2,140 235 40MB
English Pages [282] Year 2018
Table of contents :
Title
Contents
1 Introduction to Financial Management
2 Time Value of Money
3 Financing Decision
4 Investment Decisions
5 Dividend Decisions
6 Working Capital Management
Model Question Paper
Appendix
Financial Management For Bangalore University (As per CBCS Syllabus 201415 as Revised in March 2017) B.COM SEMESTER III
About the Authors Dr. V. Rajesh Kumar is an M.Com graduate from Bangalore University. He obtained his PhD in the area of Strategy. While Accounting and Taxation are his areas of expertise, Finance is his area of passion. He has 25 years of experience in teaching at graduate, postgraduate and professional levels, and has served at various institutions in different capacities—Mount Carmel Institute of Management, Department of Commerce, Bangalore University, and Alliance Business Academy, to name a few. He is a faculty for Strategic Financial Management and Tax Laws at the Institute of Chartered Accountants of India, Bangalore. He has coauthored textbooks on Accounting and Taxation for the requirements of various universities. He has presented papers at various national and international conferences and published articles in reputed journals. His paper on Capital Asset Pricing Model was selected for an international conference at Harvard University, Cambridge, United States of America, during May–June 2011. Dr. Rajesh also has a rich experience in research, consultancy and training—both at the academic and corporate levels. He has conducted student development programmes and faculty development programmes at various educational institutions, and has conducted training programmes for executives and managers of various companies like Wipro, Godrej, FCG, Honeywell, KPCL, Fouress Engineers, Triveni Engineering,
Bangalore. He is the founder of Vittam Pravina Gurushala (Finance Expert Academy)—an academy engaged in
Presently, he is working as a Finance and Academic Consultant and visits different management institutions
Dr. Y. Nagaraju is currently working as a Professor at Canara Bank School of Management Studies. He is a postgraduate from the Department of Management, Bangalore University and received his PhD from Bangalore University. He has over 20 years of teaching experience at postgraduate level. His areas of research include Accounting, Corporate Reporting and Capital Markets. He has published study material on Accounting for Managers and Financial Markets and Institutions for MBA students. He has published more than 30 articles in peer reviewed and refereed journals of national and international repute. He is a member of various boards of different universities.
Financial Management For Bangalore University (As per CBCS Syllabus 201415 as Revised in March 2017) B.COM SEMESTER III
Dr. V. Rajesh Kumar Professor and Managing Partner Vittam Pravina Gurushala Bangalore
Dr. Y. Nagaraju Professor, Canara Bank School of Management Studies Bangalore University
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Financial Management Copyright © 2018 by McGraw Hill Education (India) Private Limited. No part of this publication may be reproduced or distributed in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise or stored in a database or retrieval system without the prior written permission of the publishers. The program listings (if any) may be entered, stored and executed in a computer system, but they may not be reproduced for publication. This edition can be exported from India only by the publishers, McGraw Hill Education (India) Private Limited Print Edition: ISBN13: 9789353160647 ISBN10: 9353160642 1 23456789
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Dedicated to Our teachers who taught us this subject Our students who made us learn it better Our friends who encouraged us to write this book
Preface
 Northrop Frye Business and Financial Intelligence are not picked up within the four walls of school. You can pick them up on the streets. In school, you are taught how to manage other peoples’ money. On the streets, you learn how to make money  Ajaero Tony Martins Finance is the life blood of a business enterprise. Financial Management is a core function of every
relevant and appropriate decisions. Among many expectations corporate sector has from present and skills for applying that knowledge. While acquiring the knowledge and skills calls for pursuing various courses, a strong foundation is essential to go further—which a student ought to get at the graduation level. This book intends to provide the reader a strong foundation on the subject Bangalore University, and hence, does not cover the entire ambit of the subject. However, the topics factor about the subject. While the chapters in the book are presented in the order of the prescribed syllabus, we suggest the students to read Chapter 4 after Chapters 1 and 2, and continue with Chapters 3, 5 and 6. Complete care has been taken to make the book errorfree. However, mistakes might have crept in inadvertently. We request our readers to bring to our notice, any such errors, omissions and mistakes, for enabling us to rectify in future editions.
viii
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We thank Dr. M. Ramachandra Gowda, Registrar, Bangalore Central University, for his encouragement, motivation and support in our academic endeavours. We would also like to thank Suman Sen of McGraw Hill Education (India) for giving us the opportunity and constant encouragement to pursue this project, Shehla Mirza for her innovative ideas, constant support, follow up and guidance in bringing out quality content, and Anjali Chakravarty for giving wonderful and appealing style and presentation to the book. Our acknowledgements are also due to Mrs. Meera Rajesh, Mrs. Manjula Nagaraju, Trishala, completed by the deadline. Last but not the least, our acknowledgements are due to the Almighty God who has blessed us with the knowledge and given us strength for spreading the same. Dr. V. Rajesh Kumar Dr. Y Nagaraju
Syllabus Financial Management Semester III Bangalore University (As per CBCS Syllabus 201415 as Revised in March 2017) AC.6.6. Financial Management (Semester III)
(IA: 30 M + Written: 70M)
Chapter in the Book
Unit 1: INTRODUCTION FINANCIAL MANAGEMENT Introduction – Meaning of Finance – Business Finance – Finance Function – Aims of Finance Function – Organization structure of Finance Department – Financial Management – Goals of Financial Management – Financial Decisions – Role of a Financial Manager – Financial Planning – Steps in Financial Planning – Principles of Sound Financial Planning – Factors influencing a sound financial plan.
Chapter 1
Unit 2: TIME VALUE OF MONEY Introduction – Meaning & Definition – Need – Future Value (Single Flow – Uneven Flow & Annuity) – Present Value (Single Flow – Uneven Flow & Annuity) – Doubling Period – Concept of Valuation: Valuation of Bonds, Debentures and shares – Simple Problems.
Chapter 2
Unit 3: FINANCING DECISION Introduction – Meaning of Capital Structure – Factors influencing Capital Structure – Optimum Capital Structure – Computation & Analysis of EBIT, EBT, EPS – Leverages. Simple Problems.
Chapter 3
Unit 4: INVESTMENT & DIVIDEND DECISION Investment Decision: Introduction – Meaning and Definition of Capital Budgeting – Features – Significance – Process – Techniques: Payback Period, Accounting Rate of Return, Net Present Value, Internal Rate of Return and profitability index Simple Problems. Dividend Decision: Introduction – Meaning and Definition – Determinants of Dividend Policy – Types of Dividends – Bonus share.
Chapter 4 and 5
Unit 5: WORKING CAPITAL MANAGEMENT Introduction – Concept of Working Capital – Significance of Adequate Working Capital – Evils of Excess or Inadequate Working Capital – Determinants of Working Capital – Sources of Working Capital.
Chapter 6
Skill Development ∑ Draw the organization chart of Finance Function of a company. ∑ Evaluate the NPV of an investment made in any one of the capital projects with imaginary figures for five years.
∑ Capital structure analysis of companies in different industries ∑ Imaginary figures prepare an estimate of working capital requirements
Question Paper Pattern Financial Management Semester III Bangalore University (As per CBCS Syllabus 201415 as Revised in March 2017) Maximum Marks: 70 Note: 1. 2. 3. 4.
Duration: 03 Hours
Question paper consists of three sections: Section A, B and C Question 1 carries 10 marks Questions 2 to 6 each carries 6 marks Questions 7 to 11 each carries 14 marks Particulars
SECTIONA (Conceptual Questions) Q1: Answer any five sub questions out of seven (a) (b) (c) (d) (e) (f) (5Q ¥ 2 marks) SECTIONB (Analytical Questions) Answer any three questions out of five Q2 Q3 Q4 (3Q ¥ 6 marks) Q5 Q6 SECTIONC (Essay Type Questions) Answer any three questions out of five Q7 Q8 Q9 (3Q ¥ 14 marks) Q10 Q11 Gross Total
(g)
Marks
Nature of Question
10 marks
Theoretical
18 marks
Numerical
42 marks
Numerical
70 Marks
Contents
About the Authors Preface Syllabus Question Paper Pattern
Chapter 1
ii vii ix xi
Introduction to Financial Management
1.1–1.10 1.1
1.2 Objectives of Financial Management 1.2 1.2.1 Primary Objectives 1.2 1.2.2 Secondary Objectives 1.3 1.3 Scope of Financial Management 1.4 1.3.1 Investment Decisions 1.4 1.3.2 Financing Decisions 1.4 1.3.3 Dividend Decisions 1.4 1.4 Functions of Financial Management or the Role 1.5 1.5 Organisation of Finance Function 1.6 1.6 Financial Planning 1.7 1.6.1 Steps in Financial Planning 1.7 1.6.2 Principles of Sound Financial Planning 1.8 1.8 Summary 1.9 Multiple Choice Questions 1.9 Answer Key 1.10
xiv
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Chapter 2 Time Value of Money 2.1 2.2 Reason for Time Value of Money 2.1 2.3 Need for Time Value of Money 2.2 2.4 Components of Time Value of Money 2.2 2.5 Compounding (or General Compounding) or Finding Future Value 2.3 2.5.1 Annual Compounding 2.4 2.5.2 Continuous Compounding 2.5 2.5.3 Effective Rate of Interest 2.10 2.6 Discounting (or General Discounting) or Finding Present Value 2.11 2.6.1 Discounting Single Cash Flow 2.12 2.6.2 Discounting a Series of Cash Flows 2.16 2.7 Annuity 2.21 2.7.1 Future Value of Annuity or Terminal Value of Annuity 2.7.2 Present Value of Annuity 2.26 2.8 Perpetuity 2.30 2.8.1 Present Value of Perpetuity 2.31 2.8.2 Present Value of Growing Perpetuity 2.32 2.9 Doubling Period 2.34 2.9.1 Rule 72 2.35 2.9.2 Rule 69 2.36 2.10 Valuation 2.37 2.10.1 Valuation of Bonds and Debentures 2.37 2.10.2 Valuation of Shares 2.43 Summary 2.48 Snapshot of Formulae 2.49 Exercises 2.50 Multiple Choice Questions 2.53 Answer Key 2.54
Chapter 3
Financing Decision 3.1 Introduction 3.1 3.2 Types of Financing or Sources of Finance 3.1 3.2.1 Longterm Sources of Finance 3.2 3.2.2 Mediumterm Sources of Finance 3.2
2.1–2.54
2.22
3.1–3.79
�
xv
3.2.3 Shortterm Sources of Finance 3.2 3.3 Sources of Longterm Finance 3.2 3.4 Capital Structure Decisions 3.6 3.6 3.6 Scope of this Chapter 3.11 3.7 EBITEPS Analysis 3.12 3.8 Leverages 3.14 Summary 3.72 Snapshot of Formats and Formulae 3.73 Exercises 3.74 Multiple Choice Questions 3.78 Answer Key 3.79
Chapter 4
Investment Decisions
4.1–4.76
4.1 Introduction 4.1 4.2 Capital Budgeting 4.1 4.2 4.4 Inputs or Factors for Capital Budgeting Decisions 4.3 4.3 4.3 4.4.3 Hurdle Rate (or Discount Rate) 4.5 4.5 Techniques of Capital Budgeting 4.6 4.5.1 NonDiscounted Cash Flow Techniques 4.6 4.5.2 Discounted Cash Flow Techniques 4.6 4.6 Measurement and Decision Making Under Each Technique 4.7 4.6.1 Payback Period 4.7 4.6.2 Average Rate of Return or External Rate of Return Method or Accounting Rate of Return 4.9 4.6.3 Discounted Payback Period 4.10 4.6.4 Net Present Value 4.11 4.13 4.6.6 Internal Rate of Return 4.14 4.7 Capital Rationing 4.16 Summary 4.67 Snapshot of Formats and Formulae 4.68 Exercises 4.69 Multiple Choice Questions 4.74 Answer Key 4.76
xvi
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Chapter 5
Dividend Decisions
5.1–5.8
Introduction 5.1 Meaning of Dividends 5.1 Dividend Policy 5.2 Determinants of Dividend Policy 5.4 5.4.1 External Factors 5.4 5.4.2 Internal Factors 5.5 5.5 Forms or Types of Dividend 5.6 5.5.1 Cash Dividend 5.6 5.5.2 Stock Dividend 5.6 Summary 5.7 Multiple Choice Questions 5.8 Answer Key 5.8 5.1 5.2 5.3 5.4
Chapter 6 Working Capital Management
6.1–6.15
6.1 Introduction 6.1 6.2 Working Capital Management 6.2 6.3 Estimation of Working Capital Requirement 6.2 6.3.1 Need for Adequate Working Capital 6.3 6.3 6.3.3 Methods for Estimation of Working Capital Requirement 6.4 6.4 Sources of Working Capital 6.6 6.5 Components of Working Capital Management 6.12 Summary 6.13 Multiple Choice Questions 6.14 Answer Key 6.15
Model Question Paper1 Model Question Paper2 Model Question Paper3 Question Paper (November/December 2017) Appendix
M1.1– M1.3 M2.1– M2.3 M3.1– M3.3 QP1.1– QP1.4 A1.11.6
1
Introduction to Financial Management
CHAPTER OVERVIEW 1.1 Meaning and Deﬁnition of Financial Management 1.2 Objectives of Financial Management 1.3 Scope of Financial Management 1.4 Functions of Financial Management or the role of Chief Financial Ofﬁcer (CFO)
1.1
MEANING AND DEFINITION OF FINANCIAL MANAGEMENT
Financial Management comprises of the forecasting, planning, organising, directing, coordinating and controlling of all activities relating to acquisition and application of the
1.5 Organisation of Finance Function 1.6 Financial Planning
– Raymond Chambers Financial Management is concerned with the managerial decisions that result in the acquisition – Phillippatus
1.2
�
THEORY QUESTIONS Section A (Bangalore University, B.Com, November 2014–2016)
OBJECTIVES OF FINANCIAL MANAGEMENT
1.2
1.2.1
Primary Objectives
TABLE 1.1
P
�
1.2.2
1.3
Secondary Objectives
THEORY QUESTIONS Section A
(Bangalore University, B.Com, November 2013)
(Bangalore University, B.Com, November 2014–2015)
Section B
(Bangalore University, B.Com, November 2014–2015)
1.4
�
SCOPE OF FINANCIAL MANAGEMENT
1.3
1.3.1
Investment Decisions
1.3.2
Financing Decisions
1.3.3
Dividend Decisions
THEORY QUESTIONS Section A
Section B
�
1.4
1.5
FUNCTIONS OF FINANCIAL MANAGEMENT OR THE ROLE OF CHIEF FINANCIAL OFFICER (CFO)
� � � � � � � � � � � �
THEORY QUESTIONS Section A (Bangalore University, B.Com, November 2014)
Section B
1.6
�
(Bangalore University, B.Com, November 2016)
ORGANISATION OF FINANCE FUNCTION
1.5
CHIEF FINANCIAL OFFICER OR VICEPRESIDENT (FINANCE)
Treasurer
Controller
Cash Manager Credit Manager Capital Budgeting Manager Fund Raising Manager Portfolio Manager
Financial Accounting Manager Cost Accounting Manager Tax Manager Data Processing Manager Internal Auditor
Structure of Finance Function
�
1.7
THEORY QUESTIONS Section A
Section B
FINANCIAL PLANNING
1.6
1.6.1
Steps in Financial Planning
1.8
�
1.6.2
Principles of Sound Financial Planning
THEORY QUESTIONS Section A (Bangalore University, B.com, November 2014) (Bangalore University, B.Com, November 2015)
Section B (Bangalore University, B.Com, November 2016)
Section C (Bangalore University, B.Com, November 2013)
�
SUMMARY �
�
� � –A
A A A A
�
� �
MULTIPLE CHOICE QUESTIONS
1.9
1.10
�
ANSWER KEY
Time Value of Money
2
2.1
CHAPTER OVERVIEW
Time Value of Money
2.1 Meaning and Deﬁnition 2.2 Reason for Time Value of Money 2.3 Need for Time Value of Money 2.4 2.5 2.6 2.7
MEANING AND DEFINITION
Components of Time Value of Money Compounding or Finding Future Value Discounting or Finding Present Value Annuity
THEORY QUESTIONS
2.8 Perpetuity 2.9 Doubling Period 2.10 Valuation
Section A (Bangalore University, B.Com, November 2015)
REASON FOR TIME VALUE OF MONEY
2.2
return
`
`
`
interest
`
2.2
�
`
Opportunity Cost.
NEED FOR TIME VALUE OF MONEY
2.3
THEORY QUESTIONS Section A
Section B
COMPONENTS OF TIME VALUE OF MONEY
2.4
�
2.3
Compounding Discounting Indexing
Compounding Discounting
THEORY QUESTIONS Section A
(Bangalore University, B.Com, November 2016)
Section B
COMPOUNDING (OR GENERAL COMPOUNDING) OR FINDING FUTURE VALUE
2.5 Compounding
Future Value
Annual Compounding Continuous Compounding Effective Rate of Interest
2.4
�
2.5.1
Annual Compounding
Annual Compounding ` `
Year 1 `
`
(`)
¥ Balance in the account at the end of Year 1 Year 2
1,10,000
¥ Balance in the account at the end of Year 2 Year 3
1,21,000
¥ Balance in the account at the end of Year 3
`
`
`
(`)
1,33,100
`1,33,100.
FV = PV (1 + i)n
` Problem 1
Problem on Annual Compounding
` SOLUTION FV = PV (1 + i)n
`
¥
`1,33,100.
�
`
` ` ¥ `1,52,087.50 Problem 2
Problem on Annual Compounding
` SOLUTION FV = PV (1 + i)n `
` ` ¥ `78,676
2.5.2
Continuous Compounding Continuous Compounding. `
(`)
6ˆ Ê ÁË `10,00,000 ¥ 10% ¥ ˜¯ 12 Balance in the account at the end of 6 months (`)
6ˆ Ê ÁË `10,50,000 ¥ 10% ¥ ˜¯ 12 Balance in the account at the end of year 1
2.5
2.6
�
(`)
6ˆ Ê ÁË `11,02,500 ¥ 10% ¥ ˜¯ 12 Balance in the account at the end of year 1.5
11,57,625 (`)
6ˆ Ê ÁË `11,57,625 ¥ 10% ¥ ˜¯ 12 Balance in the account at the end of year 2
iˆ Ê FV = PV Á 1 + ˜ Ë f¯
`
n¥f
È Ê 0.10 ˆ ˘ Í1 + ÁË 2 ˜¯ ˙ Î ˚
` ` ¥ `12,15,506.25 Problem 3
Problem on Continous Compounding
` SOLUTION
iˆ Ê FV = PV Á 1 + ˜ Ë f¯
n¥f
2¥2
12,15,506.25
�
`
ÈÊ 0.10 ˆ 1 ¥ 4 ˘ ÍÁ1 + ˜ ˙ 4 ¯ ˚ ÎË
`
` ` ¥ `1,10,381.29 Problem 4
Problem on Continous Compounding
` SOLUTION
iˆ Ê FV = PV Á 1 + ˜ Ë f¯
n¥f
`
`
Ê 0.20 ˆ ÁË1 + ˜ 2 ¯
2¥2
` ` ¥ `1,464.10 Problem 5
Problem on Continous Compounding
`
2.7
2.8
�
SOLUTION (i) When compounding is done annually FV = PV(1 + i)n `
` ` ¥ `3,19,440 iˆ Ê FV = PV Á 1 + ˜ Ë f¯
n¥f
`
`
È 0.10 ˘ ÍÎ1 + 2 ˙˚
3¥ 2
` ` ¥ `3,21,624 Problem 6
Problem on Calculation of rate of interest and continuous compounding
`
`
SOLUTION `
`
�
iˆ Ê FV = PV Á 1 + ˜ Ë f¯
n¥f
` `
`
È Ê i ˆ˘ Í1 + ÁË 2 ˜¯ ˙ Î ˚
`
` 25,250 ` 20,000
È Ê i ˆ˘ Í1 + ÁË 2 ˜¯ ˙ Î ˚ È Ê i ˆ˘ Í1 + ÁË 2 ˜¯ ˙ Î ˚
2¥2
4
4
È Ê i ˆ˘ Í1 + ÁË 2 ˜¯ ˙ Î ˚ i 2 ¥
12%
iˆ Ê FV = PV Á 1 + ˜ Ë f¯
`
n¥f
2.9
2.10
�
È Ê 0.12 ˆ ˘ Í1 + ÁË 4 ˜¯ ˙ Î ˚
`
2¥4
` ` ¥ `25,336
2.5.3
Effective Rate of Interest
`
iˆ Ê FV = PV Á 1 + ˜ Ë f¯
n¥f
1¥ 2
`
È Ê 0.10 ˆ ˘ Í1 + ÁË 2 ˜¯ ˙ Î ˚
` ` ¥ `1,10,250 ` `
`
2
` `
`
` Ê `10,250 ˆ ÁË `1,00,000 ˜¯ ¥ 100
10.25%
effective rate of interest Ê Effective Rate of Interest = ÁË 1 +
È Ê 0.10 ˆ ˘ Í1 + ÁË 2 ˜¯ ˙ Î ˚
f
iˆ ˜ –1 f¯
2
2
10.25%
�
Problem 7
2.11
Problem on Calculation of Effective Rate of Interest
SOLUTION Ê ÁË1 +
iˆ ˜ f¯
f
B È Ê 0.12 ˆ ˘ Í1 + ÁË 2 ˜¯ ˙ Î ˚
2
È Ê 0.12 ˆ ˘ Í1 + ÁË 4 ˜¯ ˙ Î ˚
4
2
THEORY QUESTIONS Section A
Section B
2.6 Discounting
DISCOUNTING (OR GENERAL DISCOUNTING) OR FINDING PRESENT VALUE
2.12
�
2.6.1
Discounting Single Cash Flow `
`
FV = PV(1 +
PV =
i)n
iˆ Ê or PV Á 1 + ˜ Ë f¯
n¥f
FV FV or n È Ê i ˆ n¥f ˘ (1 + i) Í1 + ÁË ˜¯ ˙ f Î ˚
Rate of Discount
Problem 8
Problem on Calculation of Present Value
` SOLUTION PV =
FV (1 + i)n
`
`1,00,000 (1 + 0.1) 2 `1,00,000 1.21 `82,644.63 Note:
`
`
�
` `
`
` `
Problem 9
Problem on Calculation of Present Value
` SOLUTION PV =
FV È Ê i ˆ n¥f ˘ Í1 + ÁË ˜¯ ˙ f Î ˚
`
`1,00,000 È Ê 0.10 ˆ 2 ¥ 2 ˘ Í1 + ÁË ˙ ˜ 2 ¯ Î ˚
`1,00,000 (1.05) 4 `1,00,000 1.2155 `82,270.68
Problem 10
` ` ` `
Problem on Calculation of Present Value
2.13
2.14
�
SOLUTION Case (a)
PV =
FV (1 + i)n
`
`2,000 (1 + 0.1) 2
`2,000 1.12 `2,000 1.21 `1652.89 Case (b)
PV =
`
`5000 È Ê 0.09 ˆ 1 ¥ 4 ˘ Í1 + ÁË ˜ ˙ 4 ¯ ˚ Î `5000
(1.0225)4 `5000 1.093083 `4,574.22
FV È Ê i ˆ n¥f ˘ Í1 + ÁË ˜¯ ˙ f Î ˚
�
Case (c)
PV =
FV È Ê i ˆ n¥f ˘ Í1 + ÁË ˜¯ ˙ f Î ˚
`
`1000 È Ê 0.08 ˆ 0.5 ¥ 12 ˘ Í1 + ÁË ˙ ˜ 12 ¯ Î ˚ `1000
(1.0067 )6 `1000 1.040879 `960.73 Case (d)
PV =
`
`4000 È Ê 0.12 ˆ 1 ¥ 12 ˘ Í1 + ÁË ˙ ˜ 12 ¯ Î ˚ `4000
(1.01)12
FV È Ê i ˆ n¥f ˘ Í1 + ÁË ˜¯ ˙ f Î ˚
2.15
2.16
�
`4000 1.1268 `3549.88 logarithms
Note:
2.6.2
Discounting a Series of Cash Flows ` ` `
`1,00,000 `3,00,000 ` 2,00,000 + + (1.12)1 (1.12)2 (1.12)3 `
`
`
`4,70,799,92
`4,70,800 (approx.)
` `
Calculation of Present Value of `
`
1 (1 + i)1
`
1 1 = 2 [(1 + i) (1 + i)] (1 + i) 1 (1 + i)1
`
PV of ` 1 at the End of Year 1 (1 + i)
�
1
`
(1 + i)
3
=
1 [(1 + i) (1 + i) (1 + i)]
1 (1 + i) 2
`
PV of ` 1 at the End of Year 2 (1 + i) ` `1 (1 + i)
PV of `1 of cash flow at the end of Year 1 (1 + i) PV of `1 of cash flow at the end of Year 2 (1 + i)
PV of `1 of cash flow at the end of Year 3 (1 + i) PV of `1 of cash flow at the end of Year 4 (1 + i) Problem 11
Problem on Calculation of Present Value of `1
` SOLUTION Year End
Present Value of `1 at Discount Rate of 10%
1
1 1.1
2
0.9091 1.1 0.8264 1.1 0.7513 1.1 0.6830 1.1
2.17
2.18
�
Notes: `
`
Problem 12
Problem on Calculation of Present Value of `1
` SOLUTION Year End
Present Value of `1 at Discount Rate of 12%
1
1 1.12
2
0.8929 1.12 0.7972 1.12 0.7118 1.12 0.6355 1.12 0.5674 1.12 0.5066 1.12 0.4523 1.12
Notes: `
`
�
Problem 13
Problem on Calculation of Present Value of `1
` SOLUTION Year End
Present Value of `1 at Discount Rate of 15%
1
1 1.15
2
0.8696 1.15 0.7561 1.15 0.6575 1.15 0.5718 1.15 0.4972 1.15
Notes: `
`
Problem 14
Problem on Calculation of Present Value of Series of Cash Flows
Year 1 2
`)
2.19
2.20
�
SOLUTION Year
Cash
PV of `1 at 10% (`)
`)
PV of
`)
1 2
8,06,750
Problem 15
Problem on Calculation of Present Value of Series of Cash Flows
Year
Projected Cash `)
1 2
SOLUTION Year (`)
PV of `1 at 12% (`)
PV of
`)
1 2
33,36,181
�
Problem 16
2.21
Problem on Calculation of Present Value of Series of Cash Flows
Year
Projected Cash `)
1 2
SOLUTION Year (`)
PV of `1 at 8% (`)
PV of Cash `)
1 2
1,06,135.62
THEORY QUESTIONS Section A
ANNUITY
2.7 Annuity same annuity
regular intervals
given
2.22
�
2.7.1
Future Value of Annuity or Terminal Value of Annuity
` `
Future Value of Annuity
Terminal Value of Annuity
`
` `
¥
`
¥
`
¥
`1331 `
2
`
¥
`1210 `
`
¥
1
`
¥
`1100
is `1000 `
`
` `4641.
P[(1 + i)n  1] i
`
`4641
�
[`1000{(1 + 0.1) 4  1}] 0.1
[`1000 ¥ {1.14  1}] 0.1 [`1000 ¥ {1.4641  1}] 0.1
[`1000 ¥ 0.4641] 0.1
`464.10 0.1 `4641 Notes:
Ï P[(1 + i)n  1] ¸ Ì ˝ ¥ (1 + i) i Ó ˛
n¥f ˘ ÈÊ iˆ P ÍÁ 1 + ˜ ˙1 f¯ ÎË ˚ Ê iˆ ÁË ˜¯ f
Problem 17
`
ÈÏ Ê i ˆ ¸n ¥ f ˘ P ÍÌ1 + Á ˜ ˝ ˙  1 iˆ ÍÎÓ Ë f ¯ ˛ ˙˚ Ê ¥ Á1 + ˜ Ë f¯ Ê iˆ ÁË ˜¯ f
Problem on Calculation of Terminal Value of Annuity
2.23
2.24
�
SOLUTION When Investment is Made at the End of Each Year P[(1 + i)n  1] i `
{`1,00,000[(1 + 0.12)5  1]} 0.12
{`1,00,000 ¥ [(1.12)5  1]} 0.12 {`1,00,000 ¥ [1.7623  1]} 0.12
(`1,00,000 ¥ 0.7623) 0.12 `76,230 0.12 `6,35,250 When Investment is Made at the Beginning of Each Year Ï P[(1 + i)n  1] ¸ Ì ˝ ¥ (1 + i) i Ó ˛ `
Ï{`1,00,000[(1 + 0.12)5  1]}¸ ˝ ¥ (1 + 0.12) Ì 0.12 Ó ˛
Ï{`1,00,000 ¥ [(1.12)5  1]}¸ ˝ ¥ 1.12 Ì 0.12 Ó ˛
{
}
{`1,00,000 ¥ [1.7623  1]} ¥ 1.12 0.12
�
{ {
}
(`1,00,000 ¥ 0.7623) ¥ 1.12 0.12
}
`76,230 ¥ 1.12 0.12
`
¥
`7,11,480
Problem 18
Problem on Calculation of Terminal Value of Annuity
` SOLUTION
P[(1 + i)n  1] i `
{` 4,000[(1 + 0.10) 4  1]} 0.10
{` 4,000[(1.1) 4  1]} 0.10 {` 4,000 ¥ [1.4641  1]} 0.10
(` 4,000 ¥ 0.4641) 0.10
`186.40 0.10 `18,564
2.25
2.26
�
2.7.2
Present Value of Annuity ` ` Present Value of Annuity.
Year
PV of
PV of `1 at 10% (`)
(`)
`)
1 2
37,900
P ¥ Present Value of Annuity of `1 at i% for n years ¥
`
` `37,900.
`
` ‘Annuity’
È Ï 1 ¸˘ P Í1  Ì n ˝˙ Î Ó (1 + i) ˛ ˚ i
Discount Rate
ÏÔ È Ê ˆ ˘ ¸Ô 1 `10,000 1 Í Ì Á 5 ˜ ˙˝ ÍÎ Ë (1 + 0.1) ¯ ˙˚ Ô˛ ÔÓ 01
�
Ï È Ê 1 ˆ ˘¸ Ì`10,000 Í1  ÁË 5 ˜¯ ˙ ˝ 1.1 ˚ ˛ Î Ó 0.1
{`10,000[1  0.621]} 0.1 {`10,000[0.379]} 0.1
`3790 0.1 `37,900 Notes:
Ï È Ê 1 ˆ˘¸ Ô P Í1  Á ˙Ô Ì ÍÎ Ë (1 + i)n ˜¯ ˙˚ ˝ Ô ¥ (1 + i) Ô i ˛ Ó
È Ï 1 P Í1  Ô n¥f Í Ì ÊÁ 1 + i ˆ˜ ÍÎ ÔÓ Ë f¯ Ê iˆ ÁË ˜¯ f
Problem 19
Ï È Ê 1 ˆ˘¸ Ô P Í1  Á n¥f ˜ ˙ Ô ÔÔ Í Á ÊÁ 1 + i ˆ˜ ˜ ˙ ÔÔ ¯ ˙˚ ˝ Ê Ì ÍÎ Ë Ë f¯ Ô Ô ¥ ÁË 1 + Ê iˆ Ô Ô ÁË ˜¯ ÔÓ Ô˛ f
Problem on Calculation of Present Value of Annuity
` SOLUTION
¸˘ Ô˙ ˝˙ Ô˙ ˛˚
iˆ ˜ f¯
2.27
2.28
�
Method One Year
PV of
PV of `1 at 15% (`)
(`)
`)
1 2
8,38,250
¥
`
`
` ` Method Three
`
¥
`8,38,250
È Ï 1 ¸˘ P Í1  Ì n ˝˙ Î Ó (1 + i) ˛ ˚ i
`
ÏÔ È Ê ˆ ˘ ¸Ô 1 Ì`2,50,000 Í1  Á 5 ˜ ˙˝ ÍÎ Ë (1 + 0.15) ¯ ˙˚ ˛Ô ÓÔ 0.15 Ï È Ê 1 ˆ ˘¸ Ì`2,50,000 Í1  ÁË ˜ ˙˝ 1.155 ¯ ˚ ˛ Î Ó 0.15 {`2,50,000 [1  0.497]} 0.15
�
2.29
{`2,50,000[0.503]} 0.15
`1,25,750 0.15 `8,38,333.33 `
Note:
Problem 20
Problem on DecisionMaking, involving Present Value of Annuity
`
`
SOLUTION ` ` `
Option One `
`5,00,000.
`
Ê `6,15,000 ˆ ÁË 6 years ˜¯
` `
Year (`)
PV of `1 at 12% (`)
PV of `)
1 2
4.112
4,21,480.00
2.30
�
¥ ` ¥ ` ¥ `4,21,480
` `
` `
THEORY QUESTIONS Section A (Bangalore University, B.Com, November 2013)
PERPETUITY
2.8 Perpetuity same
P
regular intervals forever
Perpetuity
�
2.8.1
Present Value of Perpetuity `
approximate P i
Note:
Problem 21
Problem on Calculation of Present Value of Perpetuity
`
P SOLUTION
P i `
`60 0.08 Problem 22
P
`750
Problem on Calculation of Present Value of Perpetuity
`
SOLUTION P i
2.31
2.32
�
`
`1000 0.10 Problem 23
`10,000
Problem on Calculation of Present Value of Perpetuity
` SOLUTION P i `
`1000 0.10
`10,000
`
`10, 000 (1.12) 2
`10, 000 1.2544
`7,971.94
2.8.2
Present Value of Growing Perpetuity
P1 (i  g ) P1
�
Note:
Problem 24
Problem on Calculation of Present Value of Growing Perpetuity
`
SOLUTION
P1 (i  g )
P1
`
`10, 000 (0.12  0.08)
`10, 000 0.04 `2,50,000 Problem 25
Problem on Calculation of Present Value of Growing Perpetuity
`
2.33
2.34
�
SOLUTION
P4 (i  g ) P
`
`10, 000 (0.12  0.08)
`10, 000 0.04
`2,50,000 `
`2, 50, 000 (1.12)3 `2, 50, 000 1.404928 `1,77,945.06
THEORY QUESTIONS Section A
DOUBLING PERIOD
2.9 Doubling Period ` `
`
�
Year 1 `
`
`
`
`
`
`
`
(`)
¥ Balance in the account at the end of Year 1 Year 2
1,100.00
¥ Balance in the account at the end of Year 2 Year 3
1,210.00
¥ Balance in the account at the end of Year 3 Year 4
1,331.00
¥ Balance in the account at the end of Year 4 Year 5
1,464.10
¥ Balance in the account at the end of Year 5 Year 6
1,610.51
¥ Balance in the account at the end of Year 6 Year 7
1,771.56
¥ Balance in the account at the end of Year 7 Year 8
1,948.72
(`)
(`)
(`)
(`)
(`)
(`)
(`)
¥ Balance in the account at the end of Year 8
2,143.59
`
2.9.1
Rule 72 72 . I
2.35
2.36
�
72 10
2.9.2
7.2 years
Rule 69
Ê 69 ˆ 0.35 + Á ˜ . Ë I¯
Ê 69 ˆ ÁË ˜¯ 10 Problem 26
7.25 years
Problem on Calculation of Doubling Period
SOLUTION As per Rule 72 72 I 72 12
6 years
As per Rule 69 Ê 69 ˆ ÁË ˜¯ I Ê 69 ˆ ÁË ˜¯ 12
THEORY QUESTIONS Section A
6.10 years
�
2.37
VALUATION
2.10
Valuation
2.10.1
Valuation of Bonds and Debentures
1. Coupon Bonds or Plain Vanilla Bonds
Plain Vanilla Bonds ` `
`
`
rate of return expected by the investor
2.38
�
Value of Coupon Bond = [ C ¥ PV of Annuity of `1 at i% for n years] + [M ¥ PV of `1 receivable at the end of nth year, at i%]
Problem 27
Problem on Valuation of Coupon Bond
`
SOLUTION
Method 1 Year
PV of
PV of `1 at 10% (`)
(`)
`)
1 2
924.20
Method 2 ¥
` ¥
`
` `
` `
�
` ¥ ` `924.20 Problem 28
`
2.39
¥
`
Problem on Valuation of Coupon Bond
` SOLUTION ¥
` ¥
`
`
`
`
`
Calculation of Present Value at 16% Year
PV of `1 at 16%
1 2
3.684
` ` ¥ ` `93.40
`
¥
`
2. Zero Coupon Bonds
Zero Coupon Bonds Deep Discount Bonds
2.40
�
Amount Receivable on Maturity of Bond (usually Face Value) (1+ i) n
Problem 29
Problem on Valuation of Zero Coupon Bond
` SOLUTION Amount Receivable on Maturity of Bond (usually Face Value) (1+ i) n `
`5, 00, 000 (1 + 0.12)5 `5, 00, 000 1.125 `5, 00, 000 1.7623 `2,83,720.14 3. Irredeemable Bonds or Perpetual Bonds
Irredeemable Bonds
Perpetual Bonds
�
C i
Problem 30
Problem on Valuation of Perpetual Bond
`
`
SOLUTION C i
`
`60 0.10
`600
4. Selfamortising Bonds
` `
Problem 31
Problem on Valuation of Selfamortising Bond
`
2.41
2.42
�
SOLUTION Year End
Principal Repaid (`)
Interest Paid (`)
1
`
2
` `
`
`
`
`
`
to the Investor (`)
PV of `1 at 12% (`)
Value of the Bond
Problem 32
PV of Cash `)
1046.59
Problem on Valuation of Selfamortising Bond
`
`
(Bangalore University, B.Com, November 2013) SOLUTION
Year End
Principal Repaid (`)
Interest Paid (`)
1
`
2
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
to the Investor (`)
PV of `1 at 20% (`)
Value of the Bond
PV of Cash `)
7096.40
�
THEORY QUESTIONS Section A
Section B
2.10.2
Valuation of Shares
Ke.
2.43
2.44
�
Problem 33
Problem on
`
`
SOLUTION
` ` `218
`218 (1 + 0.12)1
`218 1.12 `194.64 Problem 34
Problem on
` ` SOLUTION
Year
Cash
PV of `1 at 10% (`)
`)
PV of `)
1 2
3.790
50.2975
`50.30 2. When Shares are Meant for Perpetual Holding and There is no Growth Expected in Dividends (No Growth Model)
�
2.45
D Ke Ke Problem 35
Problem on Valuation of Shares under No Growth Model
` SOLUTION
D Ke ` Ke `16 0.12
`133.33
3. When Shares are Meant for Perpetual Holding and Dividends are Expected to Grow at a Constant Rate (Constant Growth Model)
D1 (k e  g) 1
Ke
2.46
�
Problem 36
Problem on Valuation of Shares Under Constant Growth Model
`
SOLUTION D1 (k e  g)
1
`
Ke `2 (0.15  0.05) Problem 37
`2 0.10
`20
Problem on Valuation of Shares Under Constant Growth Model
` SOLUTION D1 (k e  g)
1
`
Ke `2 (0.14  0.06) Problem 38
`2 0.08
`25
Problem on Valuation of Shares Under Constant Growth Model
` `
�
SOLUTION
2.47
D1 (k e  g) `
1
Ke `3.50 (0.15  0.10) Problem 39
`3.50 0.05
`70
Problem on Valuation of Shares Under Constant Growth Model
` (Bangalore University, B.Com, November 2013) SOLUTION D1 (k e  g) `
1
Ke `2.00 (0.30  0.10) Problem 40
`2.00 0.20
`10
Problem on Valuation of Shares Under Constant Growth Model
`
SOLUTION D1 (k e  g)
1
` Ke
`
`3.48
2.48
�
`3.48 (0.20  0.16)
`3.48 0.04
`87
THEORY QUESTIONS Section A (Bangalore University, B.Com, November 2013)
Section B
SUMMARY � � � Compounding
�
� � Discounting � Annuity
� Perpetuity
�
� Doubling Period
�
� Value of Financial Assets �
Bonds
� Valuation of Shares
models
SNAPSHOT OF FORMULAE FV = PV(1+i)n iˆ Ê FV = PV Á 1 + ˜ Ë f¯
n ×f
f
iˆ Ê ÁË 1 + ˜¯  1 f
PV =
P
FV n
(1 + i)
or PV =
[(1 + i)n  1] i
FV Ê ÁË 1 +
iˆ ˜ f¯
n×f
È ÏÔ 1 ¸Ô˘ Í1  Ì n ˝˙ Í ÓÔ (1 + i ) ˛Ô˙˚ PÎ i P i P1 (i  g) 72 I Ê 69 ˆ 0.35 + Á ˜ Ë I¯ [C ¥ PV of Annuity of `1 at i% for n years] + [M `PV of `1 at the end of nth year, at i%] Amount Receivable on Maturity (1 + i )n C i D Ke D1 (K e  g)
2.49
2.50
�
EXERCISES Compounding ` `14,04,928] ` `5,87,731.23]
Continuous Compounding `
15% (a)
20% (b)
`
`3,19,440; (b) `3,21,622.95] ` `1,11,015 and `36,015] ` `2,575.10] `
` `12,670]
Effective Rate of Interest
Present Value ` `68,301.35]
�
2.51
` ` (Bangalore University, B.com, November 2014) `17,888.02] ` `70,496.05] ` `1518.67 (b) `1294.37] ` ` ` ` `1,652.89 (b) `4,574.22 (c) `960.92 (d) `2,795.70]
Year
1
2
3
4
5
6
7
`7,732.32]
Year
1
2
3
4
5
` `1,745.49, `1,537.69, and `1,404.56]
Terminal Value of Annuity or Future Value of Annuity `
` `1,257.79] `
Present Value of Annuity `
`2.673]
2.52
�
` `8,38,038.80] ` `614.46] ` `
`6,728.88, (b) `11,069.64]
Perpetuity `
`83.33] ` `750]
` `10,000] ` (Bangalore University, B.Com, November 2016) `2500] ` `6,643.28] ` `28,821.84]
Growing Perpetuity `
`14,28,571.43] `
`11,86,300.41]
Doubling Period
11.85 years, 7.25 years, 5.10 years and 4.18 years]
�
2.53
Valuation of Bonds ` `1126.87] ` `31,775.90] ` `666.67] `
`95.356]
Valuation of Shares ` ` ` `132.47] ` `133.33] ` `50] ` `
`288.5705, (b) `381.50]
MULTIPLE CHOICE QUESTIONS
2.54
�
3. Reason for Time Value of Money is
4. When ‘Interest’ is calculated more than once in a year, it is called
5. Same amount of receipts or payments, happening in regular intervals for a given period of time is called
intervals forever, it is called
8. Bonds having all regular or normal features are called
ANSWER KEY
Financing Decision
3
3.1
CHAPTER OVERVIEW 3.1 Introduction 3.2 Types of Financing or Sources of Finance 3.3 Sources of Longterm Finance 3.4 Capital Structure Decisions 3.5 Factors inﬂuencing Capital Structure Decisions 3.6 Scope of this chapter 3.7 EBITEPS Analysis 3.8 Leverages
INTRODUCTION
Financing Decisions refer to decisions regarding funding of the business enterprise. It involves
the amount of funds to be mobilised from each source. This chapter is discussed under the following two headings: 1. Types of Financing or Sources of Finance 2. Capital Structure Decisions
TYPES OF FINANCING OR SOURCES OF FINANCE
3.2 the following categories: I. Longterm Sources II. Mediumterm Sources III. Shortterm Sources
3.2
3.2.1 1. 2. 3. 4. 5. 6. 7. 8.
Longterm Sources of Finance Equity Shares Preference Shares Retained Earnings Debentures/Bonds Loans from Financial Institutions Loans from State Financial Corporations Loans from Commercial Banks Venture Capital Funding
3.2.2 1. 2. 3. 4. 5. 6. 7.
Mediumterm Sources of Finance Preference Shares Debentures/Bonds Public Deposits Loans from Commercial Banks Loans from Financial Institutions Loans from State Financial Corporations Lease Financing/Hire Purchase Financing
3.2.3 1. 2. 3. 4. 5. 6. 7. 8. 9.
Shortterm Sources of Finance Trade Credit Loans from Banks and Financial Institutions Loans from Indigenous Bankers Customer Advances Accrued Expenses Pledging of Receivables Commercial Papers Debt Securitisation Factoring of Receivables
SOURCES OF LONGTERM FINANCE
3.3 A. Equity Shares B. Preference Shares
3.3
C. D. E. F.
Retained Earnings Debentures Loans from Banks and Financial Institutions Venture Capital
Each of these sources is explained along with its merits and limitations in the following sections.
A. Equity Shares
The following are some of the advantages of Equity Capital Financing: (a) They provide security to other fund providers.
(c) There are no committed payments to be made.
tax implications in the form of dividend distribution tax. (d) Too much dependence on equity shares reduces the earnings available to owners and dilutes the control of the management.
B. Preference Shares holders of these instruments have preference in payment of dividends and in repayment of capital.
(a) There is no dilution of Earnings per Share or in the control of management by issue of these shares. (c) The risk for the company issuing Preference Shares is minimal.
(b) Cumulative Preference Shares might result in additional burden to the company.
3.4
C. Retained Earnings “Retained Earnings”. No risk is associated with retained earnings and there is no dilution of control from this
D. Debentures
offered as security for the amount borrowed by issue of debentures.
(c) It does not result in dilution of control in management.
of investment.
E. Loans from Banks and Financial Institutions
and (e) managerial. The rates of interest charged by the institutions differ for various schemes. These secured loans are to be repaid according to a given repayment schedule.
F. Venture Capital Financing
invests in the Equity or Debt of an entrepreneur (promoter/venture capital undertaking) who has a
3.5
the undertaking when the initial returns are not assured or are not attractive. (b) Conditional Loan: A conditional Loan is repayable in the form of a royalty after the venture is able to generate Sales. No interest is paid on such Loans. The rate of interest may be based
Loan and conditional Loan. The undertaking has to pay both interest and royalty on Sales. undertaking on which interest in the startup and commissioning phase would be nil; during the interest would be very high.
membership.
THEORY QUESTIONS Section A
4. List any two limitations of Equity Shares. 5. State the meaning of Preference Shares. 7. State the limitations of Preference Shares. 9. State any three advantages of Debentures.
12. List the different forms of Venture Capital Financing.
Section B Equity Shares.
Section C their pros and cons.
3.6
CAPITAL STRUCTURE DECISIONS
3.4 Capital Structure Decisions refer to deciding on the quantum of funds to be mobilised from each source or proportion of each source in the total capital of the company. source in the total capital) depends on various factors.
FACTORS INFLUENCING CAPITAL STRUCTURE DECISIONS
3.5 Designing Capital Structure involves deciding upon the quantum or proportion of debt and equity.
2. Risk associated with the structure 3. Cost of Capital of the structure
6. Marketability of the instruments 7. Size of the company
10. Nature of investors 11. Requirements of investors A detailed explanation of each factor is given below:
share. The formulae for calculation of Earning per Share and Market Value per share are given below: Profits available to Equity shareholders EPS = hares outstanding Number of Equity Sh Market Value per share = EPS ¥
P Ratio E
3.7
Interest and Tax (EBIT) and Indifference Point. Indifference Point refers to the amount of EBIT at which two different Capital Structures result in same EPS.
debt would lead to higher earnings per share. ‘Trading on Equity’. used is ‘EBITEPS Analysis’.
It refers to the extent of risk faced by the company on account of its Capital Structure. A business and combined or total risk. The extent of risk is measured with the help of leverages. There are three types of leverages:
Operating Leverage of changes in Sales on its EBIT. Degree of Operating Leverage (DOL) is calculated using the following formulae: Ê % Change in EBIT ˆ Ê Contribution ˆ OR Á DOL = Á ˜¯ ˜ Ë EBIT Ë % Change in Sales ¯
Financial Leverage Leverage (DFL) is calculated using the following formulae: Ê % Change in EPS ˆ Ê EBIT ˆ OR Á DFL = Á ˜ Ë EBT ˜¯ Ë % Change in EBIT ¯
debt as a source of fund.
3.8
Combined Leverage (DCL) is calculated using the following formulae: Ê % Change in EPS ˆ Ê Contribution ˆ OR Á DCL = Á ˜¯ OR (DOL ¥ DFL) Ë EBT Ë % Change in Sales ˜¯
Leverage is low and the Degree of Financial Leverage is high.
3. Cost of Capital It refers to the rate of return given by the company to those who have contributed funds. It is calculated using the following formulae:
(i) In case of Debt: I(1  T) SV
(a) Irredeemable Debt:
Kd =
(b) Redeemable Debt:
È Ê f + d i + Pr  Pi ˆ ˘ ˜¯ ˙ ÍI(1  T) + ÁË N ˚ Kd = Î È (RV + SV) ˘ ÍÎ ˙˚ 2
T = Tax Rate SV = Sale Value or Issue Price RV = Redeemable Value f = Flotation Costs d = Discount on Issue Pr = Premium on Redemption Pi = Premium on Issue N = Maturity Period (ii) In case of Preference Shares: (a) Irredeemable Preference Shares: Kp =
D SV
3.9
(b) Redeemable Preference Shares:
È Ê f + d i + Pr  Pi ˆ ˘ ˜¯ ˙ ÍD + ÁË N ˚ Kp = Î È (RV + SV) ˘ ˙˚ ÍÎ 2
SV = Sale value or Issue Price N = Maturity Period f = Flotation Cost di = Discount on Issue Pr = Premium on Redemption Pi = Premium on Issue RV = Redeemable Value (iii) In case of Equity Shares: (a) Dividend Growth Model
ÊD ˆ Ke = Á 1 ˜ + g Ë P0 ¯
(b) Capital Asset Pricing Model
Ke = Rf + b( Rm – Rf )
1
= Next Year Dividend
P0 = Market Price Per Share g = Growth Rate Rf = Riskfree Rate b = Beta Rm = Market Rate of return (iv) In case of Retained Earnings:
Kr = Ke
(B
Ko = KdWd + KpWp + KeWe an important factor that must be considered in deciding upon Capital Structure.
4. Tax Implications
savings on account of interest.
3.10
exempt from Tax. both the company and the shareholders.
5. Government Policies
6. Marketability of the Instruments
7. Size of the Company
rely more on owners’ funds.
8. Purpose of Financing
be a better choice.
9. Period of Financing
10. Nature of Investors
3.11
11. Requirement of Investors
considered.
designing Capital Structure.
THEORY QUESTIONS Section A (Bangalore University, B.Com, November 2014, November 2015–2016)
Trading on E Cost of C
(Bangalore University, B.Com, November 2015–2016)
Section B capital structure decisions.
(Bangalore University, B.Com, November 2014)
Section C
SCOPE OF THIS CHAPTER
3.6 A Capital Structure is said to be ideal when it gives maximum possible minimum cost of capital and matches with risk policy of the company.
the technique for measuring risk is Leverages. A. EBITEPS Analysis B. Leverages
3.12
EBITEPS ANALYSIS
3.7
Capital Structure with maximum EPS or maximum Market Price per Share is chosen. The format for calculating EPS is as follows: (`) Earnings before Interest and Tax (EBIT) Less: Interest on borrowings Earnings before Tax (EBT) Less: Tax Earnings after Tax (EAT) Less: Dividends on Preference Shares Earnings available to Equity Shareholders or Net Income Earnings per Share =
XXXX XXXX XXXX XXXX XXXX XXXX XXXX
Net Income Number of Equity Shares outstanding
Market Price per Share = Earnings per Share ¥
P Ratio E
Note: Operating Revenues. Operating Cost includes Cost of Goods Sold and Other Operating Expenses. Fixed Costs. Variable Costs are costs which vary proportionately with production or Sales.
calculated using the following format: (`) Sales or Revenues Less: Variable Cost Contribution Less: Fixed Cost Earnings Before Interest and Tax
XXXX XXXX XXXX XXXX XXXX
3.13
or
P Ratio V
P Ê Contribution ˆ Ratio = Á ˜¯ ¥ 100 Ë V Sales
EBIT Ê ˆ ÁË Total Capital Employed ˜¯ ¥ 100. lated using the following formula: EBIT = ROI ¥ Total Capital Employed 4. Interest on borrowings must be considered when the Capital Structure has borrowings.
interest on all borrowings must be considered in the format. ` Borrowings of ` `
`
`
`
`
corporate assesses can be assumed. represents ‘Net Income’. 7. Number of outstanding equity shares refers to equity shares issued and fully paidup. P Ratio E
8. c
P P ratio is given. Ratio can be calculated using E E
the following formula: Market Price per Share P Ratio = Earnings per Share E
3.14
THEORY QUESTIONS Section A 2. Draw the format for calculation of EPS.
(Bangalore University, B.Com, November 2014)
P E Section B
LEVERAGES
3.8 Leverage A. Business Risk C. Total Risk
A. Business Risk or Operating Risk Business Risk or Operating Risk cost refers to the cost which has to be incurred irrespective of the level of activity or production. be the operating risk. ` ` of the company will be:
`
3.15 (`) Sales or Revenues Less: Variable Cost Contribution Less: Fixed Cost Earnings before Interest and Tax
When Sales Revenue increases by 20%
When Sales Revenue falls by 20%
(`)
(`)
Sales or Revenues Contribution Less: Fixed Cost Earnings before Interest and Tax
The Present EBIT is ` `
`
from the Present EBIT. following manner:
È (` 2,80,000  ` 2,00,000) ˘ Í ˙ ¥ 100 ` 2,00,000 Î ˚ ` Present EBIT. following manner:
È (` 2,00,000  `1,20,000) ˘ Í ˙ ¥ 100 ` 2,00,000 Î ˚ `
be operating risk.
`
3.16
The measure of operating risk is called ‘Operating Leverage’
% Change in EBIT % Change in Sales
Degree of Operating Leverage (DOL) =
40% =2 20% The shortcut formula for calculating Degree of Operating Leverage is: Degree of Operating Leverage =
Contribution EBIT
` 4,00,000 =2 ` 2,00,000 ` will be:
` 4,00,000 ` 4,00,000 = =4 (` 4,00,000  `3,00,000) `1,00,000 80 per cent change in operating 80 per cent
.
B. Financial Risk
Financial Risk.
` ` statement would appear as:
3.17 (`) Earnings before Interest and Tax (EBIT) Less: Interest on borrowings Earnings before Tax (EBT) Earnings after Tax (EAT) Less: Dividends on Preference Shares Earnings available to Equity Shareholders
Nil
Number of outstanding Equity Shares Earnings Per Share `7.00
`70,000 10,000 shares
When EBIT increases by 20% (`)
When EBIT decreases by 20% (`)
Earnings before Interest and Tax (EBIT) Less: Interest on borrowings Earnings before Tax (EBT) Earnings after Tax (EAT) Less: Dividends on Preference Shares Earnings available to Equity Shareholders
Nil
Nil
`9.80
`4.20
Number of outstanding Equity Shares Earnings per Share =
`70,000 10,000 shares
The present EPS is `7.00. `
È
40 per cent Íi.e.,
Î
{
}
˘ (`9.80  `7.00) ¥ 100˙. `7.00 ˚
`2.80 or by
3.18
`
{
`2.80 or by 40 per cent
}
˘ È (`7.00  ` 4.20) ¥ 100˙ . Íi.e., `7.00 ˚ Î burden of `
. Degree of Financial Leverage can be measured using the following formula:
Degree of Financial Leverage (DFL) =
% Change in EPS % Change in EBIT
40% =2 20% The shortcut formula for calculating Degree of Operating Leverage is: Degree of Financial Leverage =
EBIT EBT
` 2,00,000 =2 `1,00,000 Suppose the Interest on borrowings in the above example is ` Leverage will be:
` 2,00,000 ` 2,00,000 = =4 `50,000 (` 2,00,000  `1,50,000) 80 per cent 80 per cent loss in earnings to shareholders.
.
3.19
favourable Degree of Financial Leverage when the Return on Capital debt as a source of fund.
calculated using the following formula:
Degree of Financial Leverage =
EBIT Ê Preference Dividend ˆ EBT  Á ˜¯ 1  Tax Rate Ë `
` 2,00,000 ˘ È DFL = Í Ï `35,000 ˆ ¸ ˙ Í Ì`1,00,000  ÊÁ ˝˙ Ë 1  0.3 ˜¯ ˛ ˙˚ ÍÎ Ó ` 2,00,000 = (`1,00,000  `50,000) =
` 2,00,000 =4 `50,000 `
`
`
C. Total Risk or Combined Risk Total Risk or Combined Risk of Operating Risk and Financial Risk.
to Total Risk. ` ` be as follows:
`
3.20 (`) Sales or Revenues Contribution Less: Fixed Cost Earnings before Interest and Tax Less: Interest on borrowings Earnings before Tax Earnings after Tax Number of Outstanding Equity Shares Earnings per Share
`7.00
will be: When Sales Revenue increases by 20% (`)
When Sales Revenue decreases by 20% (`)
Sales or Revenues Contribution Less: Fixed Cost Earnings before Interest and Tax Less: Interest on borrowings Earnings before Tax Earnings after Tax Number of Outstanding Equity Shares Earnings per Share
`12.60
`1.40
The present EPS is `7.00. `
{
`5.60
}
˘ È (`12.60  `7.00) or by 80 per cent Íi.e., ¥ 100˙ . `7.00 ˚ Î `
È
80 per cent Íi.e.,
Î
{
}
˘ (`7.00  `1.40) ¥ 100˙. `7.00 ˚
`5.60 or by
3.21
Fixed Cost of `
`
risk. The measure of total risk is called Combined Leverage or Degree of Combined Leverage. Degree of Combined Leverage can be measured using the following formula:
Degree of Combined Leverage (DCL) =
% Change in EPS % Change in Sales
80% =4 20% The shortcut formula for calculating Degree of Operating Leverage is:
Degree of Combined Leverage =
Contribution or (DOL ¥ DFL) EBT
` 4,00,000 =4 `1,00,000 OR DOL =
Contribution ` 4,00,000 =2 = EBIT ` 2,00,000
DFL =
EBIT ` 2,00,000 =2 = EBT `1,00,000
DCL = DOL ¥ DFL = 2 ¥ 2 = 4
do not get any earnings.
.
3.22
THEORY QUESTIONS Section A 1. List the different types of risks that a business entity is exposed to.
4. State the meaning of combined risk and the formula for its calculation. (Bangalore University, B.Com, November 2014) (Bangalore University, B.Com, November 2015)
Section B
4. Explain the meaning and measurement of Combined Leverage.
Section C
in Capital Structure decisions.
PROBLEMS ON EBITEPS ANALYSIS Problem 1
Problem on Calculation of Earnings per Share
The following data relates to two companies P Ltd. and Q Ltd. P Ltd.
Q Ltd.
Equity Share Capital in shares of `10 each Earnings before Interest and Tax Return on Capital Employed
(Bangalore University, B.Com, November 2015)
3.23
SOLUTION Plan 1
2
Existing Capital Structure Equity Share Capital Number of Equity Shares Ê Equity Share Capital ˆ ÁË ˜¯ ` 10 Calculation of EPS EBIT Less: Interest
Nil Earnings before Tax Earnings after Tax
Less: Preference Dividends Net Income
Nil 50,000
Nil 38,750
`1
`1.55
Earning per Share Net Income Ê ˆ ÁË Total Number of Equity Shares ˜¯ Problem 2
Problem on Calculation of Earnings per Share
data relates to them: Firm X
Firm Y
Assets 0 Equity share capital Number of shares Rate of return on assets
(Bangalore University, B.Com, November 2013)
3.24
SOLUTION
` EBIT EBIT ˆ Ê ˆ Ê ROI = Á ¥ 100 or Á ˜ ¥ 100 ˜ Ë Total Assets ¯ Ë Total Capital Employed ¯ ¥ ROI EBIT = `
¥
`1,00,000 Plan 1
2
Existing Capital Structure Equity Share Capital Number of Equity Shares (given) Calculation of EPS EBIT Less: Interest
Nil Earnings before Tax
Earnings after Tax Less: Preference Dividends Net Income
Nil
Nil
50,000
38,750
`1
`1.55
Earning per Share Net Income Ê ˆ ÁË Total Number of Equity Shares ˜¯
Capital Structure Equity Share Capital
3.25
Number of Equity Shares ÊÁ `1,25,000 ˆ˜ Ë `10 ¯ Calculation of EPS EBIT Less: Interest Earnings before Tax Earnings after Tax Less: Preference Dividends
Nil 33,125
Net Income Earning per Share Net Income Ê ˆ ÁË Total Number of Equity Shares ˜¯
Problem 3
`
`2.65
Problem on Choosing Capital Structure on the Basis of Earnings per Share
`
`
(i) It can raise the entire capital by issuing equity shares of `100 each. ` ` share capital. Assume that EBIT is ` SOLUTION (`) Financial Plans 1 Existing Capital Structure Equity Share Capital (`100 each)
2
3
4
3.26 Proposed Capital Structure for additional funds Equity Shares (`100 each)
Total Interest on Borrowings
Nil
Preference Dividends
Nil
Nil Nil
Nil
Total Number of Equity Shares Existing ÊÁ `10,00,000 ˆ˜ Ë `100 ¯ Ê Amount to be mobilised by Issue of Equity ˆ New Á ˜¯ Ë `100 EBITEPS Analysis EBIT Less: Interest
Nil
Nil
Earnings before Tax Earnings after Tax Less: Preference Dividends Net Income
Nil 84,000
Nil 66,500
Nil 42,000
59,000
`4.20
`4.43
`4.20
`3.93
Earning per Share Net Income Ê ˆ ÁË Total Number of Equity Shares ˜¯
Financial plan 2 is recommended for mobilising additional funds of ` Problem 4
Problem on Choosing Capital Structure on the basis of Earnings per Share
`
`
` retained Earnings amount to ` for which a sum of ` able to achieve the same return on investment as at present. The funds required for expansion can
3.27
Required: (a) the additional funds were raised as debt (b) the additional funds were raised by issue of equity shares SOLUTION A. Present Capital Structure (`) `10 each) Retained Earnings
Ê `1,20,000 ˆ ÁË ˜ 12% ¯
Note: The problem states that the Interest Liability is ` ` of Debenture Capital is
`
`1,20,000 =` 12%
B. Calculation of Present and Postexpansion EBIT ` `
`
=` = `4,20,000
`
achieve the same return on investment as at present’. EBIT Ê ˆ Return on Investment (ROI) = Á ¥ 100 Ë Total Capital Employed ˜¯
Ê ` 4,20,000 ˆ Present ROI = Á ¥ 100 = 14% Ë `30,00,000 ˜¯ ` will be `
3.28
Postexpansion EBIT will be: Total Capital Employed ¥ ROI = `
¥
`4,76,000
C. EBITEPS Analysis (`) Plan 1
2
Nil 2,15,600
Nil 2,49,200
`2.695 = `2.70 (approx.)
`2.077 = `2.08 (approx.)
Existing Capital Structure Equity Share Capital Retained Earnings
Proposed Capital Structure for additional funds Equity Shares of `10 each
` `
Total Number of Equity Shares Existing New ÊÁ ` 4,00,000 ˆ˜ Ë `10 ¯ EBITEPS Analysis EBIT Less: Interest Earnings before Tax Earnings after Tax Less: Preference Dividends Net Income Earning per Share Net Income Ê ˆ ÁË Total Number of Equity Shares ˜¯
3.29
Plan 1 is recommended for mobilising additional funds of ` Problem 5
Problem on Choosing Capital Structure on the basis of Market Price per Share
(`) Sales (production capacity of `
2 ˆ Ê Variable cost Á 66  %˜ Ë 3 ¯
Net Income Earnings per Share
`9
The expansion programme is estimated to cost ` P ratio E
rate through P ratio will be 12 times. Expansion will E Fixed Cost would be needed to meet the
`100 per share and generate additional Sales of ` expansion operation.
SOLUTION A. Existing Capital Structure ` ` a Net Income is `
is
`1,00,000 = `12,50,000 8% `9
3.30
Earnings per Share =
Net Income Total Number of Outstanding Equity Shares Net Income EPS =
` 4,50,000 `9
be sold at ` the face value per share is taken as `100. ¥ `100 per share = `50,00,000 (`) `100 each) 62,50,000
B. Calculation of Postexpansion EBIT Present EBIT is ` an additional Sales of `
`
(`) Sales Revenue (`
`
Less: Variable Cost (66 2 3 % of Sales ) Contribution Less: Fixed Cost Earnings before Interest and Tax
C. EBITEPS ANALYSIS (`) Alternative 1 Existing Capital Structure Equity Share Capital
2
3.31 Proposed Capital Structure for additional funds Equity Shares of `100 each Total Interest on B ` `
Total Number of Equity Shares Existing
Ê `5,00,000 ˆ New Á Ë `100 ˜¯ EBITEPS Analysis EBIT (Refer point B above) Less: Interest Earnings before Tax Earnings after Tax Less: Preference Dividends Net Income Earning per Share
Nil 6,25,000
Nil 6,50,000
`12.50
`11.82
10
12
`125.00
`141.84
Net Income Ê ˆ ÁË Total Number of Equity Shares ˜¯
P Market Price per Share ÊÁ EPS ¥ Ratioˆ˜ ¯ Ë E
Alternative 2 is recommended for mobilising additional funds required for expansion.
3.32 Problem 6
Problem on Choosing Capital Structure on the basis of Market Price per Share
The Existing Capital Structure of ABC Ltd. is as follows: Equity Shares of `100 each Retained Earnings
` ` ` ` `
`
`25 per share
P E and 2 SOLUTION A. Calculation of Present and Postexpansion EBIT is called Return on Investment (ROI) or Return on Capital Employed (ROCE). EBIT Ê ˆ ROI = Á ¥ 100 Ë Total Capital Employed ˜¯ ¥ ROI) Total Capital Employed at present is ` (`
¥
`12,00,000
Total Capital Employed postexpansion will be ` be (` ¥ ` B. EBITEPS Analysis Alternative 1 Existing Capital Structure Equity Share Capital (of `100 each) Retained Earnings
2
3
3.33 Proposed Capital Structure for additional funds `125 each)
` `
Total Preference Dividends On Existing Preference Shares (` On New Preference Shares (`
¥ ¥
Total Number of Equity Shares Existing ÊÁ ` 40,00,000 ˆ˜ Ë `100 ¯ New


7,02,500
5,27,500
4,77,500
`11.71
`13.19
`11.94
19
17
20
`222.49
`224.23
`238.80
EBITEPS Analysis EBIT (See point A above) Less: Interest Earnings before Tax Earnings after Tax Less: Preference Dividends Net Income Earning per Share Net Income Ê ˆ ÁË Total Number of Equity Shares ˜¯
P Market Price per Share ÊÁ EPS ¥ Ratioˆ˜ Ë ¯ E
P E this c
Alternative 3 issue of Preference Shares.
3.34 Problem 7
Problem on Choosing Capital Structure on the basis of Market Price per Share
below: Balance Sheet of XYZ Company as on 31 March 2018 Liabilities
Assets
(`)
(`)
Total Assets Equity Shares (`10 per share) Earned Surplus Total
Total
Income Statement for the year ended 31 March 2018 (`)
`33.33 and the price/earnings ratio of all the outstanding shares will remain 12. at assumed sales of `
`
`80 lakh and `
SOLUTION A. Existing Capital Structure (`) Equity Share Capital (`10 per share) Retained Earnings 20,00,000
3.35
B. Funds required for expansion and alternatives `
` `
Alternative 2: Issuing ` equity shares)
`
C. EBITEPS Analysis Alternative 1
2
Existing Capital Structure Equity Share Capital Retained Earnings
Proposed Capital Structure for additional funds Equity Shares of `33.33 each
` `
Total Number of Equity Shares Existing ÊÁ `10,00,000 ˆ˜ Ë ¯ `10 New ÊÁ `10,00,000 ˆ˜ Ë `33.33 ¯ (`in Lakh) When Sales Revenue is
Less: Interest EBT EAT or Net Income
`20 Lakh Alt 1 Alt 2 2.00 2.00 0.80 0.20 1.20 1.80 0.42 0.63
`40 Lakh Alt 1 Alt 2 4.00 4.00 0.80 0.20 3.20 3.80 1.12 1.33
`80 Lakh Alt 1 Alt 2 8.00 8.00 0.80 0.20 7.20 7.80 2.52 2.73
0.78
2.08
4.68
1.17
2.47
5.07
`100 Lakh Alt 1 Alt 2 10.00 10.00 0.80 0.20 9.20 9.80 3.22 3.43 5.98
6.37
3.36 Number of Equity Shares (in Lakh) Earnings per Share (Net Income/Number of Shares)
1
1.3
1
1.3
1
1.3
1
1.3
0.78
0.90
2.08
1.90
4.68
3.90
5.98
4.90
10
12
10
12
10
12
10
12
7.80
10.80
20.80
22.80
46.80
46.80
59.80
58.80
Market Price per Share (`)
P Ê ˆ ÁË EPS ¥ Ratio˜¯ E
`20 lakh and ` ` ` Problem 8
Problem on
Alpha Ltd. has the following Capital Structure: Equity Share Capital (`10 each) Retained Earnings Other information: Market Price per Equity Shares
`150 lakh `100 lakh `50 lakh `49
Alpha Ltd. is considering an expansion plan and needs `100 lakh. If expansion programme is tax. The company has the following alternatives available for raising funds required for expansion. (i) Issue equity shares at `50 each ` `
SOLUTION A. Calculation of Present and Postexpansion EBIT P Ratio is given as 7 times E
`50 each `50 each
3.37
Market Price per Share =7 Earnings per Share Market Price per Share is given as `49. Market Price per Share Price  Earnings ratio =
`49 = `7 7 `
Equity Share Capital is `
is
`150 lakh = 15 lakh. `10 Total number of Equity shares ¥ = 15 lakh shares ¥ `7 per share = `105 lakh
=
`150 lakh = `150 lakh 70%
`
`100 lakh) = `
`10 lakh
`160 lakh
`
`160 lakh) = `200 lakh
B. EBITEPS Analysis (`in lakh) Alternative Existing Capital Structure Equity Share Capital (of `10 each) Retained Earnings
Proposed Capital Structure for additional funds Equity Shares (of `50 each)
I
II
III
150 50 100 300
150 50 100 300
150 50 100 300
100
50 50
40
100
100
60 100
3.38
`100 lakh)
Total Preference Dividends On existing Preference Shares
10
10 6
10
10
16
10
Nil
Nil
Nil
Nil
Nil 5.40 5.40
15 2
15 1
15.0 0.8
17
16
15.8
200.00 10.00 190.00 57.00 133.00 Nil 133.00
200.00 16.00 184.00 55.20 128.80 Nil 128.80
200.00 10.00 190.00 57.00 133.00 5.40 127.60
`7.82
`8.05
`8.08
7.5
7
7.25
`58.65
`56.35
`58.58
Total number of Equity Shares (in lakh) existing ÊÁ `150 lakh ˆ˜ Ë `10 ¯ new
Amount mobilised by issue of Equity `50
EBITEPS Analysis EBIT (Refer point A) Less: Interest Earnings before Tax Earnings after Tax Less: Preference Dividends Net Income Earnings per Share Net Income Ê ˆ ÁË Total Number of Equity Shares ˜¯
P Market Price per Share ÊÁ EPS ¥ Ratioˆ˜ Ë ¯ E
consider mobilising the additional funds of `100 lakh in accordance with alternative III lakh by issue of equity shares and `60 lakh by issue of Preference Shares). Problem 9
Problem on
A company requires ` `
`40
3.39
equity shares plus raising a debt of ` price per share is ` to exceed `
`
` `
Up to `2,50,000
`2,50,000 to `10,00,000
More than `10,00,000
Cost of Borrowings
to the company. SOLUTION EBITEPS Analysis (`) Alternative I
II
III
22,50,000 150
15,00,000 150
10,00,000 125
= 15000
= 10000
= 8000
Nil 3,32,500
Nil 2,53,750
Nil 1,83,750
Proposed Capital Structure
Total Number of Equity Shares
Ê Amount mobilised by issue of shares ˆ ˜¯ ÁË Market Price per Share is ` borrowings will exceed `
`
EBITEPS Analysis EBIT Less: Interest Earnings before Tax Earnings after Tax Less: Preference Dividends Net Income
3.40 Earnings per Share Net Income Ê ˆ ÁË Total Number of Equity Shares ˜¯
`22.17
It is advisable to mobilise ` shares. Problem 10
`25.38
`22.97
`
Problem on
` ` Number of Equity Shares (` Earning per Share Ruling Price in the market Price/Earnings Ratio
`3 `30 10
The company has undistributed reserves of ` ` expansion. This amount will earn at the same rate as funds already employed. You are informed debt (debt + equity)
t
P ratio down to 8 and E
r probable price of the share: (i) if the additional funds are raised as debt; and (ii) if the amount is raised by issuing equity shares. SOLUTION A. Existing Capital Structure (`) Equity Share Capital (40000 shares of `10 each) Reserves Ê ` 60,000 ˆ ÁË ˜ 12% ¯
B. Calculation of Postexpansion EBIT Total Capital Employed at present is ` `
3.41
Ê `3,00,000 ˆ ÁË `15,00,000 ˜¯ ¥ 100 = 20%
Funds required for expansion is ` `
`
`
Earnings before Interest and Tax (postexpansion) = Postexpansion Capital Employed ¥ ROI =` ¥ = `3,40,000 C. EBITEPS Analysis (`) Alternative 1
2
Existing Capital Structure Equity Share Capital (40000 shares of `10 each) Reserves
Proposed Capital Structure for additional funds Debt Equity Shares
Total Debt as a percentage of Total Capital Employed
Ê `7,00,000 ˆ Ê `5,00,000 ˆ ÁË `17,00,000 ˜¯ ¥ 100 ÁË `17,00,000 ˜¯ ¥ 100 = 41.18%
` ` of Interest on additional debt is 14%
Total Number of Equity Shares Existing
` 2,00,000 Ê ˆ New Á Ë Market Price per Share  `30 ˜¯
= 29.41%
3.42 EBITEPS Analysis EBIT (Refer (ii)) Less: Interest Earnings before Tax Earnings after Tax Less: Preference Dividends Net Income
Nil 1,26,000
Nil 1,40,000
`3.15
`3.00
8
10
`25.20
`30
Earnings per Share Net Income Ê ˆ ÁË Total Number of Equity Shares ˜¯
c I considered
P ratio is 8. E P ratio itself is E
P Ê ˆ Market Price per Share Á EPS ¥ Ratio˜ Ë ¯ E
It is advisable for the company to mobilise the additional funds required for expansion by issue of equity shares.
PROBLEMS ON LEVERAGES Problem 11
Problem on Calculation of Leverages
Name of the Firm M N P Q R
Change in Revenue
Change in Operating Income
Change in Earnings per Share
3.43
(a) Degree of Operating Leverage (c) Degree of Combined Leverage SOLUTION Degree of Operating Leverage =
Change in Operating Income (i.e., EBIT) Change in Revenue
Degree of Financial Leverage =
Change in EPS Change in Operating Income
Degree of Combined Leverage =
Change in EPS Change in Revenues
Name of the Firm
Degree of Operating Leverage
Degree of Financial Leverage
Degree of Combined Leverage
M N P Q R
0.9286 1.2593 1.5200 1.8696 1.6000
1.2308 0.7647 0.6053 0.6279 0.7000
1.1429 0.9630 0.9200 1.1739 1.1200
Note: Degree of Operating Leverage ¥ Degree of Financial Leverage = Degree of Combined Leverage Problem 12
Problem on Calculation of Leverages
An analytical statement of X Ltd. is shown below. It is shown on the basis of output level of 800 units. (`) Less Variable Cost Less Fixed Cost Less Interest
Net Income
50,000
3.44
SOLUTION Degree of Operating Leverage =
Contribution ` 4,00,000 = 2.5 = `1,60,000 EBIT
Degree of Financial Leverage =
EBIT `1,60,000 = 1.6 = EBT `1,00,000
Degree of Combined Leverage =
Contribution ` 4,00,000 =4 = `1,00,000 EBT OR
Degree of Combined Leverage = Degree of Operating Leverage ¥ Degree of Financial Leverage = 2.5 ¥ 1.6 = 4 Problem 13
Problem on Calculation of Leverages
` `
`
`
`45 lakh. Required:
SOLUTION Income Statement (`) Sales Less: Variable Cost Contribution Less: Fixed Cost Earnings before Interest and Tax `30 lakh) Earnings before Tax
Notes:
1. Degree of Operating Leverage =
Contribution `15,00,000 = 1.6667 = EBT `9,00,000
2. Degree of Financial Leverage =
EBIT `9,00,000 = 1.5 = EBT `6,00,000
Debt of
3.45
3. Degree of Combined Leverage =
Contribution `15,00,000 = 2.5 = EBT `6,00,000 OR
Degree of Combined Leverage = Degree of Operating Leverage ¥ Degree of Financial Leverage = 1.6667 ¥ 1.5 = 2.5. Problem 14
Problem on Calculation of Leverages
Annual sales of a company is ` than interest is `
`
SOLUTION Income Statement (`) Sales Ê2 ˆ Less: Variable Cost Á of Sales  See Note˜ Ë3 ¯ Contribution Less: Fixed Cost Earnings before Interest and Tax `30 lakh) Earnings before Tax
Notes: Sales to Variable cost ratio is 150 per cent. If Variable cost were `
Ê `100 ˆ ÁË ˜ ¥ 100 `150 ¯
S
rd
Degree of Operating Leverage =
Contribution ` 20,00,000 = 1.3333 = EBIT `15,00,000
Degree of Financial Leverage =
EBIT `15,00,000 = 1.2821 = EBT `11,70,000
Degree of Combined Leverage =
Contribution ` 20,00,000 = 1.7094 = EBT `11,70,000
`150.
3.46 Problem 15
Problem on Calculation of Leverages
Degree of Combined L P
Q
R
Output (units) Fixed cost (`) `) `) Interest expenses (`)
5 7.5
2 7
7.50 10
SOLUTION Income Statement P
Q
R
Sales (Output ¥ Selling price per unit) Less: Variable Cost (Output ¥ Variable cost per unit) Contribution Less: Fixed Cost EBIT Less: Interest EBT
Nil
Calculation of Leverages P
Q
R
5
1.6667
2.1429
2.5
1.0714
1.00
12.5
1.7857
2.1429
Degree of Operating Leverage Contribution EBIT
Degree of Financial Leverage EBIT EBT
Degree of Combined Leverage Contribution EBT
3.47 Problem 16
Problem on Calculation of Leverages
The capital structure of progressive corporation consists of an ordinary share capital of ` (`100 par value) and ` ` ` expenses amount to ` You are required to calculate the following: (i) Percentage increase in earnings per share
SOLUTION Income Statement For 1,00,000 Units
For 1,20,000 Units
¥ `10 per unit) ¥ `6 per unit) Contribution Less: Fixed Cost Earnings before Interest and Tax ` Earnings before Tax Earnings after Tax Number of Equity Shares ÊÁ `10,00,000 ˆ˜ Ë `100 ¯ Earnings per share Earnings after Tax Number of shares
`5.00
`9.00
2
1.71
Degree of Operating Leverage Ê Contribution ˆ ÁË ˜¯ EBIT
3.48 2
Degree of Financial Leverage
1.56
Ê EBIT ˆ ÁË ˜ EBT ¯
Percentage change in Earnings per Share
È (`9  `5) ˘ = 80% ÍÎ `5 ˙˚ ¥ 100
Degree of Operating Leverage and Degree of Financial Leverage. Problem 17
Problem on C
A company had the following balance sheet as on 31 March 2018: Liabilities
Assets
(`)
Equity Share Capital of `10 each Reserves and Surplus
(`)
Fixed assets (net) Current assets
Current liabilities
Additional information given is as follows: Fixed costs per annum (excluding Interest) Total assets turnover ratio Required: Calculate the following and comment: (i) Operating Leverage (ii) Financial Leverage (iii) Combined Leverage (iv) Earnings Per Share SOLUTION A. Preparation of Income Statement Problem states that Total Assets Turnover Ratio is 2.5 Ê Turnover ˆ ÁË ˜ = 2.5 Total Assets ¯
` 2.5
3.49
`
Turnover = 2.5 `1,60,00,000 `
¥ 2.5 = `4,00,00,000
Income Statement ` Sales Contribution Less: Fixed Cost Earnings before Interest and Tax `80 Lakhs) Earnings before Tax Earnings after Tax Number of Equity Shares ÊÁ ` 40,00,000 ˆ˜ Ë ¯ `10 Earnings per Share Ê Earnings after Tax ˆ ÁË Number of Shares ˜¯
`11.40
B. Calculation of Leverages Degree of Operating Leverage =
Contribution `1,20,00,000 = 1.36 = EBIT `88,00,000
Degree of Financial Leverage =
EBIT `88,00,000 = 1.16 = EBT `76,00,000
Degree of Combined Leverage =
Problem 18
Problem on Interpretation of Operating Leverage
` `
Contribution `1,20,00,000 = 1.58 = EBT `76,00,000
`
`
3.50
SOLUTION Income Statement (`) Sales Less: Variable Cost Contribution Less: Fixed Cost Earnings before Interest and Tax ` Earnings before Tax
Degree of Operating Leverage =
Contribution `3,00,000 =3 = EBIT `1,00,000
Degree of Financial Leverage =
EBIT `1,00,000 =2 = EBT `50,000
Degree of Operating Leverage =
Change in EBIT Change in Sales
DOL = 3 Change in EBIT =3 Change in Sales Change in EBIT 100% = = 33.33% 3 3 ` will be doubled). Income Statement (`) Sales ˘ È `7,00,000 ˆ Less: Variable Cost ÍÊÁ ˜¯ ¥ `13,33,333˙ Ë ` 10,00,000 ˚ Î
Contribution
Less: Fixed Cost Earnings before Interest and Tax
` has doubled).
`
3.51 Problem 19
Problem on Interpretation of Operating Leverage
`
`
Present Sales are 1000 units. Required: (a) Find out: (i) DOL
SOLUTION A. Calculation of DOL Change in EBIT Income Statement (`) Sales (1000 units ¥ `10 per unit) Contribution Less: Fixed Cost Earnings before Interest and Tax
Degree of Operating Leverage =
DOL =
Contribution `3,000 = 1.5 = EBIT ` 2,000
Change in EBIT Change in Sales
DOL = 1.5 ¥ 1.5) `
`
DOL =
`
Change in EBIT Change in Sales
DOL = 1.5
`
`3,200
3.52
`
–
`
`
`
¥ 1.5) `800
Income Statement Present Sales
When Sales increase by 40%
When Sales fall by 40%
Sales Contribution Less: Fixed Cost
800 800
Earnings before Interest and Tax
The Present EBIT is `
DOL =
Change in EBIT Change in Sales
DOL = 1.5 Change in EBIT = 1.5 Change in Sales Change in EBIT 100% = = 66.67% (i.e., 2/3rd) 1.5 1.5 `
Income Statement (`) Sales (`
` Contribution
Less: Fixed Cost Earnings before Interest and Tax
Nil
3.53 Problem 20
Problem on Interpretation of Financial Leverage
A company has an EBIT of ` Equity Share Capital (of `10 each)
` ` `
SOLUTION Income Statement (`) Earnings before Interest and Tax (given) ` Earnings before Tax Earnings after Tax ` Net Income Number of Equity Shares Ê ` 4,00,000 ˆ ÁË ` 10 ˜¯ Net Income Ê ˆ Earnings per share Á ˜¯ Number of equity shares Ë
the following formula: Degree of Financial Leverage =
EBIT [EBT  PreTax Preference Dividend]
Earnings before Tax = `6,00,000 PreTax Preference Dividends = =
Preference Dividends (1  Tax Rate) `78,000 =` (1  0.35)
`7.80
3.54
`7,50,000 (`6,00,000  `1,20,000) =
DFL =
`7,50,000 = 1.5625 ` 4,80,000
Change in EPS Change in EBIT
DFL = 1.5625 ¥ DFL ¥ 1.5625) = 39.0625% EPS = ` =`
DFL =
`7.80) `3.05 = `10.85 (approx.)
Change in EPS Change in EBIT
DFL = 1.5625 ¥ DFL ¥ 1.5625) = 39.0625% EPS = `7.80 – `7.80) =` `3.05 = `4.75 (approx.) Income Statement Present
Earnings before Interest and Tax ` Earnings before Tax Earnings after Tax ` Net Income
When EBIT increases by 25%
When EBIT decreases by 25%
3.55 Number of Equity Shares ÊÁ ` 4,00,000 ˆ˜ Ë `10 ¯ Earnings per Share Net Income Ê ˆ ÁË Number of Equity Shares ˜¯
Problem 21
`7.80
`10.85
Problem on
Consider the following information for Strong Ltd. ` `320 lakh `700 lakh
EBIT PBT Fixed Cost
SOLUTION Change in EPS with change in Sales is measured by degree of combined leverage Degree of Combined Leverage =
Contribution EBT
EBT is `320 lakh (given)
`
`700 lakh = `
Degree of Combined Leverage =
`1,820 lakh = 5.6875 `320 lakh
Degree of Combined Leverage =
Change in EPS Change in Sales
¥ Degree of Combined Leverage ¥ 5.6875 = 28.4375%
`4.75
3.56
Income Statement (` in lakh) Present
Contribution Less: Fixed Cost
When Sales increases by 5%
700
700.00
800 320 96 224
800.00 411.00 123.30 287.70
10
10
`22.40
`28.77
Earnings before Interest and Tax Earnings before Tax Earnings after Tax Number of Equity Shares (in lakh) Earnings per Share Net Income Ê ˆ ÁË Number of Equity Shares ˜¯
Note:
`
`
`
È (` 28.77  ` 22.40) ˘ ÍÎ ˙˚ ¥ 100 = 28.4375% ` 22.40 Problem 22
Problem on Scenario Analysis
information is as follows:
Selling price per unit Variable cost per unit Fixed Cost Situation A: ` Situation B: `
`30 `20
`91 = `1,911 lakh
3.57
Capital Structure of the company is as follows: Plan XY (`)
Plan XM (`)
SOLUTION Preparation of Income Statement and calculation of Leverages Plan XY
Sales (10000 units ¥
Plan XM
Situation A (`)
Situation B (`)
Situation A (`)
Situation B (`)
1.5
1.71
1.5
1.71
1.14
1.16
1.03
1.04
1.70
1.99
1.55
1.78
¥ `30)
(6000 units ¥ `20) Contribution Less: Fixed Cost EBIT Less: Interest EBT Degree of Operating Leverage = Contribution EBIT
Degree of Financial Leverage = EBIT EBT
Degree of Combined Leverage = Contribution EBT
The company would be exposed to lower risk when it can maintain Fixed Cost at `
3.58 Problem 23
Problem on Scenario Analysis
Actual production and sales Selling price per unit Variable cost per unit Fixed Cost Situation A: Situation B: Situation C:
800 units `15 `10
` ` `
Capital Structure Plan I (`)
Plan II (`)
Plan III (`)
SOLUTION Preparation of Income Statement and calculation of Leverages (for 800 Units) Plan 1
Plan 2
Plan 3
Situation
Situation
Situation
A
B
C
A
B
C
A
B
C
600
600
600 400
300
300
300 700
900
100
100 100
Sales (@ `15) (@ `10) Contribution Fixed Cost EBIT Less: Interest EBT
3.59 Degree of Operating Leverage = Contribution EBIT
1.33
2.00
4.00
1.33
2.00
4.00
1.33
2.00
4.00
1.25
1.43
2.5
1.11
1.18
1.43
1.43
1.82
10
1.67
2.86
10
1.48
2.35
5.71
1.90
3.64
40
Degree of Financial Leverage = EBIT EBT
Degree of Combined Leverage = Contribution EBT
are to be carried out that can help in minimising operating risk. Problem 24
Problem on
` SOLUTION Degree of Combined Leverage =
Contribution EBT
(5000 units ¥ `60) EBT
`3,00,000 = `12,500 24
(`) Earnings before Tax Earnings after Tax
3.60 Problem 25
Problem on
Income Statement for the year ended 31 March 2018: Financial Leverage Interest Operating Leverage
2 ` 3
SOLUTION For preparing Income S � � � � �
Sales Variable Cost Fixed Cost Tax
The amount of interest on borrowings and Tax rate is given in the problem. The remaining Degree of Financial Leverage is 2 DFL =
EBIT EBT
DFL =
EBIT (EBIT  Interest)
EBIT =2 (EBIT  `2, 000) ` ` EBIT = `4,000 ` Tax
` `
`2,000 `600
Degree of Operating Leverage is 3 Contribution DOL = EBIT
3.61
EBIT is ascertained to be ` Contribution =3 ` 4, 000 Contribution= `
¥ 3 = `12,000
`
`
`25.
Contribution is ascertained as `
`12,000 = `48,000 25% `
` Fixed Cost = `
`
`8,000
Income Statement (`) Sales Contribution Less: Fixed Cost Earnings before Interest and Tax Less: Interest Earnings before Tax Earnings after Tax Problem 26
600 1,400
Problem on P
follows: A
B
C
75
50
Variable Expenses as a percentage of Sales
66
Interest
`200
`300
Degree of Operating Leverage
5
6
2
Degree of Financial Leverage
3
4
2
Income Tax Rate
`
3.62
(b) SOLUTION A Degree of Financial Leverage = EBIT (EBIT  Interest)
Degree of Operating Leverage = Contribution EBIT
C
EBIT EBIT EBIT =3 =4 =2 (EBIT  `1, 00) (EBIT  `200) (EBIT  `300) `600 2 EBIT = `600 EBIT = `300
Interest on Loan
B
` 3 EBIT = ` EBIT = `400
` EBIT = `2,000
`200
`300
`1000
`100
`100
`1000
`50
`50
`50
Contribution =5 `300
Contribution =6 `400
Contribution =2 `2, 000
Contribution = `1,500
Contribution = `2,400
Contribution = `4,000
Variable Expenses as a percentage of Sales
66
75
50
Contribution as a percentage of Sales (Compliment of the above percentage)
33
25
50
Sales =
`1,500 Contribution ˆ 33.33% Ê ÁË percentage of Contribution to Sales ˜¯ = `4,500
`2,400 25%
`4,000 50%
= `9,600
= `8,000
3.63
Income Statement A (`)
B (`)
300 200
400 300
100 50 50
100 50 50
C (`)
Sales Contribution Earnings before Interest and Tax Less: Interest Earnings before Tax Earnings after Tax Problem 27
Problem on Calculation of Leverages
Equity Share Capital of `10 each `1000 each Sales Fixed Cost (excluding interest) Financial Leverage
`25 lakh `18.5 lakh `42 lakh `3.48 lakh 1.39
You are required to calculate: (a) Operating leverage (c) Earnings per share SOLUTION A. Preparation of Income Statement P Ratio is percentage of Contribution on Sales V P Ê Contribution ˆ Ratio = Á ˜¯ ¥ 100 Ë V Sales P V `
`
500 500
3.64
Income Statement (`) Sales Contribution Less: Fixed Cost Earnings before Interest and Tax ` Earnings before Tax Earnings after Tax
3,39,040
Number of Equity Shares
Ê ` 25 lakh ˆ ÁË `10 per share ˜¯ Earnings per Share Ê Earnings after Tax ˆ ÁË Number of Shares ˜¯
1.36
B. Calculation of Leverages Degree of Operating Leverage =
Contribution `10,73,100 = = 1.48 EBIT `7,25,100
Degree of Combined Leverage =
Contribution `10,73,100 = 2.06 = EBT `5,21,600
Problem 28
Problem on
` respectively. It has borrowed `
(e) If the sales drop to `
`
` `
3.65
SOLUTION Income Statement (`) Sales Less: Variable Cost Contribution Less: Fixed Cost Earnings before Interest and Tax ` Earnings before Tax
(a) Calculation of ROI Ê Earnings before Interest and Tax ˆ Return on Investment (ROI) = Á ˜¯ ¥ 100 Total Capital Employed Ë EBIT = ` Total Capital Employed Equity Funds Total Capital Employed
` ` `
Ê ` 27,00,000 ˆ ÁË `1,00,00,000 ˜¯ ¥ 100 = 27% (b) Calculation of Leverages Degree of Operating Leverage =
Contribution `33,00,000 = 1.22 = ` 27,00,000 EBIT
Degree of Financial Leverage =
EBIT ` 27,00,000 = 1.18 = EBT ` 22,95,000
Contribution `33,00,000 = 1.44 = ` 22,95,000 EBT (c) Favourability of Financial Leverage Degree of Combined Leverage =
(d) Asset Leverage Asset Turnover Ratio =
Turnover (i.e., Sales) Total Assets
3.66
Turnover = ` Total Assets = Total Capital Employed = `
`75,00,000 = 0.75 `1,00,00,000 a turnover of `3. `0.75.
Change in EBIT with change in Sales is measured by Degree of Operating Leverage DOL =
Change in EBIT Change in Sales
Present Sales is `
`
È (`75,00,000  `50,00,00) ˘ Í ˙ ¥ 100 `75,00,000 Î ˚ Change in EBIT = Change in Sales ¥ DOL ¥ 1.22 = 40.74% ` `
`
` ` = `16,00,000
EBT will be Zero when EBIT = Interest ` ` Fixed Cost is `
If EBIT has to be ` `
Contribution = ` ` = `10,05,000 `
3.67
Ê `33,00,000 ˆ ÁË `75,00,000 ˜¯ ¥ 100 = 44% (This ratio is called
or
P Ratio) V `
`10,05,000 = `22,84,100 (approx.) 44% Problem 29
Problem on
Operating Leverage Combined Leverage Fixed Cost (excluding interest) Sales `100 each Equity Share Capital of `10 each
1.4 2.8 `2.04 lakh `30.00 lakh `21.25 lakh `17.00 lakh
Required:
(ii) Calculate
P ratio and Earnings per Share V
SOLUTION (a) Calculation of Financial Leverage Problem provides information on Degree of Operating Leverage and Degree of Combined Leverage. DCL = DOL ¥ DFL DCL 2.8 = =2 DOL 1.4
3.68
(b) Calculation of
P Ratio and Earnings per Share V
� Sales � Variable Cost � Fixed Cost � � Tax The amount of interest on borrowings and Tax rate is given in the problem. The remaining Degree of Financial Leverage is 2 EBIT EBT
DFL =
DFL =
EBIT (EBIT  Interest) `21.25 lakh = `2.55 lakh
EBIT =2 (EBIT  ` 2.55 lakh) `5.10 lakh `5.10 lakh EBIT = `5,10,000 `
`
`2,55,000
Tax ` `76,500 Degree of Operating Leverage is 1.4 DOL =
Contribution EBIT
EBIT is ascertained to be ` Contribution = 1.4 `5,10,000 Contribution = `
¥ 1.4 = `7,14,000
3.69
Income Statement (`) Sales Contribution Less: Fixed Cost Earnings before Interest and Tax Less: Interest Earnings before Tax Earnings After Tax
1,78,500
Number of Equity Shares
Ê `17 lakh ˆ ÁË `10 per Share ˜¯ Earnings per Share Ê Earnings after Tax ˆ ÁË Number of Shares ˜¯
`1.05
ÊP ˆ Ê Contribution ˆ ÁË Ratio˜¯ = ÁË ˜¯ ¥ 100 V Sales
Ê `7,14,000 ˆ =Á ¥ 100 Ë `30,00,000 ˜¯ = 23.8% (c) Asset Leverage Asset Turnover Ratio =
Turnover (i.e., Sales) Total Assets
Turnover = ` Total Assets = Total Capital Employed = `
`
`
`30,00,000 = 0.784 `38,25,000 a turnover of `1.5. `0.78.
3.70
EBT will be Zero when EBIT = Interest ` ` Fixed Cost is `
If EBIT has to be `
Contribution = ` ` = `4,59,000 P V
Required Contribution is ` Sales at which Contribution will be `
Required Contribution Profit =
`4,59,000 23.8%
= `19,28,571.43 Problem 30
Problem on
A wellestablished company’s most recent balance sheet is as follows: Liabilities Equity Capital (`10 per share)
Assets
(`)
(`)
Net Fixed Assets Current Assets
Retained Earnings Current Liabilities Total
Total
` (a) Calculate all the three types of leverages for the company. (b) Determine the likely level of EBIT if the EPS is (i) `1 (ii) `3 (iii) Nil
3.71
SOLUTION A. Preparation of Income Statement Total Assets Turnover Ratio = 3 T ¥3 Total Assets are ` `
¥ 3 = `6,00,000 Income Statement (`)
Sales Contribution Less: Fixed Cost Earnings before Interest and Tax ` Earnings before Tax Earnings after Tax
1,26,000
Number of Equity Shares
Ê `60,000 ˆ ÁË `10 per share ˜¯ Earnings per Share Ê Earnings after Tax ˆ ÁË Number of Shares ˜¯
`21
B. Calculation of Leverages Degree of Operating Leverage =
Contribution `3,60,000 = 1.385 = ` 2,60,000 EBIT
Degree of Financial Leverage =
EBIT ` 27,00,000 = 1.031 = EBT ` 22,95,000
Degree of Combined Leverage =
Contribution `33,00,000 = 1.429 = EBT ` 22,95,000
3.72
C. Calculation of EBIT for given EPS The present EPS is ` help of Degree of Financial Leverage. EPS. EPS =
[(EBIT  Interest) (1  T)] Number of Equity Shares
(i) EBIT for EPS of `1 `1 =
[(EBIT  `8,000) (1  0.5)] 6000
` 0.5 EBIT = `
` `
`
`10,000 = `20,000 0.5 (ii) EBIT for EPS of `3 `3 =
[(EBIT  `8,000) (1  0.5)] 6000
` 0.5 EBIT = `
` `
`
`22,000 = `44,000 0.5 (iii) EBIT for EPS of `Zero
[(EBIT  `8,000) (1  0.5)] 6000 ` ` 0.5 EBIT = ` `0 = ` `0 =
`4,000 = `8,000 0.5
SUMMARY � Financing Decisions refer to decisions regarding funding of the business enterprise. It involves amount of funds to be mobilised from each source.
3.73 � Venture Capital Financing. �
� Owners and Risk. � � � Business or Operating Risk is measured by Degree of Operating Leverage; Financial Risk is measured by Degree of Financial Leverage; and Total Risk is measured by Degree of Combined Leverage.
SNAPSHOT OF FORMATS AND FORMULAE 1. The format for EBITEPS Analysis is: (`) Earnings before Interest and Tax (EBIT)
XXXX
Less: Interest on Borrowings
XXXX XXXX XXXX
Earnings before Tax (EBT) Less: Tax Earnings after Tax (EAT) Less: Dividends on Preference Shares Earnings available to Equity Shareholders or Net Income Earnings Per Share =
Net Income Number of Equity Shares Outstanding
Market Price per Share =
Earnings per Share ¥ P Ratio E
2. Contribution = 3. Contribution – Fixed Cost = Earnings Before Interest and Tax 4.
Ê Contribution ˆ =Á ˜¯ ¥ 100 Ë Sales
Ê Earnings before Interest and Tax ˆ 5. Return on Investment = Á ˜¯ ¥ 100 Total Capital Employed Ë
XXXX XXXX XXXX
3.74 6. Degree of Operating Leverage =
7. Degree of Financial Leverage =
Change in EBIT Contribution or Change in Sales EBIT
Change in EPS EBIT or Change in EBIT EBT
8. Degree of Combined Leverage =
Change in EPS Contribution or Change in Sales EBT
EXERCISES Section A ` (Bangalore University, B.Com, November 2013) `2,00,000] ` (Bangalore University, B.Com, November 2015) `10]
Section B 1. Calculate Operating and Financial Leverage from the following: `5 per unit Variable Cost Fixed Cost Interest Expenditure
`1 per unit ` ` (Bangalore University, B.Com, November 2013)
Interest expenses Degree of Operating Leverage Degree of Financial Leverage
`300 6 4
Prepare Income Statement. (Bangalore University, B.Com, November 2013) `2,400, Sales – `9,600, EBIT – `400, Fixed Cost – `2000]
3.75 3. Given the following data: ` `50 ` `
Sales (`100 per unit) Variable Cost per unit Finance Expenses Fixed Cost
(Bangalore University, B.Com, November 2014) 4. The following information is available in respect of a product: `10 ` `6
Sales Price per unit Fixed Cost Variable Cost per unit
` Calculate all types of leverages. (Bangalore University, B.Com, November 2015) 5. Consider the following data of XYZ Ltd. `60 `10 ` `
Selling Price per unit Variable Cost per unit Fixed Cost Interest Burden
(Bangalore University, B.Com, November 2016) 6. The data relating to two companies are given below: Company A Equity Capital Output (units) per annum Selling Price per unit Fixed Costs per annum Variable Cost per unit
two companies.
Company B
` `
` ` `30
`
`250 `
`10
`75
3.76 7. Alpha Ltd. has an average selling price of `20 per unit. Its Variable Costs are `14 per unit and Fixed Costs are ` `
Section C 1. The Capital Structure of the Progressive Corporation Ltd. consists of an Equity Share Capital of ` `10 each) and ` ` `6 per unit ` You are required to calculate the following: (a) Percentage increase in EPS.
(Bangalore University, B.Com, November 2013) 2. Omax Auto Ltd. has an Equity Share Capital of ` to raise further ` (a) All Equity Shares (b) `
`
(d) `
`
`100 each. It wishes
The company’s EBIT is ` (Bangalore University, B.Com, November 2014–2015) `12.50 (b) `15 (c) `17 and (d) `13.33] (Hint: It is assumed that EBIT will be ` 3. A company had the following Balance Sheet as on 31 March 2018 Liabilities Equity Share Capital (50 lakh shares of `10 each) Reserves and Surplus Current Liabilities
`In crore
Assets Fixed Assets (net) Current Assets
5 1 10 4 20
`In crore 12.5 7.5
20
3.77 The additional information given is as follows: Fixed Costs per annum (excluding interest)
`4 crore
Total Assets Turnover Ratio
2.5
Calculate the following and comment: (a) (b) (c) (d)
Earnings per Share Operating Leverage Financial Leverage Combined Leverage
`
4. Alpha Ltd. has furnished the following Balance Sheet as on 31 March 2018: Liabilities
Assets
(`)
(`)
Fixed Assets Current Assets
equity shares of `10 each) General Reserve Current Liabilities Total
Total
Additional information: (i) Annual Fixed Cost other than interest (iii) Total Assets Turnover Ratio
` 2.5
You are required to calculate: (a) Earning per Share and (b) Combined Leverage
`11.06 and 3.04 times]
5. Delta Ltd. currently has an Equity Share Capital of ` ` of ` Equity shares of `10 each Equity shares of `10 each and the balance through longterm borrowing Equity shares of ` Equity shares of ` Shares
`
3.78 The EBIT of the company is expected to be ` (a) Calculate EPS in each of the aforementionedplans. (b) Ascertain the Degree of Financial Leverage in each plan. `1.50, `1.61, `1.72 and ` ` ` Fixed Cost other than interest is ` `
`
You are required to: ` `
`2 and (iii) `0 (November 2009) `27,65,714, `16,22,857 and `4,80,000]
MULTIPLE CHOICE QUESTIONS 1. Equity Share Capital is a
2. Customer Advances, Commercial Papers and Factoring are sources of
(b) There are no committed payments to be made. (c) They provide security to other fund providers
(a) It has lower cost of capital (b) It increases the risk of the concern (d) It does not result in dilution of control and management. (a) Equity Financing (b) Participating Debentures (c) Commercial Papers (d) Conditional Loan 6. Deciding on the quantum of funds to be mobilised from each source is called (a) Investment Decision (b) Operating Decision (c) Dividend Decision (d) Capital Structure Decision (a) Tax savings on account of borrowings (c) Return on Equity
(b) Earnings per Share (d) Market Price per Share
3.79 8. Degree of Operating Leverage measures (a) Business Risk (b) (c) Total Risk (d) 9. Degree of Financial Leverage measures (a) Business Risk (b) (c) Total Risk (d) 10. Degree of Combined Leverage measures (a) Business Risk (b) (c) Total Risk (d) 11. Contribution expressed as a percentage of Sales is
Financial Risk None of these Financial Risk None of these Financial Risk None of these
(c) Solvency Ratio (d) Return on Investment 12. Market Price per Share ∏ Earnings per Share is called (c) Return on Equity (d) PriceEarning Ratio 13. The purpose of EBITEPS Analysis is to identify the Capital Structure
(d) None of these
ANSWER KEY 1. (a) 6. (d) 11. (b)
2. (c) 7. (a) 12. (d)
3. (d) 8. (a) 13. (c)
4. (b) 9. (b)
5. (c) 10. (c)
Investment Decisions
4
4.1
CHAPTER OVERVIEW 4.1 Introduction 4.2 Capital Budgeting 4.3 Importance or Signiﬁcance of Capital Budgeting 4.4 Inputs or Factors for Capital Budgeting Decisions 4.5 Techniques of Capital Budgeting 4.6 Measurement and DecisionMaking under each Technique 4.7 Capital Rationing
INTRODUCTION
Investment Decisions refer to decisions relating to utilisation of funds. Deciding upon where to invest, when to invest, on what to invest, how much to invest, for how long to invest, etc., form the crux of investment decisions. Investment Decisions are broadly of two types – Longterm Investment Decisions and Shortterm Investment Decisions. Longterm Investment Decisions are decisions relating to investments in projects, assets and
These decisions are also called Capital Budgeting Decisions. Shortterm Investment Decisions are decisions relating to investment in daytoday operations of the business. These decisions are also called Working Capital Management Decisions. In this chapter, the discussion is focused on Capital Budgeting.
CAPITAL BUDGETING
4.2 Capital budgeting decisions involves the following: 1. Deciding on whether to invest or not, given an investment opportunity (Accepting or Rejecting Independent Proposals).
4.2
2. Deciding on the best investment alternative among mutually exclusive investment alternatives. 3. Deciding on the extent and proportion of investment among various nonmutually exclusive investment alternatives (Capital Rationing).
THEORY QUESTIONS Section A 1. What is Capital Budgeting? 2. What does Capital Budgeting involve?
Section B 1. Explain the meaning of Capital Budgeting with appropriate examples.
IMPORTANCE OR SIGNIFICANCE OF CAPITAL BUDGETING
4.3 The importance of Capital Budgeting can be understood from the following points: 1. Cost: Initial Investment is substantial. Hence, commitment of resources should be made properly. 2. Time: The effect of decision is known only in the near future and not immediately. 3. Irreversibility: Decisions are irreversible and commitment should be made on proper evaluation. 4. Complexity: of future events involves application of statistical and probabilistic techniques. Careful judgment and application of mind is necessary. 5. Risk and Uncertainty involved in Appraisal: Evaluation of capital expenditure proposal involves projections of the future. Future is always uncertain. Nobody can say with certainty
uncertainty while carrying out the capital budgeting exercise. Risk and return have a direct relationship. Higher the return from the project, higher would be the risk normally and vice versa. It is, therefore, necessary that the capital budgeting exercise should attempt to optimise both the return and risk factors.
THEORY QUESTIONS Section A 1. List the points, which highlight the importance of Capital Budgeting.
Section B business enterprise.
4.3
INPUTS OR FACTORS FOR CAPITAL BUDGETING DECISIONS
4.4 For making capital budgeting decisions, the following are the inputs required:
3. Hurdle Rate (Discount Rate) An elaborate explanation of each factor (or input) is given in the following paragraph:
can be ascertained using the following format: (`) XXXX project, till it becomes operational
XXXX
becomes operational XXXX XXXX XXXX
Note:
using the following format:
opportunity cost of the
4.4 (`) XXXXX Less: Cost of Goods Sold (i.e., Material Cost + Conversion Cost)
XXXXX XXXXX XXXXX XXXXX
Less: Depreciation
XXXXX XXXXX XXXXX XXXXX XXXXX
Add: Depreciation
Notes:
Any noncash item must not be included under these headings, rather must be shown separately. end of its Useful Life. Straight Line basis, the amount of
year is calculated as follows:
(Cost of the Asset  Salvage Value of the Asset at the end of Useful Life) Useful Life of the Asset tax rate can be considered as 30%, which is the base rate of tax
5. Depreciation is initially deducted and later added for tax purposes. Since Depreciation is
on hand or for any other reason), then Earnings Before Depreciation and Tax (i.e., EBDT) itself represents . 7. Where the amount of tax need not be calculated, rather readily given or made available, then . expected or estimated for any year, must be added. The following are the cases of other Cash
4.5
salvage of the asset or project at the end of the Useful Life, must be added to the Cash
usually happen, at the time of procurement of the asset. H appropriate since the value of money changes with time. Hence, the standard practice is to convert converted into Present Value for ease of decisionmaking. is required. Such rate is called Hurdle Rate or Discount Rate. The following are considered as Hurdle Rate or Discount Rate in practice: is considered as Discount Rate. is considered as Discount Rate. from the asset or project must be considered as Discount Rate.
THEORY QUESTIONS Section A 1. List the inputs required for making Capital Budgeting Decisions.
4. What is Depreciation?
7. What is the meaning of Hurdle Rate? 8. What must be considered as Hurdle Rate in making Capital Budgeting Decisions?
Section B
4.6
6. What is Hurdle Rate in the context of Capital Budgeting Decisions? What must be considered as Hurdle Rate, in general?
Section C 1. What is Capital Budgeting? State the importance of Capital Budgeting Decisions and explain in detail the various inputs that are required in making such decisions.
TECHNIQUES OF CAPITAL BUDGETING
4.5 For making various capital budgeting decisions, with the help of inputs explained earlier, knowledge of the following techniques is required. These techniques simplify the decisionmaking and provide a logical and rational basis for the decisions. There are many techniques which help in capital 1. NonDiscounted Cash Flow Techniques 2. Discounted Cash Flow Techniques
NonDiscounted Cash Flow Techniques include 1. Payback Period 2. Average Rate of Return
decisionmaking. Discounted Cash Flow Techniques include 1. Discounted Payback Period 2. Net Present Value 4. Internal Rate of Return Note: are listed here.
4.7
THEORY QUESTIONS Section A 1. 2. 3. 4.
List the various techniques for making Capital Budgeting Decisions. State the various NonDiscounted Cash Flow techniques of capital budgeting. List the popular Discounted Cash Flow techniques of capital budgeting. State the difference between Discounted and NonDiscounted Cash Flow techniques.
Section B 1. What is Capital Budgeting? List out the various techniques useful for making Capital Budgeting Decisions.
MEASUREMENT AND DECISION MAKING UNDER EACH TECHNIQUE
4.6 The meaning of each technique, measurement and decisionmaking under each technique is provided in the following paragraphs:
Payback Period refers to the period in which the project will generate the necessary cash to recoup the Initial Investment. That is, Payback Period refers to the period required for the project to recover the investment. Calculation of Payback Period
the project) Payback Period =
project) Step 1 2 3 4 5
Initial Investment (i.e., Cash Outflow ) Annual Cash Inflow
4.8
Criterion for Decisionmaking
accept if the Payback Period is less than cutoff period. . Merits of Payback Period
1. This method is simple to understand and easy to operate.
3. This method is suitable in the case of industries where the risk of technological obsolescence is very high and hence only those projects, which have shorter Payback Periods should be
increases, risk and uncertainty also increase. Thus, Payback Period tries to eliminate or minimise risk factor. very useful evaluation tool in case of liquidity crunch and high Cost of Capital. 6. The Payback Period can be compared to a breakeven point, the point at which the costs are Limitations of Payback Period
Period. Hence, it is not a good measure to evaluate where the comparison is between two projects, one involving a long gestation period and the other yield quick results but only for a short period. 3. This method becomes an inadequate measure of evaluating two projects where the Cash
because of longer payback. 4. This method ignores the time value of money. Cash Flows occurring at all points of time are
THEORY QUESTIONS Section A 1. What is Payback Period? 3. What is the criterion for decisionmaking on the basis of Payback Period? 4. State any three merits of Payback Period method of Capital Budgeting. 5. List any three limitations of Payback Period.
4.9
Section B 1. What is Payback Period? How can it be calculated? 3. What is Payback Period? State the advantages of Payback Period Method of decisionmaking. 4. Explain the meaning of Payback Period and list the various limitations of this technique of Capital Budgeting.
Average Rate of Return on investment generated by the project is the basis for decisionmaking.
basis for calculating the rate of return, this method is also called External Rate of Return. Calculation of Average Rate of Return
Ê Average Profits After Tax ˆ Average Rate of Return = Á ¥ 100 Ë Average Investment ˜¯ Total of Profits After Tax of all the years of the Project Life Average Investment is calculated in the following manner: È (Original Investment  Scrap Value) ˘ ÍÎ ˙˚ + Scrap Value + Net Working Capital 2 Criterion for Decisionmaking
accept if the Average Rate of Return is greater than hurdle rate or any
.
return. Merits of Average Rate of Return
1. The method is superior to Payback Period, as it takes into account savings over the entire economic life, even though estimates of distant future may be subject to wide margin of errors. 2. The projects differing widely in character can be compared properly.
4.10
3. The method embodies the concept of Net Earnings after allowing for Depreciation, as it is of vital importance in the appraisal of a proposal. Limitations of Average Rate of Return
1. The method suffers from the fundamental weakness as that of payback method, i.e., it ignores the fact that receipts occur at different time intervals – it ignores time value of money. If earnings from different investments accrue at the same time, this method can be safely used. 2. The method has different variants, each of which emerge different rate of return for one proposal. This situation arises due to diverse concepts of investments, as well as earnings. 3. Some analysts are of the opinion that as the method takes into account earnings after decisionmaking purpose.
THEORY QUESTIONS Section A 1. 2. 3. 4. 5.
What is Average Rate of Return? What is External Rate of Return? State the meaning of Accounting Rate of Return? State the formula for calculation of Average Rate of Return. How should Average Investment be calculated in the context of calculation of Average Rate of Return? 6. State the criteria for decisionmaking in Average Rate of Return method. 7. List any three merits of Accounting Rate of Return method. 8. State any three demerits of Accounting Rate of Return method.
Section B 1. What is Average Rate of Return? How is it better than Payback Period method of capital budgeting? state the advantages of this method.
Section C 1. What are Capital Budgeting Decisions? Explain in detail, the different NonDiscounted Cash Flow techniques, which help in such decisions, and bring out the merits and demerits of each method.
Discounted Payback Period refers to the Payback Period calculated considering discounted cash
4.11
Calculation of Discounted Payback Period Step 1 2 3 4 5 6
Criterion for Decisionmaking
accept if the discounted Payback Period is less than cutoff period. .
THEORY QUESTIONS Section A 1. What is Discounted Payback Period? 2. How is Discounted Payback Period superior to Payback Period? Elucidate.
Section B 1. State and explain the steps involved in calculating of Discounted Payback Period.
4.6.4
Net Present Value
effective and popular technique for making capital budgeting decisions. Calculation of Net Present Value Step 1 2 3 4 5 6
4.12
Criterion for Decisionmaking
Where Net Present Value > Zero, accept the proposal Net Present Value = Zero, accept the proposal Net Present Value < Zero, reject the proposal Merits of Net Present Value
evaluation. 3. Net Present Value constitutes addition to the wealth of shareholders and thus focuses on the
be compared on Net Present Value basis. Thus, each project can be evaluated independent of others on its own merit. Limitations of Net Present Value
1. It involves complex calculations. Present Value depends on accurate estimation of these two factors, which may be evaluated independent of others on its own merit. 3. Net Present Value and ranking of project may differ at different discount rates, causing inconsistency in decisionmaking. mutually exclusive projects.
THEORY QUESTIONS Section A 1. 2. 3. 4. 5. 6.
Explain the meaning of Net Present Value? What is Net Present Value of a Project? How can Net Present Value be calculated? State the criteria for decisionmaking in Net Present Value method. List any three merits of Net Present Value method of capital budgeting. State any three limitations of Net Present Value method.
Section B Value. 2. Explain the decisionmaking criterion in Net Present Value method. State the advantages and limitations of this method of capital budgeting technique.
4.13
exclusive projects.
Step 1 2 3 4 5 6 Total Present Value of Cash Inflows Total Present Value of Cash Outfloows
Criterion for Decisionmaking
1. This method considers the time value of money. 2. It is a better evaluation technique than Net Present Value and helps in ranking projects. 3. It focuses on maximum return per rupee of investment and hence is useful in case of investment in divisible projects, when funds are not fully available.
large project with high Net Present Value is selected, possibility of accepting several small projects which together may have higher Net Present Value than the single project is excluded.
total Net Present Value in such case being more than the one with a project with the highest
4.14
THEORY QUESTIONS Section A
3. What is Desirability Factor? List three merits of this method of capital budgeting.
Section B
method.
Internal Rate of Return refers to the rate of return on investment, which is calculated considering rate of return on investment, based on
, as against External Rate of Return,
zero. project are reinvested at Internal Rate of Return.
Step 1 2 3 Payback Factor = 4
Cash Outflows Average Cash Inflow per annum
Identify IRR Range with the help of annuity tables. That is, identify in the annuity tables against the life of the project, the rates between which the Payback Factor falls.
5 6 IRR = Lower Rate of IRR Range + [Difference between Higher Rate and Lower Rate ¥ (Present
Range)]
4.15
Criterion for Decisionmaking
Where, Internal Rate of Return > Hurdle Rate, accept the proposal Internal Rate of Return = Hurdle Rate, accept the proposal Internal Rate of Return < Hurdle Rate, reject the proposal
1. Time value of money is taken into account. 3. Decisions are immediately taken by comparing IRR with the hurdle rate.
to the IRR may not be practically valid.
THEORY QUESTIONS Section A 1. 2. 3. 4. 5. 6. 7.
What is Internal Rate of Return? How does Internal Rate of Return differ from External Rate of Return? What is the feature of Internal Rate of Return? State the underlying assumption of Internal Rate of Return Method of Capital Budgeting. Explain the decisionmaking criteria in Internal Rate of Return Method of Capital Budgeting. State any three merits of Internal Rate of Return technique of Capital Budgeting. State any thee limitations of Internal Rate of Return.
Section B 1. What is Internal Rate of Return? Explain the steps involved in calculation of Internal Rate of Return. 2. Explain the decisionmaking criteria in Internal Rate of Return method and bring out the merits and limitations of this method of Capital Budgeting.
Section C 1. List and explain in detail the various Discounted Cash Flow Techniques of Capital Budgeting, highlighting the merits and demerits of each technique. highlighting the decisionmaking criteria in each.
4.16
CAPITAL RATIONING
4.7 Capital Rationing refers to deciding about allocation of limited funds available among projects or assets, which are not mutually exclusive. Capital Rationing Decision is based on whether the projects are divisible or indivisible. Divisible projects are those wherein investment can be made in a part of the project as well;whereas,indivisible projects are those where the investment has to be made in the entire project. Value.
THEORY QUESTIONS Section A 1. What is Capital Rationing? 2. State the different situations in which Capital Rationing Decisions are made.
PROBLEMS ON CAPITAL BUDGETING Problem 1
Problem on
VRK Ltd. is planning to buy machinery. The cost of the machinery is `10,00,000. It is expected to have a Salvage Value of `1,00,000 at the end of its Useful Life of 9 years. The cost of transporting the machinery to the factory premises is `1,00,000 and the installation cost is `1,50,000. For maintenance of the machinery, a spare part inventory worth `1,00,000 has to be purchased. For the purchase of machinery, VRK Ltd. has to borrow a loan of `8,00,000 at the rate of 12% per annum. It is estimated that the machine can be made operational only after one month from the date of borrowing the loan. Working Capital requirement for the machinery is estimated at `2,50,000. SOLUTION
(`) Cost of the Machinery Transportation Charges Installation Charges Cost of Spare Part Inventory Interest on Loan Borrowed towards purchase of machinery till the date the machinery is
12 1ˆ Ê operational Á `8,00,000 ¥ ¥ ˜ Ë 100 12 ¯ Working Capital Requirement
10,00,000 1,00,000 1,50,000 1,00,000
8,000 2,50,000
4.17 Problem 2
Problem on
ABC Ltd. is evaluating the purchase of a new project with a depreciable base of `1,00,000; expected economic life of 4 years and earnings before taxes and depreciation of `45,000 in year 1, `30,000 in year 2, `26,000 in year 3 and `35,000 in year 4. Assume straight line method of depreciation and SOLUTION
Depreciation =
(Cost of the Project  Salvage Value) Useful Life
In this case, Cost of the Project = `1,00,000 Salvage Value = Nil Useful Life = 4 years
Ê `1,00,000  Nil ˆ Hence, Depreciation = Á ˜¯ = ` 4 Years Ë
(`)
Earnings Before Depreciation and Taxes Less: Depreciation Earnings Before Tax Less: Tax @ 20% Earnings After Tax Add: Depreciation
Problem 3
Year 1
Year 2
Year 3
Year 4
45,000 25,000
30,000 25,000
26,000 25,000
35,000 25,000
20,000 4,000
5,000 1,000
1,000 200
10,000 2,000
16,000 25,000
4,000 25,000
800 25,000
8,000 25,000
Problem on
XYZ Ltd. is evaluating the purchase of a new project with a depreciable base of `4,00,000; expected economic life of 4 years and Earnings Before Taxes and Depreciation of `80,000 in Year 1, `1,50,000 in Year 2, `1,44,000 in Year 3 and `1,30,000 in Year 4. Assume straight line
4.18
SOLUTION
Depreciation =
(Cost of the Project  Salvage Value) Useful Life
In this case, Cost of the Project = `4,00,000 Salvage Value = Nil Useful Life = 4 year
Ê `4,00,000  Nil ˆ Hence, Depreciation = Á ˜¯ = ` 4 Years Ë
(`) Year 1
Year 2
Year 3
Year 4
80,000 1,00,000
1,50,000 1,00,000
1,44,000 1,00,000
1,30,000 1,00,000
Earnings Before Tax (–) 20,000 Less: Tax @ 20% (See Note) Nil Earnings After Tax (–) 20,000 Add: Depreciation 1,00,000
50,000 9,000 41,000 1,00,000
44,000 13,200 30,800 1,00,000
30,000 9,000 21,000 1,00,000
Earnings Before Depreciation and Taxes Less: Depreciation
In Year 1, there is a loss. Hence the tax liability is nil. `50,000. However, for tax purposes, loss of any year can be carried `20,000 of Year 1 is setoff `30,000 (i.e., `50,000 – `20,000). Tax liability is 30% of `30,000 = `9,000. these years. Problem 4
Problem on Calculation of Payback Period
A company purchased an asset worth `10,00,000. The life of the asset is 5 years and each year, it `3,50,000. Calculate Payback Period and Postpayback Period.
4.19
SOLUTION `10,00,000 `3,50,000 formula: Payback Period =
Cash Outflows Cash Inflows p.a.
`10,00,000 So, Payback Period = = `3,50,000 9 days) can be ascertained in the following manner: Postpayback Period = Life of the asset – Payback Period = 5 years – 2.86 years = 2.14 Years Problem 5
Problem on Calculation of Payback Period
A company is considering purchase of a machinery costing `15,00,000. It has a life of 6 years and
Year
1
2
3
4
5
PAT (`)
2,00,000
5,00,000
3,00,000
3,00,000
2,00,000
Ascertain the Payback Period and Postpayback Period. SOLUTION `15,00,000 B.
straight line method, Depreciation can be calculated using the following formula:
So,
Depreciation =
(Cost of the Asset  Salvage) Useful Life
Depreciation =
(`15,00,000  Nil) =` 6 years
1,00,000
4.20
(`)
Add: Depreciation
Year 1
Year 2
Year 3
Year 4
Year 5
2,00,000 2,50,000 4,50,000
5,00,000 2,50,000 7,50,000
3,00,000 2,50,000 5,50,000
3,00,000 2,50,000 5,50,000
2,00,000 2,50,000 4,50,000
1,00,000 2,50,000 3,50,000
manner: Year
Cash `)
1 2 3 4 5 6
4,50,000 7,50,000 5,50,000 5,50,000 4,50,000 3,50,000
Cumulative Cash `) 4,50,000 12,00,000 17,50,000 23,00,000 27,50,000 31,00,000
Payback Period is the period required for recovery of investment. The investment in this project is `15,00,000. By the end of the second year, `12,00,000 would be recovered. The balance of `3,00,000 can be recovered in the third year. However, the entire third year is not required for recovering ` during the third year is `5,50,000.
`3,00,000
= The portion of the third year required for recovering the balance `3,00,000 = `5,50,000 0.55 years (i.e., 6.6 months approximately) Hence, approximately).
is 2 years + 0.55 years = 2.55 years (i.e., 2 years, 6 months and 18 days
Note: throughout the year. Postpayback Period = Life of the Asset – Payback Period = 6 years – 2.55 years = 2.45 Years Problem 6
Problem on DecisionMaking on the basis of Payback Period
An engineering company is considering the purchase of a new machine for its immediate expansion programme. There are three possible machines at same cost, which are suitable for the purpose, the details of which are given as follows:
4.21 Machine I (`)
Machine II (`)
Machine III (`)
6,00,000
6,00,000
6,00,000
40,000 50,000 60,000 20,000 10,000 1,80,000
50,000 30,000 50,000 10,000 10,000 1,50,000
48,000 36,000 58,000 10,000 10,000 1,67,000
5,00,000
4,00,000
4,50,000
Capital Cost Direct Material Direct Labour Administration Cost Selling and Distribution Cost Total Sales per annum
The economic life of machine I is 4 years, while it is 6 years for the other two, after which they are expected to have a Scrap Value of `80,000; `48,000 and `60,000 for machines I, II and III respectively. Sales are expected to be at the rates shown for each year during their full economic life. Total tax to be paid is estimated at 35% of net earnings each year. You are required to show which investment would be most preferable on the basis of Payback Period method. SOLUTION (`) Machine I
Machine II
Machine III
6,00,000
6,00,000
6,00,000
(i.e., Capital Cost)
(`6,00,000  `80,000) (`6,00,000  ` 48,000) (`6,00,000  `60,000) 6 Years 4 Years 6 Years (Cost of the Asset  Salvage) ` ` `
Depreciation =
Useful Life
per annum Sales Less: Cost of production EBDT Less: Depreciation EBT Less: Tax @ 35% Add: Depreciation
5,00,000 1,80,000 3,20,000 1,30,000 1,90,000 66,500 1,23,500 1,30,000
4,00,000 1,50,000 2,50,000 92,000 1,58,000 55,300 1,02,700 92,000
4,50,000 1,67,000 2,83,000 90,000 1,93,000 67,550 1,25,450 90,000
4.22
the asset 2,53,500 80,000
1,94,700 48,000
2,15,450 60,000
3,33,500
2,42,700
2,75,450
`6,00,000 ` 2,53,500
`6,00,000 `1,94,700
`6,00,000 ` 2,15,450
4 years – 2.37 years
6 years – 3.08 years
6 years – 2.78 years
Add: Realisation of Salvage
Payback Period = Ê Cash Outflows ˆ ÁË Cash Inflows p.a.˜¯
Postpayback Period = Life of the Asset – Payback Period
Note: In case, the recovery of investment had to happen in the last year of the life of the asset, Suggestion: Machine I has the lowest Payback Period. That is, investment in Machine I can be recovered sooner or earlier than in other machines. Hence, on the basis of Payback Period, Machine I is the most preferred choice. Problem 7
Problem on DecisionMaking on the basis of Payback Period
have been collected. 3”
4”
5”
16
24
36
64
150
5
8
15
30
50
Estimated life of the installation (in years)
10
10
10
10
10
Taxation rate (%)
50
50
50
50
50
Investment Required (in lakh rupees) Gross Annual Savings in operating cost before depreciation (in lakh rupees)
Calculate Cash Flow and on this basis indicate the proposal that has the shortest Payback Period.
4.23
SOLUTION (` in lakh) 3”
4”
5”
16.00
24.00
36.00
64.00
150.00
1.60
2.40
3.60
6.40
15.00
5.00 1.60 3.40 1.70 1.70 1.60
8.00 2.40 5.60 2.80 2.80 2.40
15.00 3.60 11.40 5.70 5.70 3.60
30.00 6.40 23.60 11.80 11.80 6.40
50.00 15.00 35.00 17.50 17.50 15.00
Ê Cash Outflows ˆ Payback Period = Á Ë Cash Inflows p.a.˜¯
4.85 years
4.62 years
3.87 years
3.52 years
4.62 years
Postpayback Period = Life of the Asset – Payback Period
5.15 years
5.38 years
6.13 years
6.48 years
5.38 years
Depreciation =
(Cost of the Asset  Salvage) Useful Life
Depreciation Less: Depreciation EBT Less: Tax @ 50% Add: Depreciation
Note: Depreciation and Tax”. Suggestion: The pipeline of diameter 6 has the lowest Payback Period (3.52 years). Hence, that can be considered as the best proposal among the alternatives. Problem 8
Problem on DecisionMaking on the basis of Postpayback Period
The manager of AB Co. Ltd. is considering three mutually exclusive investment projects – A, B and `20,000 per annum for an Initial Investment of `1,00,000. The useful lives are as follows: Project A – 5 years; Project B – 6 years; and Project C – 7 years. Advise the management regarding the choice of the project.
4.24
SOLUTION
Ê Cash Outflows ˆ Payback Period = Á Ë Cash Inflows p.a.˜¯
Machine A
Machine B
Machine C
`1,00,000
`1,00,000
`1,00,000
`20,000
`20,000
`20,000
5 years
5 years
5 years
Nil
1 year
2 years
Postpayback Period = Life of the Asset – Payback Period
All the Machines have the same Payback Period and hence choosing the best alternative on the basis of Payback Period is not a possibility. Since the life of each machine is known and Postpayback Period can be ascertained, decision can be made on this basis. which has can be considered as a better alternative. Note: Problem 9
Problem on Calculation of Average Rate of Return
The cost of machinery is `10,00,000. It is estimated to have a life of 4 years at the end of which the Salvage Value estimated is `50,000. The machinery needs `1,00,000 as Working Capital for its operations. Year 1 Year 2 Year 3 Year 4
`1,20,000 `1,85,000 `2,05,000 `1,62,500
Calculate the Average Rate of Return from the machinery. SOLUTION Ê Average Profits After Tax ˆ ÁË Average Investment ˜¯ ¥ 100 So, the inputs required for calculating Average Rate of Return (ARR) are:
4.25
(`1,20,000 + `1,85,000 + ` 2,05,000 + `1,62,500) 4 years `6,72,500 =` = 4 years =
B. Average Investment Average Investment is calculated in the following manner: È (Original Investment  Scrap Value) ˘ ÍÎ ˙˚ + Scrap Value + Net Working Capital 2 In this case, Average Investment
È (`10,00,000  `50,000) ˘ =Í ˙˚ + `50,000 + `1,00,000 2 Î È `9,50,000 ˘ =Í ˙˚ + `1,50,000 2 Î = `4,75,000 + `1,50,000 =`
Ê `1,68,125 ˆ ARR = Á ¥ 100 = Ë `6,25,000 ˜¯ Problem 10
Problem on DecisionMaking on the basis of Average Rate of Return
Two projects A and B, each requiring an investment of `10,00,000, have an economic life of are expected to be as follows: Year 1 2 3 4 5 6
Machine A (`) 5,00,000 4,00,000 3,00,000 1,00,000 – –
Machine B (`) 1,00,000 2,00,000 3,00,000 4,00,000 4,00,000 1,00,000
Which project is advisable on the basis of Average Rate of Return? Assume a tax rate of 30%.
4.26
SOLUTION Ê Average Profits After Tax ˆ Average Rate of Return = Á ¥ 100 Ë Average Investment ˜¯ Machine A 1. Depreciation = In this case, Depreciation = 2.
(Cost of the Asset  Salvage Value) Useful Life
(`10,00,000  Nil) =` 4 years
A (`)
Less: Depreciation Less: Tax @ 30%
Year 1
Year 2
Year 3
Year 4
5,00,000 2,50,000 2,50,000 75,000
4,00,000 2,50,000 1,50,000 45,000
3,00,000 2,50,000 50,000 15,000
1,00,000 2,50,000 (–) 1,50,000 Nil
Note: There is no tax liability in case of loss. 3.
(`1,75,000 + `1,05,000 + `35,000  `1,50,000) 4 `1, 65, 000 = =` 4 Average Investment = È (Original Investment  Scrap Value) ˘ ÍÎ ˙˚ + Scrap Value + Net Working Capital 2 In this case, there is no information on scrap or Working Capital. Therefore, Average Investment =
`10,00,000 =` 2
Ê ` 41,250 ˆ ¥ 100 = Average Rate of Return = Á Ë `5,00,000 ˜¯
4.27
Machine B
Depreciation =
(Cost of the Asset  Salvage Value) Useful Life
(`10,00,000  Nil) =` 6 years (For Years 1 and 2, Depreciation is considered as `1,66,666 per annum, since the total Depreciation must be equal to `10,00,000). In this case, Depreciation =
(`) Year 1
Year 2
Year 3
Year 4
Year 5
1,00,000 1,66,666 – 66,666 Less: Tax @ 30% (see note) Nil
2,00,000 1,66,666 33,334 Nil
3,00,000 1,66,667 1,33,333 30,000
4,00,000 1,66,667 2,33,333 70,000
4,00,000 1,66,667 2,33,333 70,000
1,00,000 1,66,667 – 66,667 Nil
– 66,666
33,334
1,03,333
1,63,333
1,63,333
– 66,667
and Tax Less: Depreciation
Notes: 1. There is no tax liability in case of loss. 3. In this case, loss of Year 1 is `66,666. It is carried forward to Year 2 for setoff. ` `33,334. 5. The balance of loss of year 1 (i.e., `66,666 – `33,334 = `33,332) is carried forward to Year 3 and setoff. `1,33,333. After settingoff the remaining broughtforward loss of ` `1,00,001. 7. At the rate of 30%, tax on `1,00,0001 is `30,000 (rounded off) for Year 3.
(  `66,666 + `33,334 + `1,03,333 + `1,63,333 + `1,63,333  `66,667) 6 `3,30,000 = =` 6
4.28
Average Investment = È (Original Investment  Scrap Value) ˘ ÍÎ ˙˚ + Scrap Value + Net Working Capital 2 In this case, there is no information on scrap or Working Capital. Therefore, Average Investment =
`10,00,000 =` 2
Ê `55,000 ˆ Average Rate of Return = Á ¥ 100 = Ë `5,00,000 ˜¯ Suggestion: Machine B is earning higher ARR than Machine A. Hence, it is suggested to consider investing in Machine B. Problem 11
Problem on Techniques
YN Ltd. is considering two alternative projects for investment. The projects are mutually exclusive. Advice the company with the help of the following details:
Cost of the Project Useful Life of the Project Estimated Salvage Value at the end of life Working Capital Requirement Year 1 Year 2 Year 3 Year 4 Year 5
`10,50,000
`12,00,000
4 years
5 years
`50,000
`1,00,000
`2,50,000
`3,00,000
(`) 1,00,000 2,50,000 4,70,000 3,40,000 –
(`) 2,10,000 4,40,000 5,70,000 3,20,000 1,60,000
SOLUTION NonDiscounted Cash Flow methods include Payback Period Method and Average Rate of Return Method.
4.29
Investment. Ascertainment of inputs and calculation of the measures are shown in the following steps:
Cost of the Project Working Capital Required
(`)
(`)
10,50,000 2,50,000 13,00,000
12,00,000 3,00,000 15,00,000
Average Investment = È (Original Investment  Scrap Value) ˘ ÍÎ ˙˚ + Scrap Value + Net Working Capital 2
È (`10,50,000  `50,000) ˘ Average Investment = Í ˙˚ + `50,000 + `2,50,000 2 Î È `10,00,000 ˘ = Í ˙˚ + `3,00,000 2 Î = `5,00,000 + `3,00,000 =`
È (`12,00,000  `1,00,000) ˘ Average Investment = Í ˙˚ + `1,00,000 + `3,00,000 2 Î È `11,00,000 ˘ =Í ˙˚ + `4,00,000 2 Î = `5,50,000 + `4,00,000 =`
Depreciation =
(Cost of the Project  Salvage Value) Useful Life
4.30
Depreciation =
(`10,50,000  `50,000) =` 4
Depreciation =
(`12,00,000  `1,00,000) =` 5
Add: Depreciation
Add: Depreciation
Year 1
Year 2
Year 3
Year 4
1,00,000 2,50,000
2,50,000 2,50,000
4,70,000 2,50,000
3,40,000 2,50,000
3,50,000
5,00,000
7,20,000
5,90,000
Year 1
Year 2
Year 3
Year 4
Year 5
2,10,000 2,20,000
4,40,000 2,20,000
5,70,000 2,20,000
3,20,000 2,20,000
1,60,000 2,20,000
4,30,000
6,60,000
7,90,000
5,40,000
3,80,000
(`1,00,000 + ` 2,50,000 + ` 4,70,000 + `3,40,000) 4 `11,60,000 = =` 4 (` 2,10,000 + ` 4,40,000 + `5,70,000 + `3,20,000 + 1,60,000) 5 `17,00,000 =` = 5
4.31
(`)
Cumulative Cash `)
3,50,000 5,00,000 7,20,000 5,90,000
3,50,000 8,50,000 15,70,000 21,60,000
Year 1 2 3 4
The investment in project Y is `13,00,000. By the end of the second year, `8,50,000 is recovered. The balance of `4,50,000 can be recovered in the third year. However, the entire third year is not required for recovering ` for Year 3 is `7,20,000. The portion of the third year required for recovering the balance `4,50,000 =
` 4,50,000 = 0.625 years (i.e., 7.5 months approximately) `7,20,000
is 2 years + 0.625 years = Hence, 15 days approximately).
Year 1 2 3 4 5
(i.e., 2 years, 7 months and
(`)
Cumulative Cash `)
4,30,000 6,60,000 7,90,000 5,40,000 3,80,000
4,30,000 10,90,000 18,80,000 24,20,000 28,00,000
The investment in project Y is `15,00,000. By the end of the second year, `10,90,000 is recovered. The balance of `4,10,000 can be recovered in the third year. However, the entire third year is not required for recovering ` for Year 3 is `7,90,000. The portion of third year required for recovering the balance `4,10,000.
4.32
` 4,10,000 = 0.518 years (i.e., 6.22 months approximately) `7,90,000 Hence, is 2 years + 0.518 years = (i.e., 2 years, 6 months and 7 days approximately). =
Ê Average Profits After Tax ˆ Average Rate of Return = Á ¥ 100 Ë Average Investment ˜¯
Ê ` 2,90,000 ˆ Average Rate of Return = Á ¥ 100 = Ë `8,00,000 ˜¯ Ê `3,40,000 ˆ Average Rate of Return = Á ¥ 100 = Ë `9,50,000 ˜¯ Summary
Payback Period Average Rate of Return
2.625 years 36.25%
2.518 years 35.79%
Analysis Payback Period is lower for Project N while Average Rate of Return is higher for Project Y. when there is contradiction between Payback Period and Average Rate of Return, decision based on ARR is a better choice since it is a better technique than Payback Period. Suggestion: YN Ltd. can consider investing in Problem 12
.
Problem on Calculation of Discounted Payback Period
Project X has an Initial Investment of ` `3,00,000, `3,60,000, `3,00,000, `2,64,000 and `2,40,000. Determine the payback period assuming a discount rate of 10% per annum. SOLUTION
4.33
(`) Year 1 2 3 4 5
`1 3,00,000 3,60,000 3,00,000 2,64,000 2,40,000
0.909 0.826 0.751 0.683 0.621
2,72,700 2,97,360 2,25,300 1,80,312 1,49,040
2,72,700 5,70,060 7,95,360 9,75,672 11,24,712
Note: 3 or 4 digits after decimal can be considered in calculation of Present Value of `1 The investment is `10,00,000. By the end of 4th year, `9,75,672 is recovered. The Balance of `24,328 can be recovered in the 5th year. However, entire 5th year is not required for recovering ` for Year 5 is `1,49,040 The portion of the 5th year required for recovering the balance `24,328 is =
` 24,328 = 0.16 years (i.e., 2 months approximately) `1,49,040
Hence, the discounted payback period is 4 years + 0.16 years = 2 months approximately). Problem 13
Problem on Calculation of Net Present Value)
Investment in a project is `10,00,000.
Year 1 2 3 4 5
3,00,000 3,50,000 3,30,000 2,60,000 1,40,000
Considering a discount rate of 12%, calculate Net Present Value of the project.
(i.e., 4 years and
4.34
SOLUTION The discount rate is given as 12%. NPV for the project is: Year 1 2 3 4 5
`1 3,00,000 3,50,000 3,30,000 2,60,000 1,40,000
0.893 0.797 0.712 0.636 0.567
2,67,900 2,78,950 2,34,960 1,65,360 79,380 10,26,550 10,00,000 26,550
Problem 14
Problem on Calculation of Net Present Value)
A project involves an investment of `10,00,000 and the amount has to be spent as follows: Beginning of second year Beginning of third year Beginning of fourth year
`2,50,000 `2,50,000 `2,50,000 `2,50,000
First Year Second Year Third Year Fourth Year Fifth Year
`2,30,000 `2,28,000 `2,78,000 `2,33,000 `80,000
Calculate Net Present Value of the project, assuming Cost of Capital as 10%. SOLUTION
4.35
(`) Year 1 2 3 4 5
`1 2,30,000 2,28,000 2,78,000 2,33,000 80,000
0.909 0.826 0.751 0.683 0.621
2,09,070 1,88,328 2,08,778 1,59,139 49,680
(`) Year 0 1 2 3
`1 2,50,000 2,50,000 2,50,000 2,50,000
1.000 0.909 0.826 0.751
2,50,000 2,27,250 2,06,500 1,87,750
`1 today is `1 itself.
Note: Net Present Value = `8,14,995 – `8,71,500 = Problem 15
`
Problem on DecisionMaking on the basis of Net Present Value
The Finance Manager of CD Ltd. is considering an investment project costing `3,00,000 and it will have a Scrap Value of `20,000 at the end of 5 years of life. Transportation costs are expected to be `10,000 and installation costs `50,000. If the project is accepted, spare parts inventory of `10,000 must also be acquired and maintained. It is estimated that the spare parts will have an estimated Scrap Value after 5 years amounting to 60% of their initial cost. Annual revenue from the project is expected to be `3,40,000 and annual Labour, Material and Maintenance Expenses are estimated to be `30,000; `1,00,000; and `10,000 respectively. The Depreciation and Taxes for each of the 5 years will be as follows: Year Depreciation (`) Taxes (`)
1
2
3
4
5
1,44,000
86,400
64,800
43,200
1,600
22,400
45,440
54,080
62,720
79,360
4.36
of interest. SOLUTION
is Net Present Value Method. Hence, decision in this case, is made using Net Present Value (NPV) Method. The inputs required for decisionmaking using NPV are:
C. Discount Rate
(`) Cost of the Project Transportation Charges Installation Charges Cost of Spare Part Inventory
3,00,000 10,000 50,000 10,000
Year 1
Year 2
Year 3
Year 4
Year 5
Annual Revenues
3,40,000
3,40,000
3,40,000
3,40,000
3,40,000
Labour Material Maintenance Expenses
30,000 1,00,000 10,000 2,00,000 1,44,000 56,000 22,400 33,600 1,44,000 – –
30,000 1,00,000 10,000 2,00,000 86,400 1,13,600 45,440 68,160 86,400 – –
30,000 1,00,000 10,000 2,00,000 64,800 1,35,200 54,080 81,120 64,800 – –
30,000 1,00,000 10,000 2,00,000 43,200 1,56,800 62,720 94,080 43,200 – –
30,000 1,00,000 10,000 2,00,000 1,600 1,98,400 79,360 1,19,040 1,600 20,000 6,000
EBDT Less: Depreciation EBT Less: Tax (given) Add: Depreciation Add: Salvage on the Project Add: Realisation of Scrap on spare parts
4.37
Notes: 1. Spare parts inventory of `10,000 is expected to realise a scrap of 60% of the initial cost after `10,000 = `6,000. 2. Depreciation is deducted initially and later added back for facilitating calculation of tax. manner: Year 1
Year 2
Year 3
Year 4
Year 5
3,40,000
3,40,000
3,40,000
3,40,000
3,40,000
30,000 1,00,000 10,000 EBDT 2,00,000 Less: Tax 22,400 56,000 Add: Salvage on the project – Add: Realisation of Scrap on Spare Parts –
30,000 1,00,000 10,000 2,00,000 45,440 1,54,560 – –
30,000 1,00,000 10,000 2,00,000 54,080 1,45,920 – –
30,000 1,00,000 10,000 2,00,000 62,720 1,37,280 – –
30,000 1,00,000 10,000 2,00,000 79,360 1,20,640 20,000 6,000
Annual Revenues Labour Material Maintenance Expenses
Discount rate is given as 12%. Year 1 2 3 4 5
`1
1,77,600 1,54,560 1,45,920 1,37,280 1,46,640
0.893 0.797 0.712 0.636 0.567
1,58,596.80 1,23,184.32 1,03,895.04 87,310.08 83,144.88 5,56,131.12 3,70,000.00
Decision:
4.38 Problem 16
Problem on DecisionMaking on the basis of Net Present Value
Alpha Co. Ltd. is considering the purchase of a new machine. Two alternative machines A and B have been suggested, each costing `4,00,000. Earnings After Tax, but before Depreciation are expected to be as follows: Year
Machine A (`)
Machine B (`)
1
40,000
1,20,000
2
1,20,000
1,60,000
3
1,60,000
2,00,000
4
2,40,000
1,20,000
5
1,60,000
80,000
The company has a target of 10% return on capital. Suggest the company as to the best alternative. SOLUTION
Note:
Year 1 2 3 4 5
`1 40,000 1,20,000 1,60,000 2,40,000 1,60,000
0.909 0.826 0.751 0.683 0.621
36,360 99,120 1,20,160 1,63,920 99,360 5,18,920 4,00,000
4.39
Year 1 2 3 4 5
`1 1,20,000 1,60,000 2,00,000 1,20,000 80,000
0.909 0.826 0.751 0.683 0.621
1,09,080 1,32,160 1,50,200 81,960 49,680 5,23,080 4,00,000
Suggestion: Net Present Value of Machine B is higher than Machine A. Hence, Machine B is the best alternative. Problem 17
Problem on C
Life of the Project: Discount Rate:
`9,00,000 5 years `2,50,000 10%
SOLUTION Total PV of Cash Inflows Total PV of Cash Outflows `9,00,000
Year 1 2 3 4 5
`1 2,50,000 2,50,000 2,50,000 2,50,000 2,50,000
0.909 0.826 0.751 0.683 0.621 3.790
2,27,250 2,06,500 1,87,750 1,70,750 1,55,250
4.40
¥ PV of Annuity of `1 @ i% for n years In this case, `2,50,000 ¥ PV of Annuity of `1 @ 10% for 5 years = `2,50,000 ¥ 3.790 =`
`9,47,500 = `9,00,000 Interpretation: Every one rupee invested in this project will fetch ` Problem 18
Problem on
`1,00,000 Present Value of annuity of `1 for 4 years @ 10% is 3.169.
SOLUTION Total PV of Cash Inflows Total PV of Cash Outflows 1.1235 =
Total PV of Cash Inflows . `1,00,000
= `1,00,000 ¥ 1.1235 = `
So,
¥ PV of Annuity of `1 @ i% for n years In this case, ¥ 3.169
`
`1,12,350 =` 3.169 Problem 19
Problem on

A company has the choice of continuing making a product on the existing machine or obtaining one of the two alternatives in lieu of it. The following details are available:
4.41
Machine
Machine E (`)
(`)
Book Value
50,000
–
–
Resale Value
55,000
–
–
–
90,000
1,00,000
45,000
54,000
66,000
1.50
0.75
1.25
Units produced per hour
8
8
12
Selling Price per unit
10
10
10
Purchase Price Fixed Cost per annum (including Depreciation) Variable Running Cost per unit (including Labour)
Additional Information: Material Cost per unit: `5 Annual Working Hours: 2000 Life of each machine (as from now): 5 years Residual value is negligible. Depreciation is to be calculated by Straight Line Method, using book value or purchase price as the case may be. (f) The sales manager believes that extra production from Machine F will need an extra expenditure of `4,000 on advertising to be sold in full.
(a) (b) (c) (d) (e)
SOLUTION Discount rate is given as 9%. Present Value of `1 @ 9% for 5 years is Year 1 2 3 4 5
` 0.917 0.842 0.772 0.708 0.650
4.42 Machine E Machine (In case of Present Machine, the resale value (which
Depreciation =
(Cost  Salvage) Useful Life
(In case of existing machine, Depreciation is calculated on the basis of book value) Annual Working Hours Number of Units Produced per hour Annual Production Selling Price per unit Annual Sales Revenue
Annual Revenues EBDT Less: Depreciation EBT Less: Tax @ 50% Add: Depreciation
¥ PV of Annuity of `1 @ 9% for )
`90,000
`1,00,000
`50,000 5 `
`90,000 5 `
`1,00,000 5 `
2000 8 16000 `10
2000 8 16000 `10
2000 12 24000 `10
`
Material Cost (@ `5 per unit) Labour and other Variable Cost (Number of Units ¥ Rate per unit) Fixed Cost (excluding Depreciation) Advertising Expenditure
5 years (i.e.,
`55,000
`
`
80,000 24,000
80,000 12,000
1,20,000 30,000
35,000 –
36,000 –
46,000 4,000
1,60,000 1,39,000 21,000 10,000 11,000 5,500 5,500 10,000 15,500
1,60,000 1,28,000 32,000 18,000 14,000 7,000 7,000 18,000 25,000
2,40,000 2,00,000 40,000 20,000 20,000 10,000 10,000 20,000 30,000
`60,279.50
`97,225.00
`1,16,670
4.43
60,279.50 55,000.00
97,225.00 90,000.00
1,16,670.00 1,00,000.00
Total PV of Cash Inflows Total PV of Cash Outflows
Decision: operations on the existing machine, but to replace the present machine with Problem 20
Problem on Calculation of Discounted Payback Period, Net Present
both machines is as follows:
Cost of Machine Expected Life Annual Income (Before Tax and Depreciation)
Machine I
Machine II
`15,00,000
`20,00,000
5 years
5 years
`6,25,000
`8,75,000
Depreciation is to be charged on Straight Line basis. You are required to calculate: (a) Discounted Payback Period (b) Net Present Value SOLUTION For calculating the three measures required, the following inputs are required:
3. Discount Rate
4.44
Discount rate is given as 12%. PV of `1 @ 12% is as follows: Year 1 2 3 4 5
`1 0.893 0.797 0.712 0.636 0.567
Depreciation =
(Cost of the Asset  Salvage Value) : Useful Life
For Machine I:
Depreciation =
(`15,00,000  Nil) =` 5 years
For Machine II:
Depreciation =
(` 20,00,000  Nil) =` 5 years
Less: Depreciation Less: Tax @ 30% Add: Depreciation
Machine I
Machine II
6,25,000 3,00,000
8,75,000 4,00,000
3,25,000 97,500 2,27,500 3,00,000
4,75,000 1,42,500 3,32,500 4,00,000
4.45
(`) Year
Machine I
`1
1 2 3 4 5
0.893 0.797 0.712 0.636 0.567
5,27,500 5,27,500 5,27,500 5,27,500 5,27,500
Machine II
4,71,057.50 4,20,417.50 3,75,580.00 3,35,490.00 2,99,092.50
7,32,500 7,32,500 7,32,500 7,32,500 7,32,500
6,54,122.50 5,83,802.50 5,21,540.00 4,65,870.00 4,15,327.50
(`) Year
1 2 3 4 5
Machine I
4,71,057.50 4,20,417.50 3,75,580.00 3,35,490.00 2,99,092.50
Machine II
4,71,057.50 8,91,475.00 12,67,055.00 16,02,545.00 19,01,637.50
6,54,122.50 5,83,802.50 5,21,540.00 4,65,870.00 4,15,327.50
6,54,122.50 12,37,925.00 17,59,465.00 22,25,335.00 26,40,662.50
For Machine I: The investment is `15,00,000. By the end of the third year, `12,67,055 is recovered. The balance of `2,32,945 can be recovered in the fourth year. However, the entire fourth year is not required for recovering `2,32,945 since the discounted `3,35,490. The portion of the fourth year required for recovering the balance `2,32,945 = Hence, the
` 2,32,945 = 0.69 years `3,35,490 is 3 years + 0.69 years =
4.46
For Machine II: The investment is `20,00,000. By the end of the third year, `17,59,465 is recovered. The balance of `2,40,535 can be recovered in the fourth year. However, the entire fourth year is not required for recovering `2,40,535 since the discounted `4,65,870. The portion of fourth year required for recovering the balance `2,40,535 =
` 2,40,535 = 0.52 years ` 4,65,870 is 3 years + 0.52 years = 3.52 years
Hence, the
For Machine I: NPV = `19,01,637.50 – `15,00,000 = ` For Machine II: NPV = `26,40,662.50 – `20,00,000 = ` Total PV of Cash Inflows Total PV of Cash Outflows For Machine I:
`19,01,637.50 = `15,00,000 For Machine II:
` 26,40,662.50 = ` 20,00,000 Summary
Discounted Payback Period Net Present Value
Machine I
Machine II
3.69 years `4,01,637.50 1.2678
3.52 years `6,40,662.50 1.3203
4.47
Decision: compared to Machine 1. Hence, Machine 2 is a better choice. Problem 21
Problem on Calculation of Payback Period, Discounted Payback Period,
Year
1
2
3
4
5
Project A (`)
(2,00,000)
35,000
80,000
90,000
75,000
20,000
Project B (`)
(2,00,000)
2,18,000
10,000
10,000
4,000
3,000
Ignore taxation. An amount of `35,000 will be spent on account of sales promotion in Year 3, in case of Project A. You are required to calculate for each project: (a) (b) (c) (d)
Payback Period Discounted Payback Period Net Present Value Desirability Factor
SOLUTION
for year 3 in case of Project A is `55,000 (i.e., `90,000 – `35,000) (`) Year
1 2 3 4 5
`
0.909 0.826 0.751 0.683 0.621
35,000 80,000 55,000 75,000 20,000
31,815 66,080 41,305 51,225 12,420
2,18,000 10,000 10,000 4,000 3,000
1,98,162 8,260 7,510 2,732 1863
4.48
(`)
Year
Cumulative
Cumulative
1
35,000
35,000
2,18,000
2,18,000
2
80,000
1,15,000
10,000
2,28,000
3
55,000
1,70,000
10,000
2,38,000
4
75,000
2,45,000
4,000
2,42,000
5
20,000
2,65,000
3,000
2,45,000
The investment in project A is `2,00,000. By the end of the third year, `1,70,000 is recovered. The balance of `30,000 can be recovered in the fourth year. However, the entire fourth year is not required for recovering ` for Year 4 is `75,000 The portion of fourth year required for recovering the balance `30,000 = Hence, the
`30,000 = 0.4 years `75,000
is 3 years + 0.4 years = 3.4 years
The investment in project B is `2,00,000. `2,18,000.
The period required for recovering `2,00,000 = Hence, the
is
` 2,00,000 = ` 2,18,000
4.49
(`) Year Discounted
Cumulative Discounted
Discounted
Cumulative Discounted
1
31,815
31,815
1,98,162
1,98,162
2
66,080
97,895
8,260
2,06,422
3
41,305
1,39,200
7,510
2,13,932
4
51,225
1,90,425
2,732
2,16,664
5
12,420
2,02,845
1863
2,18,527
The investment in Project A is `2,00,000. By the end of fourth year, `1,90,425 is recovered. The balance of ` `9,575 since the discounted Cash `12,420. `9,575 = Hence, the
`9,575 = 0.77 years `12,420 is 4 years + 0.77 years =
The investment in Project B is `2,00,000. `1,98,162 is recovered. The balance of `1,838 can be recovered in the second year. However, the entire second year is not required for recovering `1,838, since the discounted `8,260. The portion of the second year required for recovering the balance `1,838 = Hence, the
`1,838 = 0.22 years `8,260 is 1 year + 0.22 years = 1.22 years
4.50
In case of Project A: NPV = `2,02,845 – `2,00,000 = ` In case of Project B: NPV = `2,18,527 – `2,00,000 = `
Total PV of Cash Inflows Total PV of Cash Outflows In case of Project A:
` 2,02,845 = ` 2,00,000 In case of Project B:
` 2,18,527 = ` 2,00,000 Summary
Payback Period
3.4 years
0.92 years
Discounted Payback Period
4.77 years
1.22 years
`2,845
`18,527
1.01423
1.09264
Net Present Value
Decision: Since Project B has lower Payback Period and Discounted Payback Period, and higher Net investing in Problem 22
Problem on DecisionMaking using different Techniques of Capital Budgeting
X Ltd. is considering the following two mutually exclusive projects. The details are as follows:
4.51
Investment in Machinery
`15,00,000
`10,00,000
Working Capital
`5,00,000
`5,00,000
6 years
4 years
Scrap Value of Machinery
10%
10%
Tax Rate
30%
30%
(`) 15,00,000 9,00,000 15,00,000 8,00,000 6,00,000 3,00,000
(`) 8,00,000 8,00,000 8,00,000 8,00,000 – –
Life of Machinery
Income Before Depreciation and Taxes: First Year Second Year Third Year Fourth Year Fifth Year Sixth Year
Advise the company as to the best alternative using the following methods: (a) (b) (c) (d)
Payback Period Method Average Rate of Return Method Discounted Payback Period Method Net Present Value Method
Consider Cost of Capital of 12%. SOLUTION (`)
Cost of Machinery Working Capital
considered.
15,00,000 5,00,000
10,00,000 5,00,000
Depreciation =
(Cost of the Asset  Scrap) Useful Life
Depreciation =
(`15,00,000  `1,50,000) =` 6 years
In case of Project X:
4.52
In case of Project Y: Depreciation =
Year 1
Year 2
Year 3
Year 4
Year 5
9,00,000 2,25,000 6,75,000 2,02,500
15,00,000 2,25,000 12,75,000 3,82,500
8,00,000 2,25,000 5,75,000 1,72,500
6,00,000 2,25,000 3,75,000 1,12,500
3,00,000 2,25,000 75,000 22,500
4,72,500 2,25,000 –
8,92,500 2,25,000 –
4,02,500 2,25,000 –
2,62,500 2,25,000 –
52,500 2,25,000 1,50,000
–
–
–
–
5,00,000
0.893
0.797
0.712
0.636
0.567
0.507
9,97,928
5,55,908
7,95,660
3,99,090
2,76,413
4,70,243
Income Before Depreciation and Taxes (EBDT) 15,00,000 Less: Depreciation 2,25,000 EBT 12,75,000 Less: Tax @ 30% 3,82,500 EAT 8,92,500 Add: Depreciation 2,25,000 Add: Scrap Realisation – Add: Working Capital Recovery – PV of `1 @ 12%
(`10,00,000  `1,00,000) =` 4 years
(rounded off)
Income Before Depreciation and Taxes (EBDT) Less: Depreciation EBT Less: Tax @ 30% EAT Add: Depreciation Add: Scrap Realisation Add: Working Capital Recovery PV of `1 @ 12% (rounded off)
Year 1
Year 2
Year 3
Year 4
8,00,000 2,25,000
8,00,000 2,25,000
8,00,000 2,25,000
8,00,000 2,25,000
5,75,000 1,72,500 4,02,500 2,25,000 – –
5,75,000 1,72,500 4,02,500 2,25,000 – –
5,75,000 1,72,500 4,02,500 2,25,000 – –
5,75,000 1,72,500 4,02,500 2,25,000 1,00,000 5,00,000
0.893
0.797
0.712
0.636
5,60,358
5,00,118
4,46,780
7,80,690
4.53
(`) Year Cumulative 1 2 3 4 5 6
11,17,500 6,97,500 11,17,500 6,27,500 4,87,500 9,27,500
11,17,500 18,15,000 29,32,500 35,60,000 40,47,500 49,65,000
Cumulative 6,27,500 6,27,500 6,27,500 12,27,500
6,27,500 12,55,000 18,82,500 31,10,000
The investment in Project X is `20,00,000. By the end of the second year, `18,15,000 is recovered. The balance of `1,85,000 can be recovered in the third year. However, the entire third year is not required for recovering ` for Year 3 is `11,17,500. The portion of third year required for recovering the balance `1,85,000 = Hence, the
`1,85,000 = 0.17 years `11,17,500
is 2 years + 0.17 years =
The investment in Project Y is `15,00,000. By the end of the second year, `12,55,000 is recovered. The balance of `2,45,000 can be recovered in the third year. However, the entire third year is not required for recovering ` for Year 3 is `6,27,500. The portion of third year required for recovering the balance `2,45,000 = Hence, the
` 2,45,000 = 0.39 years `6,27,500
is 2 years + 0.39 years = 2.39 years
Ê Average Profits After Tax ˆ Average Rate of Return = Á ¥ 100 Ë Average Investment ˜¯
4.54
Project X:
(`8,92,500 + ` 4,72,500 + `8,92,500 + ` 4,02,500 + ` 2,62,500 + `52,500) 6 years `29,75,000 = 6
=
=` Project Y:
(` 4,02,500 + ` 4,02,500 + ` 4,02,500 + ` 4,02,500) 4 years `16,10,000 = 4
=
=`
È (Cost of the Asset  Scrap) ˘ Average Investment = Í ˙˚ + Scrap + Working Capital 2 Î Project X: È (`15,00,000  `1,50,000) ˘ Average Investment = Í ˙˚ + `1,50,000 + `5,00,000 2 Î
Ê `13,50,000 ˆ =Á ˜¯ + `6,50,000 Ë 2 = `6,25,000 + `6,50,000 =` Project Y:
È (`10,00,000  `1,00,000) ˘ Average Investment = Í ˙˚ + `1,00,000 + `5,00,000 2 Î Ê `9,00,000 ˆ =Á ˜¯ + `6,00,000 Ë 2 = `4,50,000 + `6,00,000 =`
4.55
Ê ` 4,95,833.33 ˆ Project X: Á ¥ 100 = Ë `12,75,000 ˜¯ Project Y:
Ê ` 4,02,500 ˆ ÁË `10,50,000 ˜¯ ¥ 100 =
(`) Year
1 2 3 4 5 6
Discounted
Cumulative Discounted
Discounted
Cumulative Discounted
9,97,928 5,55,908 7,95,660 3,99,090 2,76,413 4,70,243
9,97,928 15,53,836 23,49,496 27,48,586 30,24,999 34,95,242
5,60,358 5,00,118 4,46,780 7,80,690
5,60,358 10,60,476 15,07,256 22,87,946
The investment in Project X is `20,00,000. By the end of the second year, `15,53,836 is recovered. The balance of `4,46,164 can be recovered in the third year. However, the entire third year is not required for recovering `4,46,164, since the discounted `7,95,660. The portion of third year required for recovering the balance `4,46,164 = Hence, the
` 4,46,164 = 0.56 years `7,95,660 is 2 years + 0.56 years =
The investment in Project Y is `15,00,000. By the end of the second year, `10,60,476 is recovered. The balance of ``4,39,524 can be recovered in the third year. However, the entire third year is not required for recovering `4,39,524 since the discounted `4,46,780.
4.56
The portion of third year required for recovering the balance `4,29,524 = Hence, the
` 4,39,524 = 0.98 years ` 4,46,780 is 2 years + 0.98 years =
In case of Project X: NPV = `34,95,242 – `20,00,000 = ` In case of Project Y: NPV = `22,87,946 – `15,00,000 = ` When two alternatives having conclusion. In such cases,
are to be compared, NPV leads to wrong must be compared.
Equated NPV refers to Average NPV per annum It is calculated using the following formula: Equated NPV =
NPV PV of Annuity of `1 @ i% for n years
Equated NPV =
14,95,242 PV of Annuity of `1 @ 12% for 6 years
=
Equated NPV =
=
`14,95,242 =` 4.112 `7,87,946 PV of Annuity of `1 @ 12% for 4 years
`7,87,946 =` 3.038
Total PV of Cash Inflows Total PV of Cash Outflows
4.57
In case of Project X:
`34,95,242 = ` 20,00,000 In case of Project Y:
` 22,87,946 = 1.5253 `15,00,000 Summary
Payback Period
2.17 years
2.39 years
38.89%
38.33%
Discounted Payback Period
2.56 years
2.98 years
Net Present Value
`14,95,242
`7,87,946
`3,63,628.89
`2,59,363.40
1.7476
1.5253
Average Rate of Return
Equated Net Present Value
Decision: Since all the measures are favouring Project X, it is advisable for the company to invest in . Problem 23
Problem on Calculation of Internal Rate of Return
A project costs an Initial Investment of ` of `1,60,000 for 4 years. Calculate Internal Rate of Return. SOLUTION Step 1: Payback Factor =
In this case, Payback Factor =
Cash Outflow Average Cash Inflow p.a.
` 4,00,000 = `1,60,000
Step 2: Life of the project is 4 years. In the annuity tables (annexed at the end of the book), check against fourth year and trace the rates between which the Payback Factor falls.
4.58
A snapshot of the annuity table for fourth year is given as follows:
PV of Annuity of `1 for fourth year
2.7432
2.6901
2.6386
2.5887
2.5404
2.4936
2.4483
2.4043
2.3616
The Payback Factor, 2.5000, is between 2.5404 and 2.4936, which are the annuity values at 21% and 22%. Hence, Step 3: manner: ¥ PV of Annuity of `1 @ i% for n years `1,60,000 ¥ 2.5404 = ` `1,60,000 ¥ 2.4936 = ` Step 4: (PV of Cash Inflows at LR  CO) ˘ È IRR = LR + Í(HR  LR) ¥ (PV of CIs at LR  PV of CIs at HR) ˙˚ Î LR = Lower Rate of IRR Range = 21% HR = Higher Rate of IRR Range = 22% `4,00,000. `4,06,464. `3,98,976
È (22%  21%) ¥ (` 4,06,464  ` 400,000) ˘ So, IRR = 21% + Í ˙ (` 4,06,464  `3,98,976) Î ˚
È1% ¥ `6,464 ˘ = 21% + Í ˙ Î `7,488 ˚ = 21% + 0.86% = Note: outside the IRR range.
need not be within the IRR range. It could be any value within or
4.59 Problem 24
Problem on Calculation of Internal Rate of Return
An investment of ` Year `)
1
2
3
4
5
30,000
40,000
60,000
30,000
20,000
Find the Internal Rate of Return. SOLUTION Step 1: Payback Factor =
Cash Outflow Average Cash Inflow p.a. `1,38,500
(`30,000 + ` 40,000 + `60,000 + `30,000 + ` 20,000) 5 `1,80,000 = =` 5 So,
Payback Factor =
`1,38,500 = `36,000
Step 2: Life of the project is 5 years. between which the Payback Factor falls.
PV of Annuity of ` year
4.3295
4.2123
4.1002
3.9927
3.8896
3.7907
3.6959
3.6048
3.5172
The Payback Factor, 3.8472, is between 3.8896 and 3.7907, which are the annuity values at 9% and 10%. Hence,
4.60
Step 3: (`) Year `1 1 2 3 4 5
30,000 40,000 60,000 30,000 20,000
0.9174 0.8417 0.7722 0.7084 0.6499
`1 27,522 33,668 46,332 21,252 12,998
0.9091 0.8264 0.7513 0.6830 0.6209
27,273 33,056 45,078 20,490 12,418
Step 4: (PV of Cash Inflows at LR  CO) ˘ È IRR = LR + Í(HR  LR) ¥ (PV of CIs at LR  PV of CIs at HR) ˙˚ Î LR = Lower Rate of IRR Range = 9% HR = Higher Rate of IRR Range = 10% `1,38,500 `1,41,772 `1,38,315
(`1,41,772  `1,38,500) ˘ È So, IRR = 9% + Í(10%  9%) ¥ (`1,41,772  `1,38,315) ˙˚ Î
È1% ¥ `3,272 ˘ = 9% + Í ˙ Î `3,457 ˚ = 9% + 0.95% = Problem 25
Problem on DecisionMaking on the basis of Net Present Value and Internal Rate of Return
A sole trader plans to install machinery for the production of a luxury article, the demand for which is expected to last for only 5 years. The total capital put in by the trader is: Machinery Working Capital
`2,70,500 `40,000 `3,10,500 `
4.61
estimated to be as follows. Provide your suggestions on the basis of Net Present Value and Internal Rate of Return. Year
1
2
3
4
5
90,000
1,30,000
1,70,000
1,16,000
19,500
20,000
30,000
40,000
26,000
5,000
and Taxes Tax Payable
Consider a hurdle rate of 15%. SOLUTION `3,10,500.
Tax Payable
EBDT (given) Less: Taxes Add: Scrap Realisation Add: Working Capital Recovery
Year 1 2 3 4 5
Year 1
Year 2
Year 3
Year 4
Year 5
90,000 20,000 70,000 – –
1,30,000 30,000 1,00,000 – –
1,70,000 40,000 1,30,000 – –
1,16,000 26,000 90,000 – –
19,500 5,000 14,500 5,500 40,000
`1 70,000 1,00,000 1,30,000 90,000 60,000
0.870 0.756 0.658 0.572 0.497
60,900 75,600 85,540 51,480 29,820 3,03,340 3,10,500
Suggestion: Since NPV is negative, investing is the machinery is not advisable.
4.62
Step 1: Payback Factor =
Cash Outflow Average Cash Inflow p.a. `3,10,500
(`70,000 + `1,00,000 + `1,30,000 + `90,000 + `60,000) 5 year `4,50,000 = =` 5 So,
Payback Factor =
`3,10,500 = `90,000
Step 2: Life of the project is 5 years. between which the Payback Factor falls.
PV of Annuity of ` year
3.8896
3.7907
3.6959
3.6048
3.5173
3.4332
3.3522
3.2743
3.1993
The Payback Factor 3.4500 is between 3.5173 and 3.4332, which are the annuity values at 13% and 14%. Hence, Step 3: (`) Year `1 1 2 3 4 5
70,000 1,00,000 1,30,000 90,000 60,000
0.8850 0.7831 0.6931 0.6133 0.5428
`1 61,950 78,310 90,103 55,197 32,568
0.8772 0.7695 0.6750 0.5921 0.5194
61,404 76,950 87,750 53,289 31,164
4.63
Step 4: Calculation of IRR (PV of Cash Inflows at LR  CO) ˘ È IRR = LR + Í(HR  LR) ¥ (PV of CIs at LR  PV of CIs at HR) ˙˚ Î LR = Lower Rate of IRR Range = 13% HR = Higher Rate of IRR Range = 14% `3,10,500 `3,18,128 `3,10,557
(`3,18,128  `3,10,500) ˘ È So, IRR = 13% + Í(14% 13%) ¥ (`3,18,128  `3,10,557) ˙˚ Î È1% ¥ `7,628 ˘ = 13% + Í ˙ Î `7,571 ˚ = 13% + 1.008% = Suggestion: Since the Internal Rate of Return is less than the Hurdle Rate, it is not advisable to invest in the machinery. Problem 26
Problem on DecisionMaking on the basis of Net Present Value and Internal Rate of Return
The management of P Ltd. is considering selecting a machine out of the two mutually exclusive Details of the machine are as follows:
Cost of machine Expected life Annual income before tax and Depreciation
Machine I
Machine II
`10,00,000 5 years `3,45,000
`15,00,000 6 years `4,55,000
Depreciation is to be charged on straight line basis. (a) Calculate Net Present Value and Internal Rate of Return for each machine. (b) Advise the management of P Ltd., as to which machine they should take up.
4.64
SOLUTION
Depreciation per annum =
(Cost of the Asset  Scrap) Life
Earnings Before Depreciation and Taxes (given) Less: Depreciation Less: Tax @ 30% Add: Depreciation Present Value of Annuity of `1 @ 12% for life of 5 years and 6 years
¥ PV of Annuity)
e NPV Equated NPV = PV of Annuity
Cash Outflow Payback Factor = Average Cash Inflow p.a.
Machine I
Machine II
`10,00,000
`15,00,000
`2,00,000
`2,50,000
3,45,000 2,00,000 1,45,000 43,500 1,01,500 2,00,000
4,55,000 2,50,000 2,05,000 61,500 1,43,500 2,50,000
3.605
4.112
10,86,907.50 10,00,000.00
16,18,072.00 15,00,000.00
`86,907.50 3.605 =`
`1,18,072.00 4.112 =`
`10,00,000 `3,01,500
`15,00,000 `3,93,500
`10,10,688 `9,87,201
`15,73,056 `15,30,203
IRR Range (from annuity tables) Based on sixth year Annuity Values for Machine II
(See Working Note)
4.65
LR HR HR – LR
15% 16% 1% `10,688 `23,487
(PV of CIs at LR – PV of CIs at HR)
13% 14% 1% `73,056 `42,853
(PV of Cash Inflows at LR  CO) ˘ È IRR = LR + Í(HR  LR) ¥ (PV of CIs at LR  PV of CIs at HR) ˙˚ Î
1. Machine I PV of Annuity of `1 @ 15% for 5 years is 3.3522. `3,01,500 ¥ 3.3522 = `10,10,688 PV of Annuity of `1 @ 16% for 5 years is 3.2743. `3,01,500 ¥ 3.2743 = `9,87,201 2. Machine II PV of Annuity of `1 @ 13% for 6 years is 3.9976. `3,93,500 ¥ 3.9976 = `15,73,056 PV of Annuity of `1 @ 14% for 6 years is 3.8887. `3,93,500 ¥ 3.8887 = `15,30,203 Analysis: The life of the two machines is not the same. Hence, must be used for decisionmaking. Machine II, having higher equated NPV, is a better choice. However, IRR is higher in case of Machine I and hence on the basis of IRR, Machine I is a better choice. In case of such contradiction, the alternative suggested by NPV Method must be considered. Hence, it is advisable for the company to consider investing in Machine II. Problem 27
Problem on Finding of Missing Information
Data on a capital project M is given as follows: Annual Cash Flows Useful Life Internal Rate of Return
`60,000 4 years 15%
Salvage Value
Zero
4.66
You are required to calculate for the project M: (a) (b) (c) (d)
Cost of Project Payback Period Cost of Capital Net Present Value
SOLUTION
¥ PV of Annuity of `1 @ 15% for 4 years PV of Annuity of `1 @ 15% for 4 years = 2.8550 (From Annuity Tables) `60,000 ¥ 2.855 = `1,71,300 `
formula:
So,
Payback Period =
Cash Outflows Cash Inflow p.a.
Payback Period =
`1,71,300 = `60,000
`1,71,300 Total PV of Cash Inflows Total PV of Cash Outflows Total PV of Cash Inflows `1,71,300
That is,
1.064 =
Hence,
`1,71,300 ¥ 1.064 = `1,82,263.20 NPV = `1,82,263.20 – `1,71,300 = `
Cost of Capital is the Hurdle Rate considered in calculating NPV. ¥ PV of Annuity of `1@ i% for n years In this case, `1,82,263.20
4.67
`60,000 So, PV of Annuity of ` =
`1,82,263.20 `60,000
= Life of the project is 4 years. In the fourth year, PV of Annuity of `1 is 3.0377 at 12% (from annuity tables). Hence,
SUMMARY � Capital budgeting decisions involves the following:
� Deciding on whether to invest or not, given an investment opportunity (Accepting or Rejecting Independent Proposals). � Deciding on the best investment alternative among mutually exclusive investment alternatives. � Deciding on the extent and proportion of investment among various nonmutually exclusive investment alternatives (Capital Rationing). � Hurdle Rate or Discount Rate. � � � required. Such rate is called Hurdle Rate or Discount Rate. The following is considered as Hurdle Rate, in practice:
� is considered as Discount Rate. is
� considered as Discount Rate.
Expected from the asset or project must be considered as Discount Rate. � For making capital budgeting decisions, a variety of techniques are used. These techniques are
�
Cash Flow Techniques. � NonDiscounted Cash Flow Techniques include Payback Period and Average Rate of Return Methods. � Discounted Cash Flow Techniques include Discounted Payback Period, Net Present Value, � � Average Rate of Return refers to the return on investment given by the asset or project. Its calculation
4.68 � � � � Internal Rate of Return refers to the return on investment in the project, calculated on the basis of � Capital Rationing refers to deciding about allocation of the limited funds available, among projects or assets, which are not mutually exclusive.
SNAPSHOT OF FORMATS AND FORMULAE
(`) XXXX Add: Transportation Cost, Installation Cost and all other costs incurred XXXX date the asset becomes operational.
XXXX XXXX XXXX
(`) XXXXX Less: Cost of Goods Sold (i.e., Material Cost + Conversion Cost) Distribution expenses) Less: Depreciation
Add: Depreciation
Note:
XXXXX XXXXX XXXXX XXXXX XXXXX XXXXX XXXXX XXXXX XXXXX
4.69
Payback Period =
Cash Outflows Cash inflows p.a.
Ê Average PAT ˆ ¥ 100 ARR = Á Ë Average Investment ˜¯ È (Cost of the Asset  Scrap) ˘ Average Investment = Í ˙˚ + Scrap + Working Capital Î 2
Total PV of Cash Inflows Total PV of Cash Outflows (PV of CIs at LR  CO) ˘ È Internal Rate of Return = LR + Í(HR  LR) ¥ ˙ (PV of CIs at LR PV of CIs at HR) ˚ Î
EXERCISES
Section A 1. A project costs ` before tax at 50%. Calculate Payback Period.
`40,000, after Depreciation at 12% p.a., but `
2. Cost of plant is ` respectively. Express Payback Period in terms of years.
`10,000, `40,000 and `60,000
3. Initial Investment in a project is `20,00,000. Expected scrap is `4,00,000 at the end of its working life of 5 years. Additional Working Capital required is `2,00,000. Calculate Average Investment. [Ans: `
4.70
Section B 1. Suresh Electronics Ltd. is considering purchase of a machine. Two alternatives are available – Machine ` Year
Machine Easy (`)
Machine Quick (`)
1 2 3 4 5
30,000 40,000 60,000 70,000 50,000
40,000 50,000 60,000 60,000 50,000
Calculate Payback Period and advise the management.
`12,000 and the estimated annual `4,000. Its economic life is 5 years. The second alternative costs ` `4,000 per annum Its economic life is however only 4 years. Advise the management by using Payback Period.
(Hint: Alternative I, having almost same Payback Period but higher Postpayback Period, can be a better choice) 3. A company is requiring a machine, which needs an investment of `1,60,000. The net income before tax and Depreciation is estimated as follows: Year
1
2
3
4
5
(`)
56,000
48,000
30,000
64,000
80,000
Depreciation is to be charged on Straight Line basis. The tax rate is 40%. Calculate Average Rate of Return. ` `
4. A project costs an Initial Investment of ` `4,00,000 for 4 years. Calculate Internal Rate of Return. 5. A project costs ` Calculate Internal Rate of Return.
`4,000 each year, for 5 years.
4.71
Section C 1. A company is considering purchasing a machine. Two alternative machines are available – Machine X and Machine Y, each costing `50,000. Earnings After Taxation are expected to be as follows: Year
Machine X (`)
Machine Y (`)
1 2 3 4 5
15,000 20,000 25,000 15,000 10,000
5,000 15,000 20,000 30,000 20,000
Evaluate the two alternatives according to: (a) Payback Period (b) Average Rate of Return (c) Net Present Value @ 10% Assume Straight Line Method of Depreciation `
`
2. ABC Ltd. is considering investing in a project that costs `7,00,000. Tax rate is 50%. The company uses tax as follows: Year
(`)
1 2 3 4 5
1,20,000 1,40,000 2,00,000 2,50,000 3,00,000
` 0.909 0.826 0.751 0.683 0.621
Calculate the following: (a) Payback Period (b) Net Present Value at 10% (c) Accounting Rate of Return ` (Hint: In Year 1, there is a loss of `
are given as follows:
4.72
(`)
(`)
Investments
1,40,000
1,40,000
Year 1 Year 2 Year 3 Year 4 Year 5
20,000 40,000 60,000 90,000 1,20,000
1,20,000 80,000 40,000 20,000 20,000
Compute: (a) Payback Period (b) Net Present Value `
`
(Hint: NPV and PI are almost same. However, Project Y has a very low Payback Period. Hence, Project Y could be a better choice) 4. Consider the following mutually exclusive projects: `) A B C D
C – 10,000 – 10,000 – 3,500 – 3,000
C1 6,000 2,500 1,500 0
C2 2,000 2,500 2,500 0
C3 2,000 5,000 500 3,000
C4 12,000 7,500 5,000 6,000
Required: (a) Calculate the Payback Period for each project. (b) If the standard Payback Period is 2 years, which project will you select? Will your answer differ, if standard Payback Period is 3 years? (c) If the Cost of Capital is 10%, compute the discounted Payback Period for each project. Which projects will your recommend, if standard discounted Payback Period is (i) 2 years; (ii) 3 years? (d) Compute the NPV of each project. Which project would your recommend on the NPV criterion? The Cost of Capital is 10%. What will be the appropriate choice criteria in this case?
(d) `
`
`
`
5. A company has to make a choice between two projects, namely A and B. The initial capital outlay of two projects are `1,35,000 and `2,40,000 respectively for A and B. There will be no Scrap Value at the end of the life of both the projects. The opportunity Cost of Capital of the company is 16%. The annual
4.73 Year
1
2
3
Project A

30,000
Project B
60,000
84,000
4
5
1,32,000
84,000
84,000
96,000
1,02,000
90,000
You are required to calculate for each project: (a) Discounted Payback Period (c) Net Present Value `
`
machines is as follows:
Cost of Machine
Machine I
Machine II
`15,00,000
`20,00,000
5 years
5 years
`6,25,000
`8,75,000
Expected Life Annual Income (Before Tax and Depreciation) Depreciation is to be charged on Straight Line basis. You are required to calculate: (a) Discounted Payback Period (b) Net Present Value `
`
7. Zenith Industries Ltd. is thinking of investing in a project costing `20,00,000. The life of the project
Year
1
2
3
4
5
EBDT (`in lakh)
4
6
8
8
10
You are required to determine the: (a) Payback Period of the investment (b) Average Rate of Return (c) Net Present Value, assuming a discount rate of 10% (d) Internal Rate of Return
`
8. The management of a company is considering two alternative proposals. Project A requires capital outlay of `12,00,000 and Project B requires ` for 5 years:
4.74 Project A: `4,00,000 per year and Project B: `5,80,000 per year. The Cost of Capital is 10%. Show which of the two projects is preferable from the viewpoint of (a) Net Present Value Method (c) Internal Rate of Return Method `
`
9. The details of Project C are given as follows: Cost of the Project Useful Life
`2,28,400 4 years
Internal Rate of Return Salvage Value
15% Zero
You are required to calculate: (a) (b) (c) (d)
Annual Cash Flow Cost of Capital Net Present Value Discounted Payback Period [Ans: (a) `
`
10. ANP Ltd. is providing the following information: Annual Cost Savings Useful Life
`96,000 5 years
Internal Rate of Return
15%
You are required to calculate: (a) Cost of the Project (b) Payback Period (d) Cost of Capital
[Ans: (a) `
`
MULTIPLE CHOICE QUESTIONS
(a) Deciding on whether to invest or not in a given investment opportunity. (b) Choosing the best alternative among various mutually exclusive alternatives. (c) Capital rationing
4.75
(c) Hurdle Rate (a) (b) (c) (d)
(d) All of these
Cost of Asset Cost of Goods Sold Transportation and Installation Cost of the Asset Interest on loan borrowed for investing in the asset, till the asset becomes operational.
(a) EBITDA
(b) EBIT
(a) EBIT – Tax –
(b) EBITDA – Tax Liability
must be (a) Weighted Average Cost of Capital (c) Cost of Debt
(b) Cost of Equity (d) None of these
must be (a) Weighted Average Cost of Capital (c) Cost of Debt
(b) Cost of Equity (d) None of these
(a) Net Present Value Method (c) Average Rate of Return Method
(a)
Cost of the Asset 2
(b)
(Cost of the Asset + Working Capital) 2
(c)
(Cost of the Asset  Scrap Value) 2
(b) Internal Rate of Return Method (d) Discounted Payback Period Method
È (Original Investment  Scrap Value) ˘ (d) Í ˙˚ + Scrap Value + Net Working Capital Î 2
4.76
¥ ∏ (d) None of these (a) Deciding on whether to invest or not in a given investment opportunity (b) Choosing the best alternative among various mutually exclusive alternatives (c) Choosing the suitable alternatives among various nonmutually exclusive alternatives
ANSWER KEY 1. (d) 6. (c) 11. (c)
2. (d) 7. (a) 12. (c)
3. (b) 8. (b)
4. (a) 9. (c)
5. (b) 10. (d)
Dividend Decisions
5
INTRODUCTION
5.1
CHAPTER OVERVIEW 5.1 Introduction 5.2 Meaning of Dividends 5.3 Dividend Policy 5.4 Determinants of Dividend Policy 5.5 Forms or Types of Dividend
MEANING OF DIVIDENDS
5.2
retained earnings dividends
THEORY QUESTIONS Section A
5.2
DIVIDEND POLICY
5.3
A. Constant Dividend Policy `
B. Constant Dividend Payout Policy
Ê Dividends ˆ ÁË ˜ ¥ 100 Profits after Tax ¯ or Ê Dividend per Share ˆ ÁË Earning per share ˜¯ ¥ 100
5.3
C. Constant Dividend Plus Policy
`
D. Residual Approach
minus
THEORY QUESTIONS Section A
Section B
5.4
DETERMINANTS OF DIVIDEND POLICY
5.4
5.4.1
External Factors
1. General State of Economy
2. Trend in the Industry
3. State of Capital Market
4. Legal Restrictions
5. Contractual Restrictions
6. Tax Policy
up to `10 lakh
5.5
5.4.2
Internal Factors
1. Desire of the Shareholders
� � � 2. Financial Needs of the Company
3. Nature of Earnings
4. Desire of Control
5. Liquidity Position
5.6
THEORY QUESTIONS Section A
Section B
Section C
(Bangalore University, B.Com, November 2014–2015)
FORMS OR TYPES OF DIVIDEND
5.5
5.5.1
Cash Dividend
5.5.2
Stock Dividend
5.7
THEORY QUESTIONS Section A (Bangalore University, B.Com, November 2014–2015)
(Bangalore University, B.Com, November 2013–2016)
Section B (Bangalore University, B.Com, November 2013)
SUMMARY � � � � � � � � � �
5.8 � � � �
MULTIPLE CHOICE QUESTIONS
2. Which of the following is not a type of Dividend Policy?
3. Which of the following is the correct formula for calculating Dividend Payout Ratio? Ê EPS ˆ ÁË ˜ ¥ 100 PAT ¯
Ê DPS ˆ ÁË ˜ ¥ 100 EPS ¯
Ê DPS ˆ ÁË ˜ ¥ 100 PAT ¯ 4. Which of the following is not an external factor in determining Dividend Policy?
5. Which of the following is not an internal factor in determining Dividend Policy?
6. Stock Dividends are also referred as
ANSWER KEY
6
Working Capital Management
6.1
CHAPTER OVERVIEW
INTRODUCTION
Working Capital refers to the capital required for the daytoday working of a business enterprise. It is of different types, which have been explained as follows:
6.1 Introduction 6.2 Working Capital Management 6.3 Estimation of Working Capital Requirement
1. Gross Working Capital: It refers to the
6.4 Sources of Working Capital 6.5 Components of Working Capital Management
2. Net Working Capital: It refers to the excess of total current assets over total
operations, etc.
THEORY QUESTIONS Section A 1. What is working capital? 2. State the different types of working capital.
6.2 3. What is gross working capital?
(Bangalore University, B.Com, November 2014)
Section B
WORKING CAPITAL MANAGEMENT
6.2
This chapter covers discussion on Estimation of Working Capital Requirement and Sources of Working Capital.
THEORY QUESTIONS Section A
ESTIMATION OF WORKING CAPITAL REQUIREMENT
6.3 This topic covers discussion on the following: A. Need for adequate working capital or Dangers of inadequate and Excessive working capital.
6.3
6.3.1
Need for Adequate Working Capital
inadequate working capital are as follows:
(d) Low liquidity could lead to insolvency of the business.
excessive working capital are as follows: (b) There could be pileup of unnecessary inventories.
debts, etc.
THEORY QUESTIONS Section A 1. What is working capital? State the need for adequate working capital. 3. State any two dangers of excessive working capital. (Bangalore University, B.Com, November 2013)
Section B with inadequate or excessive working capital.
(Bangalore University, B.Com, November 2016)
Whether the working capital required is high or low depends on various factors, which have been explained in the following Table 6.1: TABLE 6.1 Factor 1. Production policies
High Working Capital High production during peak season e.g., diaries, calendars, etc.
Low/Moderate Working Capital
6.4 2. Production process
Labourintensive process
Capitalintensive process
Long
Short and quick
process 4. Nature of business 5. Credit policy
Trading Liberal and relaxed None or Low
suppliers Newly established concerns 8. Inventory policy
High stockholding period period
10. Pricelevel changes conditions 11. Business cycle recessionary conditions
THEORY QUESTIONS Section A
Section B (Bangalore University, B.Com, November 2013)
Section C
(Bangalore University, B.Com, November 2017)
6.5
Regression Method
Operating Cycle or Cash Cycle Method
Cash Cycle ˆ Ê ÁË Total Operating Cost ¥ ˜¯ + Desired Cash Balance 12 � Total Operating Cost = Cost of Goods Sold + Operating Expenses � � �
cash. That is, Operating Cycle refers to the duration between the date of spending cash and its realisation on
Average Stock of Raw Material Raw Material consumption per day
W=
Average Stock of Workinprogress y Cost of Production per day
6.6
Average Stock of Finished Goods Average Cost of Goods Sold per day
D=
Average Accounts Receivable Average Sales per day
C=
Average Accounts Payable Average Purchases per day
Policy Method
THEORY QUESTIONS Section A
SOURCES OF WORKING CAPITAL
6.4 A. Trade Credit
E. Accrued Expenses
H. Debt Securitisation
6.7
A. Trade Credit
advantages are: there are no explicit costs associated with the credit period allowed; it is available and keeps on
(a) Loans: transfer to the current account of the borrower. Interest and other charges like inspection, insurance, processing charges, etc., are charged to this account. (b) Cash Credit: T
(c) Bank Overdraft: When the borrowed funds are no longer required, they can be quickly and easily repaid.
(d) Bill Discounting:
is discount. (e) Advances against Documents of Title to Goods: title to goods, when its possession is considered possession of goods itself and granted
Maximum Permissible Bank Finance
� � �
6.8
are rigid and stringent.
E. Accrued Expenses
F. Pledging of Receivables
is higher.
Papers:
corporate bodies registered or incorporated in India, unincorporated bodies, nonresident
6.9
` worth, as per the latest audited Balance Sheet, is not less than `4 crore, it has been sanctioned
strong.
H. Debt Securitisation
The following is the process of Securitisation:
receivables of the originator. Purpose Vehicle (SPV) or Special Purpose Entity (SPE), for which the SPV or SPE pays the
6.10
lien on the underlying asset pool. (d) Usually, the risk of defaults is borne by investors and the issuer is under an obligation to pay
Advantages of Securitisation
(A) To the Originator: (i) The assets are shifted off the balance sheet, thus giving the Originator recourse to offbalance sheet funding. (ii) It converts illiquid assets to a liquid portfolio.
(iv) The credit rating of the originator enhances. (B) To the Investor:
I. Factoring of Receivables
The procedure for factoring is as under: 1. The borrower sells his accounts receivables to the factor.
collection of debts, credit protection, riskbearing, etc.
6.11
(a) Accounts receivables are easily converted into cash. (b) (c) undertaken by the factor. (d) The following Table 6.2 shows TABLE 6.2 Differences B Bill Discounting 1. Parties
Buyer of Goods = Drawee Seller of Goods = Drawer
Factoring Buyer of Goods = Debtor Seller of Goods = Client
2. Nature debts/receivables. change is discounted and provided at transaction, and provides the balance at
4. Additional services
vide any additional service other than services and other services like providing advance. Debtors’ followup, Debtors’ Ledger
Banker earns discounting charges on the transaction. services. 6. Statute applicable.
J. Forfaiting of Receivables
6.12
THEORY QUESTIONS Section A (Bangalore University, B.Com, November 2013) 3. What is trade credit? 4. What is cash credit?
11. 12. 13. 14.
What is debt securitisation? What is factoring? State any two differences between factoring and bill discounting. What is forfaiting?
Section B
(Bangalore University, B.Com, November 2014–2015)
its advantages. 7. Distinguish between factoring and bill discounting.
Section C entity.
COMPONENTS OF WORKING CAPITAL MANAGEMENT
6.5
6.13
The following T TABLE 6.3 Receivables Management
Inventory Management
Cash Management
1. Ensuring continuity in production associated costs associated costs associated cost Associated Costs
1. Capital Cost 2. Collection Cost 3. Delinquency Cost 4. Default Cost
1. Purchase Cost 2. Ordering Cost 3. Carrying Cost or Holding Cost
Areas or Scope of
1. Credit Standards 2. Credit Period 3. Cash Discount 4. Collection Efforts
2. Storage 3. Issues
1. Transaction Cost 2. Opportunity Cost
Cash Balance Tools or Techniques 1. Decision Trees
1. EOQ
3. Ageing Schedule 4. VSN Analysis 5. Stock Levels
8. Average Cost
SUMMARY � � �
1. Cash Budgets 2. Concentration Banking
6.14 � �
� �
�
MULTIPLE CHOICE QUESTIONS 1. Working Capital refers to funds required for (b) Investing in stocks and real estate (d) None of these 2. Which of the following is not a component of Working Capital Management?
3. Which of the following are the problems of excessive working capital? (a) Higher Incidence of Bad Debts (b) Pile up of inventory 4. Which of the following are the problems of inadequate working capital?
5. Which of the following is not a factor in determining working capital requirement?
6. Which of the following is not a method for estimation of Working Capital Requirement?
7. In estimation of working capital, the formula R + W + F + D – C represents (a) Tricycle (b) Bicycle (c) Operating Cycle (d) Cash Cycle (a) Venture Capital
(b) Trade Credit
6.15 9. Which of the following is not the method of calculating Maximum Permissible Bank Finance?
(d) None of these 10. The terms Originator, Obligor and Special Purpose Vehicle are relating to
11. “Minimisation of associated costs” is the objective of
ANSWER KEY 1. (c) 6. (a) 11. (d)
2. (b) 7. (d)
3. (d) 8. (a)
4. (d) 9. (d)
5. (c) 10. (b)
Model Question Paper1 III Semester B.Com Examination COMMERCE 3.4: Financial Management Time: 3 hours
Max. Marks: 70
SECTION A 1. Answer any subquestions. Each question carries two marks. (a) List any four objectives of Financial Management. (b) What is Financial Planning? (c) Explain the concept of Continuous Compounding.
(5 ¥ 2 = 10)
(e) State the differences between Discounted and Nondiscounted techniques of Capital Budgeting. (f) State the different types of Dividend Policies. (g) What are Commercial Papers?
SECTION B Answer any
questions. Each question carries six marks.
(3 ¥ 6 = 18)
India. `
`
[Ans: ` 12,670]
M1.2
5. The data relating to two companies is given as follows: Company A
Company B
` `
` `
Equity Capital 12% Debentures Output (units) per annum Selling Price per unit Fixed Costs per annum Variable Cost per unit
` 30
` 250
`
` ` 10
` 75
of the two companies. [Ans: DOL – 2.4 and 2.14; DFL – 1.11 and 1.07; DCL – 2.56 and 2.29] 6. Suresh Electronics Ltd. is considering purchase of a machine. Two alternatives are available ` as follows: (`)
(`)
1 2 3 4 5
Calculate Payback Period and advise the management.
SECTION C Answer any
questions. Each question carries
marks.
(3 ¥ 14 = 42)
7. “The working capital requirement of a business enterprise depends on various factors”. 8. X Ltd. just declared a dividend of ` 14.00 per share. Mr B is planning to purchase the share the market price of this share to be ` 360.00 after 3 years. You are required to determine: per annum.
annum.
[Ans: (i) `
`
M1.3
` sales revenue from the project is ` ` ` 10 each and 12% debentures of ` You are required to: ` ` 2 and (c) ` 0 ` 27,65,714, `
`
`
outlay of two projects are ` ` no scrap value at the end of the life of both the projects. The opportunity cost of capital of the
1 Project A
2
4
5
–
Project B
You are required to calculate for each project: (i) Discounted Payback Period (iii) Net Present Value `
`
which is expected to last for only 5 years. The total capital put in by the trader is: Machinery Working Capital
` ` `
` are estimated to be as follows. Provide your suggestions on the basis of Net Present Value and
1
2
4
5
Tax Payable
Consider a hurdle rate of 15%. [Ans: NPV – () ` 7,160 and IRR – 14%]
Model Question Paper2 III Semester B.Com Examination COMMERCE 3.4: Financial Management Time: 3 hours
Max. Marks: 70
SECTION A 1. Answer any
subquestions. Each question carries two marks.
(5 ¥ 2 =10)
SECTION B Answer any
questions. Each question carries six marks.
(3 ¥ 6 = 18)
decisions of a company. 4. An investor deposits ` 1,000 in a saving institution. Each payment is made at the end of the [Ans: 3,374.62]
M2.2 Firm X 5,00,000 0 5,00,000 50,000 20%
Assets
Number of Shares Rate of Return on Assets
Firm Y 5,00,000 2,50,000 2,50,000 25,000 20%
[Ans: Firm X = ` 1 and Firm Y = ` 1.55] 6. A company is considering purchase of a machinery costing `
`)
1 2,00,000
2 5,00,000
3 3,00,000
4 3,00,000
5 2,00,000
6 1,00,000
Ascertain the Payback Period and Postpayback Period.
SECTION C Answer any
questions. Each question carries
marks.
(3 ¥ 14 = 42)
8. A company is proposing to issue a 5year debenture of ` 1000 at 14% rate of interest per
[Ans: ` 1046.59]
(`) ` 60,00,000 at
30,00,000 Interest @ 8%
1,00,000
Net Income Earnings per Share
4,50,000 4,50,000 `
M2.3
` P E
t
` 100 per share and
P E
`
1
`
` 141.84]
` 2,28,400
(iv) Discounted Payback Period [Ans: (i) ` 80,000, (ii) 13%, (iii) ` `
` 18,00,000. Both are estimated
`
`
`
`
Model Question Paper3 III Semester B.Com Examination COMMERCE 3.4: Financial Management Time: 3 hours
Max. Marks: 70
SECTION A 1. Answer any subquestions. Each question carries two marks. (5 ¥ 2 =10) (a) What is Financial Management? What are its functions? (b) Enumerate the objectives of Financial Management. (c) What are the features of Plain Vanilla Bonds? (d) What is Trading on Equity? (e) What is Desirability Factor? List three merits of this method of Capital Budgeting. (f) What is Residual Approach of Paying Dividends? (g) State the various methods of estimating Working Capital Requirement.
SECTION B Answer any
questions. Each question carries six marks.
(3 ¥ 6 = 18)
2. What are Dividends? Explain the different forms of Dividend Payment. 4. A doctor is planning to buy an Xray machine for his hospital. He has two options. He can either purchase it by making cash payment of ` 5 lakh or ` 6,15,000 is to be paid in six equal annualinstallments. Which option do you suggest to the doctor, assuming the rate of return is 12%? [Ans: Option II] 5. Annual sales of a company are ` other than interest is ` 5,00,000 per annum. Company has 11% debentures of ` 30,00,000. You are required to calculate the Operating, Financial and Combined Leverages of the company. [Ans: 1.33, 1.28 and 1.70]
M3.2
6. The cost of machinery is ` 10,00,000. It is estimated to have a life of 4 years, at the end of which, the salvage value estimated is ` 50,000. The machinery needs ` 1,00,000 as working capital for its operations. ` 1,20,000 ` 1,85,000 ` 2,05,000 ` 1,62,500
Year 1 Year 2 Year 3 Year 4
Calculate the Average Rate of Return from the machinery.
[Ans: 26.9%]
SECTION C Answer any
questions. Each question carries
marks.
(3 ¥ 14 = 42)
highlighting their pros and cons. (i) (ii) (iii) (iv)
` 2,000 to be received at the end of 2 years @ 10%, compounded annually. ` 5,000 to be received at the end of 1 year at 9%, compounded quarterly. ` 1,000 to be received at the end of 6 months @ 8%, compounded monthly. ` 4,000 to be received at the end of 3 years at 12%, compounded monthly. [Ans: (i) ` 1,652.89, (ii) ` 4,574.22 (iii) ` ` 2,795.70]
9. A company had the following balance sheet as on 31 March 2018. ` Equity Share Capital (50 lakh shares of ` 10 each) Reserves and Surplus 15% Debentures Current Liabilities
` 5 1 10 4 20
Fixed Assets (net) Current Assets
Fixed Costs per annum (excluding interest) Variable operating costs ratio Total assets turnover ratio Income tax rate
12.5 7.5
20
` 4 crore 65% 2.5 30%
M3.3
(i) (ii) (iii) (iv)
Earnings per Share Operating Leverage Financial Leverage Combined Leverage
[Ans: ` 16.80; 1.296; 1.125 and 1.458]
10. Delta Ltd. currently has an equity share capital of ` 10,00,000, consisting of 1,00,000 equity shares of ` 10 each. The company is going through a major expansion plan, requiring to raise funds to the tune of ` ` 10 each ` 10 each and the balance through longterm borrowing at 12% interest p.a. ` 10 each and 3,000 ` 100, 9% debentures ` 10 each and the balance through 6% preference shares The EBIT of the company is expected to be ` 4,00,000 p.a. Assume corporate tax rate of 40%. Calculate EPS in each of the above plans. [Ans: EPS – ` 1.50, ` 1.61, ` 1.72 and ` 1.71] 11. A project involves an investment of ` Beginning of second year Beginning of third year Beginning of fourth year
` 2,50,000 ` 2,50,000 ` 2,50,000 ` 2,50,000
First Year Second Year Third Year Fourth Year Fifth Year
` 2,30,000 ` 2,28,000 ` 2,78,000 ` 2,33,000 ` 80,000
Calculate Net Present Value of the project, assuming cost of capital as 10%. [Ans: NPV: () ` 56,505]
III Semester B.Com Examination, November/December 2017 (CBCS) (Semester Scheme) (2015–16 and Onwards) (F + R) COMMERCE 3.4: Financial Management Time: 3 hours
Max. Marks: 70
SECTION A 1. Answer any
subquestions. Each subquestion carries two marks. (5 ¥ 2 = 10 Marks)
(a) Give the meaning of Finance.
(d) Expand EAT, EBIT and PAT.
period of one year.
` 1,000, if it is invested at 8% interest, for a [Ans: ` 1080]
SECTION B Answer any
questions. Each question carries six marks.
(3 ¥ 6 = 18 marks)
QP1.2
at 10% rate of interest: (i) ` (ii) ` 5,000 at the end of second year (iii) ` 6,000 at the end of third year (iv) ` 7,000 at the end of fourth year (v) ` [Ans: ` 5856.40, ` 6655, ` 7260, ` 7700 and ` 8,000; Total ` 35471.40] for 4 years, 3 years, 2 years, 1 year and 0 year for payments made at the end of year 1, 2,3,4
` 1,00,000 at ` 5 per unit ` 1 per unit ` 1,00,000 ` 20,000
Fixed Cost Interest Expenditure
[Hint: Contribution is ` 80,000, EBIT is () ` 20,000 and EBT is () ` 6. Rajesh and Co. is considering the purchase of a machine. Two machines A and B, each costing `
1 2 3 4 5
`
`
15,000 20,000 25,000 15,000 10,000
5,000 15,000 20,000 30,000 20,000
SECTION C Answer any
questions. Each question caries
marks.
(3 ¥ 14 = 42)
QP1.3
Fixed Cost Interest
` 20,00,000
` 30,00,000
` 5,00,000 ` 1,00,000
` 7,00,000 ` 1,25,000
[Ans:
1.714 1.167 2.000
Investment
`
`
1,00,000
1,00,000
20,000 30,000 40,000 50,000 60,000
45,000 40,000 30,000 10,000 8,000
1.500 1.098 1.647
QP1.4
1 2 3 4 5
20%
29%
9%
15%
0.833 0.694 0.579 0.483 0.402
0.775 0.601 0.466 0.361 0.280
0.917 0.842 0.772 0.708 0.650
0.870 0.750 0.658 0.572 0.497
P V 1
`
0 1 2 3 4 5
(2,00,000) 20,000 30,000 60,000 80,000 30,000
` ` 1.000 0.909 0.826 0.751 0.683 0.621
` ` 13,870]
1%
0.9901
0.9803
0.9706
0.9610
0.9515
0.9420
0.9327
0.9235
0.9143
0.9053
0.8963
0.8874
0.8787
0.8700
0.8613
0.8528
0.8444
0.8360
0.8277
0.8195
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
0.6730
0.6864
0.7002
0.7142
0.7284
0.7430
0.7579
0.7730
0.7885
0.8043
0.8203
0.8368
0.8535
0.8706
0.8880
0.9057
0.9238
0.9423
0.9612
0.9804
2%
0.5537
0.5703
0.5874
0.6050
0.6232
0.6419
0.6611
0.6810
0.7014
0.7224
0.7441
0.7664
0.7894
0.8131
0.8375
0.8626
0.8885
0.9151
0.9426
0.9709
3%
0.4564
0.4746
0.4936
0.5134
0.5339
0.5553
0.5775
0.6006
0.6246
0.6496
0.6756
0.7026
0.7307
0.7599
0.7903
0.8219
0.8548
0.8890
0.9246
0.9615
4%
Present Value of `1
Year
TABLE A
0.3769
0.3957
0.4155
0.4363
0.4581
0.4810
0.5051
0.5303
0.5568
0.5847
0.6139
0.6446
0.6768
0.7107
0.7462
0.7835
0.8227
0.8638
0.9070
0.9524
5%
0.3118
0.3305
0.3503
0.3714
0.3936
0.4173
0.4423
0.4688
0.4970
0.5268
0.5584
0.5919
0.6274
0.6651
0.7050
0.7473
0.7921
0.8396
0.8900
0.9434
6%
0.2584
0.2765
0.2959
0.3166
0.3387
0.3624
0.3878
0.4150
0.4440
0.4751
0.5083
0.5439
0.5820
0.6227
0.6663
0.7130
0.7629
0.8163
0.8734
0.9346
7%
0.2145
0.2317
0.2502
0.2703
0.2919
0.3152
0.3405
0.3677
0.3971
0.4289
0.4632
0.5002
0.5403
0.5835
0.6302
0.6806
0.7350
0.7938
0.8573
0.9259
8%
0.1784
0.1945
0.2120
0.2311
0.2519
0.2745
0.2992
0.3262
0.3555
0.3875
0.4224
0.4604
0.5019
0.5470
0.5963
0.6499
0.7084
0.7722
0.8417
0.9174
9%
0.1486
0.1635
0.1799
0.1978
0.2176
0.2394
0.2633
0.2897
0.3186
0.3505
0.3855
0.4241
0.4665
0.5132
0.5645
0.6209
0.6830
0.7513
0.8264
0.9091
10%
Appendix
11%
0.9009
0.8116
0.7312
0.6587
0.5935
0.5346
0.4817
0.4339
0.3909
0.3522
0.3173
0.2858
0.2575
0.2320
0.2090
0.1883
0.1696
0.1528
0.1377
0.1240
Year
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
0.1037
0.1161
0.1300
0.1456
0.1631
0.1827
0.2046
0.2292
0.2567
0.2875
0.3220
0.3606
0.4039
0.4523
0.5066
0.5674
0.6355
0.7118
0.7972
0.8929
0.0868
0.0981
0.1108
0.1252
0.1415
0.1599
0.1807
0.2042
0.2307
0.2607
0.2946
0.3329
0.3762
0.4251
0.4803
0.5428
0.6133
0.6931
0.7831
0.8850
13%
0.0728
0.0829
0.0946
0.1078
0.1229
0.1401
0.1597
0.1821
0.2076
0.2366
0.2697
0.3075
0.3506
0.3996
0.4556
0.5194
0.5921
0.6750
0.7695
0.8772
14%
0.0611
0.0703
0.0808
0.0929
0.1069
0.1229
0.1413
0.1625
0.1869
0.2149
0.2472
0.2843
0.3269
0.3759
0.4323
0.4972
0.5718
0.6575
0.7561
0.8696
15%
Present Value of `1
12%
TABLE A (Cont.)
0.0514
0.0596
0.0691
0.0802
0.0930
0.1079
0.1252
0.1452
0.1685
0.1954
0.2267
0.2630
0.3050
0.3538
0.4104
0.4761
0.5523
0.6407
0.7432
0.8621
16%
0.0433
0.0506
0.0592
0.0693
0.0811
0.0949
0.1110
0.1299
0.1520
0.1778
0.2080
0.2434
0.2848
0.3332
0.3898
0.4561
0.5337
0.6244
0.7305
0.8547
17%
0.0365
0.0431
0.0508
0.0600
0.0708
0.0835
0.0985
0.1163
0.1372
0.1619
0.1911
0.2255
0.2660
0.3139
0.3704
0.4371
0.5158
0.6086
0.7182
0.8475
18%
0.0308
0.0367
0.0437
0.0520
0.0618
0.0736
0.0876
0.1042
0.1240
0.1476
0.1756
0.2090
0.2487
0.2959
0.3521
0.4190
0.4987
0.5934
0.7062
0.8403
19%
0.0261
0.0313
0.0376
0.0451
0.0541
0.0649
0.0779
0.0935
0.1122
0.1346
0.1615
0.1938
0.2326
0.2791
0.3349
0.4019
0.4823
0.5787
0.6944
0.8333
20%
0.0221
0.0267
0.0323
0.0391
0.0474
0.0573
0.0693
0.0839
0.1015
0.1228
0.1486
0.1799
0.2176
0.2633
0.3186
0.3855
0.4665
0.5645
0.6830
0.8264
21%
0.0187
0.0229
0.0279
0.0340
0.0415
0.0507
0.0618
0.0754
0.0920
0.1122
0.1369
0.1670
0.2038
0.2486
0.3033
0.3700
0.4514
0.5507
0.6719
0.8197
22%
0.0159
0.0196
0.0241
0.0296
0.0364
0.0448
0.0551
0.0678
0.0834
0.1026
0.1262
0.1552
0.1909
0.2348
0.2888
0.3552
0.4369
0.5374
0.6610
0.8130
23%
0.0135
0.0168
0.0208
0.0258
0.0320
0.0397
0.0492
0.0610
0.0757
0.0938
0.1164
0.1443
0.1789
0.2218
0.2751
0.3411
0.4230
0.5245
0.6504
0.8065
24%
0.0115
0.0144
0.0180
0.0225
0.0281
0.0352
0.0440
0.0550
0.0687
0.0859
0.1074
0.1342
0.1678
0.2097
0.2621
0.3277
0.4096
0.5120
0.6400
0.8000
25%
A1.2
26%
0.7937
0.6299
0.4999
0.3968
0.3149
0.2499
0.1983
0.1574
0.1249
0.0992
0.0787
0.0625
0.0496
0.0393
0.0312
0.0248
0.0197
0.0156
0.0124
0.0098
Year
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
0.0084
0.0107
0.0135
0.0172
0.0218
0.0277
0.0352
0.0447
0.0568
0.0721
0.0916
0.1164
0.1478
0.1877
0.2383
0.3027
0.3844
0.4882
0.6200
0.0072
0.0092
0.0118
0.0150
0.0193
0.0247
0.0316
0.0404
0.0517
0.0662
0.0847
0.1084
0.1388
0.1776
0.2274
0.2910
0.3725
0.4768
0.6104
0.7813
28%
0.0061
0.0079
0.0102
0.0132
0.0170
0.0219
0.0283
0.0365
0.0471
0.0607
0.0784
0.1011
0.1304
0.1682
0.2170
0.2799
0.3611
0.4658
0.6009
0.7752
29%
0.0053
0.0068
0.0089
0.0116
0.0150
0.0195
0.0254
0.0330
0.0429
0.0558
0.0725
0.0943
0.1226
0.1594
0.2072
0.2693
0.3501
0.4552
0.5917
0.7692
30%
Present Value of `1
0.7874
27%
TABLE A (Cont.) 31%
0.0045
0.0059
0.0077
0.0101
0.0133
0.0174
0.0228
0.0299
0.0392
0.0513
0.0672
0.0880
0.1153
0.1510
0.1979
0.2592
0.3396
0.4448
0.5827
0.7634
32%
0.0039
0.0051
0.0068
0.0089
0.0118
0.0155
0.0205
0.0271
0.0357
0.0472
0.0623
0.0822
0.1085
0.1432
0.1890
0.2495
0.3294
0.4348
0.5739
0.7576
33%
0.0033
0.0044
0.0059
0.0078
0.0104
0.0139
0.0185
0.0245
0.0326
0.0434
0.0577
0.0768
0.1021
0.1358
0.1807
0.2403
0.3196
0.4251
0.5653
0.7519
34%
0.0029
0.0038
0.0052
0.0069
0.0093
0.0124
0.0166
0.0223
0.0298
0.0400
0.0536
0.0718
0.0962
0.1289
0.1727
0.2315
0.3102
0.4156
0.5569
0.7463
35%
0.0025
0.0033
0.0045
0.0061
0.0082
0.0111
0.0150
0.0202
0.0273
0.0368
0.0497
0.0671
0.0906
0.1224
0.1652
0.2230
0.3011
0.4064
0.5487
0.7407
36%
0.0021
0.0029
0.0039
0.0054
0.0073
0.0099
0.0135
0.0184
0.0250
0.0340
0.0462
0.0628
0.0854
0.1162
0.1580
0.2149
0.2923
0.3975
0.5407
0.7353
37%
0.0018
0.0025
0.0035
0.0047
0.0065
0.0089
0.0122
0.0167
0.0229
0.0313
0.0429
0.0588
0.0806
0.1104
0.1512
0.2072
0.2839
0.3889
0.5328
0.7299
38%
0.0016
0.0022
0.0030
0.0042
0.0058
0.0080
0.0110
0.0152
0.0210
0.0289
0.0399
0.0551
0.0760
0.1049
0.1448
0.1998
0.2757
0.3805
0.5251
0.7246
39%
0.0014
0.0019
0.0027
0.0037
0.0051
0.0072
0.0099
0.0138
0.0192
0.0267
0.0371
0.0516
0.0718
0.0997
0.1386
0.1927
0.2679
0.3724
0.5176
0.7194
40%
0.0012
0.0017
0.0023
0.0033
0.0046
0.0064
0.0090
0.0126
0.0176
0.0247
0.0346
0.0484
0.0678
0.0949
0.1328
0.1859
0.2603
0.3644
0.5102
0.7143
A1.3
7.3255
8.1622
1.9704
2.9410
3.9020
4.8534
5.7955
6.7282
7.6517
8.5660
9.4713
10.3676
2
3
4
5
6
7
8
9
10
11
2%
3%
13.8651 12.8493 11.9379 11.1184 10.3797
14.7179 13.5777 12.5611 11.6523 10.8378 10.1059
15.5623 14.2919 13.1661 12.1657 11.2741 10.4773
16.3983 14.9920 13.7535 12.6593 11.6896 10.8276 10.0591
17.2260 15.6785 14.3238 13.1339 12.0853 11.1581 10.3356
18.0456 16.3514 14.8775 13.5903 12.4622 11.4699 10.5940
16
17
18
19
20
9.8986 9.7122
9.2950
9.7632
9.4466
9.1079
8.7455
8.3577
7.9427
13.0037 12.1062 11.2961 10.5631
8.8527
8.3838
7.4987
7.0236
6.5152
5.9713
5.3893
4.7665
4.1002
3.3872
2.6243
1.8080
15
9.3936
8.8633
7.8869
7.3601
6.8017
6.2098
5.5824
4.9173
4.2124
3.4651
2.6730
1.8334
7% 0.9346
14
9.9856
9.3851
8.3064
7.7217
7.1078
6.4632
5.7864
5.0757
4.3295
3.5460
2.7232
1.8594
6% 0.9434
11.2551 10.5753
8.7605
8.1109
7.4353
6.7327
6.0021
5.2421
4.4518
3.6299
2.7751
1.8861
5% 0.9524
12.1337 11.3484 10.6350
9.9540
4% 0.9615
13
9.2526
8.5302
7.7861
7.0197
6.2303
5.4172
4.5797
3.7171
2.8286
1.9135
0.9709
12
9.7868
8.9826
6.4720
5.6014
4.7135
3.8077
2.8839
1.9416
0.9804
1%
0.9901
1
Present Value of Annuity of `1
Year
TABLE B 8%
9.8181
9.6036
9.3719
9.1216
8.8514
8.5595
8.2442
7.9038
7.5361
7.1390
6.7101
6.2469
5.7466
5.2064
4.6229
3.9927
3.3121
2.5771
1.7833
0.9259
9%
9.1285
8.9501
8.7556
8.5436
8.3126
8.0607
7.7862
7.4869
7.1607
6.8052
6.4177
5.9952
5.5348
5.0330
4.4859
3.8897
3.2397
2.5313
1.7591
0.9174
10%
11%
8.5136 7.9633
8.3649 7.8393
8.2014 7.7016
8.0216 7.5488
7.8237 7.3792
7.6061 7.1909
7.3667 6.9819
7.1034 6.7499
6.8137 6.4924
6.4951 6.2065
6.1446 5.8892
5.7590 5.5370
5.3349 5.1461
4.8684 4.7122
4.3553 4.2305
3.7908 3.6959
3.1699 3.1024
2.4869 2.4437
1.7355 1.7125
0.9091 0.9009
12%
7.4694
7.3658
7.2497
7.1196
6.9740
6.8109
6.6282
6.4235
6.1944
5.9377
5.6502
5.3282
4.9676
4.5638
4.1114
3.6048
3.0373
2.4018
1.6901
0.8929
13%
7.0248
6.9380
6.8399
6.7291
6.6039
6.4624
6.3025
6.1218
5.9176
5.6869
5.4262
5.1317
4.7988
4.4226
3.9975
3.5172
2.9745
2.3612
1.6681
0.8850
14%
6.6231
6.5504
6.4674
6.3729
6.2651
6.1422
6.0021
5.8424
5.6603
5.4527
5.2161
4.9464
4.6389
4.2883
3.8887
3.4331
2.9137
2.3216
1.6467
0.8772
15%
6.2593
6.1982
6.1280
6.0472
5.9542
5.8474
5.7245
5.5831
5.4206
5.2337
5.0188
4.7716
4.4873
4.1604
3.7845
3.3522
2.8550
2.2832
1.6257
0.8696
A1.4
16%
0.8621
1.6052
2.2459
2.7982
3.2743
3.6847
4.0386
4.3436
4.6065
4.8332
5.0286
5.1971
5.3423
5.4675
5.5755
5.6685
5.7487
5.8178
5.8775
5.9288
Year
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
5.6278
5.5845
5.5339
5.4746
5.4053
5.3242
5.2293
5.1183
4.9884
4.8364
4.6586
4.4506
4.2072
3.9224
3.5892
3.1993
2.7432
2.2096
1.5852
0.8547
19%
20%
3.7057 3.6046
5.3527 5.1009 4.8696
5.3162 5.0700 4.8435
5.2732 5.0333 4.8122
5.2223 4.9897 4.7746
5.1624 4.9377 4.7296
5.0916 4.8759 4.6755
5.0081 4.8023 4.6106
4.9095 4.7147 4.5327
4.7932 4.6105 4.4392
4.6560 4.4865 4.3271
4.4941 4.3389 4.1925
4.3030 4.1633 4.0310
4.0776 3.9544 3.8372
3.8115
3.4976 3.4098 3.3255
3.1272 3.0576 2.9906
2.6901 2.6386 2.5887
2.1743 2.1399 2.1065
1.5656 1.5465 1.5278
0.8475 0.8403 0.8333
18%
22%
23%
4.6567 4.4603 4.2786
4.6346 4.4415 4.2627
4.6079 4.4187 4.2431
4.5755 4.3908 4.2190
4.5364 4.3567 4.1894
4.4890 4.3152 4.1530
4.4317 4.2646 4.1082
4.3624 4.2028 4.0530
4.2784 4.1274 3.9852
4.1769 4.0354 3.9018
4.0541 3.9232 3.7993
3.9054 3.7863 3.6731
3.7256 3.6193 3.5179
3.5079 3.4155 3.3270
3.2446 3.1669 3.0923
2.9260 2.8636 2.8035
2.5404 2.4936 2.4483
2.0739 2.0422 2.0114
1.5095 1.4915 1.4740
0.8264 0.8197 0.8130
21%
Present Value of Annuity of `1
17%
TABLE B (Cont.)
4.1103
4.0967
4.0799
4.0591
4.0333
4.0013
3.9616
3.9124
3.8514
3.7757
3.6819
3.5655
3.4212
3.2423
3.0205
2.7454
2.4043
1.9813
1.4568
0.8065
24%
26%
3.0833
3.9539 3.8083
3.9424 3.7985
3.9279 3.7861
3.9099 3.7705
3.8874 3.7509
3.8593 3.7261
3.8241 3.6949
3.7801 3.6555
3.7251 3.6059
3.6564 3.5435
3.5705 3.4648
3.4631 3.3657
3.3289 3.2407
3.1611
2.9514 2.8850
2.6893 2.6351
2.3616 2.3202
1.9520 1.9234
1.4400 1.4235
0.8000 0.7937
25%
3.6726
3.6642
3.6536
3.6400
3.6228
3.6010
3.5733
3.5381
3.4933
3.4365
3.3644
3.2728
3.1564
3.0087
2.8210
2.5827
2.2800
1.8956
1.4074
0.7874
27%
3.5458
3.5386
3.5294
3.5177
3.5026
3.4834
3.4587
3.4272
3.3868
3.3351
3.2689
3.1842
3.0758
2.9370
2.7594
2.5320
2.2410
1.8684
1.3916
0.7813
28%
3.4271
3.4210
3.4130
3.4028
3.3896
3.3726
3.3507
3.3224
3.2859
3.2388
3.1781
3.0997
2.9986
2.8682
2.7000
2.4830
2.2031
1.8420
1.3761
0.7752
29%
3.3158
3.3105
3.3037
3.2948
3.2832
3.2682
3.2487
3.2233
3.1903
3.1473
3.0915
3.0190
2.9247
2.8021
2.6427
2.4356
2.1662
1.8161
1.3609
0.7692
30%
A1.5
31% 0.7634 1.3461 1.7909 2.1305 2.3897 2.5875 2.7386 2.8539 2.9419 3.0091 3.0604 3.0995 3.1294 3.1522 3.1696 3.1829 3.1931 3.2008 3.2067 3.2112
Year
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
3.1129
3.1090
3.1039
3.0971
3.0882
3.0764
3.0609
3.0404
3.0133
2.9776
2.9304
2.8681
2.7860
2.6775
2.5342
2.3452
2.0957
1.7663
1.3315
0.7576
3.0202
3.0169
3.0124
3.0065
2.9987
2.9883
2.9744
2.9559
2.9314
2.8987
2.8553
2.7976
2.7208
2.6187
2.4828
2.3021
2.0618
1.7423
1.3172
0.7519
33%
2.9327
2.9299
2.9260
2.9209
2.9140
2.9047
2.8923
2.8757
2.8534
2.8236
2.7836
2.7300
2.6582
2.5620
2.4331
2.2604
2.0290
1.7188
1.3032
0.7463
34%
2.8501
2.8476
2.8443
2.8398
2.8337
2.8255
2.8144
2.7994
2.7792
2.7519
2.7150
2.6653
2.5982
2.5075
2.3852
2.2200
1.9969
1.6959
1.2894
0.7407
35%
2.7718
2.7697
2.7668
2.7629
2.7575
2.7502
2.7403
2.7268
2.7084
2.6834
2.6495
2.6033
2.5404
2.4550
2.3388
2.1807
1.9658
1.6735
1.2760
0.7353
36%
Present Value of Annuity of `1
32%
TABLE B (Cont.)
2.6977
2.6959
2.6934
2.6899
2.6852
2.6787
2.6698
2.6576
2.6409
2.6180
2.5867
2.5437
2.4849
2.4043
2.2939
2.1427
1.9355
1.6516
1.2627
0.7299
37%
2.6274
2.6258
2.6236
2.6206
2.6164
2.6106
2.6026
2.5916
2.5764
2.5555
2.5265
2.4866
2.4315
2.3555
2.2506
2.1058
1.9060
1.6302
1.2497
0.7246
38%
2.5606
2.5592
2.5573
2.5546
2.5509
2.5457
2.5386
2.5286
2.5148
2.4956
2.4689
2.4317
2.3801
2.3083
2.2086
2.0699
1.8772
1.6093
1.2370
0.7194
39%
2.4970
2.4958
2.4941
2.4918
2.4885
2.4839
2.4775
2.4685
2.4559
2.4383
2.4136
2.3790
2.3306
2.2628
2.1680
2.0352
1.8492
1.5889
1.2245
0.7143
40%
A1.6