financialmar kets capitalmar kets, 785 cashf lowsb etweenfir man d, 8 private equity market (SeeP rivate equitymar ket) “Financial”me rgers, 704,705 Financialp lanning EastCo astY achtsc ase, 84–86 exampleo f, 67–68 “Procrustesa pproach”to , 75–76,76n short-term( See Short-term financial planning) simplemo delso f, 62–63 Financialp lanningmo dels, 62–68 caveatsr egarding, 75–76,76n MonteCar losim ulation, 214–218 percentageo f sale sa pproach, 63–68 simple, 62–63 Financialp olicy asd eterminanto f gr owth, 71–74,75 flexibilityo f, 805–808 internalgr owthr atean d, 70,71 restrictive, 806,807 salesgr owthan d, 63 short-term, 804–810 sustainablegr owthr atean d, 70,71–72 Financialr atios. SeeR atioan alysis Financialslac k, 540 Financialsta tement(s), 20–35 balancesh eet( SeeB alancesh eet(s)) cashf lowman agementan d, 34 creditin formationf oundin , 858 financial cash flow and, 21, 28–31, 30n incomesta tement( SeeIn come statement) netw orkingc apitalan d, 28 statement of cash flows (SeeS tatement of cash flows) taxesan d, 26–28

Financialsta tementan alysis, 44–48 common-sizeb alancesh eets, 45–46 common-sizein comesta tements, 46–48 ratioan alysis( SeeR atioan alysis) standardizingsta tements, 44–45 Financial subsidies, 429, 553–554, 557, 564,564n Financingtyp ep rojects, 145,146 Finishedgo odsin ventory, 861 FINRA(F inancialIn dustryR egulatory Authority), 249 Firmc ommitmento ffer, 619,620, 623,646 Firms all-debtfir ms, 413,413n all-equityfir ms( SeeAll-e quityf irms) cashf lowswith fin ancialmar kets, 8 controlo f,sh areholderin terestsan d, 15 control of firm, 13n, 13–16, 877, 877n, 894 corporations( SeeCo rporation(s)) growing,d ebt–equityr atioin , 541n, 541–542,542n indifferenceto e quityo rd ebt, 543 no-dividendfir ms, 284n,284–285 no-growthfir ms, 540n,540–541 ,542 partnerships, 4–5,6 valueo f ( SeeV alueo f fir m) FirstCityP roperties, 896 First-in,first-o ut(F IFO)ac counting, 286–287,453 First-roundfin ancing, 644 Fiscaly ear, 60 FiservIn c., 401 Fishere ffect, 255–257,948n ,948–949,950 FitchR atings, 16n,248,477 FiveC’ so f c redit, 859 Fixedasse ts, 1,21–22,29 Fixedc osts, 208 Fixed-ratelo an, 785–786 Flat-ratetax, 27 FleetF inancialGr oup, 902 Flexibility, 585,709 of fin ancingstr ategy, 809–810 of sh ort-termfin ancialp olicies, 805–808 Flexibletar gets, 546 Float, 826–832,842,847 collectionf loat, 827–828,829 costo f, 829–831,830n disbursementf loat, 826–827,829, 837–838 ethicalan dle galissu es, 831,837 –838 managemento f, 828–831 measuring, 828–829 netf loat, 827–828 steady-statef loat, 830,830n Floating-rateb onds(f loaters), 477–478 Floating-ratelo ans, 785–786 Floor(s), 788

Subject Index

Floorac tivity, 289–290 Floorb rokers, 289 Floortr aders, 289 Flotationc osts, 417–419,420,563–564 Flowto e quity(F TE)a pproach, 557–560 calculatingd iscountr ate, 556 calculatingL CF, 555n,555–556 estimatingc osto f c apital, 561–562 guidelinef oru se, 558–559 summaryo f, 560 valuation, 556 FMC(F ordM otorCr edit), 856 Forbes Magazine, 15,408 Force conversion, 757 Ford Motor Company, 45, 335, 339, 433, 437, 469, 824, 825, 917 FordM otorCr edit(F MC), 856 Forecasts, 397,406 Foreignb onds, 480 Foreignc urrencies, 457 Foreignc urrencya pproach, 949,950–951, 951n Foreigne xchange, 933 Foreigne xchangemar kets, 934–935 Foreigne xchanger ates. SeeE xchange rate(s) Foreigne xchange(F X)s waps, 786 Form8K(S EC), 16 Form10K(S EC), 16 Form10Q(S EC), 16 Forwardc ontract(s), 764–765,790 futuresc ontractsc ompared, 765, 767–769 majorf lawin , 768–769 pricing, 772–773,773n Forwardc ontractp ricing, 772–773,773n Forwarde xchanger ates, 939,947,953 Forwardtr ade, 939 Fourth-roundfin ancing, 645 Fox, 410 FoxMeyerHe alth, 861 Fractionalc ouponp eriod, 252n FranklinE lectronicP ublishers, 654 FreddieM ac, 300 Freec ashf low, 31,507,507n ,884,884n Freec ashf lowh ypothesis, 277n agencyc ostsan d, 536–537,537n rolein me rgers, 902 unprofitablec arve-outsan d, 908 “Freelu nch”sto ry, 754–755 Freeport-McMoRanCo pper& GoldIn c., 720,721 Freeze-outp eriod, 721,723 Frequencyd istribution, 310–311,312 Friendlytak eovers, 893–895,909 FTE. See Flow to equity (FTE) approach Funding, 473n Futuresc ontracts, 765–769,768n ,773n , 773–774,790

989

forwardc ontractsc ompared, 765, 767–769 longh edgein , 770n,770–771,771n marked-to-the-marketp rovisionsin , 767, 768, 769, 773 shorth edgein , 769–771 Futuresp otr ates, 947 Futurev alue(F V), 88,91–94,122 Future value of annuity of $1 table, 111,967 Futurev alueo f $1 table, 93,966 Future value of $1 with continuously compoundedr ates, 105 Future value of $1 with continuously compoundedr ateta ble, 105,968–969 FV(fu turev alue), 88,91–94,122 FX(f oreigne xchange)s waps, 786

G GAAP(ge nerallyac ceptedac counting principles), 9,22,22n ,24 TheGa p, 438,439 GatewayCo mputer, 804 GE. SeeGe neralE lectric GECo mmercialF inance, 652 Generalc asho ffer, 617,619 GeneralDyn amics, 14–15 General Electric (GE), 26, 61, 171, 339, 348, 356, 380n, 410, 527, 652, 824, 825,856,886 GeneralGr owthP roperties,In c., 918 Generallyac ceptedac countingp rinciples (GAAP), 9,22,22n ,24 General Motors Corp. (GM), 45, 53, 335, 347, 352, 433, 437, 471, 531–532, 881, 908, 917, 918, 919, 953 Generalp artnership, 4 The General Theory of Employment, Interest, and Money(K eynes), 824 Gentex, 604 Geometrica verager eturn, 315,316–317 Geometricse ries, 106 GettyOil, 524–525,881 GibsonGr eetingCar ds(GGC), 906 Gillette, 897 Gilts, 934 GlobalCr ossing, 454 Globalissu es bankruptcy, 922,924n equityrisk p remium, 318–319,320, 321n financialc risiso f 2 008, 300,321–322 IPOu nderpricing, 626 rightso fferings, 637,637n shareholderp rotection, 13,13n taxb ooksvs .sto ckholders’b ooks, 179 Globalization, 934 GM. SeeGe neralM otorsCo rp. Goff Co mputer,In c.,c ase, 426–427

“Goingd ark,” 16n,16–17,607 Goingo nmar gin, 351,494 Going-privatetr ansactions, 877–878, 905,909 Goldenp arachutes, 895–896 The Goldman Sachs Group, Inc., 7, 14, 616, 619, 720, 721, 875 GoodweekT iresc ase, 204–205 Goodwill, 904 Google, 44, 60–61, 284, 285, 287, 469, 620–621,622 Governmentb onds, 244n,244–245 holdingp eriodr eturnso n, 304 intermediate-term, 312 long-term, 304,307,312 municipal(“m unis”), 244,244n ,245, 261 taxe xemptions, 244,244 n totalan nualr eturns, 312 Treasuryb onds( See U.S. Treasury bonds) yieldso n, 246 GreatDe pression, 923 Greenin itiatives, 171 Greenmail, 896,897 GreenS hoeCo rp., 621n GreenS hoep rovision, 621,631 Growingan nuity, 115–116,122 Growingfir ms, 541n,541–5 42,542n Growingp erpetuity ingr owingfir m, 541n presentv alueo f, 107–109,108n ,271 simplifyingf ormulaf or, 107–109, 108n,122 Growth debt–equityr atioan d, 540n,540–542 determinantso f, 73–74,7 5 EFNan d, 68–71 financialp olicyan d, 71–74,75 Growtho pportunities, 278–285,280n discountingd ividendsvs .e arnings, 284 earningsan dd ividendsc ompared, 281–282 no-dividendfir ms, 284n,284–285 NPVGO( See Net present value of growtho pportunities) PEr atioan d, 285–286,2 87 of real-world companies, 280n, 280–281 retentionr atioan d, 282–284 Growthr ates ind ividendd iscountmo del, 273–275, 274n of d ividends,e stimating, 406 EFNf or, 69–70 ingr owingp erpetuityf ormula, 108 internal, 70,71,75 paymento f d ividendsan d, 285 retentionr atioan d, 283–284 sustainable, 70,71–72,74–75 totalr eturnd ependentu pon, 276–277

990

Subject Index

Growthsto ck(s), 449n,449–450,450n Growthsto ckp ortfolios, 384–385

H Healthcaree quipmentin dustry, 804 Hedges, 382n Hedging, 336–337,763,769–771,790 durationh edging, 778–784 exchanger ates, 953–954 interestr ateh edging, 774–778, 776n longh edge,e xampleo f, 770n, 770–771,771n of p oliticalrisk , 956 shorth edge,e xampleo f, 769–770 shortvs .lo ng, 777n,777–778 Hewlett-Packard(HP ), 15,281,804 High-dividendp olicy, 590–594 Hockeystic k diagram, 678 Holdingp eriod, 269 Holdingp eriodr eturns, 304–307 Holdouts, 927,927n ,929 Homec urrencya pproach, 949,950 HomeDe pot, 58,347,356 Homemaded ividends, 580,581 Homemadele veragestr ategy, 494–495 Homogeneouse xpectations, 354,354n Honda, 795,918,954 HoneywellIn ternational, 347 Horizontalac quisition, 877,881 HormelF oods, 371 Hostiletak eovers, 893–835,909 Hostiletar get, 894 HovnianE nterprises, 20 HP(He wlett-Packard), 15,281,804 HughesAir craft, 881

I Ibbotson SBBI 2009 Classic Yearbook, 304,304n IBM, 286, 335, 339, 352, 410, 438, 652, 677,678,856 Ideale conomy, 808,813–814 Idiosyncraticrisk , 348 IFE(in ternationalF ishere ffect), 948n, 948–949,950 Illegalac ts, 34,454,589,589n IlukaR esources,L td., 953 ImCloneS ystems, 17 Immunizationto in terestr aterisk , 774, 782–783,783n Impaireda bilityto c onductb usiness, 524n,524–525 Impairmento f asse ts, 905 Income, 175, 176,178 accountingin come, 669 netin come, 31,47 operatingi ncome, 547 Incomeb onds, 478

Incomesta tement common-size, 46–48 noncashite msin , 23–24,25,25n percentageo f sale sa pproach, 63–64 prof orma, 62–63,64 timean dc osts, 25–26 Increasedd ebtc apacity, 883,883n Incrementalc ashf lows, 171–174,193 allocatedc osts, 173–174 discounting, 171–172 IRRan d, 149–152,160 opportunityc osts, 172–173 sidee ffectso f, 173 sunkc osts, 172 switchingc reditp olicies, 853 synergyan d, 878n,878–879 IncrementalIRR, 151 Indenture, 474n,474–477 callp rovisions, 476–477 protectivec ovenantsin , 477,528–529, 529n security, 475,475n seniority, 476 sinkingfu ndarr angements, 476 termso f b ond, 474–475 Independentd emand, 862 Independentle asingc ompanies, 652,670, 784 Independentp rojects, 155 Indexfu nds, 441–442 Indiana Jones and the Kingdom of the Crystal Skull(film), 206 Indifference tod ividendo rr epurchase, 583–584,608 tod ividendp olicy, 579–580 toe quityo rd ebt, 543 tome rger, 887,888 Indifferencep roposition, 579–582,584, 608 Indirectc osts, 14 of fin anciald istress, 524n,524–525,548 forn ewsto ckissu es, 629 Indirecte xchanger ate, 936 Individualr etirementac count(IRA), 111 Indivisibilities, 157 IndustrialCo mpositeIn dex (VL), 397 Industryb etas, 400n,400–401,401n , 415n,420 Inefficientman agement, 881,881n Inflation, 181–186,193,312 cashf lowan d, 183–184 discounting: nominal vs. real rates, 184–186 expectede xchanger atean d, 943n, 943–944 interestr atesan d, 181–183 term structure of interest rates and, 257–260,258n TIPS, 254–255,255n year-by-year, 308

Inflatione scalatorc lause, 769 Inflation-linkedb onds, 254–255,25 5n Inflationp remium, 258,259,261 Inflationr ate Fishere ffectan d, 255–257 nominalr ateo nb ondsan d, 253 relative purchasing power parity and, 943n,943–944 Inflationrisk , 254–255,255n ,372 Information asymmetric, 538 diversificationan d, 347 ond ividends,c ontento f, 592n,5 92–593 lacko f,fin anciald istressan d, 928 inmar ketp rices, 457–459,457n –459n, 460 new,r eactionsto , 431–432 privatevs .p ublic, 435 public,E MHan d, 439,440 public, mutual fund performance and, 441,443 randomw alkan d, 434,434n sourceso f c reditin formation, 858–859 Informationc ontente ffect, 592n,5 92–593 Infrequentan nuity, 113 Initialp ublico ffering(IP O), 408,616, 617, 619, 619n deviationsfr omp arityan d, 446–447 Dutchau ctionu nderwriting, 620 followingL BO, 906 investoro verenthusiasm, 625,627,627n opinionso f CF Os, 627–628 techb ubblein , 428 timingd ecisiono f, 454,456 venturec apitalfin ance, 645,645n “Inp lay,” 895 Insidertr ading, 16–17 Insolvency, 918,918n Insurancec ompanies, 856 Intangibleasse ts, 22 IntelCo rporation, 281 Intercept(alp ha), 398 Interest on bonds, no tax exclusion for, 588n compound, 91,92,94 simple( SeeS implein terest) taxd eductible, 411,472 Interestc overager atio(T IEr atio), 51 Intereste xpense, 29,34 Interesto nin terest, 91,92,192 Interest-onlylo an, 236 Interestr ate(s), 122 onb onds( See Bond interest rates) calculating, 97–98 callo ptionv aluean d, 689 coveredin terestarb itrage, 945–946,953 Fishere ffectan d, 255–257 inflationan d, 181–183 puto ptionv aluean d, 690 realo rn ominal, 182,183

Subject Index

risk-freer ate, 419,735 solvingf or, 93–94 stated annual interest rate, 102, 103–104 termstru ctureo f, 257–260,258n tiedto L IBOR, 812 Interestr ateb ets, 456 Interestr atefu turesc ontracts, 771–778, 773n,790 forwardc ontractp ricing, 772–773, 773n futuresc ontracts, 773n,773–774 futuresh edging, 774–778,776n shortvs .lo ngh edging, 777n,777–778 U.S.T reasuryb ondp ricing, 771 Interestr atefu turesh edging, 774–778,776n Interestr atein dexes, 478 Interestr atep arity(IRP ), 946n, 946–947,956 Interestr aterisk (se nsitivity) onb onds, 238–240 immunizationstr ategies, 774, 782–783,783n interestr ateh edging, 774–775,790 onsh ort-termse curities, 840 Interestr aterisk p remium, 258,258n , 259,261 Interestr ates waps, 784n,784–786 Interestsu bsidies, 562–565 Intermediate-termd ebt, 473n Internale quity, 419 Internalfin ancing, 539 Internalgr owthr ate, 70,71,75 Internalr ateo f r eturn(IRR), 141–154, 159 benefitso f, 154 calculationo f, 141–143 costo f c apitalan d, 395,407 incremental, 151 independent and mutually exclusive projects, 144–145 modified, 147–148 NPVan alysisc ompared, 141–143,149, 151–154 problemswith , 144–154 spreadsheeta pplications, 144 InternalR evenueCo de, 589,882 InternalR evenueS ervice(IRS ), 7,179,882 ond eductionsf orle ases, 656 penaltiesf ortaxa voidance, 589,590 onv erylo ng-termb onds, 240 Internationalb onds, 480 Internationalc apitalb udgeting, 949n, 949–952,957 costo f c apital, 951–952 foreignc urrencya pproach, 949, 950–951,951n homec urrencya pproach, 949,950 unremittedc ashf lows, 951

991

See also Capital budgeting; Internationalc orporatefin ance Internationalc orporatefin ance, 933–957 capitalb udgeting, 949n,949–952 coveredin terestarb itrage, 945–946,953 currencys waps, 784,786 EastCo astY achtsc ase, 961–962 exchanger aterisk , 933,952–955,957 foreigne xchangemar kets, 934–935 foreign exchange rates (SeeE xchange rate(s)) interestr atep arity, 946n,946–947 internationalF ishere ffect, 948n, 948–949,950 politicalrisk , 952,955–956,957 purchasingp owerp arity, 939–944 terminology, 934 unbiasedf orwardr ates, 947,952 uncoveredin terestp arity, 948,948n Internationalc orporations, 7,933 InternationalF ishere ffect(IF E), 948n, 948–949,950 InternationalP aperCo ., 478 Internetsto cks, 286,607,893 indexo f, 450–451 techb ubble, 428,444,626 Intervals, 731–733,732n “Inth emo ney,” 677,748 Inventory accountingme thods, 286–287,453 blanketin ventorylie n, 813 carrying costs of, 862, 863, 864, 866 just-in-timein ventory, 862,869 kindso f, 861 liquidityo f, 21,862 omittedfr omq uickr atio, 50 sizeo f, 805,805n stockouts, 180 Inventoryd epletion, 864 Inventorylo ans, 813 Inventoryman agement, 861–869,870 ABCa pproachto , 863 derived-demandin ventories, 869 EOQmo del, 863–869 inventoryc osts, 862 inventoryp olicy, 861 just-in-timein ventory, 869 materialsr equirementsp lanning, 869 typeso f in ventory, 861–862 Inventoryp eriod, 798,801,801n ,803,849 Inventorytu rnoverr atio, 52,801, 801n,802 Inversef loater, 787 Investingtyp ep rojects, 145,146 Investment(s) cashin vestment, 839–841 in current assets, size of, 804–806, 805n, 806n,807 holdingp eriodr eturnso n, 304–305 netin vestment, 274

in real projects, options and, 707–709, 709n inr eceivables, 847–848 forr etirement, 111 selfishin vestmentstr ategies, 525–528 inw orkingc apital, 175,177–178,277n Investmentb anks, 619–620 role in public issue of stock, 622n, 622–623,623n See alsoUn derwriting Investmentd ecisions, 68,27 8 Investmentgr adelo ans, 480 Investmentgr ader ating, 642 Investmentp olicy, 582 Investmentru les, 135–160 behavioralfin ancean d, 591 discounted payback period method, 141 IRRme thod, 141–154 NPVru le, 135–138,147, 159,189 paybackp eriodme thod, 138–141 practice of capital budgeting and, 157–159 profitabilityin dex, 155–157 Investmenttaxc redit, 453 Investors ind istressedd ebt, 923 indifferentto d ividendp olicy, 579–580 irrationalityo f, 432–433 note asilyf ooled, 429 overenthusiasma boutIP Os, 625, 627,627n undoingd ividendp olicy, 580,581 Invoice, 848 Invoiced ate, 848–849 Involuntaryb ankruptcy, 921 Involuntaryp etition, 925 IPO. SeeIn itialp ublico ffering IRA(in dividualr etirementac count), 111 IRP(in terestr atep arity), 946n, 946–947,956 IRR. See Internal rate of return Irrationality, 432–433,444,444n ,451 IRS. SeeIn ternalR evenueS ervice ISDEX, 428 Itron, 629 ITT, 886

J Jargon, 22n JIT(ju st-in-time)in ventory, 862,869 Jobp rospects, 15 JohnDe ere, 575 Johnson&J ohnson, 473,47 4,476–477 Jointsto ckc ompanies. See Corporation(s) JPMorganCh ase, 616,629 Juniord ebt, 926–927 “Junk”b onds, 248,260–261,522 “Junk”lo ans, 479 Just-in-time(J IT)in ventory, 862,869

992

Subject Index

K Kanbansyste ms, 869 KeaferM anufacturingc ase, 822–823 Keiretsu, 869 Kerr-McGee (KM), 894–895 k-Factormo del, 374 KitchenAid, 846 KM(K err-McGee), 894–895 Kohl’s, 329 KrispyKr emeDo ughnuts, 745

L Large-companyc ommonsto cks, 304,306, 310,312,317 Largesto ckd ividends, 604,606 Last-in,first-o ut(L IFO)ac counting, 286–287,453 “Lawo f o nep rice,” 940 Lawyers, 522,523n ,523–524,524n , 525,583 LBOs. SeeL everagedb uyouts LCF(le veredc ashf low), 555n,555–557 Lease(s), 652–654,671 automobilele ases, 479 basicso f, 652 capitalle ases, 655 financialle ases, 653–654 IRSc oncernsa bout, 656 operatingl eases, 652–653,669,671 sales-typele ases, 652 Leasevs .b uyd ecision, 656–658,657n , 660–661 Leasing, 652–671 accountingan d, 654–656 accountingin comean d, 669 associationwith h ighd ebt, 670,670n badr easonsf or, 669–670 cashf lowsfr om, 656–658,657n debt displacementan d, 661–664 effectso nd ebt, 661–662,662n goodr easonsf or, 666–669 by manufacturers and third parties, 652,670,784 nontaxin centivesf or, 670,670n oneh undredp ercentfin ancingan d, 669 possibleb enefitso f, 665n,665–666 risklessc ashf lowsan d, 658–660 taxesan d, 656,666–668,671 transactionc ostso f, 666,669,669n types of leases (SeeL ease(s)) Warf Co mputersc ase, 675 Ledgerb alance, 826 Legacye ffect, 604 Legalissu es, 831,837–838,876n Legislation, 16n,16–18 antitrustla ws, 898 Bankruptcy Abuse Prevention and Consumer Protection Act of 2005, 924,924 n

Bankruptcy Reform Act of 1978, 921, 922, 924, 924n Check Clearing for the 21st Century Act of 2004 (Check 21), 832 Omnibus Budget Reconciliation Act of 1993, 26 Sarbanes-OxleyAc to f 2002, 17n, 17–18,627 “Sayo nP ay”b ill(2007), 1 SecuritiesAc to f 19 33, 16 SecuritiesE xchangeAc to f 1934, 16–17 Tax Reform Act of 1986, 26, 180, 181 WilliamsAc to f 1968, 893–894 LehmanB rothersHo ldings,In c., 875,918 Lending. SeeL oan(s) Lessee, 667–668 Lessor, 652,668,670 Lettero f c omment, 617 Levelc ouponb ond, 234–235 Leverage betaan d, 565–568,566n financial( SeeF inancialle verage) homemadestr ategy, 494–495 operating,b etaan d, 404,420 targetamo unto f, 539 taxb enefito f, 558 WACCu naffectedb y, 498 Leveragedb uyouts(L BOs), 536,536n APVa pproachp referredf or, 559 organizationalc hangean d, 884 valuec reationin , 905–906,909 Leveragedle ases, 654 Leveragedr ecapitalization, 897,920 Leveragedsyn dicatedlo ans, 480 Leverager atios cashc overager atio, 51–52 charto f, 57 timesin tereste arned(T IE), 51 totald ebtr atio, 51,51n Leveredb eta, 566n Leveredc ashf low(L CF), 555n,555–557 Leveredfir ms adjustedp resentv aluean d, 553–555, 554n,555n CheekP roductsc ase, 573–574 flowto e quityan d, 555–556 valuation and capital budgeting for, 553–568 valueo f, 489–490,505,506–508 weighted average cost of capital, 556–557 Lexmark, 467 Liabilities, 22 currentlia bilities, 2,796 matchingwith asse ts, 782–784,784n shownin b alancesh eet, 20,21 unpaidd ebtas , 472 Liability–equityr atio, 660–661 LIBOR. See London Interbank OfferedR ate

Lifec ycleth eory, 602 Lifein surancec ompanies, 784 LIFFE(L ondonIn ternationalF inancial Futuresan dOp tionsE xchange), 765 LIFO(last-in ,first-o ut)ac counting, 286–287,453 Limitedlia bilityc ompany(L LC), 7 Limitedlia bilityin struments, 678 Limitedp artnerships, 4,643 Lindt, 607 Linearin terpolation, 697,697n Linearityo f CAP M, 360 Linens‘n T hings, 846 Liquidasse ts, 806 Liquidatingd ividend, 575 Liquidation(b ankruptcy), 921n, 921–924,931 Liquidity, 21–22,862 futuresc ontractsan d, 768,773 holdingc ashf or, 825 of in ventory, 21,862 managemento f, 825–826,826n short-term,r atiosasme asureo f, 49 trade-off th eoryan d, 806,806n Liquidityp remium, 258n,261 Liquidityr atios cashr atio, 50 charto f, 57 currentr atio, 49–50 quick(ac id-test)r atio, 50 LittonIn dustries, 886 LLC(limite dlia bilityc ompany), 7 Loan(s) amortizationo f, 116–120 “bridge”lo ans, 479 interest-only, 236 investmentgr ade, 480 “junk”lo ans, 479 lenders( SeeCr editors) nonrecourselo an, 654 “paydaylo ans,” 103 riskless, 350–353 securedo ru nsecured, 812,813 syndicatedb anklo ans, 479–480,480n Loana greement(d ebt), 2,474n Loangu arantees, 702–703 Lockboxes, 833–837 LockheedCo rporation, 703 “Lock-in”e ffect, 604 Lockups, 622 LondonIn terbankOf feredR ate (LIBOR), 934 interestr atestie dto , 812 swapsan d, 785–786,787,788 LondonIn ternationalF inancialF utures andOp tionsE xchange(L IFFE), 765 LondonS tockE xchange, 18 Longh edges, 790 exampleo f, 770n,770–771,771n shorth edgec ompared, 777n,777–778

Subject Index

Long-termb onds, 240,304,307,312 Long-termd ebt, 2 Long-terme xposureto risk , 953–954 Long-termfin ancing, 467–484 bonds( SeeB ond(s)) casho utflowsf or, 811 corporatelo ng-termd ebt, 472–477 internationalb onds, 480 patternso f, 480–482 stockfe atures, 467–471 stockissu ance( See Initial public offering; Public issue of stock) syndicatedb anklo ans, 479–480,480n trends in capital structure and, 482–483 Long-termle ases, 655 Lotteries, 110 Low-dividendsto ck, 407–408 Lowerb ound, 685–686 Lowe’sCo mpanies, 58 LTVIn dustries, 886 LyondellCh emicalCo ., 918

M MACRS(M odifiedAc celeratedCo st RecoveryS ystem), 176,178 Macy’s, 339,929 Magnificationfac tor, 355–356 Mailingtime , 828,829,833 “Make-whole”c all, 476 Makingd elivery, 764 Management,c orporate agencyc ostsan d, 14 aligningwith sh areholder interests, 723 of bidding firms, shareholders and, 901n,901–902,902n “carrotan dstic k,” 906 compensationasin centivef or, 14–15, 15n goalso f, 10–12,14,18 incentivesto f oolp ublic, 14,594 inefficient,e liminationo f, 881,881n interestsin c orporations, 5–6 mergersan d, 879,902 pursuito f se lfishgo als, 592 stockholderin terestsan d, 14–15 of target firms, shareholders and, 902n, 902–903 turnover in, stock performance and, 458–459 varyingd ividendp olicy, 580,581 view of payback period method, 139, 140 Managerialin formation, 628–629 Manpower,In c., 50 Manufacturersasle ssors, 652,670 MarathonOil, 878n,886 Marginalfir ms, 927

993

Marginaltaxr ates, 26–28 Marked-to-the-marketp rovisions, 767, 768, 769, 773, 790 Market(s) responsivenessto , 355–356,402,403 See also specific markets Marketablec laims, 532 Market“b ubbles,” 428,444 Marketc apitalizationr atio, 56 Marketd ebtr atio, 482–483 Markete fficiency. SeeE fficient capital markets; Efficient market hypothesis Markete quilibrium, 353–357 Marketh istory equityrisk p remium, 318,318n , 319–321,320n marketrisk p remium, 396 pricein formation, 434 rateso f r eturn, 304,317 returno ne quityr atio, 274–275 riskan dr eturn, 300–302 Marketingb yu nderwriter, 623 Marketinggain s, 879 “Marketmak ers,” 288–289,290 Marketmo delo f r eturns, 374,374n Marketo verhang, 642 Marketp ortfolio, 354 defined, 353–354,354n riskin ( SeeP ortfoliorisk ) single-factormo delo f, 380n, 380–381 S&P500In dexf or, 354,356n Marketrisk , 347–348 Marketrisk p remium, 396–397,397n , 407,407n Marketsh are, 11 Market-to-bookr atio, 56,641 Marketv alue(s), 22,23,483,640–641 Marketv alueb alancesh eet, 499–501, 509n,511,512 Marketv alued ilution, 640–641 Marketv aluer atios, 55–57 enterprisev alue, 56–57 enterprisev aluem ultiples, 57 marketc apitalization, 56 market-to-bookr atio, 56,641 price–earnings(P E)r atio, 56,285n , 285–287,292 Marketv aluew eights, 414 Matchingp rinciple, 24 Materialsr equirementsp lanning (MRP), 869 Matrixa pproach, 337,345–346,361 Maturityh edging, 810 Maturityo f b onds, 235 corporateb onds, 473,476 interestr aterisk an d, 238–240 nominalvs .r ealv alue, 253–255 verylo ng-termb onds, 240

Maturityo f se curities, 840 MBAd ecisionc asestu dy, 134 MBS(mo rtgage-backedse curity), 234, 475,479 McDonald’s, 144–145,152, 281,303,339, 347, 438, 624, 803, 941–943 McGraw-HillCo ., 268,356 McKenzieCo rporationc ase, 552 Measuremente rror, 407,407n Medicare, 804 Memberso f NY SE, 288–289 Mercedes, 954 Merck, 347,438 Merger(s), 875–876,876n ,908 agreemento f me rger, 878n analyzingv alueo f, 898–903 BirdieGo lf–HybridGo lf c ase, 915–916 cashan dsto ckc ompared, 892n, 892–893 forc ashc onsideration, 889n,889–890 forc ommonsto ck, 891–892 debtc apacityan d, 883,8 83n defined, 875,876 friendlyvs .h ostiletak eovers, 893–895, 909 indifferenceto , 887,888 managersvs .sto ckholders, 901–903 NPVan alysiso f, 889–893 optionsan d, 703–705 returnsto b idders, 899–900 valueto tar getc ompany, 900n, 900–901 See alsoAc quisitions;Di vestitures Mergerp remium, 900,900n Mergerso f e quals(M OEs), 902,902n Merrill Lynch & Co., Inc., 478, 618, 720, 721,875 MesaAirGr oup, 467 MesaP artnersII, 897–898 MesaP etroleum, 881 MexcoE nergyCo rp., 300 Mezzaninefin ancing, 645 MicrosoftCo rporation, 60,70–71,278, 281, 285, 287, 329, 399, 401, 402, 408, 410, 467, 577, 604, 606, 824 MicrosoftE xcel. SeeS preadsheet applications Middleo f mo nth(M OM)d ating, 849 Milkingth ep roperty, 527 Minic ases. See Case studies; specific cases Minimumv ariancep ortfolio, 340–341,342 Miningin dustry, 222–223 Minneapolis Star Tribune, 488 Minorityp articipation, 468,468n MIRR(mo difiedIRR), 147–148 Mispricing, 445,446–447,4 57 Mitchells, 524

994

Subject Index

MMP ropositionI, 513,538,586 convertibled ebtan d, 754 underc orporatetax es, 507n, 507–508,512 equalb orrowingc osts, 495,495n homemadele verage, 493n,493–495 PropositionIIc ompared(e xample), 498–502 summaryo f, 504,512 WACCin , 496,496n MMP ropositionII, 495–504,513,538 underc orporatetax es, 508–510, 509n,512 interpretationo f, 502n,502–504,504n PropositionIc ompared(e xample), 498–502 requiredr eturnto e quityholders, 496n, 496–502,497n riskto e quityholders, 491,492, 495–496 summaryo f, 504,512 Mobil, 877 ModifiedAc celeratedCo stR ecovery System(M ACRS), 176,178 ModifiedIRR(M IRR), 147–148,148n Modiglianian dM illerth eory high-dividendp olicyan d, 590 indifferencep ropositionan d, 579–582, 584,608 See also MM Proposition I; MM PropositionII MOEs(me rgerso f e quals), 902,902n MOM(mid dleo f mo nth)d ating, 849 Moneymar ket, 838,851 Moneymar ketm utualfu nds, 838 Moneymar ketse curities, 840–841 Monitoring, 623 Monopolyp ower, 880 MontanaM illsB readCo mpany,In c., 745 MonteCar losim ulation, 214–218,225 Moody’sIn vestorsS ervice, 16n,247–248, 483,840 MorganS tanley, 619,875,902 Morningstar, 329 Mortgage(s), 475,475n ,774–776 Mortgage-backedse curities(M BS), 234, 475,479 Mortgagetru stin denture, 475 Motionp icturein dustry, 150–151, 158–159, 206, 220, 410 Motorola, 15 MRP(ma terialsr equirements planning), 869 Multifactormo delo f AP T, 382 Multinationalc orporations, 933 Multiperiodc ashf lowv aluation, 91–101 algebraicf ormulaf or, 101 findingn umbero f p eriods, 98–100 futurev aluean dc ompounding, 91–94 powero f c ompounding, 94n,94–95

presentv aluean dd iscounting, 95–98 spreadsheeta pplications, 99 MultipleIRRs , 145,148–149 Multipler ateso f r eturn, 147,147n Multiyearc ompounding, 104 Municipalb onds, 244,244n ,245,261 Mutualfu nds casestu dy, 391 closed-end,p arityd eviationsin , 446 expectedr eturno nb onds, 246 moneymar ketfu nds, 838 performance relative to stock market, 442–443 repackagingtr ansactions, 590 semistrongf orme fficiencyan d, 441–443 standardd eviationso f, 313–314 tradingv olumeo f, 606–607 Mutuallye xclusivep rojects, 145,160 applicationo f P I, 155–156 internalr ateo f r eturnan d, 144–145 aso ptions, 705–707 problemswith , 149–154 scalep robleman d, 149–152 timingp robleman d, 152–154

N NAL(n etad vantageo f le asing), 664 NASDAQ, 288,292,428,633 delistingb y, 607,62 7 financialc risiso f 2 008, 300 openedto E CNs, 290–291 NASDAQCa pitalM arket, 291 NASDAQGlo balM arket, 291 NASDAQGlo balS electM arket, 291 NationalAsso ciationo f S ecurities Dealers Automated Quotations. SeeN ASDAQ Nationallyr ecognizedsta tisticalr ating organizations(NRS ROs), 16n NationalP ayday, 103 Naturalr esourced evelopment, 956 NCAA(“No Co uponAtAll”), 248,477 Near-cash, 825 Negativec apitalgain s, 300,301 Negativec ashc ycle, 799 Negativec orrelation, 334,335 Negativec ovenants, 477,528 Negatived ependency, 333 NegativeNP V, 280,281–282,292,641 NegativeNP Vp rojects, 281–284,587, 587n,902,902n NegativeNP VGO, 281–282 Negotiatedo ffer, 622,623 NesteOil, 135 Netad vantageo f le asing(N AL), 664 Netc reditp eriod, 848 Netf loat, 827–828,842 Netin come, 31,47

Netin vestment, 274 Neto peratinglo sses(NOL ), 882,8 82n Netp resentv alue(NP V), 88–89,1 22 of ac celeratedc ollections, 837 analysis of lease vs. buy decision, 660–661 BaldwinCo mpanyc ase, 178–179 calculatingNP V, 89,100,209 discounted payback period method and, 141 flotationc ostsan d, 418–419 flow-to-equitya pproachan d, 556 of gr antingc redit, 857,858 ineffectivef oro ptionv aluation, 690–691 IRRc ompared, 141–143,149, 151–154 of le ase,c alculating, 664 of me rger, 889–893 inM onteCar losim ulation, 218,218n negative, 280,281–2 82,292,641 negativeNP Vp rojects, 281–284,587, 587n, 902, 902n nominalvs .r eal, 185–186 optionsan d, 705–707 paybackp eriodme thodc ompared, 138–141 presentv alued istinguishedfr om, 554 top ricef orwardc ontracts, 772 of project, unlevered betas and, 567–568 realo ptionsan d, 218–223 of reducing or eliminating float, 830–831 inse nsitivityan alysis, 208–209 spreadsheeta pplications, 137 of s witchingc reditp olicies, 853–854 usein c apitalb udgeting, 135–138,159 Net present value of financing side effects (NPVF), 553 Net present value of growth opportunities (NPVGO), 278–280,280n negative, 281–282 PEr atior elatedto , 285 forr eal-worldc ompanies, 280n, 280–281 Netw orkingc apital, 2–3,175 additionsto , 30 BaldwinCo mpanyc ase, 175,17 9–180 changein , 28 componentso f, 796 short-termfin anciald ecisionsan d, 795 short-termfin ancialp lanning, 796–797 See alsoW orkingc apital NewCe nturyF inancialCo rp., 918 NewsCo rporation, 410 NewY orkKn icks, 25 NewY orkM ercantileE xchange (NYM), 765 NewY orkR angers, 25

Subject Index

NewY orkS tockE xchange(NY SE), 248, 288–290, 292, 545, 627 classeso f sto ck, 469 floorac tivity, 289–290 memberso f, 288–289 NASDAQlar gerth an, 291 operations, 289 small-companyc ommonsto cks, 304 The New York Times, 15n,488 NewY orkY ankees, 101 Nintendo, 862 “NoCo uponAtAll” (NCAA), 248,477 No-dividendfir ms, 284n,284–285 No-dividendsto ck, 407–408 No-growthfir ms, 540n,540–541,542 NOL(n eto peratinglo sses), 882,882n Nominalc ashf low, 183 Nominalin terestr ate, 182,183 onb onds, 253–254 Fishere ffectan d, 255–257 Nominalv alueo f b onds, 253–255 Noncashite ms, 23–24,25,25n Noncumulatived ividends, 471 Nonmarketablec laims, 532 Non-market-ratefin ancing, 565 NoNob onds, 478 Nonpayment,p robabilityo f, 852 Nonrecourselo an, 654 Nontraditionalc asho ffer, 619 Normald istribution, 314,315 NortelNe tworks, 520 Notches, 247n Note(s), 475 Not-for-profitse ctor, 12 NPV. SeeNe tp resentv alue NPVan alysis. SeeNe tp resentv alue NPVF (net present value of financing side effects), 553 NPVGO. See Net present value of growth opportunities NPVru le, 135–138,147,159,189 NRSROs(n ationallyr ecognizedsta tistical ratingo rganizations), 16n NYM(Ne wY orkM ercantileE xchange), 765 NYSE. See New York Stock Exchange NYSEGr oup,In c., 288

O OCF. SeeOp eratingc ashf low Odd lot, 606 Offeringp rice, 288,623–624 OID(o riginal-issued iscount)b ond, 242n Olympia&Y orkR ealtyCo rp., 918 Omnibus Budget Reconciliation Act of 1993, 26 One-factor model, 374–378, 380n, 380–381 Openac count, 851 Openin terest, 765,766

995

Openmar ketp urchases, 583 Operatingc ashf low(OCF ), 31,32 alternatived efinitionso f, 186n, 186–189,187n bottom-upa pproachto , 187–188 computing, 29 short-term, 2–3 taxsh ielda pproachto , 188–189 top-downa pproachto , 187 Operatingc osts, 884–885 Operatingc ycle, 797–804 calculating, 800,801n ,801–802 defined, 798 firm’so rganizationc hartan d, 800 inv ariousin dustries, 803–804 See alsoCash c ycle Operatingin come, 547 Operatingle ases, 652–653,669,671 Operatingle verage, 404,420 Opportunityc osts, 172–173 inb reak-evenan alysis, 213–214 carryingc ostsan d, 805 of c reditp olicy, 855 ine quivalentan nualc ostme thod, 192 exampleo f, 177 of e xcessc ash, 825 of lo werr eturns, 826,826n Opportunityse ts, 341,344,344n ,351 Optimalc apitalstru cture, 543 Optimalc reditp olicy, 854–856,870 Optimald ebtle vel, 542 lease vs. buy decision and, 662n, 662–664,663n risklessc ashf lowsan d, 660,660n trade-off th eoryan d, 530–531 Optimalp ortfolio, 352–353 Option(s), 676 callo ptions( SeeCallo ptions) capitalb udgetingan d, 705–707 ClissoldIn dustriesc ase, 718 combinationso f, 682–685,685n corporated ecisionsan d, 703–707 diversificationan d, 703–705 as executive compensation (See Executive stock options) investment in real projects and, 707–709,709n loangu aranteesan d, 702–703 puto ptions( SeeP uto ptions) quotes, 681,682 rightso fferings, 633 selling, 680–681,681n stocksan db ondsas , 698–703 valuationo f ( SeeOp tionv aluation) valueo f c onvertibleb ond, 751n, 751–752 Optionp ricingf ormula, 690–698 Black–Scholesmo del( SeeB lack– Scholes option pricing model) two-statemo del, 691–693

Optionv aluation, 685n,685 –690,709–710 binomialmo del( See Two-state option model) boundingv alueo f c all, 685–686 executivesto cko ptions, 720–723,722n factorsin c allo ptionv alues, 687–689 factors in put option values, 690, 690n NPVin effectivef or, 690–691 risk-neutralp robabilitiesin , 728,728n , 730,730n roleo f c ontractsin , 728–729 See also Black–Scholes option pricing model OracleCo rporation, 15,329,401,410, 720,721 OrangeCo unty,Calif ornia, 523,523n Orderc osts, 806 Orderf low, 289 Ordinaryan nuity, 113,122 Organizationalstru cture, 3,884 Organizationc hart, 800 Original-issued iscount(OID)b ond, 242n Originationfe e, 774 OTC(o ver-the-counter)mar kets, 248–249, 291,934–935 “Outo f th emo ney,” 677,75 8 Overreaction, 431–432 Oversubscribedissu e, 624 Oversubscriptionp rivilege, 637 Over-the-counterc ollection, 833 Over-the-counter(O TC)ma rkets, 248–249,291,934–935 Owners’e quity, 12,18 Ownership,d ispersiono f, 13,13n

P PacificGas&E lectricCo ., 918 PaladinE nergy,L td., 744 PalmIn c., 446–447 Paperlessp aymentme chanisms, 825 Paramount, 206,410 Parentc orporations, 410 Parity deviationsfr om, 445–446 interestr atep arity(IRP ), 946n, 946–947,956 purchasingp owerp arity, 939–944,956 relative, 943n,943–944,9 56 uncovered interest parity, 948, 948n, 950 Partnerships, 4–5,6,643,64 4 Parv alueo f b onds, 235,474 Payablesp eriod, 802,803 Payablestu rnoverr atio, 802 Payback, 138 Paybackp eriodme thod, 138–141 definingru le, 138–139 managerialp erspectiveo f, 139,140 problemswith , 139–140 summary, 141

996

Subject Index

Paybackp eriodru le, 139 Paychex,In c., 401 “Paydaylo ans,” 103 Payment(s) balloonp ayments, 118,656 of c ashd ividends, 575–578 leasep ayments, 656,665,665n paperlessme chanisms, 825 afterp aybackp eriod, 139 preauthorized, 833 reservationp ayment, 667–668 Paymentd ate, 576 Paymenth istory, 859 Payoffs, 680 Payoutp olicy, 603 Payoutr atio, 274–275 PCAOB(P ublicCo mpaniesAc counting OversightB oard), 17 PeachHo ldings, 18 Pecking-orderth eory, 537n,537–540, 538n,548 Pennzoil, 524–525 Pensionfu nds, 606–607,784 PeopleSoft(P S), 896 PepsiCo, 676,953 P/E(p rice-earnings)r atio, 56,285n , 285–287,292 Percentage-of-completionme thod, 286 Percentageo f sale sa pproach, 63–68,69 Percentager eturns, 302–304 Perfectn egativec orrelation, 334,342–343, 343n Performance-relatedc ompensation, 15 Periodc osts, 26 Perishability, 849 Perpetuity growing( SeeGr owingp erpetuity) simplifyingf ormulaf or, 106–107,122 Perquisites, 535 Personaltax es, 542–544,548 basicso f, 542–543 dividendp ayoutd ecisionan d, 588,608 effecto nc apitalstru cture, 543–544,544n issuing stock to pay dividends and, 586–587 summaryo f, 589–590 See alsoCo rporatetax es;T ax(es) PeugeotS A, 7 Pfizer, 286,438 Pharmaceuticalin dustry, 547 PhillipsP etroleum, 881 PI(p rofitabilityin dex), 155–157,160 Piemo del, 488–489,531–532 Plannede xpenditures, 840 Plowbackr atio, 64 Poisonp ills, 896 Politicalrisk , 952,955–956,957 Porsche, 941

Portfolio(s), 335–339,361 betaso f, 360,375–376 CAPMv alidf or, 360 diversificatione ffectin , 338n,338–339 diversified, 376–378,377n ,378n ,386 efficientse tf ortw oasse ts, 339–344 expectedr eturno n, 335–336,360,361 Fama–Frenchth ree-factormo delo f, 385 of gr owthsto cks, 384–385 of man yasse ts, 339,345–347 marketp ortfolio( SeeM arketp ortfolio) matrixa pproachto , 337,345–346 minimumv ariancep ortfolio, 340–341, 342 one-factormo delan d, 374–378 optimal, 352–353 standardd eviationo f r eturn, 337, 337n,339 stylep ortfolios, 384–385 valuep ortfolios, 384,385 varianceo f, 336–337,338,345–347,361 Portfoliorisk , 354–356,356n ,361 equityrisk p remium, 358 reductionin , 887 tolerancef or, 341,353 uncertaintyin , 376 Portfolioth eory, 723 Positivec orrelation, 334,335 Positivec ovenants, 477,528 Positived ependency, 333 PPP(p urchasingp owerp arity), 939–944, 956 Pratt’s Guide to Venture Capital, 645 Preauthorizedp ayment, 833 Precautionarymo tives, 824–825 Preemptiverigh ts, 469–470 Preferredsto ck averagec osto f c apitalan d, 413n costo f, 412 featureso f, 470–471,484 highd ividendyie ldso n, 841 privatep lacemento f, 643 Premiumb onds, 237 Prepackagedb ankruptcy, 928n,928–929, 929n,931 Presentv alue(P V), 88–89,122 of an nuity( SeeAn nuity(ies)) inb reak-evenan alysis, 212–214 discountingan d, 95–98 formulaf or, 96 of gr owingp erpetuity, 107–109, 108n,271 of p erpetuity, 106–107,122 of project, NPV distinguished from, 554 of risk lessc ashf lows, 659,659n spreadsheeta pplications, 111,121 insto ckv aluation, 269 of taxsh ield, 506 Presentv aluefac tor, 95

Present value of annuity of $1 table, 110, 113,965 Presentv alueo f $1 ta ble, 97,98,96 4 Present value of $1 with continuous discountr ateta ble, 105,970–971 Price–earnings(P E)r atio, 56,285n , 285–287,292 Pricef luctuations, 437 Primary(sto ck)mar ket, 287 “Primitive,” 763 Principalv alueo f b ond, 474 Privatee quityfir ms, 643,644 Privatee quitymar ket, 617,642–645 privatee quityfir ms, 643 privatep lacement, 642–643 stages of financing in, 644n, 644–645, 645n venturec apitalists, 643–644 See also Public issue of stock Privatep artnerships, 644 Privatep lacement, 642–643 Privatew orkout, 926–928,927n Privilegedsu bscription, 619 Probabilityd istributions, 215–217 Processingd elay, 828 Procter&Gamb le, 271–272,276,880 Productc osts, 25–26 Productionc osts, 404,806 Profit, 210–212,211n ,686,940 Profitability, 11,533–534,539–540, 849–850 Profitabilityin dex(P I), 155–157,1 60 Profitabilityr atios charto f, 57 EBITDAmar gin, 54n,54–55 profitmar gin, 54 return on assets (ROA), 55, 55n, 803 return on equity (SeeR eturno ne quity) Profitmar gin, 73 Profitmar ginr atio, 54 Profitmaximiz ation, 11 Profitp otential, 940 Prof ormafin ancialsta tements, 62–63, 69,77 Projectfu nding, 280,280n costo f c apitalf or, 408–410,409 n eliminatingin fa voro f d ividends, 582 mutuallye xclusivep rojects, 525–526 WACCan d, 414 Projectrisk , 409 Promisedyie ld, 245–246 Promissoryn ote, 851 Propertyrigh ts, 908 Proportionateo wnership, 639 Prospectus, 616–617 Protectivec ovenants, 477,528–529 , 529n,548 Proxy, 469,877 Proxyfigh ts, 15,469,877,894–895 Proxyso licitors, 894

Subject Index

PS(P eopleSoft), 896 PublicCo mpaniesAc countingOv ersight Board(P CAOB), 17 Public-issueb onds, 473 Publicissu eo f sto ck, 616–646 alternativeissu eme thods, 617,617n , 619,619n basicp roceduref or, 616–617 for cash, 619–627,621n costo f n ewissu es, 629–633,631n costso f go ingp ublic, 632–633 dilutionan d, 639–641 EastCo astY achtsc ase, 651 firmc ommitmento ffer, 619,620,623 functiono f u nderwriteran d, 637n, 637–639,639n IPOs( See Initial public offering (IPO)) offeringp rice, 623–624 rightso fferings, 617,633–637 role of investment banks in, 622n, 622–623,623n seasonedn ewissu es, 628n,628–629, 629n shelf r egistration, 641–642,642n underpricing, 624–627,625n ,627n See alsoP rivatee quitymar ket Publiclimite dc ompanies. See Corporation(s) Publicp olicy, 899 Purchase method of accounting for acquisitions, 904–905 Purchasingp owerp arity(P PP), 939–944, 956 Pured iscountb onds, 258 Purefin ancialme rgers, 705 Purep lays, 410 Putb onds, 478 Put-callp arity, 683–685,702,709 Puto ptions, 678–680,709 bondholdersan d, 701,702 callo ptionsc ompared, 701–702 complexc ontracts, 682–683 exercisep riceo f, 690,700–701 factorsin o ptionv alues, 690,690n payoffs, 680 put-callp arity, 683–685,702,709 quotes, 681,682 selling, 680,681,681n stockholdersan d, 700–701 value at expiration, 678–679, 690, 690n, 700–701 Putp rovision, 478 PV. SeeP resentv alue

Q Quarterlyc ompounding, 102–103 Quick(ac id-test)r atio, 50 “Quietp eriod,” 622 Quotes, 681,682

997

R RaganE nginesc ase, 298–299 Randomw alk, 434,434n ,438–439 RANs(r evenuean ticipation notes), 841 Rateso f r eturn, 304,317 Ratioan alysis, 48–58,77 assetman agementr atios, 52–54, 801–803 charto f r atios, 57 DuP ontid entityan d, 59–61 leverager atios, 51–52 liquidityme asures, 49–50 marketv alueme asures, 55–58,285n , 285–287, 292, 641 profitabilityme asures, 54n,54–55, 55n,803 tableo f c ommonr atios, 57 Rationality, 443–444,444n ,590–591 deviationsfr om, 432–433,444, 444n,451 markete fficiencyan d, 432 inrigh tso fferings, 634,637 Rawma terialin ventory, 861 RCA, 906 Realc ashf low, 183 Realin terestr ate, 182,183,253–254 Realo ptions, 218–223,225 Realv alue, 253–255 Real-worldsitu ations clientelee ffect, 595–596,596n dividendsvs .r epurchases, 584–585 favoringh igh-dividendp olicy, 590–594 growtho pportunities, 280n,280–281 personal taxes and capital structure, 543–544,544n stock dividends and stock splits, 606,607 use of Monte Carlo simulation, 218,218n Receipto f go ods(R OG), 849 Receivables. SeeAc countsr eceivable Receivablesp eriod, 801,803,848,849 Receivablestu rnoverr atio, 53,53n ,801, 801n,802 Recordd ate, 576 Redh erring, 616–617 Refco,In c., 918 Registeredb onds, 475 Registrar, 475 Registrationsta tement, 616 Regressionan alysis, 398,405 Regressionlin e, 402–403 Regularc ashd ividends, 575 Regulation, 16n,16–18,60 RegulationA, 616 Relativep urchasingp owerp arity basicid ea, 943,956

currencya ppreciationan d depreciation, 944 resultso f, 943n,943–944 Reorderp oints, 867–869 Reorganization. SeeB ankruptcy reorganization Replacementd ecisions, 191–193,193n Reporting,to S EC, 16 Representativeness, 444,451 –452 RepublicNa tionalB ank, 240 Repurchasea greements, 841 Repurchaseo f sto ck. SeeS hare repurchases “Reputationc apital,” 622,6 23 Requiredr eturn, 275–276,393 one quity,with le verage, 496n, 496–502, 497n, 513 See also Cost of capital; Discount rates Reservationp ayment, 667–668 Residualv alue, 668 Responsivenessc oefficient, 355 Responsivenessto mar ket, 355–356,402, 403,410 Restaurantin dustry, 803 Restockingc osts, 864–865, 867 Restockingq uantity, 864 Restrictived ebtc ovenants, 757 Restrictivefin ancialp olicy, 806,807 Restructuringasse ts, 898,9 06–907, 920,931 Retentionr atio, 64,274,282–284 Retirement,in vestingf or, 111 Return(s), 300–304 ARs( SeeAb normalr eturns) correlationo f, 329,332n ,332–335 covarianceo f, 329,332n ,332–335 dispersiono f, 339 dollarr eturns, 300–302 effecto f syste maticrisk o n, 371–374 excess, 311,436–437 holdingp eriodr eturns, 304–307 marketmo delf or, 374,374n percentager eturns, 302–304 Returnan drisk . SeeRisk an dr eturn Returno nasse ts(R OA), 55,55n ,803 Returno ne quity(R OE), 55,55n ,803 ind ividendd iscountmo del, 406 DuP ontid entityan d, 59–61,60n expected,with le verage, 496n,496–502, 497n,509–510 ingr owthr atef ormula, 274 historical, 274–275 leveragean d, 491–492,496 required,with le verage, 496n,496–502 , 497n,513 sharep ricean d, 283–284 sustainablegr owthr atean d, 74–75 RevcoD .S ., 929

998

Subject Index

Revenue(s) inb reak-evenan alysis, 211,211n cyclicalityo f,b etaan d, 404 effectso f c reditp olicy, 852 modeling, with Monte Carlo simulation, 214–217 inse nsitivityan alysis, 207 Revenuean ticipationn otes(RANs), 841 Revenuee nhancement, 879–880,880n Reversal, 437–438 Reversesp lits, 607 Rewardto risk (S harpe)r atio, 314,318 RichmondCo rporationc ase, 845 Rightso fferings, 633–637,646 directo rstan dbyo ffer, 619 effecto nsh areholders, 636–637 effecto nst ockp rice, 635–636 mechanicso f, 633–634 number needed to purchase one share, 634–635 publicissu eo f sto ck, 617,633–637 subscriptionp rice, 634 underwriteran d, 637n,637–639,639n Risk betaan d( SeeB eta(s)) borneb yu nderwriter, 623 of c ashf lows, 10 controlling, 11 creditrisk , 850 of d efault( SeeDe faultrisk ) diversificationan d, 347–348,349,378 exchanger aterisk , 933,952–955,957 idiosyncratic, 348 inflationri sk, 254–255,255n ,372 interestse nsitivity( See Interest rate risk) IPOu nderpricingan d, 625,627,627n leveragean d, 493,496,502 market portfolio and (SeeP ortfolio risk) marketrisk p remium, 396–397,397n , 407,407 n NPVru lea nd, 137–138 PEr atioan d, 287 politicalris k, 952,955–956 projectrisk , 409 reducing with derivatives (See Derivatives) selectiono f d iscountr atean d, 90 systematic( SeeS ystematicrisk ) unsystematic( SeeUn systematicrisk ) tow arranth olders, 748 Riskan alysis, 206–225 break-evenan alysis, 210–214 BunyanL umberc ase, 232–233 MonteCar losim ulation, 214–218 realo ptionsan d, 218–223 scenarioan alysisan d, 210 sensitivityan alysisan d, 206–209,207n usingd ecisiontr eesin , 223–225

Risk andr eturn, 300–304,329–362 arbitragep ricingth eory, 371–386 averager eturns( SeeA verager eturns) CAPM( See Capital asset pricing model) covariancean dc orrelation, 332n, 332–335 diversificationan d, 347–350 EastCo astY achtsc ase, 327–328, 369–370 efficient set for many securities, 344n, 344–347,345n efficientse tf ortw oasse ts, 339–344 equity risk premium (See Equity risk premium) expectedr eturnan dv ariance, 330n, 330–332 financial crisis of 2008 and, 300, 321–322 individualse curitiesan d, 329 markete quilibriuman d, 353–357 marketh istory, 300–302 forp ortfolios, 335–339 returnsta tistics, 307–311 risklessb orrowingan dle nding, 350–353 risksta tistics, 312–315 Riska version homogeneouse xpectationsan d, 354,354n innovativefin ancingan d, 430 optimalp ortfolioan d, 353 valueu naffectedb y, 698 Risk-basedmo dels, 383–384 Risk-freein terestr ate, 394,396,407n , 419,735 Risk-freer eturns, 311,312 Risk-freese curities, 350–351,351n Risk-freeT reasuryb ills, 311,312, 350,396 Risk-freez eroc ouponb onds, 685 Risklessb orrowingan dle nding, 350–353 Risklessc ashf lows, 658–660,671 Riskn eutrality, 736 bankruptcyc ostsan d, 521n,521–522 probabilitiesin o ptionv aluation, 728, 728n, 730, 730n intw o-stateo ptionmo del, 692–693 Riskp remiums defaultp remium, 260,261 equity( See Equity risk premium) historical, 319 interestr atep remium, 258,258n , 259,261 marketrisk p remium, 396–397,397n , 407,407n Riskr eduction, 705,887–889 Risksta tistics, 312–315,357 Risksyn ergy, 756 Risk-taking, 525–526

Riskto lerance, 255–257,341,353,948 RJRNa bisco, 881 ROA(r eturno nasse ts), 55,55n ,803 ROE. SeeR eturno ne quity ROG(r eceipto f go ods), 849 Rolls-RoyceP LC, 7 RothIRA, 111 Roundlo t, 606 “Roundtrip tr ades,” 34 RoyalDu tchP etroleum, 445,446 Royalty-backedb onds, 479 Rule144A(S EC), 642–643 Ryder, 286

S “Safetymar gin”th eory, 758,758n ,759 Safetyr eservesc osts, 806 Safetysto cks, 867,868 Safetysu pplyo f c ash, 824,838 SagientR esearchS ystems, 607 SAIR(sta tedan nualin terestr ate), 102, 103–104 Sale,d ivestitureb y, 906–907,907n Salean dle aseback, 654 Salesforce.com, 622 Salesgr owth, 63 Sales-typele ases, 652 Salvagev alue, 175,178,192 S&P. SeeS tandard&P oor’s S&SAirc ase, 762 Sarbanes-OxleyAc to f 2002, 17n, 17–18,627 “Sayo nP ay”b ill(2007), 1 Scalee nhancement, 567–568 Scalep roblem, 149–152 Scenarioan alysis, 210 Schedule13D(S EC), 893 Scorchede arthp olicy, 898 Scotville, 896 SE(stan darde rror), 319 SearsR oebuck, 329 Seasonalac tivities, 839 Seasonalb usinesses, 60–61 Seasonald ating, 849 Seasonalsale s, 860 Seasonede quityo ffering(S EO), 454–455, 456,457 Seasonedn ewissu es, 619,620,628 n, 628–629,629n SEC. See Securities and Exchange Commission Secondary(sto ck)mar ket, 287 Second-roundfin ancing, 644 Securedc reditors, 924 Securedlo ans, 813 Securities, 329,471 costo f issu ing, 553 safest,issu ingfirst, 539 See also specific kinds of securities

Subject Index

SecuritiesAc to f 1933, 16 Securitiesan dE xchangeCo mmission (SEC), 489,813 formsr equiredb y, 16 onin sidertr ading, 443 publicissu anceo f sto ck, 616–617 “quietp eriod”r equiredb y, 622,627 registrationfe es, 633 Rule144A, 642–643 Schedule13D , 893 onsp in-offs, 907 Securitiesb rokers, 288 SecuritiesE xchangeAc to f 1934, 16–17 Securitizedb onds, 479 Securitymar ketlin e(S ML), 358–361 estimatingc osto f c apital, 561 for expectedr eturns, 379–380 marketp ortfolioo n, 380–381 for risk-adjustedd iscountr ate, 395 SecurityP acific, 880 Seedmo neysta ge, 644 Self-control, 590–591 Selfishin vestmentstr ategies, 525–528 Semiannualc ompounding, 101–102,105, 237–238,243 Semiannualc oupons, 237–238,771 Semistrongf orme fficiency, 435–436, 439–443,460,656 Seniord ebt, 476,926–927 Sensitivity. SeeIn terestr aterisk Sensitivityan alysis, 206–209,207n ,225 SEO(se asonede quityo ffering), 454–455, 456,457 Separationp rinciple, 353 Serialc orrelation, 437–438 Settlementp rice, 765,766 Severancep ackages, 895–896 Shareholder(s) bankruptcyc ostsb orneb y, 522 of bidding firms, management and, 901n,901–902,902n callo ptionsan d, 699,702,757–758 cashf lowto , 31 coinsurancee ffecto n, 887–889 conflictswith b ondholders, 591–592, 592n,608 diversificationan d, 886,886n effecto f righ tso fferingso n, 636–637 effectso f lo angu aranteeso n, 703 effectso f me rgero n, 887–889,909 exchangeo ffers, 534 expectedr eturnsto , 393–394 financialman agementgo also f, 11–12 indifferent between dividend and repurchase, 583–584,608 interestsin c orporations, 5–6 mergera pprovalb y, 876,876n new,c apitalgain sd ilutedb y, 393–394 protectiono f, 13,13n puto ptionsan d, 700–701

999

returns to, financial leverage and, 491–493, 496, 506, 506n selfishin vestmentstr ategiesb y, 525–528 of target firms, benefits to, 900n, 900–901 of target firms, management and, 902n, 902–903 Shareholderd isinterest, 437 Shareholderin terests, 5–6 aligningman agementwith , 723 controlo f fir man d, 14–15,15n financialle veragean d, 491–493,496, 506,506n maximization of firm value and, 489–490,490n Shareholderrigh ts appraisalrigh ts, 876 bankruptcyas , 705 inc ommonsto ck, 467–469,468n ,484 preemptive,in c ommonsto ck, 469–470 Sharer epurchases, 575 constantgr owthsto cks, 271–272,272n , 278n debtissu edf or, 467,482,484 dividendsign alingan d, 594,594n exampleo f, 583–584 firmgr owthan d, 541n firms with cash for dividends, 589, 589n fixedstr ategyf or, 603 real-worldc onsiderations, 584–585 “stickiness”to , 582–583 astak eoverd efense, 897 taxesan d, 586–590,602,884,884n timingo f, 455 Sharew arrants, 633 Sharper atio, 314,318 Shelf c asho ffer, 619 Shelf r egistration, 641–642,642n ,646 ShellT ransport, 445,446 ShellUKL td., 7 Shirking, 535 Shortagec osts, 805,806,813,862 Shorth edges, 790 exampleso f, 769–770,774–776 longh edgec ompared, 777n,777–778 Short-termd ebt, 2 Short-terme xposureto risk , 952 Short-termfin ancialp lanning, 2–3,18, 795–814 cashan dn etw orkingc apital, 796–797 cashb udgeting, 810–812,814 KeaferM anufacturingc ase, 822–823 operatingan dc ashc ycles, 797–804 policyasp ects, 804–810 sourceso f fu nds, 812–813 Short-termfin ancialp olicy, 804–810 alternativec urrentasse tp olicy, 808,809 appropriateamo unto f b orrowing, 809–810

size of current asset investment, 805n, 805–806,806n ,807 Short-termse curities, 840,841 Sidee ffects, 173,553 Sightd raft, 851 Signale quilibrium, 757n Signalingth eory debtsign aling, 533–534,548 dividendsign alingstr ategy, 593n, 593–594,594n informationc ontente ffect, 592n, 592–593 two-part, 602–603 SignetS olar, 553 Simplefin ancialp lanningmo dels, 62–63 Simplein terest, 91,92,94 Single-factormo del of mar ketp ortfolio, 380n,380–381 of syste maticrisk , 374–378 Sinkingfu nd, 476 Sizefac tor ina verager eturns, 448n,448–449,449n inth ree-factormo del, 385 inu seo f d erivatives, 789 “SleepingB eauty”b onds, 249 Slowr esponse, 431–432 Smallc ompanies, 536,668, 921n,929n Small-companyc ommonsto cks, 304,306, 310,312 Small-issuese xemption, 616 Smallsto ckd ividends, 604–605 SmithKlineB eecham, 446 SML. SeeS ecuritymar ketl ine Societyf orW orldwideIn terbank Financial Telecommunications (SWIFT), 935 Softwarein dustry, 400–401 Solep roprietorships, 4 SonyCo rporation, 222,410 ,908 Sourceso f c ash, 797 Sourceso f fu nds, 812–813 SouthwestAir lines, 329 Specialists, 288–289 Specialist’sp ost, 289 Speculation, 456,457,763–764 Speculativemar kets, 450–451 Speculativemo tives, 824 Speed Racer(film), 206 Spin-off, 907 Spote xchanger ate, 939 Spotr ates, 772,773,773n Spottr ades, 939 Spread, 288,620,629,633 Spreadingo verhead, 880 Spreadsheeta pplications bondp ricesan dyie lds, 243–244 calculatingIRR, 144 discountedc ashf lowv aluation, 99, 111, 119, 121 EXCELfu nctions, 696

1000

Subject Index

Spreadsheeta pplications—Cont. loanamo rtization, 119 NPVc alculation, 137 timev alueo f mo neyc alculations, 99 Stabilityo f b etas, 399n,399–400 Staffordlo ans, 118–120 Stakeholders, 15–16 Standard&P oor’s(S &P), 16n,247–248, 477,483,840 Standard & Poor’s (S&P) 500 Index, 286, 304, 397, 577 asb enchmarkf orstyle p ortfolios, 384 financialc risiso f 2008, 300,321 indexfu ndsan d, 441 Internetsto ckin dexc ompared, 450–451 formar ketp ortfolio, 354,356n inme asuringb etas, 398,399 as mirror of stock market movement, 382–383,383n standardd eviationsf or, 339 Standardd eviation diversificatione ffectan d, 338n, 338–339,341–342 of h istoricalrisk p remium, 319 normald istributionan d, 314,315 forp ortfolioo f m ultipleasse ts, 345–347 of p ortfolio’sr eturn, 337,337n ,339 of r eturn,in o ptionv aluation, 732 risklessle ndingan d, 350,351 inrisk sta tistics, 313–314 of se curities’r eturn, 329,331,332 Standarde rror(S E), 319 Standardization, 849–850 Standardizedn ormald istribution, 695 Standbyfe e, 637 Standbyrigh tso ffer, 619 Standbyu nderwriting, 637 Standstilla greements, 896 Starbucks, 286,720 Start-upc ompanies, 723–726 Start-upsta ge, 644 Stated annual interest rate (SAIR [APR]), 102,103–104 Statedv aluep referredsto ck, 471 Statemento f c ashf lows, 32–34 cash flow from financing activities, 29,33–34 cashf lowfr omin vestingac tivities, 32 cashf lowfr omo peratingac tivities, 32 Statements of Financial Accounting Standards No. 13, “Accounting for Leases,” 654,655 No. 52, “Foreign Currency Translation,” 955 Statictr ade-off th eory. SeeT rade-off theory Steady-statef loat, 830,830n StephensonR ealE statec ase, 519

“Stickiness,” 582–583 Stock common( SeeCo mmonsto ck(s)) effective tax rate on distributions, 543–544 floating,f orall-e quityfir m, 499–500 preferred( SeeP referredsto ck) priceo f ( SeeS tockp rice(s)) publiclyissu ed( See Public issue of stock) repurchasing( SeeS harer epurchases) valuationo f ( SeeS tockv aluation) Stockc ertificates, 2,745–746 Stockd ividends, 575,604–606 large,e xampleo f, 606 markete fficiencyan d, 454 small, 604–605 valueo f, 606–607 Stock-for-stocktr ansaction cashtr ansactionc ompared, 892n, 892–893 NPVo f me rgeran d, 891–892 Stockholders. SeeS hareholder(s) Stockholders’b ooks, 179,904 Stockholders’e quity. SeeE quity Stockmar ket(s) crashes,mar kete fficiencyan d, 450–451 dealersan db rokers, 287–288 NASDAQ, 290–291 NYSE( See New York Stock Exchange) perceptionso f fu ture, 285 performance of mutual funds relative to, 442–443 reporting, 291–292 rolein sto ckv aluation, 287–292 valuesr educedb yme rgers, 898–899 volatilityo f, 483 Stocko ptions. See Executive stock options Stockouts, 180,806,867 Stockp rice(s) callo ptionv aluean d, 687–688 common stock vs. convertible debt, 753–754 underc orporatetax es, 511–512 dropo ne x-dividendd ate, 577–578 effecto f d ividendp olicyo n, 594 effecto f righ tso fferingso n, 635–636 offeringp rice, 623–624 puto ptionv aluean d, 690 straightvs .c onvertibled ebt, 753 taxr atesan d, 576 underwritingan d, 627,629 Stockq uotations, 291–292 Stockr epurchase. SeeS harer epurchases Stocksp lits, 575 exampleo f, 605 markete fficiencyan d, 454 reversesp lits, 607 valueo f, 606–607

Stockv aluation, 268–292 constantgr owthsto cks, 270–272,272n differentialgr owthsto cks, 272–273 differenttyp eso f st ocks, 269–273 dividendd iscountmo del, 273–278, 282–284 dividends vs. capital gains in, 268–269, 269n growtho pportunitiesan d, 278–285, 280n link to cash flows, 277n, 277–278, 278n presentv alue, 268–273 price–earningsr atioan d, 285n,2 85–287 RaganE nginesc ase, 298–299 roleo f sto ckmar ketsin , 287–292 zerogr owthsto cks, 270 Storagec osts, 864–865 Straightb ondv alue, 750,751 Straightd ebt, 753 Straight-lined epreciation, 181,286 ,65 7 Straightv oting, 468,468n Strategies benefitso f r evenuee nhancement, 879–880,880n duplicatingstr ategy, 693–694 fixed,f orsh arer epurchases, 603 flexibilityo f fin ancingstr ategy, 809–810 homemadele verage, 494–495 immunizationstr ategies, 774,782–783, 783n for interest rate futures hedging, 775–776 signalingas , 593n,593–594,594 n See alsoS elfishin vestmentstr ategies Streets weep, 894 Stricttar gets, 546 Strikep rice, 676,681,682 Strongf orme fficiency, 435,436,443,460 Stylep ortfolios, 384–385 Subordinatedd ebt, 476 Subscriptionp rice, 634 Sunkc osts, 172 SuperDOTsyste m, 289 Superfloaters, 788 Superinverses, 788 Supermajorityp rovisions, 895 Surplusfu nds, 884,884n Sustainablegr owth, 70–71,76 Sustainablegr owthr ate, 70,71–72,74–75 Swapsc ontracts, 763,784–788,790 creditd efaults wap(CDS ), 784, 786–787 currencys waps, 784,786 exotics, 787–788 interestr ates waps, 784n,784–78 6 LIBORan d, 785–786,787,788 SWIFT (Society for Worldwide Interbank FinancialT elecommunications), 935 SymantecCo rp., 400–401

Subject Index

Symbion,In c., 632–633 Syndicate, 620 Syndicatedb anklo ans, 479–480,480n Synergy(ies), 173,704,908 costr eduction, 880–881 incrementalc ashf lowsan d, 878n, 878–879 reducedc apitalr equirements, 884–885 revenuee nhancement, 879–880 risksyn ergy, 756 sourceso f, 879n,879–885,898,906 taxgain san d, 882–884 Syntheticsto cks, 684,685 Systematicrisk betasan d, 350,354–356,356n , 371–374,374n diversificationan d, 347–348,349,378 one-factormo delo f, 374–378 Systematicv ariability, 886

T Takeover(s), 15 acquisitionb y, 877n,877–878 defensesa gainst( SeeT akeover defenses) friendlyvs .h ostile, 893–895 Takeoverd efenses, 895–898,909 assetr estructuring, 898,906–907 corporatec hartersas , 895,895n exclusionaryse lf-tenders, 897–898 goldenp arachutesas , 895–896 greenmail, 896,897 poisonp ills, 896 recapitalizationan dr epurchase, 897 standstilla greements, 896 whitek nightan dw hitesq uire, 897 Take-upfe e, 637 Tangiblefix edasse ts, 21–22 TANs(taxan ticipationn otes), 841 Targetedr epurchase, 583,896 Targetfir ms, 877 benefitsto sh areholders, 900n,900–901 hostiletar get, 894 managemento f,sh areholdersan d, 902n,902–903 premiump aidf or, 879 Targetr atio debt–equityr atios, 546n,546–547,547n inW ACCa pproach, 556 Tax(es) averagevs .mar ginalr ates, 26–28 benefitsfr omd epreciation, 904 carrybacksan dc arryforwards, 882,882n casho utflowsf or, 811 clientelee ffect, 595–596,596n on common stock dividends, 470, 470n, 597,597n corporate( SeeCo rporatetax es)

1001

debt–equityr atioan d, 547,547n deferred, 25,25n effectso nb etas, 405n effectso nd ividends, 586–590 financialsta tementsan d, 26–28 formo f ac quisitionan d, 903–904,909 penaltiesf ora voidance, 589,590 personal( SeeP ersonaltax es) onsh ort-termse curities, 840 Taxabilityp remium, 261 Taxableac quisitions, 903n,903–904 Taxad vantages disadvantageo f d ividends, 586–589 of le asing, 656,666 –668,671 of sh arer epurchases, 585 Taxan ticipationn otes(T ANs), 841 Taxb ooks, 179,904 Taxe xemptions, 244,244n ,616 Tax-freeac quisitions, 903 Taxgain s fromac quisitions, 882–884 debtc apacityan d, 883,883n neto peratinglo ssesan d, 882,882n surplusfu ndsan d, 884,884n Taxr ates averagevs .mar ginal, 26–28 corporate, 26 ond ividends,c ut, 598 effective,o nc apitalgain s, 543 effective,o nsto ckd istributions, 543–544 flat-ratetax, 27 stockp ricesan d, 576 TaxR eformAc to f 1986, 26,180,181 Taxsh ielda pproach, 188–189 increasedd ebtc apacity, 883 natureo f, 511–512 presentv alueo f, 506 Taxsu bsidies APVu sedwith , 564,564n tod ebtfin ancing, 553–554,557 Technologytr ansfer, 881 Tendero ffer, 583,876,893–894 Termp remium, 396 Termso f sale , 846,848–852 basicf orm, 848 cashd iscounts, 850–851 creditin struments, 851–852 creditp eriod, 848–850 Termstru cture, 810 Termstru ctureo f in terestr ates bondin terestr ates, 257–260,258n shiftsin , 773,773n Texaco,In c., 524–525,918 Third-partyle ssors, 652,670 Third-roundfin ancing, 645 ThornburgM ortgage,In c., 918 3Com, 446–447 3M, 356,676 Thresholdp rices, 735

Tickersymb ols, 681,682 “Tick”siz e, 259 TIE(time sin tereste arned)r atio, 51 Time effectivetime to ma turity, 776,776n incomesta tementan d, 25 mailingtime , 828,829,83 3 Timec onventions, 108n,10 8–109 Timed raft, 851 Timep remium, 686 Timesin tereste arned(T IE)r atio, 51 Timev alueo f mo ney, 87,99 TimeW arner(T W), 410,892–893,902 Timingassu mption, 108 Timingd ecision corporatefin ancean d, 454n,454–455, 455n ine quityissu ance, 538 forin itialp ublico ffering, 454,456 form utuallye xclusivep rojects, 152–154 Timingo f c ashf lows, 9–10,139,768 Timingo ptions, 222–223 TIPS(T reasuryin flation-protected securities), 254–255,255n Toehold, 893 TollB rothers, 20 Tombstonead vertisement, 617,618 Top-downa pproach, 187 TorontoS tockE xchange, 520 Totalasse ttu rnoverr atio, 54,73,803 Total cash flow of firm. See Free cash flow Totalc ost(s), 865–867 Totalc ostc urve, 806 Totalc reditc ostc urve, 855–856 Totald ebtr atio, 51,51n Totald ollarr eturn, 301 Totalin ventoryc ostc urve, 863 Totalin vestment, 274 Totalr eturns annual, 312 calculating, 303–304 dependentu pongr owthr ate, 276–277 ind ividendd iscountmo del, 275–276 onmar ket,e stimatingwi thDDM , 397 year-by-year, 308–309 ToyotaM otorCo rporation, 45,795, 869,954 Toys“R” Us , 839 TRACE (Trade Report and Compliance Engine), 249 Trackingsto cks, 908 Tradeac ceptance, 851 Tradec redit, 846 Traded iscounts, 851 Trade-off th eory agencyc ostan d, 534n,53 4–537,536n of c apitalstru cture, 530–531 corporated istressan d, 923 liquidh oldingsan d, 806,806n

1002

Subject Index

Trade Report and Compliance Engine (TRACE), 249 Tradingc osts, 806 Tradingin th e“c rowd,” 290 Tradingr ange, 606–607 Transactionc osts inf oreigne xchange, 940 high-dividendp olicyan d, 590,608 reducing,b yle asing, 666,669,669n Transactionmo tive, 825 Translatione xposure, 954–955 Transparency, 249 Transunion, 858 Treasuryb ills. SeeU .S.T reasuryb ills Treasuryb onds. SeeU .S.T reasuryb onds Treasuryin flation-protectedse curities (TIPS), 254–255,255n Treasuryyie ldc urve, 260–261 Trianglearb itrage, 938 TribuneCo mpany, 488 Trustd eed, 475 Trustr eceipt, 813 TW(T imeW arner), 410,892–893,902 Two-stateo ptionmo del, 691–693,719 amounto f b orrowingin , 692 Black–Scholesmo delc ompared, 732, 733 determiningd eltain , 692 extensionto man yd ates, 731–733,732n goldmin ee xample, 733–740 heatingo ile xample, 726–733 risk-neutralv aluation, 692–693 shutdownan dr eopeningd ecisions, 735–740 three-datee xampleo f, 729n,729–731 two-datee xampleo f, 727–729,728n valuationo f asse t, 733–734 volatilityo f r eturnan d, 734–735 TycoIn ternational, 17,34

U UALCo rp., 918 UCF (unlevered cash flow), 555n, 555–558 UFR(u nbiasedf orwardr ates)c ondition, 947,952,956,957 UIP(u ncoveredin terestp arity), 948, 948n,950 Unbiasedf orwardr ates(UF R)c ondition, 947,952,956,957 Uncertainty, 214–218,376,547,666,668 Unclassifiedb oardo f d irectors, 895 Uncoveredin terestp arity(UIP ), 948, 948n,950 Undeclaredd ividends, 470 Underinvestment, 526–527,527n “Underlying,” 763 Underpricing of IP Os, 626 of n ewsto ckissu es, 630–632

of public issue of stock, 624–627, 625n,627n Undervaluation, 585 Underwriter(s), 620 certificationb y, 623,639 functiono f, 637n,637–639,639n Underwritersp read, 629,633 Underwriting arrangementsf orrigh tso fferings, 637 “Dutchau ction,” 619,620–621 firmc ommitmento ffer, 620,646 lockups, 622 in public issue of stock, 637n, 637–639, 639n stockp ricean d, 627,629 See alsoIn vestmentb anks Underwritingd iscount, 620,629,631n Unfundedd ebt, 473,473n Uniformp riceau ction, 619,620–621 UnileverNV , 7,446 UnileverP LC, 446 U.S. bankruptcyc ode Chapter7, 921n,921–924,931 Chapter 11, 920, 922, 924n, 924–926, 925n,931 U.S. BankruptcyCo urt, 928 U.S. CensusB ureau, 158 U.S. Departmento f J ustice(DOJ ), 880,898 U.S. dollar, 300–302,939 U.S. Foodan dDru gAd ministration, 17 U.S. Navy, 669–670 U.S. Steel, 878n,886 U.S. Treasuryb ills, 840,841 rateso f r eturn, 304,307 risk-free, 311,312,350,396 termstru ctureo f in teresto n, 396 U.S. Treasuryb onds bondmar ket, 248–252 futuresc ontractsin , 774–776 priceq uotes, 251,252 pricing,in h edging, 771,772 relationto T IPS, 255,255n taxe xemptionso n, 244 See alsoGo vernmentb onds United Technologies Corporation, 720, 721 UniversalS tudios, 410 Unleveredb eta, 567–568 Unleveredc ashf low(UCF ), 555n, 555–558 Unleveredfir ms, 489 Unlimitedlia bilityf ord ebts, 4 Unocal, 881,897–898 Unremittedc ashf lows, 951 Unseasonedn ewissu e, 617,619,624 Unsecuredlo ans, 812 Unsystematicrisk diversificationan d, 347–348,349, 376–378, 378n, 380 weighteda verageo f, 377,377n

Unsystematicv ariability, 886 Unusedd ebtc apacity, 883 Upperb ound, 686 Upsta tep rices, 729–730 Useso f c ash, 797 Utilizationr atios. See Asset management ratios

V VailR esorts, 34 VAL inux, 428 Value of cash flows (See Discounted cash flowv aluation) costan d, 22n,22–23 dilutiono f, 640–641 of fir m( See Value of firm) FV( SeeF uturev alue) NPV( See Net present value) of o ptions( SeeOp tionv aluation) PV( SeeP resentv alue) Valuead ditivity, 136–137 Valuec reation cashf lowan d, 7–8 as goal of financial management, 10–12 growtho pportunitiesan d, 279–280 inle veragedb uyouts, 905–906 measuring,with e ventstu dies, 898 throughse ll-offs, 907 value-creatingd ecisions, 428–430 Valuefac tor, 385 Value Line (VL) Investment Survey, 276, 280,397 Valueo f fir m changes in capital structure and, 492, 493n,493–495 debt–equitye xchangean d, 511–512 debtfin ancingan d, 500–502 discountedc ashf lowv aluation, 120–121 effects of negative NPV projects, 281–284 effectso f w arrantso n, 746n,746–748 elementso f, 75 financialle veragean d, 491–495, 506–508, 507n, 513 high-riskp rojectsan d, 525–526 impacto f r etentionr atioo n, 282–284 leveredfir ms, 489–490,505,506–508 marketablec laimsan d, 532 maximizationo f, 489–490,490n shareholderin terestsan d, 489–490, 490n start-ups, 723–726 Valuep ortfolios, 384,385 Valuesto cks, 449n,449–450,450n Vanguard High Yield Corporate Bond Fund(HYF und), 246

Subject Index

Vanguard500in dexfu nd, 441–442 VanguardIn termediate-TermT reasury BondF und(T BF und), 246 Variablec osts, 208,209 Variables,in M onteCar losim ulation, 214–217 Variance of asset, call option value and, 688–689 calculationsr equiredf or, 330n estimating, in Black–Scholes model, 695 expectedr eturnan d, 330n,330–332 minimumv ariancep ortfolio, 340–341,342 of p ortfolios, 336–337,338, 345–347,361 asp roperme asureo f risk , 357 risklessle ndingan d, 350 inrisk sta tistics, 313–314,357 onse curities’r eturn, 329 varianceo f, 338,345–347,361 Venturec apital, 642,646 stagesin fin ancing, 644n,644–645, 645n supplierso f, 643–644 VerizonCo mmunications, 339 Verticalac quisition, 877 Verticalin tegration, 881 Viacom, 410 Visa, 616,627 Volatilityo f r eturn, 734–735 Volatilityo f sto ck, 690 Voluntaryp etition, 925 Volvo AB, 7 Votingrigh ts, 469–470 Vultures, 923

W WACC. See Weighted average cost of capital WachoviaCo rporation, 720,721 Wages, 811 Waitingp eriod, 616,617 The Wall Street Journal, 14,694 ona veraged ividendyie ld, 397 exchanger ateq uotations, 935–937 futuresc ontractlistin gs, 765,766 informationr eleasedb y, 440n stockmar ketr eportingb y, 291–292 U.S. Treasury bond price quotes, 251,252 Wal-Mart, 50,281,289–290,606

1003

WaltDisn eyCo mpany, 221,240,339, 410,908 WaMu(W ashingtonM utual), 629 Warf Co mputersc ase, 41–43,675 WarnerB rothers, 206,410 Warrants, 744n,744–745,758 onb onds, 478 callo ptionsc ompared, 744, 745–748,758 cashfr omsale o f, 746n,758 commonsto ckc ompared, 753–754 conversionv alue, 750–751 dilutionfr ome xercising, 745–747,758 gainfr ome xercising, 748n,748–749 reasonsf orissu ing, 753–757,755n , 758–759 riskto w arranth olders, 748 sharew arrants, 633 See alsoCo nvertibled ebt;W arrants WashingtonM utual(W aMu), 629 WaterfordW edgewoodP LC, 520 Weakf orme fficiency, 460 efficientmar keth ypothesisan d, 433–436,434n evidencef or, 437–439 Wealthyfamilie s, 643–644 Weighteda verage(s) calculatingf lotationc osts, 417–418 estimatingc osto f d ebt, 415–416 inp ortfolior eturnsmo del, 376 of u nsystematicrisk , 377,377n Weighted average cost of capital (WACC), 412–414,413n APV and FTE approaches compared, 557–560 capitalstru cturean d, 530,531 computing, 413–414 corporatetax esan d, 510 defined, 392 EastmanCh emicalCo .e xample, 415–416 estimatingc osto f c apital, 562 flotationc ostsan d, 417–419 guidelinef oru se, 558–559 internationalc apitalb udgeting, 949,949n forle veredfir ms, 556–557 summaryo f, 560 unaffectedb yle verage, 498 WellPoint, 604 Westinghouse, 769 Weyerhauser, 44

What-if an alysis, 206–209,2 07n What’sY ourB eef, 771,771n Whitek night, 897 Whitesq uire, 897 WilliamsAc to f 1968, 893–894 WilliamsonM ortgage,In c.c ase, 794 Winner’sc urse, 625,625n Wiretr ansfers, 835 WitCa pitalCo rporation, 618 Workingc apital investmentin , 175,177–178 mergersan d, 885 net( See Net working capital) overinvestmentin , 277n Workingc apitalman agement. SeeS horttermfin ancialp lanning “Working”th eo rder, 290 Work-in-progressin ventory, 861 Worksheets(c orporate), 175,180 WorldCom,In c., 17,454,52 3,918 WorldW restlingF ederation Entertainment,In c., 618 Write-offs, 20 Write-upo f asse ts, 903n,903–904 Wyeth, 720,721,722

X Xerox, 286

Y Yahoo!, 60–61 Yahoo!F inance, 291 YankeeCan dleCo ., 846 Yieldc urve, 260–261 Yieldto ma turity(YT M), 261 aftertaxyie lds, 244 of b onds, 235,240–242,251,252 calculating, 240–242 junkb onds, 260–261 spreadsheeta pplications, 243–244

Z Zero-balanceac counts, 838 Zeroc orrelation, 334,335 Zeroc ouponb onds, 242n,242–243 ind urationh edging, 778,778n ,779 risk-free, 685 Zerogr owthsto cks, 270 Zero-sumgame s, 681,787 Z-scoreb ankruptcyp redictionmo del, 929–931