Approaches on Firm Valuation 9781846636417, 9781846636400

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ISSN 0307-4358

Volume 33 Number 11 2007

Managerial Finance Approaches on firm valuation Guest Editors: Carlo Alberto Magni and Stefano Malagoli

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Managerial Finance

ISSN 0307-4358 Volume 33 Number 11 2007

Approaches on firm valuation Guest Editors Carlo Alberto Magni and Stefano Malagoli

Access this journal online _________________________

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Editorial advisory board___________________________

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The use of fuzzy logic and expert systems for rating and pricing firms: a new perspective on valuation Stefano Malagoli, Carlo Alberto Magni and Giovanni Mastroleo ________

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Valuing companies by cash flow discounting: ten methods and nine theories Pablo Ferna´ndez _______________________________________________

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Information transparency and valuation: can you value what you cannot see? Aswath Damodaran ____________________________________________

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Strategic options and firm value Lihui Lin and Nalin Kulatilaka ___________________________________

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Determinants of market reactions to goodwill write-off after SFAS 142 Mauro Bini and Chiara Della Bella ________________________________

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CONTENTS

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Editorial advisory board

EDITORIAL ADVISORY BOARD

Professor Kofi A. Amoateng NC Central University, Durham, USA

Professor Moses L. Pava Yeshiva University, New York, USA

Professor Felix Ayadi Jesse E. Jones School of Business, Texas Southern University, USA Professor Mohamed E. Bayou The University of Michigan-Dearborn, USA Dr Andre de Korvin University of Houston-Downtown, USA Dr Colin J. Dodds Saint Mary’s University, Halifax, Nova Scotia, Canada Professor John Doukas Old Dominion University, Norfolk, Virginia, USA

Professor George C. Philipatos The University of Tennessee, Knoxville, Tennessee, USA Professor David Rayome Northern Michigan University, USA Professor Alan Reinstein Wayne State University, Detroit, Michigan, USA Professor Ahmed Riahi-Belkaoui The University of Illinois at Chicago, USA Professor Mauricio Rodriguez Texas Christian University, Fort Worth, Texas, USA

Professor Uric Dufrene Indiana University Southeast, New Albany, Indiana, USA

Professor Salil K. Sarkar Henderson State University, Arkadelphia, Arkansas, USA

Professor Ali M. Fatemi De Paul University, Chicago, Illinois, USA

Professor Atul A. Saxena Mercer University, Georgia, USA

Professor Iftekhar Hasan New Jersey Institute of Technology, USA

Professor Philip H. Siegel Monmouth University, New Jersey, USA

Professor Suk H. Kim University of Detroit Mercy, Detroit, USA

Professor Kevin J. Sigler The University of North Carolina at Wilmington, USA

Professor John Leavins University of Houston-Downtown, USA Professor R. Charles Moyer Wake Forest University, Winston-Salem, North Carolina, USA

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Professor Gordon Wills International Management Centres, UK Professor Stephen A. Zeff Rice University, Texas, USA

Dr Khursheed Omer University of Houston-Downtown, USA

Managerial Finance Vol. 33 No. 11, 2007 p. 835 # Emerald Group Publishing Limited 0307-4358

The current issue and full text archive of this journal is available at www.emeraldinsight.com/0307-4358.htm

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The use of fuzzy logic and expert systems for rating and pricing firms

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A new perspective on valuation Stefano Malagoli and Carlo Alberto Magni Dipartimento di Economia Politica, Universita` di Modena e Reggio Emilia, Modena, Italy, and

Giovanni Mastroleo Universita` della Calabria, Cosenza, Italy Abstract Purpose – The purpose of the paper is to focus on the rating, ranking and valuing of firms. Design/methodology/approach – Fuzzy logic and expert systems are used in order to provide a score for the firm(s) under consideration, representing the firm value-creating power. Findings – The fuzzy expert system introduced is capable of dealing with both quantitative and qualitative variables and integrates financial, managerial and strategic variables. A sensitivity analysis corroborates the model. Research limitations/implications – The system is apt to rate and rank firms within a sector. Some regression analysis can lead to a determined price for the target firm. Practical implications – The expert system may be used by rating agencies for ranking firms, and by financial analysts and potential buyers to furnish a price for acquisition. Originality/value – The use of a fuzzy expert system for ranking firms within a sector and pricing firms is a first attempt at an alternative way of measuring performance and value. Keywords Organizations, Market value, Strategic evaluation, Fuzzy logic, Modelling Paper type Research paper

Managerial Finance Vol. 33 No. 11, 2007 pp. 836-852 # Emerald Group Publishing Limited 0307-4358 DOI 10.1108/03074350710823818

1. Introduction In this paper, we construct a formal model that takes into account the experience of the decision maker and combines logic and intuition to assess a firm’s ability to create value. The approach followed results in a method of rating and ranking firms, and (if an acquisition is under examination) a price for the target firm may be extracted. Furthermore, the model may be used to inform about the impact of a particular management’s decision on value creation or to compensate managers on the basis of their performance. The approach followed makes use of expert systems and fuzzy logic. An expert system is a tool meant for replicating the way of reasoning of one or more experts. Fuzzy logic is a cognitive framework that aims at formalizing the way human beings cognize the world and think about problems and situations and at formalizing qualitative and vague concepts. We think that the integration of expert systems and fuzzy logic for company valuation and, in general, for decision-making purposes represents a reliable methodology that could be appealing for managers, practitioners, analysts. The model proposed does not rest on simplistic assumptions (as often financial models do for mathematical tractability), it does not excessively simplify description of reality, it does not engage in complicated formalization and does not require advanced knowledge of mathematics, it is intuitive and comprehensible by any evaluator, it is extremely flexible (it can be changed by the evaluator), it is able to

handle both quantitative and qualitative variables, it is not restricted to a small number of variables (29 inputs are considered, but many more can be added). The evaluation derives from logical implications (‘‘if-then’’ rules). Implications are our natural cognitive tools so anyone can understand them and construct them. Our approach is just a first attempt to develop a new methodology for appraising firms and business units. We think that this path is fruitful when dealing with complex situations where a great number of value drivers must be taken into account, both qualitative and quantitative, and/or where explicit account of their interrelations must be taken for a better description and rationalization of the evaluation process. 2. Theoretical background The literature suggests that firms can derive a superior capability to create value from both the structure of the industry where the company operates (or intends to invest) and from its internal resources and core competencies. According to the StructureConduct-Performance paradigm the sources for creating a sustainable competitive advantage (Porter, 1985) have to be found in the industry structure, which determines the intensity of rivalry inside the competitive arena (Porter, 1980). These studies focus on how the structure of the sector influences firms’ strategic behavior and performance, starting from the idea that the supply and demand characteristics determine the nature of the competition (Pellicelli, 2002). An example of the use of some typical structural variables is given by the variable we call Power. This variable identifies the bargaining power of the target firm towards customers and suppliers and depends on two input variables: Customer Concentration and Supplier Concentration [1]. Power, in turn, affects (along with Processes Efficiency) the Operating Costs and (along with Product Quality) the Revenues. Further studies have postulated that firms can actually influence the industry structure’s evolution using a strategic conduct (strategic behavior) aimed at increasing their market power vis-a`-vis their rivals. Creating synergies and pre-empting competitors are typical strategies moves to this end (Vickers, 1985). In our model we take Synergies into consideration, which represent one of the three fundamental determinants of the target firm’s Rating (the other two are Equity Value and Additional Financial Value). We have decided to limit the determinants of Synergies to three input variables[2]: the presence in the target firm of complementary resources (Complementarities) and of resources and skills fundamental to compete in the specific industry (Consistency), and the Economies of Scale. We have not incorporated diversification as a determinant of Synergies, because too often the supposed purpose of reducing the risk of the business by investing in some anticyclical activity conceals some personal goals of the management not aligned with the shareholders’ interests (building empires). However, some empirical evidences showing that performance differences among firms inside the same sector were bigger than the ones among different sectors (Rumelt, 1991) can be considered as the call for a new theory. The Resource-based Theory changes the focus of the analysis, postulating that firms can derive a superior capability to create value principally from its ability to develop and exploit superior competencies and skills (Grant and Robert, 1995). The endowment of resources and capabilities are the primary sources of the firm’s profitability (Grant, 1991). In our model, we have not given priority to either of the two approach (Structural or Resource-based), believing that for building a sustainable competitive advantage it is important to consider both the structure of the industry and the resources and capabilities of the firm. Our model is therefore constructed on the assumption that it is

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equally important to identify the Strategic Assets and the Strategic Industry Factors (Amit and Schoemaker, 1993). Examples of strategic assets in our model are represented by Resources and Skills, Technology, (quality of) Management, which affect the Strategic Risk. The input Resources and Skills expresses the resources and skills owned by the target firm while Technology indicates the quality and degree of Technology present in the target firm. Both Technology and Resources and Skills have a double correlation in the model, because they also affect Product Quality, alongside the input Expenditure in Research and Development. (We are aware that a single variable can hardly express the complexity of a judgment relative to the Resources and Skills owned by the target firm and the degree of Technology, nevertheless we have decided to limit the numbers of variables to balance complexity and accuracy[3].). Additional Financial Value, one of the three fundamental building blocks of the model, identifies the financial value that could be created through an optimization of the capital structure of the target firm. The construction of the Additional Financial Value framework has been inspired by the Static trade-off approach which postulates the existence of an optimal capital structure. Due to this theory the management would move toward predetermined levels of capital structure and pay-out ratios (Myers, 1984). Additional Financial Value is affected by the Optimal (financial) Leverage, along with the Cost of Adjustment and the Current Leverage (the higher the difference between Current Leverage and Optimal Leverage, the higher the Additional Financial Value). While the latter are inputs, the Optimal Leverage is determined by both debt’s costs and benefits, also taking the need for future financial Flexibility into consideration. The debt’s benefits, for example, (Borrowing Benefits in the model) are determined by two drivers: Tax Rate and Separation. The variable Separation is a qualitative variable representative of the separation between management and shareholders and is positively correlated with Borrowing Benefits: the higher the separation, the higher the convenience of increasing (the) debt (other things equal). In fact, according to the theory of Agency Costs and Ownership Structure (Jensen and Meckling, 1976), debt should be used as a disciplinary device by the stockholders in order to control the management, avoiding cash slack and preventing management from investing in nonprofitable projects making a bad use of the excess cash (Stewart, 1991). One of the three determinants of the variable Borrowing Costs is the Bankruptcy Risk. The latter depends on the input variable Coverage Ratio (EBIT/Financial expenses), and on the Operating Risk: empirical studies confirm that the higher the operating margin volatility the higher the probability of distress, and therefore the lower the optimal financial leverage (e.g. Bradley et al., 1984). 3. Fuzzy logic and expert systems The way we cognize the world is vague and multivalued and fuzziness is often encountered in real life. In a business context, the sentence ‘‘the quality of this firm’s products is high’’ is always true at a certain degree (possibly a zero degree) as well as the sentence ‘‘the quality of this firm’s products is low’’ is always true at a certain degree (possibly zero). Fuzzy logic rests on the assumption that all things belong to a set at a certain degree (see Kosko, 1993), so the quality of a product always belongs to both the set of high-quality products and the set of low-quality products (to a certain degree), in the same sense a man always belongs to the set of old men at a certain degree (as well as to the set of young men at a certain degree). Also, variables such as quality of outputs, reputation, company image, employee morale, experience with new technology, consistency with corporate strategy, etc. may not be treated with the

classic ‘‘crisp’’ financial criteria and often are integrated in the decision process in a nonfinancial way or even neglected. Some other drivers have a direct financial impact but are not suited for mathematical tractability (at least not directly), e.g. financial Flexibility, bargaining power, customers’ loyalty, Synergies. In all these cases fuzzy logic may be used. Fuzzy logic enables us to formalize linguistic attributes such as ‘‘low’’, ‘‘high’’, ‘‘good’’, ‘‘excellent’’, ‘‘positive’’, ‘‘interesting’’, ‘‘fruitful’’, ‘‘adequate’’, and so on. For a single variable, more attributes may be used and graphically represented in the same graph. As an example, we describe the input Coverage Ratio[4] by using six linguistic attributes and the corresponding degrees: Coverage Ratio is then at one time VeryLow, Low, MediumLow, MediumHigh, High, VeryHigh. Graphically, we may represent these attributes through fuzzy numbers[5] as in Figure 1. The x-axis collects all possible numerical values for the Coverage Ratio, whose unit of measure is given by EBIT/ Financial Expenses. The y-axis collects the degrees at which a linguistic attribute is activated (membership degrees). The VeryLow attribute is represented by a trapezium (its basis ranges from 0 to 1.5) and the others are depicted as triangles (their bases range, respectively, from 1 to 2.5, from 1.5 to 5.5, from 2.5 to 8, from 8 to 9). For example, a Coverage Ratio of 1.25 is VeryLow at a degree of 80 per cent, Low at a degree of 20 per cent, MediumLow at a zero degree, MediumHigh at a zero degree, High at a zero degree, VeryHigh at a zero degree. A Coverage Ratio of 6.5 is VeryLow at a zero degree, Low at a zero degree, MediumLow at a zero degree, MediumHigh at a degree of 60 per cent, High at a degree of 40 per cent, VeryHigh at a zero degree[6]. In other words, once the decision maker fixes a value for Coverage Ratio, the latter is fuzzified (i.e. translated in fuzzy terms), and the corresponding fuzzy numbers is individuated by the pair (linguistic attribute, membership degree). The number of scientific contributions using fuzzy logic in business and finance has sharply increased in the recent past. Sugeno (1985), Tanaka (1997), Bojadziev and Bojadziev (1997) and Von Altrock (1997) show that fuzzy logic may be safely and usefully applied to business, financial, industrial applications. Zebda (1989, 1991) deals with vagueness and accounting. Abdel-Kader et al. (1998) cite a large number of nonquantifiable factors that firms consider important for investments’ decisions. Buckley et al. (2002) show economic and engineering applications of fuzzy mathematics. An expert system is a software addressed to achievements usually performed by a human expert. It consists of a knowledge base and an inferential engine. If a question is asked, the system will try to infer the answer from the knowledge base, using the logic and the heuristics of the inferential engine. The knowledge base must be represented in symbolic forms so as to be stocked and used by a computer. The most common method to this end is to use rule blocks. Fuzzy expert systems use fuzzy data, fuzzy rules and fuzzy inference, in addition to the standard ones implemented in the ordinary expert

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Figure 1.

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systems For example, a simple rule based on conditional (‘‘if-then’’) implications is the following: IF entry barriers are medium at a degree of x AND the prospective operating costs are low at a degree of y AND the prospective revenues are high at a degree of z

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THEN the prospective operating margin is high at a degree of w with x, y, z, w being real numbers in [0, 1]. If the system receives the piece of information provided by the above antecedent, it infers (using its inferential engine) the sentence ‘‘the prospective Operating Margin is high’’ and simultaneously provides a corresponding degree w that substantiates such a ‘‘high’’ value. The value of w is obtained through aggregation of the membership degrees x, y, z of the antecedent variables. To this end, fuzzy algorithms are used and automatically implemented by the expert system (see Von Altrock, 1997, for details). 4. The model Figure 2 shows that the target firm’s Rating is a function of three fundamental blocks: the stand-alone value (Equity Value), the additional value derived by the optimization of the capital structure (Additional Financial Value), the synergies realizable (Synergies). The first two provide an objective rating, the addition of the third one provides a subjective rating, which changes from investor to investor. These three variables are described by fuzzy numbers, i.e. by the pair (linguistic attribute, membership degree) as in the Coverage Ratio example. To determine the final Rating starting from the three variables, the expert system rests on a rule block containing ‘‘if-then’’ implications. Table I is an extract of such a rule block. The rule block is self-explaining. For example, row 16 says that if Additional Financial Value is High, and Equity Value is Low, and Synergies are VeryHigh, then Rating is High. Row 6 (where a blank space is left in the first column) is to be read as follows: whatever the value of Additional Financial Value, if Equity Value is VeryHigh and Synergies is High, then Rating is VeryHigh (as one may note, Rating, seen as a function of the three variables, is positively correlated to each of them: the greater one of the three, the greater the Rating). The rule block is composed by 113 rules and exhausts all possible cases, that is for each possible pair (linguistic attribute, membership degree) of the three variables we determine a corresponding pair for Rating. Therefore, Rating is described by a fuzzy number; but we need a ‘‘crisp’’ value, e.g. a normalized number in the interval [0, 1] giving us the value-creation power of the firm (the higher the Rating, the higher its capability to generate value). This step is accomplished by a defuzzification process (see Von Altrock, 1997, for details).

Figure 2.

Additional Financial Value

IF Equity Value

Synergies

THEN Rating

Zero Low MediumLow MediumHigh High

High High High High High VeryHigh VeryLow VeryLow VeryLow VeryLow VeryLow Low Low Low Low Low Medium Medium Medium Medium Medium High VeryHigh

High High High High High High VeryHigh VeryHigh VeryHigh VeryHigh VeryHigh VeryHigh VeryHigh VeryHigh VeryHigh VeryHigh VeryHigh VeryHigh VeryHigh VeryHigh VeryHigh VeryHigh VeryHigh

High High High VeryHigh VeryHigh VeryHigh MediumLow MediumLow Medium MediumHigh MediumHigh MediumLow Medium MediumHigh MediumHigh High MediumHigh MediumHigh High High VeryHigh VeryHigh VeryHigh

Zero Low MediumLow MediumHigh High Zero Low MediumLow MediumHigh High Zero Low MediumLow MediumHigh High

The three variables Equity Value, Additional Financial Value and Synergies are intermediate variables, as they depend in turn on other variables (through rule blocks of the kind above mentioned), which in turn depends on other variables and so on (see Appendix, Figures A1-A3). Take for example the Equity Value: it depends on Firm Value and Outstanding Debt. Firm Value is in turn affected by the Free Cash Flow to Firm[7], the Growth Rate and the Operating Risk. These three variables in turn depend on other variables and so on. Iterating backwards through all the intermediate variables of the system one finally gets to the very inputs of the system (the value drivers). The inputs are the starting points of the decision process: the decision maker just has to fix the appropriate values for each input, then the expert system fuzzifies the inputs and using the ‘‘if-then’’ rule blocks infers the Rating, which is then defuzzified in order to obtain a number in [0, 1], as seen. Our model incorporates 29 value drivers, 16 of them are qualitative, 13 of them are quantitative (see Appendix for description); there are 22 intermediate variables, 23 rule blocks and 730 fuzzy rules. It is worth noting that some variables affect more than one intermediate variables. For example, the Operating Risk is relevant not only for determining the Equity Value but also for computing the Additional Financial Value. In particular, it affects both the need for financial Flexibility and the Bankruptcy Risk. The same is true for the inputs Technology and Resources and Skills, as already seen. Any model needs corroboration. To this end, we have analyzed different scenarios and realized a sensitivity analysis by changing one or more inputs to verify if changes in the output are theoretically correct. Let us consider, for example, two firms with the inputs: shown in Table II which determine the following values for the intermediate

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Table I. Extract from the Rule Block ‘‘Rating’’

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Table II.

Acquisition Cost of adjustment Barriers Capital expenditures Competitive rivalry Consistency Coverage ratio Complementarities Current leverage Customer concentration Direct costs Economies of scale Expenditures in R&D Indirect costs Management Monitoring costs NonCash working cap Operating leverage Outstanding debt Price sensitivity Processes efficiency Reinvestment rate Resources and skills ROI Sensitivity to economy Separation Supplier concentration Tax rate Technology

Firm A

Firm B

0 0.1 0 0 0.05 0.4 9 0.4 0.1 0.1 0.1 0 0.8 0.4 0.8 0 0 0.1 0.1 0.1 0.8 0.1 1 0.16 0.1 1 0.1 0.6 1

0 1 0 0.8 0.5 0.7 4 0.7 0 0 0.1 0.7 0 0.4 0.8 0 0 0 0.3 0 0 0 1 0 0.7 0.5 0 0.2 0.5

variables (in alphabetical order) shown in Table III. This is so that the three fundamental blocks are valued as shown in Table IV. This which in turn determines the Rating shown in Table V. Firm A has a medium value-creation power, due to a low value of Synergies, a medium value of the stand-alone Equity Value and a very high Additional Financial Value. The low value of Synergies is due to Medium Low values of Consistency and Complementarities and nonexistent Economies of Scale. The medium value of equity is determined by a very low Outstanding Debt and a medium Firm Value. The latter is in turn determined by a low value for FCFF (which is so because even if the Operating Margin is not bad and there are no cash outputs for Reinvestment Needs, the Tax Rate is very high), medium values for growth expectations (derived from medium values of ROI and Reinvestment Rate)[8] and no Operating Risk (look at the very favorable values of the inputs affecting Business Risk, Specific Risk and Strategic Risk). As for Firm B, its Equity Value coincides with that of Firm A, because the higher value of Outstanding Debt is compensated by a slightly higher Firm Value (owing to the fact that Tax Rate is very low, Operating Margin is medium, but Reinvestment Needs are higher than in Firm A). Synergies for Firm B are significant (there are good values for the three inputs) so they are much higher than those of Firm B. However, the Additional Financial Value that may be reached with an Optimal Leverage is only medium for Firm B, especially because the cost of adjustment is very high. The net

Firm A

Firm B

0.4 0 1 0 0.05 0.25 0.5 0 0.5 0.133 0.5 0 1 0.5 1 0 0.667 0 0

0.4 0 0.25 0 0.5 0.5 0.55 0 0 0.667 0.5 0.125 0.833 1 0.5 0.333 0.667 0.167 0.133

Bankruptcy Cost Bankruptcy Risk Borrow Benefits Borrow Costs Business Risk FCFF Firm Value Needs for Flexibility Growth Operating Costs Operating Margin Operating Risk Optimal Leverage Power Product Quality Reinvestment Needs Revenues Specific Risk Strategic Risk

Firm A

Firm B

0.5 0.2 1

0.5 0.714 0.5

Equity Value Synergies Additional Financial Value

Rating

Firm A

Firm B

0.46

0.64

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Table III.

Table IV.

Table V.

effect is a higher Rating for Firm B, since Synergies for Firm A are so low that a higher Additional Financial Value is not able to compensate (and the Additional Financial Value for B is not so bad). Let us now take Firm A and consider favorable changes in the Economies of Scale, leaving other inputs unvaried. Owing to the importance of such a variable, we expect the Rating to increase. Our system complies with our expectations (Table VI). Raising from 0 to 1 the Economies of Scale, the Synergies considerably increase from 0.2 to 0.7 (while Equity and Additional Financial Value keep constant), and this reverberates on the Rating which increases from 0.46 to 0.8. Economies of Scale Synergies Rating

0 0.2 0.46

0.1 0.25 0.5

0.2 0.29 0.53

0.3 0.33 0.56

0.4 0.37 0.58

0.5 0.45 0.63

0.6 0.5 0.67

0.7 0.54 0.69

0.8 0.58 0.72

0.9 0.62 0.75

1 0.7 0.8

Table VI.

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Another simulation may be considered with Firm B. Let us check how the output changes as both Operating Leverage and Price Sensitivity changes from 0.3 to 1. A higher operating leverage means that a higher proportion of fixed costs determines an increase of Specific Risk. Likewise, if customers’ Price Sensitivity increases, customers are more likely to leave the product if price is not sufficiently low, so that the Specific Risk increases. Specific Risk affects both the Equity Value and the Additional Financial Value. In particular, we expect Equity Value to decrease, because increasing values of Specific Risk imply increasing values of Operating Risk and thus smaller values for Firm Value. The Additional Financial Value should also decrease in value, since a higher Specific Risk (and then Operating Risk) means a higher Bankruptcy Risk and therefore higher Borrowing Costs, which in turn entail a smaller Optimal Leverage (whereas Synergies is obviously untouched). As a result, the Rating should decrease. The system actually fulfills our expectations (See Table VII). (We have accomplished many other simulations, which seem to corroborate the model, but we omit them for reasons of space.) 5. From Rating to Price The value provided by the expert system is a normalized score in [0, 1]. This may be used for rating firms in a market or in a sector by a rating agency, by a financial analyst or by a decision maker willing to objectively score a class of firms with respect to their ability to generate value. As for rating agencies and financial analysts willing to rate firms so as to provide information to the market, they should fix a particular value for each input in each firm considered. An objective rating is independent of any particular potential buyer and aims at providing objective information about the firm. Because synergies have to do with beneficial interrelations between the target firm and the acquiring firm (which change from buyer to buyer) the evaluators should fix a value of zero for Consistency, Complementarities, Economies of Scale. If this is done, Synergies is nullified, i.e. it does not affect Rating, which then depends only on Additional Financial Value and Equity Value. Once all value drivers are fixed, the expert system automatically provides the final score. The firms rated can then be ranked by dividing them into classes according to their value-creation power (in the same sense as bonds are classified into risk classes). As an example, one may stipulate that firms in the interval [0, 0.2] have a very poor value-creation power, firms in the interval [0.2, 0.4] are mediocre, firms in the interval [0.4, 0.6] are medium, the interval [0.6, 0.8] is a sign of good value-creation power, [0.8, 1] is outstanding. This use of the model may provide investors in the market with helpful information. Periodic publications of firms’ rating will shed lights on the firm’s power of generating value in the future, thus helping investors to take more rational decisions. Also, this kind of rating could represent a tool which adds to the information provided by current rating agencies (bond rating) and financial analysts (multiples analysis). In this sense, the rating would inform whether a particular decision taken by the firm positively or negatively affects the value-creation power: if a particular decision results in a higher

Table VII.

Operating Leverage Price Sensitivity Equity Value Additional Financial Value Rating

0.3 0.3 0.5 0.5 0.64

0.37 0.37 0.5 0.5 0.64

0.44 0.44 0.5 0.43 0.63

0.51 0.51 0.49 0.37 0.59

0.58 0.58 0.45 0.32 0.54

0.65 0.65 0.41 0.32 0.53

0.72 0.72 0.39 0.32 0.52

0.79 0.79 0.35 0.32 0.49

0.86 0.86 0.33 0.32 0.48

0.93 0.93 0.29 0.32 0.46

1 1 0.25 0.32 0.42

Rating, this will turn into an increase of the firm’s value-creation power (beneficial to the shareholder); if Rating decreases, the public communication of this result will inform investors that the value is being destroyed. Further, in front of firms that are equally priced by the market, the expert system may be of some help to distinguish the one that generates more value (and to understand how that value is generated). If the evaluator is a decision maker willing to buy the firm (or some shares of the firm), it may be an individual or a company. In the former case the individual will act as just explained: Synergies will be nullified (there are no synergies for individuals). Conversely, in the latter case, Synergies will be taken into account; in particular, a specific value for Consistency, Complementarities, Economies of Scale should be selected to determine the value of Synergies, which now plays an important role: the value-creation power of the target firm increases with increasing values of Synergies. For example, even with a low value of both Equity Value and Additional Financial Value, Synergies is able to partially compensate if it is VeryHigh: in this case Rating is medium (see Table I). If a potential buyer intends to acquire the firm and needs to know the price at which the firm should be acquired, it is possible to convert the scoring provided by the expert system into a price. One of the possible methods to extract a price is to make use of regression analysis. As previously seen, the expert system we have constructed is conceptually and technically divided into three main blocks: Equity Value, Additional Financial Value and Synergies. It is possible to price each block separately and then sum the three shares to obtain the price an investor should pay for acquiring the firm. As for Equity Value the evaluator should comply with the following steps: (1) Choose a subclass of firms in the market that are regarded as fairly priced. (2) Isolate the value drivers that actively affect Equity Value: They are Tax Rate, Competition, Sensitivity to Economy, Operating Leverage, Price Sensitivity, Management, Reinvestment Rate, ROI, Acquisition, Capital Expenditures, NonCash Working Capital, Barriers, Processes Efficiency, Customer Concentration, Supplier Concentration, Expenditures in R&D, Resources and Skills, Technology. Fix the correct values for the firms at hand and compute, via expert system, the defuzzified Equity Value for each of these firms. (3) Associate to each Equity Value so obtained its Price/Earning ratio and plot the pairs (x, y) on an xy-plane, where x is the (defuzzified) Equity Value provided by the system and y is the Price/Earning ratio of the firm. (4) Run a (linear or quadratic) regression to infer the function y ¼ f(x) connecting Equity Value and the Price/Earning ratio. (5) Consider the target firm, compute its (defuzzified) Equity Value and put it in the analytic expression of the function as the independent variable. From the number obtained in step (5) one can get the money value of Equity, i.e. the maximum price any investor should be ready to pay in order to acquire the firm, leaving aside any consideration of synergies and assuming that capital structure remains unvaried. As for appraising the additional value due to optimal structure an analogous linear regression analysis can be conducted. The number obtained is the premium any investor should be ready to pay in order to acquire the firm, considering that an optimal financial leverage will be reached (leaving aside any consideration of synergies). As for the money value of synergies, the steps are similar and one gets the premium any investor should be ready to pay in order to acquire the firm (leaving aside

Fuzzy logic and expert systems

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any consideration about optimal structure). Summing the three values so obtained one finds the total money value of the acquisition for the potential buyer. That is the maximum price an investor should be ready to pay for the firm[9]. The price so obtained is already naturally decomposed into three components: one is the stand-alone value, another is the value added by an optimal structure, the third one is the value of the additional benefits due to synergies with the acquiring firm. The threefold partition provides additional information for the decision process: Firstly, it enables to distinguish an objective price (sum of the former two components) from a subjective price (sum of all components). Secondly, it furnishes a justification for the price, because each of the three components of the price of the firm is isolated (different firms resulting in equivalent prices may have different price decomposition). Thirdly, one may need to deduce not a total money value but a value for just one or two of the three dimensions for comparing firms on this basis. Moreover, managers themselves may be interested in knowing the money value of one or the other component of the firm, in order to take more rational decisions. 6. Managerial implications Our model is actually alternative to those existing in the literature and in practice, of which it is independent. Yet, one may be willing to use it in combination with other techniques (DCF, Real Options) in a ‘‘plurimethodological’’ approach. Unlike the standard valuation techniques, it gives a clear and clean sight on the determinants of value, specifying their relationships in an explicit and transparent way and using a rigorous formalization. The DCF approach for example shows a lack of transparency (it is not possible to understand the ‘‘background’’ of the decision process). In this sense, our approach can be particularly useful for managers and financial analysts whenever it is necessary to understand and justify a premium paid for an acquisition, to substantiate a price paid which leads to a high (or low) value of multiples, to justify managerial policies, etc. This model is therefore both an evaluation technique and a device for assessing the increase in value associated to particular decisions. Also, managers themselves may be motivated and compensated on the basis of how much they increase the value of the rating, so that the model can be used as a corporate governance tool. The class of subjects interested in the model is actually rather ample: rating agencies, financial analysts, investors (shareholders, bondholders), banks and managers. In particular, it may be used for: (1) rating listed or unlisted companies; (2) pricing firms; (3) decomposing rating and pricing into three driving factors (rating/pricing of Equity Value, rating/pricing of Synergies, rating/pricing of Additional Financial Value) for analysis purposes (two equally priced/rated firms may have very different decompositions); (4) rewarding and compensating managers; (5) evaluating and comparing business units of a firm; (6) measuring the impact of the firm’s possible policies and strategies on value creation; (7) evaluating the impact of particular decisions taken by managers on value creation;

(8) analyzing under- or overvaluation of a firm by the market; (9) helping decision makers in strategic decisions; and

Fuzzy logic and expert systems

(10) helping decision makers about selling or buying shares. 7. Conclusions Finance suggests that we need formal models for a better description and rationalization of the evaluation process, whereas business economics suggests that reality cannot be described by merely resting on mathematical models, complex in their application and simplified in their assumptions. Human intuition and experience are relevant in a decision process and individuals are highly tolerant for ambiguity (Isenberg, 1984). This paper proposes a model which seems to meet both requirements: we have a formal tool rationalizing the decision process and are, at the same time, able to fruitfully exploit human intuition and experience, overcoming difficulties in dealing with ambiguity. To this end, expert systems and fuzzy logic, combined together, seem to be an interesting tool for valuing firms[10]. The approach we offer is easy to understand and easy to implement, it does not require advanced knowledge of mathematics and does not make any particular assumption on the variables affecting the value of the option. The solution derives from logical implications (‘‘if-then’’ rules), so anyone can understand them and construct them. At the same time we have a formal model, which rationalizes the evaluation process and automatically gives the final value. Fuzzy logic seems to be a reliable tool for describing the value of a firm, since the complexity of real-life situations is handled through ‘‘vague’’ variables and ‘‘vague’’ interactions, which better replicate human mind as well as economic phenomena. Also, a fuzzy approach, unlike classical ones, seems to be capable of integrating qualitative and quantitative analysis, so that the model is not forced to limit its scope to numerical variables with well-specified units of measures but can handle any type of qualitative drivers. We are able to shape the problem so as to take explicit consideration of business, strategic, organizational, financial aspects. The system is extremely flexible, one can introduce many more value drivers and change in any moment the rules connecting drivers and intermediate variables. Notes 1. For a complete description of the value drivers used in our model see Appendix. 2. To reduce the complexity of the model we have not included the post merger costs which are often an important factor in an acquisition. Our expert system is flexible so that we can add other determinants (for example, the cultural matching between buyer and target firm). 3. Note that any input variable in our model can be the output of an accurate and deep propaedeutic study (and, possibly, the output of another expert system). 4. Coverage Ratio is to be considered as a random variable in a forward-looking perspective. 5. See Buckley et al. (2002), for a detailed introduction to fuzzy mathematics. 6. As for any value greater than nine, the system considers it VeryHigh at a degree of 100 per cent and the other linguistic attributes are activated at a zero degree. 7. A more rigorous term for what we mean is Capital Cash Flow (Ruback, 2002; Ferna`ndez, 2002). In our fuzzy perspective to use either term is a matter of convention.

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8. The fuzzy numbers we have used for ROI are such that a 16 per cent ROI is considered medium, but this judgment may change from sector to sector (the same holds for the other inputs). 9. For reasons of space, we may not concentrate on technical details such as how to infer useful data, how to select the relevant firms to run the regression, how to cope with cases where data are not available. 10. Magni et al. (2002) present a fuzzy expert system evaluating a real option. Magni et al. (2004) study a real-life firm acquisition with intrinsic options of abandon, growth and expansion. References Abdel-Kader, M.G., Dugdale, D. and Taylor, P. (1998), Investment Decisions in Advanced Manufacturing Technology: A Fuzzy Set Theory Approach, Ashgate Publishing, Aldershot. Amit, R. and Schoemaker, P.J.H. (1993), ‘‘Strategic assets and organizational rent’’, Strategic Management Journal, Vol. 14, pp. 33-46. Bojadziev, G. and Bojadziev, M. (1997), Fuzzy Logic for Business, Finance, and Management, World Scientific Publishing Co. Pte. Ltd, Singapore. Bradley, M., Gregg, A., Jarrel, G.A. and Kim, E.K. (1984), ‘‘On the existence of an optimal structure: theory and evidence’’, Journal of Finance, Vol. 39 No. 3, pp. 857-78. Buckley, J.J., Eslami, E. and Feuring, T. (2002), Fuzzy Mathematics in Economics and Engineering, Physica-Verlag, Heidelberg. Ferna´ndez, P. (2002), Valuation Methods and Shareholder Value Creation, Academic Press, San Diego, CA. Grant, R. (1991), ‘‘The resource-based theory of competitive advantage: implications for strategy formulation’’, California Management Review, Vol. 33 No. 3, pp. 114-35. Grant, R. and Robert, M. (1995), Contemporary Strategy Analysis: Concepts, Techniques, Applications, Blackwell, Oxford. Isenberg, D. (1984), ‘‘How senior managers think’’, Harvard Business Review, Vol. 62 No. 6, pp. 81-91. Jensen, M.C. and Meckling, W.H. (1976), ‘‘Theory of the firm: managerial behavior, agency costs and ownership structure’’, Journal of Financial Economics, Vol. 3 No. 4, Winter, pp. 305-60. Kosko, B. (1993), Fuzzy Thinking: The New Science of Fuzzy Logic, Hyperion, New York, NY. Magni, C.A., Mastroleo, G. and Facchinetti, G. (2002), ‘‘A fuzzy expert system for solving real option decision processes’’, Fuzzy Economic Review, Vol. VI No. 2, pp. 51-73. Magni, C.A., Mastroleo, G., Vignola, M. and Facchinetti, G. (2004), ‘‘Strategic options and expert systems: a fruitful marriage’’, Soft Computing, Vol. 8 No. 3, January, pp. 179-92. Myers, S.C. (1984), ‘‘The capital structure puzzle’’, Journal of Finance, Vol. 34 No. 3, pp. 575-92. Pellicelli, G. (2002), Strategia d’Impresa, Universita` Bocconi Editore, Milano. Porter, M.E. (1980), Competitive Strategy, The Free Press, New York, NY. Porter, M.E. (1985), Competitive Advantage, The Free Press, New York, NY. Ruback, R.S. (2002), ‘‘Capital cash flows: a simple approach to valuing risky cash flows’’, Financial Management, Vol. 31 No. 2, Summer, pp. 85-103. Rumelt, R. (1991), ‘‘How much does industry matter?’’, Strategic Management Journal, Vol. 12 No. 3, pp. 167-85. Stewart, G.B. (1991), The Quest for Value: The EVA Management Guide, HarperCollins Publishers, New York, NY. Sugeno, M. (Ed.) (1985), Industrial Application of Fuzzy Control, North-Holland, New York, NY.

Tanaka, K. (1997), An Introduction to Fuzzy Logic for Practical Applications, Springer-Verlag, New York, NY. Vickers, J. (1985), ‘‘Pre-empting patenting, joint ventures, and the persistence of oligopoly’’, International Journal of Industrial Organization, Vol. 3, pp. 261-73. Von Altrock, C. (1997), Fuzzy Logic and Neurofuzzy Applications in Business and Finance, Prentice-Hall, Englewood Cliffs, NJ. Zebda, A. (1989), ‘‘Fuzzy set theory and accounting’’, Journal of Accounting Literature, Vol. 8, pp. 76-105. Zebda, A. (1991), ‘‘The problem of ambiguity and vagueness in accounting’’, Behavioural Research in Accounting, Vol. 3, pp. 117-45. Further reading McNeil, D. and Freiberger, D. (1994), Fuzzy Logic, Touchstone-Simon & Schuster, New York, NY. Sloan, R.G. (1996), ‘‘Using earnings and free cash flow to evaluate corporate performance’’, Journal of Applied Corporate Finance, Vol. 9 No. 1, Spring, pp. 70-8. Sorensen, E.H. and Wiliamson, D.A. (1985), ‘‘Some evidence on the value of the dividend discount model’’, Financial Analysts Journal, Vol. 41, pp. 60-9. Zadeh, L.A. (1965), ‘‘Fuzzy sets’’, Information and Control, Vol. 8, pp. 338-53. Zimmermann H.J. (1996), Fuzzy Set Theory and its Applications, 3rd ed., Kluwer Academic Publishers, Boston, MA.

Appendix Value drivers Acquisition. The portion of capital expenditures represented by the target firm’s prospective external investments. This variable has been treated as a qualitative variable. Cost of Adjustment. The costs that the target firm has to sustain to pass from the current capital structure to the optimal one is treated as qualitative variable. Barriers. The entry barriers are treated as a qualitative variable. Capital Expenditures. The net capital expenditures include the fair adjustments for the capitalizations of R&D and of SG&A. One may use an average of the firm’s ratio NetCapitalExpenditures Revenues. Competitive Rivalry. This variable is considered as a typical qualitative variable. Complementarities. We use the term complementarities to identify resources and skills complementarities and market complementarities, considering the diseconomies derived from any kind of overlapping and cannibalization (qualitative variable). Consistency. The consistency between resources and skills owned by the firm and resources and skills needed to compete in the specific sector in which the firm operates (qualitative). Coverage Ratio. The ratio EBIT/Financial expenses represents a quick measure of financial rating of the target firm. Current Leverage. The current debt/equity ratio of the company. Customer Concentration. The ratio (average sales per client)/(total sales). Direct Costs. The procedure’s costs that have to be sustained in case of distress (qualitative). Economies of Scale. The economies of scale that the merger can grant. It is highly subjective and depends on the unique match between a specific buyer and the target firm (we treat it as a qualitative variable). Expenditures in R&D. Research and development expenses represent a capital expenditure. It is a quantitative variable but may be treated as a qualitative, in case monetary forecasts are not possible. Indirect Costs. Indirect costs of bankruptcy depend on the specific characteristics of the firm. This variable is qualitative. Management. The quality of management (qualitative).

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Figure A1.

Monitoring Costs. The costs that banks and bondholders have to sustain in order to control management’s activity. We treat it as a qualitative variable, due to the difficulties in quantifying these costs. NonCashWorkingCapital. Short-term investments in inventories and accounts receivable One may use an average of the firm’s ratio NonCashWorkingCapital/Revenues. Operating Leverage. The proportion of fixed costs on total costs.

Fuzzy logic and expert systems

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Figure A2.

Figure A3.

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Outstanding Debt. While we treat it as a qualitative variable in our model, one may directly use the market value of the outstanding debt, using the statistical distribution of debts’ values of the firms of the industry to define the linguistic attributes. Price Sensitivity. It expresses customers’ price sensitivity (qualitative). Processes Efficiency. A qualitative variable in our model, in some specific industry it is actually possible to find a quantitative measure identifying efficiency. Reinvestment Rate. The ratio (Capital Expenditures – depreciation þ
NonCashWorkingCapital)/[EBIT(1
t)]. Resources and Skills. Resources and skill owned by the target firm (qualitative). ROI. The ratio EBIT(1
t)/capital invested. Sensitivity to Economy. The sensitivity to macroeconomic factors is given by the unlevered beta of the industry. Separation. Separation between management and shareholder is a qualitative variable. Supplier Concentration. The ratio (average purchase cost of raw materials per supplier)/(total cost of raw materials’ purchases). Tax Rate. The marginal corporate tax rate. Technology. The quality and degree of technology owned by the firm (qualitative). Corresponding author Carlo Alberto Magni can be contacted at: [email protected]

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Valuing companies by cash flow discounting: ten methods and nine theories Pablo Ferna´ndez

Valuing by cash flow discounting

853

IESE Business School, University of Navarra, Madrid, Spain Abstract Purpose – The aim of this paper is to answer the question: Do discounted cash flows valuation methods provide always the same value? Design/methodology/approach – This paper is a summarized compendium of ten methods including: free cash flow; equity cash flow; capital cash flow; adjusted present value; business’s riskadjusted free cash flow and equity cash flow; risk-free rate-adjusted free cash flow and equity cash flow; economic profit; and economic value added. Findings – All ten methods always give the same value. Research limitations/implications – The disagreements among the various theories of firm valuation arise from the calculation of the value of the tax shields (VTS). The paper analyses nine different theories. Originality/value – The paper is an analysis of ten methods of company valuation using discounted cash flows and nine different theories about the VTS. Keywords Cash flow, Organizations, Discounted cash flow Paper type Conceptual paper

1. Introduction This paper is a summarized compendium of all the methods and theories on company valuation using discounted cash flows. Section 2 shows the ten most commonly used methods for valuing companies by discounted cash flows: (1) free cash flow discounted at the weighted average cost of capital (WACC); (2) equity cash flows discounted at the required return to equity; (3) capital cash flows discounted at the WACC before tax; (4) adjusted present value (APV); (5) the business’s risk-adjusted free cash flows discounted at the required return to assets; (6) the business’s risk-adjusted equity cash flows discounted at the required return to assets; (7) economic profit discounted at the required return to equity; (8) economic value added (EVA) discounted at the WACC;

The author thanks his colleagues Jose´ Manuel Campa and Charles Porter for their wonderful help in revising earlier manuscripts of this paper, and an anonymous referee for very helpful comments. He also thanks Rafael Termes and his colleagues at IESE for their sharp questions that encouraged him to explore valuation problems.

Managerial Finance Vol. 33 No. 11, 2007 pp. 853-876 # Emerald Group Publishing Limited 0307-4358 DOI 10.1108/03074350710823827

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(9) the risk-free rate-adjusted free cash flows discounted at the risk-free rate; and (10) the risk-free rate-adjusted equity cash flows discounted at the required return to assets. All ten methods always give the same value. This result is logical, since all the methods analyze the same reality under the same hypotheses; they differ only in the cash flows taken as the starting point for the valuation. In section 3 the ten methods and nine theories are applied to an example. The nine theories are: (1) No-cost-of-leverage. Assuming that there are no leverage costs. This theory appears in Ferna´ndez (2004a); (2) Damodaran (1994). To introduce leverage costs, Damodaran assumes that the relationship between the levered and unlevered beta is [1]:
L ¼
u þ D (1
T)
u/E; (3) Practitioners method. To introduce higher leverage costs, this method assumes that the relationship between the levered and unlevered beta is:
L ¼
u þ D
u/E; (4) Harris and Pringle (1985) and Ruback (1995). All of their equations arise from the assumption that the leverage-driven value creation or value of tax shields (VTS) is the present VTS [2] discounted at the required return to the unlevered equity (Ku). According to them, VTS ¼ PV[DKdT; Ku]; (5) Myers (1974), who assumes that the value of tax shields (VTS) is the present VTS discounted at the required return to debt (Kd). According to Myers: VTS ¼ PV½DKdT; Kd (6) Miles and Ezzell (1980). They state that the correct rate for discounting the tax shield (DKdT) is Kd for the first year, and Ku for the following years; (7) Miller (1977) concludes that the leverage-driven value creation or VTS is zero; (8) With-cost-of leverage. This theory assumes that the cost of leverage is the present value of the interest differential that the company pays over the riskfree rate; and (9) Modigliani and Miller (1963) calculate the VTS by discounting the present value of the tax savings due to interest payments of a risk-free debt (TDRF) at the risk-free rate (RF). Modigliani and Miller claim that: VTS ¼ PV½RF ; DTRF : Appendix 1 gives a brief overview of the most significant theories on discounted cash flow valuation. Appendix 2 contains the valuation equations according to these theories. Appendix 3 shows how the valuation equations change if the debt’s market value is not equal to its nominal value. Appendix 4 contains a list of the abbreviations used in the paper.

Valuing by cash flow discounting

2. Ten discounted cash flow methods for valuing companies There are four basic methods for valuing companies by discounted cash flows: Method 1. Using the free cash flow and the WACC Equation (1) indicates that the value of the debt (D) plus that of the shareholders’ equity (E) is the present value of the expected free cash flows (FCF) that the company will generate, discounted at the weighted average cost of debt and shareholders’ equity after tax (WACC): E0 þ D0 ¼ PV0 ½WACCt ; FCFt 

ð1Þ

The definition of WACC or ‘‘weighted average cost of capital’’ is given by equation (2): WACCt ¼

½Et
1 Ket þ Dt
1 Kdt ð1
TÞ ½Et
1 þ Dt
1 

ð2Þ

Ke is the required return to equity, Kd is the cost of the debt, and T is the effective tax rate applied to earnings. Et
1 þ Dt
1 are market values[3]. Method 2. Using the expected equity cash flow (ECF) and the required return to equity (Ke) Equation (3) indicates that the value of the equity (E) is the present value of the expected equity cash flows (ECF) discounted at the required return to equity (Ke): E0 ¼ PV0 ½Ket ; ECFt 

ð3Þ

Equation (4) indicates that the value of the debt (D) is the present value of the expected debt cash flows (CFd) discounted at the required return to debt (Kd): D0 ¼ PV0 ½Kdt ; CFdt 

ð4Þ

The expression that relates the FCF with the ECF is[4]: ECFt ¼ FCFt þ
Dt
It ð1
TÞ

ð5Þ


Dt is the increase in debt and It is the interest paid by the company. It is obvious that CFd ¼ It

Dt The sum of the values given by equations (3) and (4) is identical to the value provided by equation (1)[5]: E0 þ D0 ¼ PV0 ½WACCt ; FCFt  ¼ PV0 ½Ket ; ECFt  þ PV0 ½Kdt ; CFdt : Method 3. Using the capital cash flow (CCF) and the WACCBT (weighted average cost of capital, before tax) The capital cash flows[6] are the cash flows available for all holders of the company’s securities, whether these be debt or shares, and are equivalent to the ECF plus the cash flow corresponding to the debt holders (CFd). Equation (6) indicates that the value of the debt today (D) plus that of the shareholders’ equity (E) is equal to the capital cash flow (CCF) discounted at the weighted average cost of debt and shareholders’ equity before tax (WACCBT):

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856

ð6Þ

½Et
1 Ket þ Dt
1 Kdt  ½Et
1 þ Dt
1 

ð7Þ

The expression (7) is obtained by making equation (1) equal to equation (6). WACCBT represents the discount rate that ensures that the value of the company obtained using the two expressions is the same[7]: E0 þ D0 ¼ PV½WACCBTt ; CCFt  ¼ PV½WACCt ; FCFt  The expression that relates the CCF with the ECF and the FCF is equation (8): CCFt ¼ ECFt þ CFdt ¼ ECFt

Dt þ It ¼ FCFt þ It T
Dt ¼ Dt
Dt
1 ;

It ¼ Dt
1 Kdt

ð8Þ

Method 4. Adjusted present value (APV) The APV equation (9) indicates that the value of the debt (D) plus that of the shareholders’ equity (E) is equal to the value of the unlevered company’s shareholders’ equity, Vu, plus the present value of the value of the tax shield (VTS): E0 þ D0 ¼ Vu0 þ VTS0

ð9Þ

We can see in Appendixes 1 and 2 that there are several theories for calculating the VTS. If Ku is the required return to equity in the debt-free company (also called the required return to assets), Vu is given by equation (10): Vu0 ¼ PV0 ½Kut ; FCFt 

ð10Þ

Consequently: VTS0 ¼ E0 þ D0
Vu0 ¼ PV0 ½WACCt ; FCFt 
PV0 ½Kut ; FCFt  We can talk of a fifth method (using the business risk-adjusted free cash flow), although this is not actually a new method but is derived from the previous methods: Method 5. Using the business risk-adjusted free cash flow and Ku (required return to assets) Equation (11) indicates that the value of the debt (D) plus that of the shareholders’ equity (E) is the present value of the expected business risk-adjusted free cash flows (FCF\\Ku) that will be generated by the company, discounted at the required return to assets (Ku): E0 þ D0 ¼ PV0 ½Kut ; FCFt nnKu

ð11Þ

The definition of the business risk-adjusted free cash flows[8] (FCF\\Ku) is equation (12): FCFt nnKu ¼ FCFt
ðEt
1 þ Dt
1 Þ½WACCt
Kut 

ð12Þ

Likewise, we can talk of a sixth method (using the business risk-adjusted equity cash flow), although this is not actually a new method but is derived from the previous methods: Method 6. Using the business risk-adjusted equity cash flow and Ku (required return to assets) Equation (13) indicates that the value of the equity (E) is the present value of the expected business risk-adjusted equity cash flows (ECF\\Ku) discounted at the required return to assets (Ku): E0 ¼ PV0 ½Kut ; ECFt nnKu

ð13Þ

The definition of the business risk-adjusted equity cash flows [9] (ECF\\Ku) is equation (14): ECFt nnKu ¼ ECFt
Et
1 ½Ket
Kut 

ð14Þ

Method 7. Using the economic profit and Ke (required return to equity) Equation (15) indicates that the value of the equity (E) is the equity’s book value plus the present value of the expected economic profit (EP) discounted at the required return to equity (Ke): E0 ¼ Ebv0 þ PV0 ½Ket ; EPt 

ð15Þ

The term economic profit (EP) is used to define the accounting net income or profit after tax (PAT) less the equity’s book value (Ebvt
1) multiplied by the required return to equity: EPt ¼ PATt
KeEbvt
1

ð16Þ

Method 8. Using the EVA (economic value added) and the WACC (weighted average cost of capital) Equation (17) indicates that the value of the debt (D) plus that of the shareholders’ equity (E) is the book value of the shareholders’ equity and the debt (Ebv0 þ N0) plus the present value of the expected EVA, discounted at the weighted average cost of capital (WACC): E0 þ D0 ¼ ðEbv0 þ N0 Þ þ PV0 ½WACCt ; EVAt 

ð17Þ

The EVA is the Net Operating Profit After Tax (NOPAT) less the company’s book value (Dt
1 þ Ebvt
1) multiplied by the WACC. The NOPAT is the profit of the unlevered company (debt-free): EVAt ¼ NOPATt
ðDt
1 þ Ebvt
1 ÞWACCt

Valuing by cash flow discounting

ð18Þ

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Method 9. Using the risk-free-adjusted free cash flows discounted at the risk-free rate Equation (19) indicates that the value of the debt (D) plus that of the shareholders’ equity (E) is the present value of the expected risk-free-adjusted free cash flows (FCF\\ RF) that will be generated by the company, discounted at the risk-free rate (RF): E0 þ D0 ¼ PV0 ½RFt ; FCFt nnRF 

ð19Þ

The definition of the risk-free-adjusted free cash flows [10] (FCF\\RF) is equation (20): FCFt nnRF ¼ FCFt
ðEt
1 þ Dt
1 Þ½WACCt
RFt 

ð20Þ

Likewise, we can talk of a tenth method (using the risk-free-adjusted equity cash flow), although this is not actually a new method but is derived from the previous methods: Method 10. Using the risk-free-adjusted equity cash flows discounted at the risk-free rate Equation (21) indicates that the value of the equity (E) is the present value of the expected risk-free-adjusted equity cash flows (ECF\\RF) discounted at the risk-free rate (RF): E0 ¼ PV0 ½RFt ; ECFt nnRF 

ð21Þ

The definition of the risk-free-adjusted equity cash flows [11] (ECF\\RF) is equation (22): ECFt nnRF ¼ ECFt
Et
1 ½Ket
RFt 

ð22Þ

We could also talk of an 11th method; using the business risk-adjusted capital cash flow and Ku (required return to assets), but the business risk-adjusted capital cash flow is identical to the business risk-adjusted free cash flow (CCF\\Ku ¼ FCF\\Ku). Therefore, this method would be identical to Method 5. We could also talk of a 12th method; using the risk-free-adjusted capital cash flow and RF (risk-free rate), but the risk-free-adjusted capital cash flow is identical to the risk-free-adjusted free cash flow (CCF\\RF ¼ FCF\\RF). Therefore, this method would be identical to Method 9. 3. An example: valuation of the company Toro Inc. The company Toro Inc. has the balance sheet and income statement forecasts for the next few years shown in Table I. After year 3, the balance sheet and the income statement are expected to grow at an annual rate of 2 per cent. Using the balance sheet and income statement forecasts in Table I, we can readily obtain the cash flows given in Table II. Obviously, the cash flows grow at a rate of 2 per cent after year 4. The unlevered beta (
u) is one. The risk-free rate is 6 per cent. The cost of debt is 8 per cent. The corporate tax rate is 35 per cent. The market risk premium is 4 per cent. Consequently, using the CAPM, the required return to assets is 10 per cent[12]. With these parameters, the valuation of this company’s equity, using the above equations, is given in Table III. The required return to equity (Ke) appears in the second line of the table[13]. Equation (3) enables the value of the equity to be obtained by discounting the equity cash flows at the required return to equity (Ke)[14]. Likewise, equation (4)

0

1

2

3

4

5

Working capital requirements (WCR) Gross fixed assets Accumulated depreciation Net fixed assets Total assets

400 1,600 1,600 2,000

430 1,800 200 1,600 2,030

515 2,300 450 1,850 2,365

550 2,600 720 1,880 2,430

561.00 2,913.00 995.40 1,917.60 2,478.60

572.22 3,232.26 1,276.31 1,955.95 2,528

Debt (N) Equity (book value) Total liabilities

1,500 500 2,000

1,500 530 2,030

1,500 865 2,365

1,500 930 2,430

1,530.00 948.60 2,478.60

1,560.60 967.57 2,528

420 120 300 105 195

680 120 560 196 364

740 120 620 217 403

765.00 120.00 645.00 225.75 419.25

780 122 658 230.27 427.64

Income statement Margin Interest payments Profit before tax (PBT) Taxes PAT (profit after tax ¼ net income)

1 PAT (profit after tax) þ depreciation þ increase of debt
increase of working capital requirements
investment in fixed assets ECF FCF CFd CCF

195 200 0
30
200 165.00 243.00 120.00 285.00

2

3

4

5

364 250.00 0.00
85

403 270.00 0.00
35

419.25 275.40 30.00
11

427.64 280.91 30.60
11.22


500.00 29.00 107.00 120.00 149.00


300.00 338.00 416.00 120.00 458.00


313.00 400.65 448.65 90.00 490.65


319.26 408.66 457.62 91.80 500.46

enables the value of the debt to be obtained by discounting the debt cash flows at the required return to debt (Kd)[15]. Another way to calculate the value of the equity is using equation (1). The present value of the free cash flows discounted at the WACC (equation (2)) gives us the value of the company, which is the value of the debt plus that of the equity[16]. By subtracting the value of the debt from this quantity, we obtain the value of the equity. Another way of calculating the value of the equity is using equation (6). The present value of the capital cash flows discounted at the WACCBT (equation (7)) gives us the value of the company, which is the value of the debt plus that of the equity. By subtracting the value of the debt from this quantity, we obtain the value of the equity. The fourth method for calculating the value of the equity is using the APV, equation (9). The value of the company is the sum of the value of the unlevered company (equation (10)) plus the present value of the VTS[17]. The business risk-adjusted equity cash flow and free cash flow (ECF\\Ku and FCF\\Ku) are also calculated using equations (14) and (12). Equation (13) enables us to obtain the value of the equity by discounting the business risk-adjusted equity cash

Valuing by cash flow discounting

859

Table I. Balance sheet and income statement forecasts for Toro Inc.

Table II. Cash flow forecasts for Toro Inc.

MF 33,11

Equation

2

3

4

5

10.00% 10.00% 10.00% 10.00% 10.00% 10.00% 10.49% 10.46% 10.42% 10.41% 10.41% 10.41% 5,458.96 5,709.36 6,120.80 6,264.38 6,389.66 6,517.46 9.04% 9.08% 9.14% 9.16% 9.16% 9.16% 3,958.96 4,209.36 4,620.80 4,764.38 4,859.66 4,956.86

(3)

E ¼ PV(Ke; ECF)

3,958.96

4,209.36

4,620.80

4,764.38

4,859.66

4,956.86

(4)

D ¼ PV(CFd; Kd)

1,500.00

1,500.00

1,500.00

1,500.00

1,530.00

1,560.60

(6) (7)

D þ E ¼ PV(WACCBT; CCF) 5,458.96 5,709.36 6,120.80 6,264.38 6,389.66 6,517.46 WACCBT 9.81% 9.82% 9.83% 9.83% 9.83% 9.83% (6)
D ¼ E 3,958.96 4,209.36 4,620.80 4,764.38 4,859.66 4,956.86

(10) (9) (11) (12)

VTS ¼ PV(Ku; DT Ku) Vu ¼ PV(Ku; FCF) VTS þ Vu (9)
D ¼ E

623.61 4,835.35 5,458.96 3,958.96

633.47 5,075.89 5,709.36 4,209.36

644.32 5,476.48 6,120.80 4,620.80

656.25 5,608.12 6,264.37 4,764.37

669.38 5,720.29 6,389.66 4,859.66

682.76 5,834.69 6,517.46 4,956.86

D þ E ¼ PV(Ku; FCF\\Ku) FCF\\Ku (11)
D ¼ E

5,458.96

5,709.36 295.50 4,209.36

6,120.80 159.50 4,620.80

6,264.37 468.50 4,764.38

6,389.66 501.15 4,859.66

6,517.46 511.17 4,956.86

4,209.36 145.50

4,620.80 9.50

4,764.38 318.50

4,859.66 381.15

4,956.86 388.77

3,458.96 3,958.96

142.54 3,679.36 4,209.36

308.54 3,755.80 4,620.80

312.85 3,834.38 4,764.38

322.44 3,911.06 4,859.66

328.89 3,989.28 4,956.86

3,458.96 3,958.96

92.23 3,679.36 4,209.36

257.67 3,755.80 4,620.80

264.79 3,834.38 4,764.38

274.62 3,911.06 4,859.66

280.11 3,989.28 4,956.86

5,709.36 77.14 4,209.36

6,120.80
68.87 4,620.80

6,264.38 223.67 4,764.38

6,389.66 250.58 4,859.66

6,517.46 255.59 4,956.86

4,209.36
12.86

4,620.80
158.87

4,764.38 133.67

4,859.66 190.58

4,956.86 194.39

(13) (14)

E ¼ PV(Ku; ECF\\Ku) ECF\\Ku

(16)

EP PV(Ke; EP) PV(Ke; EP) þ Ebv ¼ E

(15) (18) (17) (19) (20)

Table III. Valuation of Toro Inc. No-cost-of-leverage

1

Ku Ke E þ D ¼ PV(WACC; FCF) WACC (1)
D ¼ E

(1) (2)

860

0

(21) (22)

EVA PV(WACC; EVA) E ¼ PV(WACC; EVA) þ Ebv þ N
D

3,958.96 3,958.96

D þ E ¼ PV(RF; FCF\\RF) FCF\\RF (19)
D ¼ E

5,458.96

E ¼ PV(RF; ECF\\RF) ECF\\RF

3,958.96

3,958.96

flows at the required return to assets (Ku). Another way to calculate the value of the equity is using equation (11). The present value of the business risk-adjusted free cash flows discounted at the required return to assets (Ku) gives us the value of the company, which is the value of the debt plus that of the equity. By subtracting the value of the debt from this quantity, we obtain the value of the equity. The economic profit (EP) is calculated using equation (16). Equation (15) indicates that the value of the equity (E) is the equity’s book value plus the present value of the expected economic profit (EP) discounted at the required return to equity (Ke). The EVA is calculated using equation (18). Equation (17) indicates that the equity value (E) is the present value of the expected EVA discounted at the WACC, plus the book value of the equity and the debt (Ebv0 þ N0) minus the value of the debt (D). The risk-free-adjusted equity cash flow and free cash flow (ECF\\RF and FCF\\RF) are also calculated using equations (22) and (20). Equation (21) enables us to obtain the value of the equity by discounting the risk-free-adjusted equity cash flows at the

risk-free rate (RF). Another way to calculate the value of the equity is using equation (19). The present value of the risk-free-adjusted free cash flows discounted at the required return to assets (RF) gives us the value of the company, which is the value of the debt plus that of the equity. By subtracting the value of the debt from this quantity, we obtain the value of the equity. Table III shows that the result obtained with all ten valuations is the same. The value of the equity today is 3,958.96. As we have already mentioned, these valuations have been performed according to the No-cost-of-leverage theory. The valuations performed using other theories are discussed further on. Tables IV to XI contain the most salient results of the valuation performed on the company Toro Inc. according to Damodaran (1994), Practitioners method, Harris and Pringle (1985), Myers (1974), Miles and Ezzell (1980), Miller (1977), With-cost-ofleverage theory, and Modigliani and Miller (1963). Table XII is a compendium of the valuations of Toro Inc. performed according to the nine theories. It can be seen that Modigliani and Miller gives the highest equity value (4,080.75) and Miller the lowest (3,335.35). Note that Modigliani and Miller and Myers yield a higher equity value than the No-cost-of-leverage theory. This result is inconsistent, as discussed in Ferna´ndez (2002). Table XIII is the valuation of Toro Inc. if the growth after year 3 were 5.6 per cent instead of 2 per cent. Modigliani and Miller and Myers provide a required return to equity (Ke) lower than the required return to unlevered equity (Ku ¼ 10 per cent), which is an inconsistent result because it does not make any economic sense.

Valuing by cash flow discounting

861

4. How is the company valued when it reports losses in one or more years? In such cases, we must calculate the tax rate that the company will pay, and this is the rate that must be used to perform all the calculations. It is as if the tax rate were the rate obtained after subtracting the taxes that the company must pay. Example. The company Campa S.A. reports a loss in year 1. The tax rate is 35 per cent. In year 1, it will not pay any tax as it has suffered losses amounting to 220 million. In year 0

1

2

3

4

5

391.98 398.18 405.00 412.50 420.75 429.16 VTS ¼ PV[Ku; DTKu
D(Kd
RF) (1
T)]
L 1.261581 1.245340 1.222528 1.215678 1.215678 1.215678 Ke 11.05 10.98 10.89 10.86 10.86 10.86 E 3,727.34 3,974.07 4,381.48 4,520.62 4,611.04 4,703.26 WACC WACCBT EþD

9.369 10.172 5,227.34

9.397 10.164 5,474.07

9.439 10.153 5,881.48

9.452 10.149 6,020.63

9.452 10.149 6,141.04

9.452 10.149 6,263.86

EVA EP

85.63 139.77

251.24 305.80

257.77 308.80

267.57 318.23

272.92 324.59

ECF\\Ku FCF\\Ku

126.00 276.00


10.00 140.00

299.00 449.00

361.65 481.65

368.88 491.28

ECF\\RF FCF\\RF


23.09 66.91


168.96
78.96

123.74 213.74

180.83 240.83

184.44 245.64

Table IV. Valuation of Toro Inc. according to Damodaran (1994)

MF 33,11

0 VTS ¼ PV[Ku; TD Kd
D(Kd
RF)]

862

Table V. Valuation of Toro Inc. according to the Practitioners method

142.54

144.79

2 147.27

3 150.00

4 153.00

5 156.06


L Ke E

1.431296 1.403152 1.363747 1.352268 1.352268 1.352268 11.73 11.61 11.45 11.41 11.41 11.41 3,477.89 3,720.68 4,123.75 4,258.13 4,343.29 4,430.15

WACC WACCBT EþD

9.759 10.603 4,977.89

9.770 10.575 5,220.68

9.787 10.533 5,623.75

9.792 10.521 5,758.13

9.792 10.521 5,873.29

9.792 10.521 5,990.75

EVA EP

77.82 136.37

243.67 302.45

249.55 303.91

259.31 313.15

264.50 319.41

ECF\\Ku FCF\\Ku

105.00 255.00


31.00 119.00

278.00 428.00

340.65 460.65

347.46 469.86

ECF\\RF FCF\\RF


34.12 55.88


179.83
89.83

113.05 203.05

170.33 230.33

173.73 234.93

0 VTS ¼ PV[Ku; TD Kd]
L Ke E

498.89

1 506.78

2 515.45

3 525.00

4 535.50

5 546.21

1.195606 1.183704 1.166966 1.161878 1.161878 1.161878 10.78 10.73 10.67 10.65 10.65 10.65 3,834.24 4,082.67 4,491.93 4,633.12 4,725.79 4,820.30

WACC 9.213 WACCBT ¼ Ku 10.000 EþD 5,334.24

Table VI. Valuation of Toro Inc. according to Harris and Pringle (1985) and Ruback (1995)

1

9.248 10.000 5,582.67

9.299 10.000 5,991.93

9.315 10.000 6,133.12

9.315 10.000 6,255.79

9.315 10.000 6,380.90

EVA EP

88.75 141.09

254.27 307.11

261.08 310.72

270.89 320.23

276.31 326.63

ECF\\Ku FCF\\Ku

135.00 285.00


1.00 149.00

308.00 458.00

370.65 490.65

378.06 500.46

ECF\\RF FCF\\RF


18.37 71.63


164.31
74.31

128.32 218.32

185.33 245.33

189.03 250.23

2, it will pay corporate tax amounting to 35 per cent of that year’s profit less the previous year’s losses (350-220). The resulting tax is 45.5, that is, 13 per cent of the EBT for year 2. Consequently, the effective tax rate is zero in year 1, 13 per cent in year 2, and 35 per cent in the other years. 5. Conclusion The paper shows the ten most commonly used methods for valuing companies by discounted cash flows always give the same value. This result is logical, since all the

0 VTS ¼ PV (Kd; DKdT)

1

663.92

2

675.03

3

687.04

4

700.00

714.00

5 728.28


L Ke E

1.104529 1.097034 1.087162 1.083193 1.083193 1.083193 10.42 10.39 10.35 10.33 10.33 10.33 3,999.27 4,250.92 4,663.51 4,808.13 4,904.29 5,002.37

WACC WACCBT EþD

8.995 9.759 5,499.27

9.035 9.765 5,750.92

9.096 9.777 6,163.51

9.112 9.778 6,308.12

9.112 9.778 6,434.29

9.112 9.778 6,562.97

EVA EP

93.10 142.91

258.59 308.94

265.89 313.48

275.82 323.16

281.34 329.62

ECF\\Ku FCF\\Ku

148.28 298.28

12.50 162.50

321.74 471.74

384.65 504.65

392.34 514.74

ECF\\RF FCF\\RF


11.69 78.31


157.54
67.54

135.20 225.20

192.33 252.33

196.17 257.37

3

4

0 VTS ¼ PV [Ku; TDKd] (1 þ Ku)/(1 þ Kd)

508.13

1 516.16

2 525.00

534.72

545.42

WACC WACCBT EþD

9.199% 9.985% 5,343.48

9.304% 9.987% 6,142.85

9.304% 9.987% 6,265.70

9.304% 9.987% 6,391.02

EVA EP

89.01 141.20

254.53 307.22

261.36 310.88

271.17 320.40

276.60 326.80

ECF\\Ku FCF\\Ku

135.78 285.78


0.22 149.78

308.78 458.78

371.43 491.43

378.86 501.26

ECF\\RF FCF\\RF


17.96 72.04


163.90
73.90

128.72 218.72

185.71 245.71

189.43 250.63

methods analyze the same reality under the same hypotheses; they differ only in the cash flows taken as the starting point for the valuation. The ten methods analyzed are: (1) free cash flow discounted at the WACC; (2) equity cash flows discounted at the required return to equity; (3) capital cash flows discounted at the WACC before tax; (4) APV (adjusted present value);

Table VII. Valuation of Toro Inc. according to Myers (1974)

556.33

1.190077 1.178530 1.162292 1.157351 1.157351 1.157351 10.76% 10.71% 10.65% 10.63% 10.63% 10.63 % 3,843.5 4,092.1 4,501.5 4,642.8 4,735.7 4,830.4 9.287% 9.987% 6,001.48

863

5


L Ke E

9.235% 9.986% 5,592.05

Valuing by cash flow discounting

Table VIII. Valuation of Toro Inc. according to Miles and Ezzell

MF 33,11

0 VTS ¼ 0
L Ke E ¼ Vu

864

Table IX. Valuation of Toro Inc. according to Miller

1

3

4

5

0 0 0 0 0 0 1.539673 1.503371 1.452662 1.438156 1.438156 1.438156 12.16% 12.01% 11.81% 11.75% 11.75% 11.75% 3,335.35 3,575.89 3,976.48 4,108.13 4,190.29 4,274.09

WACC ¼ Ku 10.000% WACCBT 10.869% EþD 4,835.35

10.000% 10.827% 5,075.89

10.000% 10.767% 5,476.48

10.000% 10.749% 5,608.13

10.000% 10.749% 5,720.29

10.000% 10.749% 5,834.69

EVA EP

73.00 134.21

239.00 300.33

244.50 300.84

254.25 309.95

259.34 316.15

ECF\\Ku FCF\\Ku

93.00 243.00


43.00 107.00

266.00 416.00

328.65 448.65

335.22 457.62

ECF\\RF FCF\\RF


40.41 49.59


186.04
96.04

106.94 196.94

164.33 224.33

167.61 228.81

0 VTS ¼ PV[Ku; D (KuT þ RF
Kd)]

Table X. Valuation of Toro Inc. according to the Withcost-of-leverage theory

2

267.26

1 271.49

2 276.14

3 281.25

4 286.88

5 292.61


L Ke E

1.343501 1.321648 1.290998 1.281931 1.281931 1.281931 11.37% 11.29% 11.16% 11.13% 11.13% 11.13% 3,602.61 3,847.38 4,252.61 4,389.38 4,477.16 4,566.71

WACC WACCBT EþD

9.559% 9.579% 10.382% 10.365% 5,102.61 5,347.38

9.609% 9.618% 9.618% 9.618% 10.339% 10.331% 10.331% 10.331% 5,752.61 5,889.38 6,007.16 6,127.31

EVA EP

81.82 138.13

247.54 304.18

253.75 306.43

263.53 315.76

268.80 322.08

ECF\\Ku FCF\\Ku

115.50 265.50


20.50 129.50

288.50 438.50

351.15 471.15

358.17 480.57

ECF\\RF FCF\\RF


28.60 61.40


174.40
84.40

118.40 208.40

175.58 235.58

179.09 240.29

(5) the business’s risk-adjusted free cash flows discounted at the required return to assets; (6) the business’s risk-adjusted equity cash flows discounted at the required return to assets; (7) economic profit discounted at the required return to equity; (8) EVA discounted at the WACC; (9) the risk-free rate-adjusted free cash flows discounted at the risk-free rate; and (10) the risk-free rate-adjusted equity cash flows discounted at the required return to assets.

0 VTS ¼ PV[RF; DRFT]

745.40

1 758.62

2 772.64

3 787.50

4 803.25

5 819.31


L Ke E

1.065454 1.058571 1.050506 1.045959 1.045959 1.045959 10.26% 10.23% 10.20% 10.18% 10.18% 10.18% 4,080.75 4,334.51 4,749.12 4,895.62 4,993.54 5,093.41

WACC WACCBT EþD

8.901% 9.654% 5,580.75

8.940% 9.660% 5,834.51

9.001% 9.673% 6,249.12

9.015% 9.672% 6,395.62

9.015% 9.672% 6,523.54

Valuing by cash flow discounting

865

9.015% 9.672% 6,654.01

EVA EP

94.97 143.69

260.52 309.76

268.12 314.75

278.19 324.54

283.75 331.03

ECF\\Ku FCF\\Ku

154.32 304.32

18.84 168.84

328.41 478.41

391.65 511.65

399.48 521.88

ECF\\RF FCF\\RF


8.91 81.09


154.54
64.54

138.44 228.44

195.83 255.83

199.74 260.94

(Value in t ¼ 0)

Equity value (E)

Value of tax shield (VTS)

Leverage cost

t ¼ 0 (%)

t ¼ 4 (%)

No-cost-of-leverage Damodaran Practitioners Harris and Pringle Myers Miles and Ezzell Miller With-cost-of-leverage Modigliani and Miller

3,958.96 3,727.34 3,477.89 3,834.24 3,999.27 3,843.48 3,335.35 3,602.61 4,080.75

623.61 391.98 142.54 498.89 663.92 508.13 0.00 267.26 745.40

0.00 231.63 481.07 124.72
40.31 115.48 623.61 356.35
121.79

10.49 11.05 11.73 10.78 10.42 10.76 12.16 11.37 10.26

10.41 10.86 11.41 10.65 10.33 10.63 11.75 11.13 10.18

(Value in t ¼ 0)

Equity value (E)

Value of tax shield (VTS)

Leverage cost

t ¼ 0 (%)

t ¼ 4 (%)

No-cost-of-leverage Damodaran Practitioners Harris and Pringle Myers Miles and Ezzell Miller With-cost-of-leverage Modigliani and Miller

6,615.67 6,234.21 5,823.40 6,410.27 7,086.10 6,425.48 5,588.66 6,028.81 12,284.86

1,027.01 645.55 234.75 821.61 1,497.44 836.83 0.00 440.15 6,696.20

0.00 381.46 792.27 205.40
470.43 190.19 1,027.01 586.87
5,669.19

10.29 10.63 11.03 10.47 10.00 10.45 11.29 10.82 8.15

10.23 10.50 10.81 10.37 9.94 10.36 11.01 10.65 8.17

Table XI. .

Valuation of Toro Inc. according to Modigliani and Miller

Ke

Table XII. Valuation of Toro Inc. according to the nine theories

Ke

Table XIII. Valuation of Toro Inc. according to the nine theories if growth after year 3 is 5.6 per cent instead of 2 per cent

MF 33,11

The paper also analyzes nine different theories on the calculation of the VTS, which implies nine different theories on the relationship between the levered and the unlevered beta, and nine different theories on the relationship between the required return to equity and the required return to assets. The nine theories analyzed are: (1) No-cost-of-leverage;

866

(2) Modigliani and Miller (1963); (3) Myers (1974); (4) Miller (1977); (5) Miles and Ezzell (1980); (6) Harris and Pringle (1985); (7) Damodaran (1994); (8) With-cost-of-leverage; and (9) Practitioners method. The disagreements among the various theories on the valuation of the firm arise from the calculation of the VTS. Using a simple example, we show that Modigliani and Miller (1963) and Myers (1974) provide inconsistent results. The paper contains the most important valuation equations according to these theories (Appendix 2, Table AII to Table AV) and also shows how the valuation equations change if the debt’s market value is not equal to its book value (Appendix 3, Table AVI and Table AVII). Notes 1. Instead of the relationship obtained from No-cost-of-leverage:
L ¼
u þ D(1
T) (
u

d)/E. 2. The tax shield of a given year is DKdT. D is the value of debt, Kd is the required return to debt, and T is the corporate tax rate. DKd are the interest paid in a given year. The formulas used in the paper are valid if the interest rate on the debt matches the required return to debt (Kd), or to put it another way, if the debt’s market value is identical to its book value. The formulas for when this is not the case are given in Appendix 3. 3. In actual fact, ‘‘market values’’ are the values obtained when the valuation is performed using formula (1). Consequently, the valuation is an iterative process: the free cash flows are discounted at the WACC to calculate the company’s value (D þ E) but, in order to obtain the WACC, we need to know the company’s value (D þ E). 4. Obviously, the free cash flow is the hypothetical equity cash flow when the company has no debt. 5. Indeed, one way of defining the WACC is: the WACC is the rate at which the FCF must be discounted so that equation (2) gives the same result as that given by the sum of equations (3) and (4). 6. Arditti and Levy (1977) suggested that the firm’s value could be calculated by discounting the capital cash flows instead of the free cash flow. 7. One way of defining the WACCBT is: the WACCBT is the rate at which the CCF must be discounted so that equation (6) gives the same result as that given by the sum of equations (3) and (4). 8. Expression (12) is obtained by making equation (11) equal to equation (1).

9. 10. 11. 12. 13. 14. 15.

16. 17.

18. 19. 20.

Expression (14) is obtained by making equation (13) equal to equation (3). Expression (20) is obtained by making equation (19) equal to equation (1). Expression (22) is obtained by making equation (21) equal to equation (3). In this example, we use the CAPM: Ku ¼ RF þ
uPM ¼ 6 per cent þ 4 per cent ¼ 10 per cent. The required return to equity (Ke) has been calculated according to the No-cost-ofleverage theory (see Appendix 1). The relationship between the value of the equity in two consecutive years is: Et ¼ Et
1 (1 þ Ket)
ECFt. The value of the debt is equal to the nominal value (book value) given in Table I because we have considered that the required return to debt is equal to its cost (8 per cent). The relationship between the company’s value in two consecutive years is: (D þ E)t ¼ (D þ E)t
1 (1 þ WACCt)
FCFt. As the required return to equity (Ke) has been calculated according to the No-cost-ofleverage theory, we must also calculate the VTS according to the No-cost-of-leverage theory, namely: VTS ¼ PV(Ku; DTKu). See Damodaran (1994, p. 31). One of the many places where it appears is Ruback (1995, p. 5). This formula can be completed with another parameter ’ that takes into account that the cost of leverage is not strictly proportional to debt. ’ should be lower for small leverage and higher for high leverage. Introducing this parameter, the value of tax shields is VTS ¼ PV [Ku; DT Ku
’D(Kd
RF)].

References Arditti, F.D. and Levy, H. (1977), ‘‘The weighted average cost of capital as a cutoff rate: a critical examination of the classical textbook weighted average’’, Financial Management, Fall, pp. 24-34. Copeland, T.E., Koller, T. and Murrin, J. (2000), Valuation: Measuring and Managing the Value of Companies, 3rd ed., Wiley, New York, NY. Damodaran, A. (1994), Damodaran on Valuation, John Wiley & Sons, New York, NY. Ferna´ndez, P. (2002), Valuation Methods and Shareholder Value Creation, Academic Press, Burlington, MA. Ferna´ndez, P. (2004a), ‘‘The value of tax shields is NOT equal to the present value of tax shields’’, Journal of Financial Economics, Vol. 73 No. 1, July, pp. 145-65. Ferna´ndez, P. (2004b), ‘‘The value of tax shields and the risk of the net increase of debt’’, SSRN working paper no. 506005, SSRN, New York, NY. Harris, R.S. and Pringle, J.J. (1985), ‘‘Risk-adjusted discount rates extensions form the averagerisk case’’, Journal of Financial Research, Fall, pp. 237-44. Inselbag, I. and Kaufold, H. (1997), ‘‘Two DCF approaches for valuing companies under alternative financing strategies (and how to choose between them)’’, Journal of Applied Corporate Finance, Spring, pp. 114-22. Kaplan, S. and Ruback, R. (1995), ‘‘The valuation of cash flow forecasts: an empirical analysis’’, Journal of Finance, Vol. 50 No. 4, September. Lewellen, W.G. and Emery, D.R. (1986), ‘‘Corporate debt management and the value of the firm’’, Journal of Financial Quantitative Analysis, December, pp. 415-26.

Valuing by cash flow discounting

867

MF 33,11

868

Luehrman, T.A. (1997), ‘‘What’s it worth? A general manager’s guide to valuation’’ and ‘‘Using APV: a better tool for valuing operations’’, Harvard Business Review, May-June, pp. 132-54. Miles, J.A. and Ezzell, J.R. (1980), ‘‘The weighted average cost of capital, perfect capital markets and project life: a clarification’’, Journal of Financial and Quantitative Analysis, September, pp. 719-30. Miller, M.H. (1977), ‘‘Debt and taxes’’, Journal of Finance, May, pp. 261-76. Modigliani, F. and Miller, M. (1958), ‘‘The cost of capital, corporation finance and the theory of investment’’, American Economic Review, Vol. 48, pp. 261-97. Modigliani, F. and Miller, M. (1963), ‘‘Corporate income taxes and the cost of capital: a correction’’, American Economic Review, June, pp. 433-43. Myers, S.C. (1974), ‘‘Interactions of corporate financing and investment decisions – implications for capital budgeting’’, Journal of Finance, March, pp. 1-25. Ruback, R.S. (1995), ‘‘A note on capital cash flow valuation’’, Harvard Business School Note 9-295069, Harvard Business School, Boston, MA. Tham, J. and Ve´lez-Pareja, I. (2001), ‘‘The correct discount rate for the tax shield: the N-period case’’, SSRN working paper, SSRN, New York, NY. Further reading Miles, J.A. and Ezzell, J.R. (1985), ‘‘Reequationing tax shield valuation: a note’’, Journal of Finance, Vol. XL No. 5, December, pp. 1485-92. Appendix 1. A brief overview of the most significant papers on the discounted cash flow valuation of firms There is a considerable body of literature on the discounted cash flow valuation of firms. We will now discuss the most salient papers, concentrating particularly on those that proposed different expressions for the present value of the tax savings due to the payment of interest or VTS. The main problem with most papers is that they consider the VTS as the present value of the tax savings due to the payment of interest. Ferna´ndez (2004a, b) argues and proves that the VTS is the difference between two present values: the present value of taxes paid by the unlevered firm and the present value of taxes paid by the levered firm. Modigliani and Miller (1958) studied the effect of leverage on the firm’s value. Their proposition 1 (1958, equation 3) states that, in the absence of taxes, the firm’s value is independent of its debt, i.e. E þ D ¼ Vu; if T ¼ 0

ð23Þ

E is the equity value, D is the debt value, Vu is the value of the unlevered company, and T is the tax rate. In the presence of taxes and for the case of a perpetuity, they calculate the VTS by discounting the present value of the tax savings due to interest payments on a risk-free debt (TDRF) at the risk-free rate (RF). Their first proposition, with taxes, is transformed into Modigliani and Miller (1963, p. 436, equation 3): E þ D ¼ Vu þ PV½RF ; DTRF  ¼ Vu þ DT

ð24Þ

DT is the VTS for perpetuity. This result is only correct for perpetuities. As Ferna´ndez (2004a) demonstrates, discounting the tax savings due to interest payments on a risk-free debt at the risk-free rate provides inconsistent results for growing companies. We have seen this in Table XIII. Myers (1974) introduced the APV. According to Myers, the value of the levered firm is equal to the value of the firm with no debt (Vu) plus the present value of the tax saving due to the

payment of interest (VTS). Myers proposes calculating the VTS by discounting the tax savings (DTKd) at the cost of debt (Kd). The argument is that the risk of the tax saving arising from the use of debt is the same as the risk of the debt. Therefore, according to Myers (1974): VTS ¼ PV½Kd; DTKd

ð25Þ

Luehrman (1997) recommends valuing companies using the APV and calculates the VTS in the same way as Myers. This theory yields inconsistent results for growing companies, as shown in Ferna´ndez (2004a). Ferna´ndez (2004b) shows that this theory yields consistent results only if the company will not increase its debt. Miller (1977) assumes no advantages of debt financing: ‘‘I argue that even in a world in which interest payments are fully deductible in computing corporate income taxes, the value of the firm, in equilibrium, will still be independent of its capital structure’’. According to Miller (1977), the value of the firm is independent of its capital structure, that is: VTS ¼ 0

ð26Þ

According to Miles and Ezzell (1980), a firm that wishes to keep a constant D/E ratio must be valued in a different manner from a firm that has a preset level of debt. For a firm with a fixed debt target [D/(D þ E)], they claim that the correct rate for discounting the tax saving due to debt (KdTDt
1) is Kd for the tax saving during the first year, and Ku for the tax saving during the following years. The expression of Ke is their equation (22): Ke ¼

Ku þ DðKu
KdÞ½1 þ Kdð1
TÞ ½ð1 þ KdÞE

ð27Þ

Although Miles and Ezzell do not mention what the VTS should be, equation (27) relating the required return to equity with the required return for the unlevered company implies that: VTS ¼

PV½Ku; TDKdð1 þ KuÞ ð1 þ KdÞ

ð28Þ

Lewellen and Emery (1986) also claim that the most logically consistent method is Miles and Ezzell. Harris and Pringle (1985) propose that the present value of the tax saving due to the payment of interest (VTS) should be calculated by discounting the tax saving due to the debt (KdTD) at the rate Ku. Their argument is that the interest tax shields have the same systematic risk as the firm’s underlying cash flows and, therefore, should be discounted at the required return to assets (Ku). Therefore, according to Harris and Pringle (1985): VTS ¼ PV½Ku; DKdT

Valuing by cash flow discounting

ð29Þ

Harris and Pringle (1985, p. 242) say ‘‘the MM position is considered too extreme by some because it implies that interest tax shields are no more risky than the interest payments themselves. The Miller position is too extreme for some because it implies that debt cannot benefit the firm at all. Thus, if the truth about the VTS lies somewhere between the MM and Miller positions, a supporter of either Harris and Pringle or Miles and Ezzell can take comfort in the fact that both produce a result for unlevered returns between those of MM and Miller. A virtue of Harris and Pringle compared to Miles and Ezzell is its simplicity and straightforward intuitive explanation’’. Ruback (1995) reaches equations that are identical to those of Harris and Pringle (1985). Kaplan and Ruback (1995) also calculate the VTS ‘‘discounting interest tax shields at the discount rate for an all-equity firm’’. Tham and Ve´lez-Pareja (2001), following an arbitrage argument, also claim that the appropriate discount rate for the tax shield is Ku, the required

869

MF 33,11

870

return to unlevered equity. Ferna´ndez (2002) shows that Harris and Pringle (1985) provide inconsistent results. Damodaran (1994, p. 31) argues that if all the business risk is borne by the equity, then the equation relating the levered beta (
L) to the asset beta (
u) is:
 D
uð1
TÞ ð30Þ
L ¼
u þ E It is important to note that equation (30) is exactly equation (22) assuming that
d ¼ 0. One interpretation of this assumption is that ‘‘all of the firm’s risk is borne by the stockholders (i.e. the beta of the debt is zero)’’[18]. However, we think that it is difficult to justify that the debt has no risk (unless the cost of debt is the risk-free rate) and that the return on the debt is uncorrelated with the return on assets of the firm. We rather interpret equation (30) as an attempt to introduce some leverage cost in the valuation: for a given risk of the assets (
u), by using equation (30) we obtain a higher
L (and consequently a higher Ke and a lower equity value) than with equation (22). Equation (30) appears in many finance books and is used by some consultants and investment banks. Although Damodaran does not mention what the VTS should be, his equation (30) relating the levered beta to the asset beta implies that the VTS is: VTS ¼ PV½Ku; DTKu
DðKd
RF Þð1
TÞ Another way of calculating the levered beta with respect to the asset beta is the following:
 1þD
L ¼
u E

ð31Þ

ð32Þ

We will call this method the Practitioners’ method, because consultants and investment banks often use it[19]. It is obvious that according to this equation, given the same value for
u, a higher
L (and a higher Ke and a lower equity value) is obtained than according to equation (22) and (30). One should notice that equation (32) is equal to equation (30) eliminating the (1
T) term. We interpret equation (32) as an attempt to introduce still higher leverage cost in the valuation: for a given risk of the assets (
u), by using equation (32) we obtain a higher
L (and consequently a higher Ke and a lower equity value) than with equation (30). Equation (32) relating the levered beta with the asset beta implies that the VTS is: VTS ¼ PV½Ku; DTKd
DðKd
RF Þ

ð33Þ

By comparing equations (33) to (31) it can be seen that (33) provides a VTS, that is, PV[Ku; DT(Ku
RF)] lower than equation (31). We interpret this difference as additional leverage cost (on top of the leverage cost of Damodaran) introduced in the valuation. Inselbag and Kaufold (1997) argue that if the firm targets the dollar values of debt outstanding, the VTS is given by Myers (1974) equation. However, if the firm targets a constant debt/value ratio, the VTS is given by Miles and Ezzell (1980) equation. Copeland et al. (2000) treat the APV in their Appendix A. They only mention perpetuities and only propose two ways of calculating the VTS: Harris and Pringle (1985) and Myers (1974). They conclude ‘‘we leave it to the reader’s judgment to decide which approach best fits his or her situation’’. They also claim that ‘‘the finance literature does not provide a clear answer about which discount rate for the tax benefit of interest is theoretically correct’’. It is quite interesting to note that Copeland et al. (2000, p. 483) only suggest Inselbag and Kaufold (1997) as additional reading on APV. We will consider two additional theories to calculate the VTS. We label these two theories Nocosts-of-leverage and With-costs-of-leverage. We label the first theory the No-costs-of-leverage equation because, as may be seen in Ferna´ndez (2004a), it is the only equation that provides consistent results when there are no

leverage costs. According to this theory, the VTS is the present value of DTKu (not the interest tax shield) discounted at the unlevered cost of equity (Ku):

Valuing by cash flow discounting

ð34Þ

PV½Ku; DTKu

Equation (34) is the result of considering that the VTS is the difference between two present values: the present value of taxes paid by the unlevered firm and the present value of taxes paid by the levered firm. It can be seen in Ferna´ndez (2004a). Comparing equations (31) to (34), it can be seen that equation (31) provides a VTS, that is, PV[Ku; D(Kd
RF) (1
T)] lower than equation (34). We interpret this difference as leverage cost introduced in the valuation by Damodaran. Comparing equations (33) to (34), it can be seen that equation (33) provides a VTS, that is, PV[Ku; DT(Ku
Kd) þ D(Kd
RF)] lower than equation (34). We interpret this difference as leverage cost introduced in the valuation by the Practitioners’ method. Ferna´ndez (2004b) shows that only two of them are correct:

871

(1) If the company expects to increase its debt, the VTS is the present value of DKuT discounted at the required return to unlevered equity (Ku): VTS ¼ PV [DKuT; Ku]. See Ferna´ndez (2004a). (2) If the company will not increase its debt, the VTS is: PV[DTKd; Kd]. See Myers (1974). With-costs-of-leverage. This theory provides another way of quantifying the VTS: VTS ¼ PV½Ku; DKuT
DðKd
RF Þ

ð35Þ

One way of interpreting equation (35) is that the leverage costs (with respect to equation (34)) are proportional to the amount of debt and to the difference between the required return on debt and the risk-free rate[20]. By comparing equations (35) to (34), it can be seen that equation (40) provides a VTS, that is, PV[Ku; D(Kd
RF)] lower than equation (34). We interpret this difference as leverage cost introduced in the valuation. Table AI provides a synthesis of the nine theories about the VTS applied to level perpetuities. Theories

Equation

VTS

1

No-costs-of-leverage

(34)

DT DT
½DðKd
RF Þð1
TÞ Ku D½RF
Kdð1
TÞ Ku TDKd Ku

2

Damodaran

(31)

3

Practitioners

(33)

4

Harris and Pringle

(29)

5

Myers

(25)

DT

6

Miles and Ezzell

(28)

TDKdð1 þ KuÞ ½ð1 þ KdÞKu

7

Miller (1977)

(26)

0

8

With-costs-of-leverage

(35)

DðKuT þ RF
KdÞ Ku

9

Modigliani and Miller

(24)

DT

Table AI. Perpetuities: value of tax shields (VTS) according to the nine theories

MF 33,11

Appendix 2. Valuation equations according to the main theories when the debt’s market value (D) is equal to its nominal value (N) Equations common to all methods: WACCt ¼

872

Et
1 Ket þ Dt
1 Kdt ð1
TÞ Et
1 þ Dt
1

WACCBTt ¼

Et
1 Ket þ Dt
1 Kdt Et
1 þ Dt
1

Relationships between cash flows: ECFt ¼ FCFt þ ðDt
Dt
1 Þ
Dt
1 Kdt ð1
TÞ CCFt ¼ FCFt þ Dt
1 Kdt T CCFt ¼ ECFt
ðDt
Dt
1 Þ þ Dt
1 Kdt Cash flows\\Ku: FCFnnKu ¼ FCFt
ðEt
1 þ Dt
1 ÞðWACCt ECFnnKu ¼ ECFt
Et
1 ðKet
Kut Þ
Kut Þ ¼ CCFnnKu ¼ CCFt
ðEt
1 þ Dt
1 ÞðWACCBTt
Kut Þ Cash flows\\ RF: ECFnnRF ¼ ECFt
Et
1 ðKet
RFt Þ FCFnnRF ¼ FCFt
ðEt
1 þ Dt
1 ÞðWACCt
RFt Þ ¼ CCFnnRF ¼ CCFt
ðEt
1 þ Dt
1 ÞðWACCBTt
RFt Þ ECFnnRF ¼ ECFnnKu
Et
1 ðKut
RFt Þ FCFnnRF ¼ FCFnnKu
ðEt
1 þ Dt
1 ÞðKut
RFt Þ FCFnnKu
ECFnnKu ¼ Dt
1 Kut
ðDt
Dt
1 Þ FCFnnRF
ECFnnRF ¼ Dt
1 RFt
ðDt
Dt
1 Þ

No-cost-of-leverage

Damodaran (1994)

Dð1
TÞ ðKu
KdÞ E Dð1
TÞ
L ¼
u þ ð
u

dÞ E
 Ku 1
DT E þD DTðKu
KdÞ Ku
E þD

Dð1
TÞ ðKu
RF Þ E Dð1
TÞ
L ¼
u þ
u E
 ðKd
RF Þð1
TÞ Ku 1
DT þD EþD E þD TðKu
RF Þ
ðKd
RF Þ Ku
D E þD

VTS

PV[Ku; DTKu]

PV[Ku; DTKu
D(Kd
RF)(1
T)]

ECFt\\Ku

ECFt
Dt
1(Kut
Kdt) (1
T)

ECFt
Dt
1(Ku
RF)(1
T)

FCFt\\Ku

FCFt þ Dt
1KutT

FCFt þ Dt
1KuT
Dt
1 (Kd
RF)(1
T)

ECFt\\RF

ECFt
Dt
1(Kut
Kdt) (1
T)
Et
1(Kut
RFt)

ECFt
Dt
1(Ku
RF ) (1
T)
Et
1(Kut
RFt)

FCFt\\RF

FCFt þ Dt
1KutT
(Et
1 þ Dt
1)(Kut
RFt)

FCFt þ Dt
1KuT
Dt
1(Kd
RF)(1
T)
(Et
1 þ Dt
1)(Kut
RFt)

Ke ßL WACC WACCBT

Table AII.

Ke ¼ Ku þ

Ke ¼ Ku þ

Appendix 3. Valuation equations according to the main theories when the debt’s market value (D) is not equal to its nominal or book value (N) This Appendix contains the expressions of the basic methods for valuing companies by discounted cash flows when the debt’s market value (D) is not equal to its nominal value (N). If the debt’s market value (D) is not equal to its nominal value (N), it is because the required return to debt (Kd) is different from the cost of the debt (r). The interest paid in a period t is: It ¼ Nt
1rt. The increase in debt in period t is:
Nt ¼ Nt
Nt
1. Consequently, the debt cash flow in period t is: CFd ¼ It

Nt ¼ Nt
1 rt
(Nt
Nt
1). Consequently, the value of the debt at t ¼ 0 is: D0 ¼

1 X Nt
1 rt
ðNt
Nt
1 Þ Qt t¼1 1 ð1 þ Kdt Þ

It is easy to show that the relationship between the debt’s market value (D) and its nominal value (N) is: Dt
Dt
1 ¼ Nt
Nt
1 þ Dt
1 Kdt
Nt
1 rt Consequently:
Dt ¼
Nt þ Dt
1 Kdt
Nt
1 rt The fact that the debt’s market value (D) is not equal to its nominal value (N) affects several equations given in section 1 of this paper. Equations (1, 3, 4, 6, 7, 9, 10) continue to be valid, but the other equations change. The expression of the WACC in this case is: WACC ¼

EKe þ DKd
NrT E þD

ð36Þ

The expression relating the ECF to the FCF is: ECFt ¼ FCFt þ ðNt
Nt
1 Þ
Nt
1 rt ð1
TÞ

ð37Þ

The expression relating the CCF to the ECF and the FCF is: CCFt ¼ ECFt þ CFdt ¼ ECFt
ðNt
Nt
1 Þ þ Nt
1 rt ¼ FCFt þ Nt
1 rt T Equations common to all the methods: WACC and WACCBT: WACCt ¼ WACCBTt

Et
1 Ket þ Dt
1 Kdt
Nt
1 rt T ðEt
1 þ Dt
1 Þ Nt
1 rt T
WACCt ¼ ðEt
1 þ Dt
1 Þ

WACCBTt ¼

Et
1 Ket þ Dt
1 Kdt ðEt
1 þ Dt
1 Þ

Relationships between the cash flows: ECFt ¼ FCFt þ ðNt
Nt
1 Þ
Nt
1 rt ð1
TÞ CCFt ¼ ECFt
ðNt
Nt
1 Þ þ Nt
1 rt

CCFt ¼ FCFt þ Nt
1 rt T

ð38Þ

Valuing by cash flow discounting

873

MF 33,11

Harris-Pringle (1985); Ruback (1995)

Myers (1974)

Miles and Ezzell (1980)

Ke

Ke ¼ Ku þ D ðKu
KdÞ E

Ke ¼ Ku þ Vu
E ðKu
KdÞ E

D Ke ¼ Ku þ ðKu
KdÞ  E  TKd  1
1 þ Kd

ßL


L ¼
u þ D ð
u

dÞ E


L ¼
u þ Vu
E ð
u

dÞ E

D
L ¼
u þ
u

dÞ  E  TKd  1
1 þ Kd

WACC

Ku
DKdT E þD

VTSðKu
KdÞ þ DKdT Ku
D KdT 1 þ Ku E þ D 1 þ d0 E þD VTSðKu
KdÞ ðKu
KdÞ Ku
Ku
D KdT E þ D ð1 þ Kd0 Þ E þD ð1 þ KuÞ PV[Kd; TDKd] PV½Ku; TDKd ð1 þ KdÞ ECFt
(Vu
E) (Kut
Kdt) ECF
DðKu
KdÞ

874

WACCBT Ku VTS

PV[Ku; TDKd]

ECFt\\Ku ECFt
Dt
1(Kut
Kdt)

Ku


1 þ Kdð1
TÞ ð1 þ Kd0 Þ ð1 þ KuÞ FCF þ TDKd ð1 þ KdÞ 

FCFt\\Ku FCFt þ TDt
1Kdt ECFt\\RF ECFt
Dt
1 (Kut
Kdt)
Et
1(Kut
RFt)

FCFt\\RF

FCFt
TDKd þ VTS  ðKu
KdÞ ECFt
(Vu
E) (Kut
Kdt)
Et
1 (Kut
RFt)

FCFt þ TDKd þ VTS ðKu
KdÞ
ðEt
1 þ Dt
1 Þ FCFt þ TDt
1Kdt
(Et
1 þ Dt
1)(Kut
RFt)  ðKu
R Þ t Ft

Table AIII.

Ke ßL WACC WACCBT VTS ECFt\\Ku FCFt\\Ku ECFt\\RF FCFt\\RF Table AIV.

ECF
DðKu
KdÞ 1 þ Kdð1
TÞ  ð1 þ Kd0 Þ
Et
1 ðKut
RFt Þ ð1 þ KuÞ ð1 þ KdÞ
ðEt
1 þ Dt
1 Þ ðKut
RFt Þ

FCF þ TDKd

Miller

With-cost-of-leverage

Ke ¼ Ku þ D ½Ku
Kdð1
TÞ E
L ¼
u þ D ð
u

dÞ þ D TKd E E PM Ku

Ke ¼ Ku þ D ½Kuð1
TÞ þ KdT
RF  E
L ¼
u þ D ½ð
uð1
TÞ
T
dÞ E DðKuT
Kd þ RF Þ Ku
EþD

Ku þ DKdT E þD 0 ECFt
Dt
1 [Kut
Kdt(1
T)] FCFt ECFt
Dt
1 [Kut
Kdt(1
T)]
Et
1(Kut
RFt) FCFt
(Et
1 þ Dt
1)(Kut
RFt)

D½ðKu
KdÞT þ RF
KdÞ Ku
E þD PV[Ku; D(KuT þ RF
Kd)] ECFt
Dt
1 [Kut(1
T) þ KdtT
RFt] FCFt þ Dt
1 [KutT
Kdt þ RFt] ECFt
Dt
1 [Kut(1
T) þ KdtT
RFt]
Et
1 (Kut
RFt) FCFt þ Dt
1 [KutT
Kdt þ RFt]
(Et
1 þ Dt
1)(Kut
RFt)

Ke ßL WACC

WACCBT VTS ECFt\\Ku FCFt\\Ku

Modigliani and Miller

Practitioners

h ia Ke ¼ Ku þ D Ku
Kdð1
TÞ
ðKu
gÞ VTS E D a VTSðKu
gÞ
L ¼
u þ D
u

d þ TKd
E PM DP M a DKu
ðKu
gÞVTS ðE þ DÞ DKu
ðKu
gÞVTS þ DTKda E þD PV[RF; TDRF] ½Kut
Kdt ð1
TÞ
ðKu
gÞVTS]a ECFt
Dt
1 D FCFt þ Et
1Ku þ (Ku
g)VTSa

Ke ¼ Ku þ D ðKu
RF Þ E
L ¼
u þ D
u E R
Kdð1
TÞ Ku
D F E þD

ECFt
Dt
1(Kut
RFt) FCFt þ Dt
1[RFt
Kdt (1
T)]

ECFt
Dt
1[Kut
Kdt(1
T)
(Ku
g)VTS/D]
Et
1 (Kut
RFt)a

ECFt
(Et
1 þ Dt
1) (Kut
RFt)

FCFt\\RF

FCFt þ Et
1 Ku þ (Ku
g)VTS
(Et
1 þ Dt
1)(Kut
RFt)a

FCFt þ Dt
1 [RFt
Kdt (1
T)]
(Et
1 þ Dt
1) (Kut
RFt)

Table AV.

Note: Valid only for growing perpetuities

NrT þ DTðKu
KdÞ ðE þ DÞ

Damodaran (1994)

Practitioners

NrT þ D½TðKu
RF Þ
ðKd
RF Þ ðE þ DÞ

NrT
DðKd
RF Þ ðE þ DÞ

WACC

Ku


VTS

PV[Ku; DTKu þ T(Nr
DKd)]

PV[Ku; TNr þ DT(Ku
RF)
D(Kd
RF)]

PV[Ku; TNr
D(Kd
RF)]

FCFt\\Ku

FCFt þ Dt
1 KutT þT (Nt
1rt
Dt
1Kdt)

FCFt þ Dt
1 KutT þ T(Nt
1 rt
Dt
1Kdt)
Dt
1(Kdt
RFt) (1
T)

FCFt þ T (Nt
1 rt
Dt
1Kdt) þ Dt
1 [RFt
Kdt(1
T)]

Ku


Harris and Pringle (1985); Ruback (1995)

875

Ku þ D Kd
RF E þD PV[Ku; TDKd
D(Kd
RF)]

ECFt\\RF

No-cost-of-leverage

Valuing by cash flow discounting

Myers (1974) VTSðKu
KdÞ þ NrT ðE þ DÞ

WACC

Ku
NrT ðE þ DÞ

Ku


VTS

PV[Ku; TNr]

PV[Kd; TNr]

FCFt\\Ku

FCFt þ TNt
1rt

FCFt þ TNr þ VTS(Ku
Kd)

Ku


Table AVI.

Miles and Ezzell (1980) 1 þ Ku Ku
NrT ðE þ DÞ 1 þ Kd PV½Kut ; Nt
1 rt Tð1 þ KuÞ ð1 þ KdÞ FCF þ TNrð1 þ KuÞ ð1 þ KdÞ

Table AVII.

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Appendix 4. Dictionary
d, beta of debt
L, beta of levered equity
u, beta of unlevered equity ¼ beta of assets D, value of debt E, value of equity Ebv, book value of equity ECF, equity cash flow EP, economic profit EVA, economic value added FCF, free cash flow g, growth rate of the constant growth case I, interest paid Ku, cost of unlevered equity (required return to unlevered equity) Ke, cost of levered equity (required return to levered equity) Kd, required return to debt ¼ cost of debt N, book value of the debt NOPAT, Net Operating Profit After Tax ¼ profit after tax of the unlevered company PAT, profit after tax PBT, profit before tax PM, market premium ¼ E (RM
RF) PV, present value r, cost of debt RF, risk-free rate T, corporate tax rate VTS, value of the tax shield Vu, value of shares in the unlevered company WACC, weighted average cost of capital WACCBT, weighted average cost of capital before taxes WCR, working capital requirements ¼ net current assets Corresponding author Pablo Ferna´ndez can be contacted at: [email protected]

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Information transparency and valuation: can you value what you cannot see? Aswath Damodaran

Information transparency and valuation 877

Stern School of Business, New York University, New York, New York, USA Abstract Purpose – It is clear that some firms are more forthcoming about their financial affairs than others, and that the financial statements of some firms are designed to obscure rather than reveal information about the firms. How does one reflect the transparency (or the opacity) of a firm’s financial statements in its value? This paper aims to examine both the sources of complexity in financial statements and the appropriate responses in valuation. Design/methodology/approach – The paper examines both the sources of complexity in financial statements and the appropriate responses in valuation. Findings – The paper develops a number of potential measures of complexity, ranging from a measure of opacity (developed by Price Waterhouse) to a complexity score (developed by asking a series of questions about companies). Practical implications – If the value of complex firms is consistently discounted, an incentive for simpler holding structures and more transparent financial statements will be created. Originality/value – While investors and analysts may increasingly bemoan the increasing complexity of financial statements, there is no simple measure of complexity. This paper considers some ways in which the complexity of a firm’s financial statement can be measured. Keywords Financial management, Annual reports, Financial reporting Paper type Conceptual paper

Introduction Consider the following experiment. You are analyzing two firms with the same market capitalization, the same overall market risk exposure and the same financial leverage. Assume that both firms have the same operating earnings, similar returns on capital and that you expect the same growth rate in the operating income. Finally, assume that firm A is a firm in a single business with open and easy-to-understand financial statements whereas firm B is a firm in multiple businesses with complex and difficultto-decipher financial statements. In conventional discounted cash flow valuation, we would attach the same value to both firms[1]. Most investors, however, would value firm A more highly than firm B, thus discounting the latter firm’s value for both its complexity and its opaque financial statements. Are they being irrational or are we missing an important aspect of value in discounted cash flow models? We do not think investors are irrational, and we will present an argument that we should consider these issues in valuation. We will begin by looking at the sources of and reasons for complexity in financial statements, and then look at ways in which we can adapt valuation models. Sources of complexity The financial statements of firms are made complex by a number of factors, some of which are external to the firms, like accounting standards (often designed to force more information disclosure) and some of which are the consequence of operating and financial decisions made by the firm:

Managerial Finance Vol. 33 No. 11, 2007 pp. 877-892 # Emerald Group Publishing Limited 0307-4358 DOI 10.1108/03074350710823836

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Accounting standards and practices clearly bear some of the responsibility for the increasing complexity of financial statements. There are two key problems. The first is inconsistency. The accounting rules developed for the industrial age have not traveled well into the information age. Research and development expenses at technology firms are treated as operating rather than capital expenses, operating leases are not treated as financial expenses and employee options are not considered part of compensation expenses. As a result, the choices that a firm makes on these items can make a big difference in how earnings are measured. The second is the discretionary power that is retained by firms on how they account for income and expenses exposes investors to uncertainties and risks. Aggressive accounting practices, though legal, can inflate the reported earnings for a firm. It is ironic, but the focus on increased disclosure has had an unintended and negative side effect. The financial reports of most companies have ballooned out to include often trivial details.

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Some firms are more complex than others simply because they operate in multiple businesses, often with little in common. General Electric (GE), for instance, has operations in more than ten distinct businesses, with very different margins and risk profiles. Analyzing GE is therefore more difficult than analyzing a firm like Adobe Systems, a firm that produces and sells only software. Why do firms get into different and often unrelated businesses? In the 1960s and 1970s, the impetus came from the desire to diversify, which it was argued, would reduce risk. In the 1980s, the argument was that a well-run firm could take over poorly run firms in other businesses and use its superior management to increase value. Whether these benefits actually materialize is open to question but the complexity added to financial statements is one potential cost.

.

When firms enter new markets or businesses, the way they structure these businesses can have an effect on the resulting complexity. For instance, a firm that keeps each business separate should be easier to value than a firm that envelops all the businesses into one entity. In some cases, firms can exacerbate problems by creating subsidiaries for each of their businesses and holding less than 100 per cent of these subsidiaries. A good example of complexity created by structuring would be Coca Cola’s split-up of its bottlers in the 1980s. By making these bottlers independent entities and reducing its ownership in the bottlers below the majority threshold, Coca Cola was able to take its lowest return assets of its books and report significantly higher returns on capital. In reality, however, the partial ownership of the bottlers obscures the true returns and financial leverage of the consolidated firm. After all, Coca Cola and its bottlers are a composite entity, with the value of one deriving from the existence of the other.

.

As financing choices have proliferated, and new and different ways of raising funds (convertibles, warrants and other hybrids) have come into being, the balance sheet has become more complicated. An entirely new category of funding that accountants call quasi-equity, representing hybrid securities (which are part debt and part equity) now plays a prominent role in many balance sheets. Firms have also become more inventive (with the help of investment bankers) at keeping debt off their books.

878

Reasons for complexity Firms with complicated financial statements have to bear much of the responsibility for the complexity, no matter how strong or weak the accounting standards are. This is because accounting standards establish a floor on what has to be revealed and not a ceiling. Firms that want to reveal more to their investors can always do so and it is worth considering why they do not choose to do so:

Information transparency and valuation

.

Many incumbent managers fear hostile takeovers, since they will lose their power after these takeovers. They attempt to pre-empt hostile acquirers by structuring a bewildering array of subsidiaries and holding companies to hold their assets and by creating new financial securities – common stock with different voting rights, for example. How do these actions keep hostile acquirers away? First, information that is not available to investors is also unavailable to potential hostile acquirers, making it difficult for them to detect when a firm’s assets are being poorly managed and under valued. Second, the complicated holding structure and financial instruments used by the firm can make it difficult to gain effective control of the firm. In Asia and Latin America, for instance, family run firms have used cross holdings to effectively cement control in the hands of family members. By not providing complete information on the cross holdings, they make it difficult for stockholders who want to ask them relevant questions about the profitability and value of these investments.

879

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Firms can sometimes reduce their tax burden by creating holding structures in low-tax domiciles. For instance, it is not uncommon for firms in the USA to have subsidiaries in tax-exempt locales such as the Cayman Islands and to funnel income into these subsidiaries[2]. Complex holding structures also allow firms to shift income from one subsidiary to another, using transfer pricing and intercompany loans. In other words, firms cannot afford to be transparent with shareholders if they prefer opacity when it comes to the tax authorities. As a general proposition, complexity in tax laws will generate complexity in financial statements. Legislators who bemoan the latter should consider their role in creating the former.

.

We have saved the most odious of the reasons for complexity for last. Firms sometimes create complex structures to fool investors into believing that they (the firms) are worth more than they really are or that they owe less money than they truly do. In many cases, what starts as a small evasion mushrooms over time to become a large one, and when the truth comes, as it inevitably will, there are large economic and social costs. For the deceit to work, you often need analysts who look the other way and do not ask tough questions of managers, and investors who base their investment choices on past history and little analysis.

Measuring complexity While investors and analysts may increasingly bemoan the increasing complexity of financial statements, there is no simple measure of complexity. There are some who would argue that they know complexity when they see it, but this is not a very satisfying or objective measure of complexity. In this section, we consider some ways in which we can measure the complexity of a firm’s financial statements.

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Volume of data in financial statement A simplistic (but surprisingly effective) measure of complexity is the sheer volume of data in a financial statement. For instance, the 10K filings made by firms with the SEC range in size from less than 100 pages to in excess of 400 pages. In Table I, we summarize the length of the filings for the 2000 financial year for the ten largest market capitalization firms in the USA. Using this measure, Citigroup and AIG have the most complex financial statements, whereas Microsoft, Intel and Johnson & Johnson have the least complex statements. The reason is that it is a simplistic measure, of course, is because a short 10K can reflect a simple business and financial structure or just indicate an absence of information about the firm’s operations. The opacity index In the late 1990s, Price Waterhouse developed an ‘‘opacity index’’ to measure the transparency (or absence thereof) of financial statements in different countries. Defining opacity as the ‘‘the lack of clear, accurate, formal, easily discernible, and widely accepted practices’’, Price Waterhouse looked at five factors: 1 Oi ¼
½Ci þ Li þ Ei þ Ai þ Ri  5 where i indexes the countries and: O refers to the composite O-Factor (the final score); C refers to the impact of corrupt practices; L refers to the effect of legal and judicial opacity (including shareholder rights); E refers to economic/policy opacity; A refers to accounting/corporate governance opacity; R refers to the impact of regulatory opacity and uncertainty/arbitrariness. They based the country scores for each factor on a survey of CFOs, equity analysts, bankers and Price Waterhouse employees in 35 countries in the third and fourth quarters of 2000. The survey responses were converted into a numerical score and weighted to arrive at each country’s opacity measure. Based on this measure, Singapore had the least opacity whereas China and Russia had the most opacity in their financial statements. Note that this measure is a composite measure that includes, in addition to accounting transparency, other factors such as corruption and legal practices. The survey questions that directly relate to accounting opacity provide an interesting perspective on what the survey participants view as the key accounting issues and problems in each country. Among the most common problems noted were: Company

Table I. Complexity in financial statements: US companies

General Electric Microsoft Wal-mart Exxon Mobil Pfizer Citigroup Intel AIG Johnson & Johnson IBM

Number of pages in last 10Q

Number of pages in last 10K

65 63 38 86 171 252 69 164 63 85

410 218 244 332 460 1,026 215 720 218 353

(1) Failure to disclose related party transactions, where there are potential conflicts of interests between officers of the company and its stockholders (Numerous emerging markets). (2) Reliability of exhibits: Exhibits backing up the financial statements either are missing or do not include important information (China, Russia). (3) Inflation accounting: In many cases, attempts to do inflation accounting resulted in more complicated financial statements and not more informative ones (Chile, Colombia). (4) Inconsistent rules on consolidation and treatment of goodwill (US, UK, Singapore and South Africa). (5) Dual bookkeeping: Firms maintain different financial statements for different authorities, leading to confusion about a firm’s true financial standing. An information based index One way to think about complexity is to begin with the inputs that go into the value of a company and consider all those factors that may make deriving those inputs more difficult in a measure of complexity. For instance, one of the inputs you need to value a firm is risk. It is more difficult to estimate risk parameters for firms that are in multiple businesses than it is for firms that are in a single business for two reasons – different businesses can have different risk profiles and changes in the mix can change the overall firm’s risk profile. Breaking down the valuation inputs into their main components, we can identify the factors that determine complexity: Table II represents an attempt (undoubtedly incomplete) to list out these factors. The contributions made by each of the factors to complexity vary, with some factors (such as volatile effective tax rates) being less important than others (substantial cross holdings in private companies). How much we weight each factor will depend upon how much of the value is attributable to it, and whether it makes estimation more difficult or impossible. To illustrate, operating leases and R&D expenses undoubtedly skew financial statements, resulting in misstated earnings and meaningless book values, but there is enough information usually available in financial statements for analysts to correct the problems. In contrast, earnings that are not clearly identified as non-operating or one-time earnings cannot be easily be incorporated into value. Once we have identified the factors that determine complexity, and categorize them based upon their importance, you can construct complexity scores for firms. These complexity scores should allow us to distinguish between more complex and less complex firms, and to adjust value for complexity (if necessary). Table AI in the Appendix contains one such attempt to come up with a complexity score. Consequences of complexity When financial statements are not transparent, you cannot estimate the fundamental inputs that you need to examine to value a firm. For instance, a firm’s expected growth should be a function of how much it reinvests (reinvestment rate) and how well it reinvests (its return on capital). If firms funnel their investments through holding companies that are hidden from investors, you cannot assess either of these inputs. To evaluate a firm’s cost of capital, you need to know how much debt is owed by the firm, as well as the cost of this debt. For firms that hide a significant portion of their debt,

Information transparency and valuation 881

As business mix changes, the beta will change Different risk premiums for different markets You have to estimate market value of debt Estimating default spread becomes difficult Debt ratio difficult to estimate

1. Volatile capital expenditures 2. Frequent and large acquisitions 3. Stock payment for acquisitions and investments

1. Unspecified current assets and current liabilities 2. Volatile working capital items

1. Off-balance sheet assets and liabilities (operating leases and R&D) 2. History of stock buybacks 3. Changing return on capital over time

1. Multiple businesses 2. Operations in emerging markets 3. No market traded debt

4. No bond rating 5. Off-balance sheet debt

Working capital

Expected growth rate

Cost of capital

1. Holdings in publicly traded firms 2. Holdings in private companies 3. Holdings in other entities

1. Options granted in the past 2. Continuing option grants

Cross holdings

Employee options

Insufficient information to value options Difficult to estimate expected drain in future periods

Requires that these companies be valued Impossible to get information on private company holdings Used to hide assets, debt and other unpleasant facts

Pushes down book value of equity and increases returns Makes forecasting returns more difficult

Makes measuring capital invested difficult

Becomes repository for miscellaneous assets Forecasting working capital needs is difficult

Forecasting becomes difficult Requires normalization over several years Difficult to figure out how much acquisitions cost

Different tax rates in different locales Effective tax rate is meaningless Maneuvers to reduce taxes can lead to complexity Forecasting tax rate becomes difficult

operating income difficult difficult difficult

Capital expenditures

Income from multiple locales Different tax and reporting books Headquarters in tax havens Volatile effective tax rate

it difficult to trace source of forecasting of future income forecasting of future income forecasting of future income

1. 2. 3. 4.

Makes Makes Makes Makes

Tax rate

Multiple businesses One-time income and expenses Income from unspecified sources Items in income statement that are volatile

1. 2. 3. 4.

Reasons

Operating income

Table II. Complexity factors and valuation inputs

Complexity factors

882

Valuation input

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you will underestimate the default risk that the firm is exposed to, and consequently, its cost of capital. Does this mean that the value of a complex firm is more difficult to estimate than the value of a simple firm? The answer is yes, but it does not necessarily follow that investors will discount the value of complex firms because of this uncertainty. In fact, companies like General Electric, IBM and Tyco prospered in the 1990s, even as they became more complex. While some would argue that the increase in value came in spite of their complexity, there are others who would present the case that it was because of it. In this section, we consider some of the empirical evidence on the relationship between firm value and complexity. The cost of opacity In the last section, we referred to the opacity index developed by Price Waterhouse to measure the opacity of transparency of financial statements in 35 countries. In an interesting extension, Price Waterhouse also attempted to examine the impact of the opacity index on two variables that have direct consequences for value. The first was a ‘‘tax-equivalent’’ cost, where the opacity measure was converted into an equivalent tax rate. As they note in their report, an increase in the opacity index from the Singapore level (which is the most transparent) to the Chinese level is the equivalent of an increase in the tax rate of 46 per cent. In an alternate measure of the cost of complexity, Price Waterhouse measured the default spread on sovereign bonds issued by countries over the US treasury and argued that this was a cost of complexity, since more complex companies tended to have much lower bond ratings. The conglomerate discount In the last two decades, evidence has steadily mounted that markets discount the value of conglomerates, relative to single-business (or pure play) firms. In a study, Villalonga (1999), compared the ratio of market value to replacement cost (Tobin’s Q) for diversified firms and specialized firms and reported that the former traded at a discount of about 8 per cent on the latter. Similar results were reported in earlier studies[3]. The reasons for the discount have been widely debated, with many attributing it to the lack of focus in these firms and the inefficiencies that follow. Another possible reason for the discount may be the complexity that gets added to financial statements as firms enter multiple businesses. Even the best efforts of these firms to be more transparent often cannot overcome this problem. First, conglomerates inevitably consolidate costs for some functions – after all, one reason for creating conglomerates is to create economies of scale – and these consolidated costs then have to be allocated to the multiple divisions (businesses) that the firm is in. These allocations are subjective and investors may be dubious about the resulting bottom-line numbers. Second, the absence of market prices for the individual divisions makes it difficult for investors to see the value of each division and consider the market reactions to actions taken by that division. How can we differentiate between discounts attributable to management inefficiencies and those caused by accounting complexity? We can look at market reactions to conglomerates that do break up to create independent entities run by incumbent management. If the reason for the discount is accounting complexity alone, splitting the firm into independent businesses, with their own financial statements (and perhaps their own tracking stock) while preserving incumbent management control of the overall entity should eliminate the discount. If, on the other hand, it is

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management inefficiency that is the problem, you should expect to see the discount persist even after the split-up, since only divestitures will eliminate the underlying problem of poor management. The market reaction to spin offs and divestitures tends to be positive, with the size of the reaction increasing in proportion to the spin off. This suggests that the cause of the discount may vary from firm to firm.

884

Other evidence The other evidence on complexity is scattered over a number of different studies. There is evidence that is consistent with the notion that investors do discount stock prices for complexity, though the extent of the discount is debatable: .

Morgan Stanley, in a study of annual reports, found that stock returns were inversely proportional to the number of pages in the report. Firms with long (and often expensive reports) had the worst returns among the stocks they examined. This suggests that firms often use useless detail to bury valuable facts in reports.

.

Emerging markets that change their accounting standards to increase transparency usually report strong positive reactions to these changes, with investors being willing to pay more for stocks in these markets.

.

When firms in emerging markets have ADRs listed on the US market, their stock prices react positively. While there are a number of possible explanations for this phenomenon, one is that these firms often have to restate their financial statements using generally accepted accounting principles in the USA.

.

The positive reactions associated with spin-offs, split-offs and divestitures can also be viewed as indirect evidence that market reward transparency. Linn and Rozeff (1984) examined the price reaction to announcements of divestitures by firms and reported an average excess return of 1.45 per cent for 77 divestitures between 1977 and 1982. They also noted an interesting contrast between firms that announce the sale price and motive for the divestiture at the time of the divestiture, and those that do not: in general, markets react much more positively to the first group than to the second, as shown in Table III. The market clearly seems to be rewarding transparency at least about this specific action.

Dealing with complexity Reviewing the last few sections, we can now state the three basic questions that we have to address in dealing with transparency in valuation: (1) What do we use as a measure of complexity in valuation? (2) Should we reflect this complexity in value? (3) If we decide to do so, how do we value complexity (or transparency)?

Motive announced Table III. Market reaction to divestiture announcements

Price announced

Yes (%)

No (%)

Yes No

3.92 0.70

2.30 0.37

In prior sections, we have established that while measures of complexity exist, the ultimate test is a subjective one, and that the more complex a financial statement becomes, the more difficult it is to get basic information you need to complete a valuation. We have also shown some evidence, though none of it is conclusive, that complexity does affect value negatively. In this section, we consider three possible responses to complexity when valuing a company. The first two represent the extreme views. One is to ignore assets that you cannot see through the fog of financial statements entirely. The other is to ignore complexity entirely in valuation and trust management to tell the truth about their performance and future prospect. The last approach tries to take a middle ground, where invisible assets are valued, though the value may be discounted. Do not value what you cannot see The most conservative approach to dealing with complexity is to demand information about all assets owned by a firm and all of its outstanding debt. When the information is not forthcoming or is incomplete, you view the assets as worthless. To a risk-averse investor, this may seem not only sensible but prudent. If all investors adopted this approach, firms with valuable assets would, it is argued, be forced to be forthcoming. There is some merit to this argument but it has a potential downside. If most firms have complex financial statements and other investors are less demanding than you are, you many very well end up as a bystander in the equity market. If that is not a viable option – you may be the manager of an equity mutual fund who is required to be fully invested in equities at all times – you may have to bend on these rules. The problems become even worse if you have to invest in younger or higher growth companies, where the reason for the complexity may be the business itself and not intransigent management. Even if a Cisco or a Biogen was absolutely forthcoming about their research and development expenses and acquisitions, you may still find yourself short of the information that you need to correctly assess their value. Trust the firm to reveal the truth At the other extreme, you can trust the managers of the firm with invisible assets to tell you the truth about these assets. Why would they do this? If managers are long-term investors in the company, it is argued, they would not risk their long-term credibility and value for the sake of a short-term price gain (obtained by providing misleading information). While there might be information that is not available to investors about these invisible assets, the risk should be diversifiable and thus should not have an effect on value[4]. This view of the world is not irrational but it does run into two fundamental problems. First, managers can take substantial short-term profits by manipulating the numbers (and then exercising options and selling their stock), which may well overwhelm whatever concerns they have about long-term value and credibility. Second, even managers who are concerned about long-term value may delude themselves into believing their own forecasts, optimistic though they might be. It is not surprising, therefore, that firms become sloppy during periods of sustained economic growth. Secure in the notion that there will never be another recession (at least not in the near future), they adopt aggressive accounting practices that overstate earnings. Investors, lulled by the rewards that they generate by investing in stocks during these periods, accept these practices with few questions. The downside of trusting managers is obvious. If managers are not trustworthy and firms manipulate earnings, investors who buy stock in complex companies are more

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likely to be confronted with negative surprises than positive ones. This is because managers who hide information deliberately from investors are more likely to hide bad news than good news. While these negative surprises can occur at any time, they are more likely to occur when overall economic growth slows (a recession!) and are often precipitated by a shock. In early 2002, the fall of Enron and the expose´ of its accounting practices had a domino effect on the stock prices of Tyco, Williams Energy and even GE, all viewed as complex companies[5]. Adjust the value for complexity Is there a middle road between the two extremes? Can we value assets in complex companies while considering the potential for managers to mislead markets? In this section, we will present four practical ways in which we can adjust a discounted cash flow valuation for the complexity of financial statements. They are not necessarily mutually exclusive and represent solutions to different types of disclosure problems. Adjust the cash flows. The simplest way to deal with complexity is to adjust the cashflows of firms for the complexity of their financial statements. In simple terms, you apply a discount to the expected cashflows, with the magnitude of the discount increasing for more complex companies. This process, called ‘‘haircutting the cashflows’’, is very common both in capital budgeting and valuation, though the discounts applied tend to be both arbitrary and reflect factors other than complexity (such as risk)[6]. To make this a little more objective, we would suggest the following steps: (1) Identify how much of the earnings of the firm come from assets that are invisible or not clearly identified. In particular, focus on earnings from holdings in private businesses (or special purpose entities) as well as other nonoperating income (such as income from pension funds and non-recurring transactions). (2) Assign a probability that management of the firm can be trusted with their forecasts. This is difficult to do, but it should reflect both objective and subjective factors. Among the objective factors is the history of the firm – past accounting restatements or errors will weigh against the management – and the quality of corporate governance – firms with strong and independent boards should be more likely to be telling the truth. The subjective factors come from your experiences with the management of the firm, though some managers can be likeable and persuasive, even when they are misrepresenting the facts. In fact, the conversion of opacity into an implicit tax by Price Waterhouse represents a discounting of the cashflows. You could increase the tax rate for complex firms and estimate the cashflows for the firm with the higher tax rate. The lower expected cashflows will result in lower value. This approach is most appropriate when you are unsure about the current earnings of the firm (as stated in their financial statements) and feel that they might be overstated. An alternative approach that may be simpler is to replace the inputs for the firm with more sustainable numbers. Thus, you would change the operating margin of the firm from its reported value to the industry average and the effective tax rate to the marginal tax rate. The management of the firm will complain mightily that you are being unfair in your valuation, but the onus should be on management to provide the

information that allows you to believe that they can sustain higher margins and lower tax rates. Adjust the discount rate. You can also adjust the discount rate – the costs of equity and capital – that you use to discount the cash flows for complexity. In practical terms, you will increase the costs of equity and capital for firms with more complex financial statements, relative to firms with more transparent statements. There are four ways in which you can make this adjustment: (1) Estimate the historical risk premium attached to complex firms by comparing the returns you would have made on a portfolio of complex firms historically to the returns you would have earned on a market index. For instance, if you would have earned 18.3 per cent over the last 20 years investing complex firms and only 14.1 per cent investing in the S&P 500 index, the risk premium associated with complex firms is 4.2 per cent. You can add this directly to the cost of equity of complex firms. The problems with this approach are two-fold. First, classifying firms into complex and simple firms is both difficult and subjective. Second, as firms change over time, you can have simple firms become complex (or vice versa), making it difficult to keep the portfolios intact. (2) Adjust the betas of complex firms for the lack of the transparency. If you trust markets, it is possible that the betas of complex firms will be higher than the betas of simple firms[7]. Unfortunately, the high standard errors in beta estimates and the changing nature of firms may make this difficult to do. Thus, the beta adjustment is likely to be arbitrary in most cases. (3) Relate the adjustment of the discount rate to the information that is not provided in the financial statements. You can estimate the beta of a firm by taking a weighted average of the betas of the businesses it is in. To do this, you need to be told what businesses a firm is in and how much value the firm derives from each business. If the financial statements are so opaque that you cannot get one or another of these two pieces of information for some of the businesses that the firm operates in, you should err on the side of caution and assume that these businesses are much riskier than the rest of the firm and attach a large enough weight to these businesses to make the overall beta increase. (4) If the complexity is not in the asset side of the balance sheet but on the liability side – significant off-balance sheet borrowing that is not footnoted or is referenced obliquely, for instance – you could adjust the debt to equity ratio to reflect the true leverage of the firm (including the off-balance sheet debt). This would result in a higher levered beta (and cost of equity) and a higher assessment of default risk (resulting in a higher cost of debt). Adjusting the discount rate to reflect complexity makes the most sense for firms where the complexity is obscuring the riskiness of the businesses that the firm is involved in and/or the financial leverage of the firm. Adjust expected growth/length of the growth period. In valuing any firm, two key inputs that determine value are the length of the growth period and the expected growth rate during the period. More fundamentally, it is the assumptions about excess returns on new investments made by the firm during the period that drive value. What is the relationship between complexity and these inputs? Since we derive our estimates

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of return on capital and excess returns from existing financial statements, you can argue that it is more difficult to: .

estimate the return on capital on existing assets for firms where both earnings and capital are obscured by accounting choices; and

.

make judgments on whether this return on capital can be sustained in the future.

One way to adjust the value of complex companies then is to assume a lower return on capital on future investments and assume that these excess returns will fade much more quickly. In practical terms, the lower expected growth rate and shorter growth periods that emerge will result in a lower value for the firm. Apply a complexity discount. You could do a conventional valuation of a firm, using unadjusted cashflows, growth rates and discount rates, and then apply a discount to this value to reflect the complexity of its financial statements. But how would you quantify this complexity discount? There are several options: (1) One is to develop a rule of thumb, similar to those used by analysts who value private companies to estimate the effect of illiquidity. The problem with these rules of thumb is that they are not only arbitrary but that the same discount is applied to all complex firms. (2) A slightly more sophisticated option is to use a complexity scoring system, similar the one described in Table AI (see Appendix) to measure the complexity of a firm’s financial statements and to relate the complexity score to the size of the discount. (3) You could compare the valuations of complex firms to the valuation of simple firms in the same business, and estimate the discount being applied by markets for complexity. Since it is difficult to find otherwise similar firms, you can estimate this discount by looking at a large sample of traded firms and relating a standard multiple of value (say price-to-book ratios) to financial fundamentals (such as risk, growth and cashflows) and some measure of complexity (such as the complexity score). We did this on a limited basis for the hundred largest market capitalization firms and related price earnings ratios to expected growth rates, betas, payout ratios and number of pages in the 10K for each of these firms (as a measure of complexity). The regression is summarized below: PBV ¼ 0:65 þ 15:31 ROE  0:55 Beta þ 3:04 Expected growth rate  0:003# Pages in 10K Thus, a firm with a 15 per cent return on equity, a beta of 1.15, and expected growth rate of 10 per cent and 350 pages in the 10K would have a price-to-book ratio of: PBV ¼ 0:65 þ 15:31ð0:15Þ  0:55ð1:20Þ þ 3:04ð0:10Þ  0:003ð350Þ ¼ 1:54 (4) If a firm is in multiple businesses, and some businesses are simple and others are complex, you could value the company in pieces attaching no discount to the simple pieces and a much greater discount to the more complex parts of the firm. This may be the best strategy for a firm like General Electric, where information on some parts of the firm is easy to access while other parts of the firm are more complicated and difficult to value.

Relative valuation. Most analysts value companies using multiples and comparable firms. How can this approach be modified to consider firms that are complex? While it is more difficult to assess the effect of complexity on relative value, you should consider the following options: (1) If a firm is in multiple businesses, you could value each business using a separate relative valuation and different comparable firms, rather than trying to attach one multiple to the entire company. If the firm reports revenues or earnings from unspecified businesses (where information is not provided or is withheld), your estimate of relative value for these businesses should be conservative. For instance, you could treat these earnings as both risky and low growth and apply a low multiple to estimate value. (2) As in the case of discounted cashflow valuation, you could do a conventional relative valuation (with no adjustment for complexity) and then discount the relative value for the complexity of the firm. The adjustment process would mirror that used for the discounted cashflow value. As firms become more complex, relative valuation becomes much more difficult across the board since you need pure play firms with market prices to estimate the appropriate multiples. Cures for complexity To preserve the integrity of financial markets, we must push to make the financial statements of firms both truthful and transparent. There is always the legislative route. In the aftermath of accounting scandals in the USA, legislation has inevitably followed. While the motivation for legislation is usually noble, new laws are blunt instruments that often create new problems while solving old ones. Accounting standards and rules are also usually rewritten in response to corporate failures. No matter how strict accounting standards may be, however, accounting statements will be reflections of a firm’s true standing only if accounting principles are strictly adhered to and auditors monitor this adherence. Equity research analysts have always been cautious about downgrading firms that they follow[8] and they have become far too accepting of management claims and promises in the last decade. It is the responsibility of analysts to demand information that they feel is critical in assessing the value of the firms they follow As investors, it is easy to blame loose laws, incompetent auditors and snoozing analysts for complex companies that turn into investment disasters. However, we should recognize that we bear a substantial responsibility for our failures, since we do not have to buy stocks that analysts recommend. If, as investors, we refused to buy stock in companies with complex financial statements (hence discounting value for complexity), we are providing the ultimate incentive for firms to eliminate or at least reduce complexity. Conclusion Are complex firms worth less than otherwise similar simple firms? In some cases, they are and we have examined both the sources of complexity in financial statements and the appropriate responses in valuation. Complexity is the result of business decisions made by the firm (you can diversify and make your business mix more complex), structuring decisions on how the firm is organized (holding structures and consolidation) and disclosure decisions (on how to reveal information to financial

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markets). Thus, firms can have complex financial statements even if they are in simple businesses because of accounting decisions they make. We developed a number of potential measures of complexity, ranging from a measure of opacity (developed by Price Waterhouse) to our complexity score (developed by asking a series of questions about companies). If you trust managers to be unbiased in what information they reveal to markets and when they reveal this information, you could argue that complexity by itself is not a problem since the additional uncertainty created by uncertainty is essentially firmspecific and diversifiable. If, on the other hand, managers are more likely to use complexity to hide unpleasant or bad news (losses or debt), complexity will result in more negative surprises than positive ones. In this case, it is appropriate to discount value for complexity. The discounting can occur in one of the inputs to a discounted cashflow value – cashflows, growth rates or discount rates – or can take the form of a complexity discount on conventional (unadjusted) value. It is quite clear that firms should avoid unnecessary complexity but the way to ensure this is often not new legislation or more accounting rules, since they have unintended side consequences. Instead, investors and analysts need to become more demanding of firms. If we consistently discounted the value of complex firms, we will create an incentive for simpler holding structures and more transparent financial statements. Notes 1. Since the firms have similar risk exposure and financial leverage, they should have the same cost of capital. Since their return on capital is equal, they would also have the same reinvestment rates and free cashflows to the firm. The lack of transparency would be considered diversifiable risk and would not affect the cost of capital. 2. There is clearly the sensitive issue of when tax avoidance becomes tax evasion. We do not have the legal expertise to make that legal judgment. 3. See Wernerfelt and Montgomery (1988), Lang and Stulz (1994) and Berger and Ofek (1995). 4. This follows from the assumption that managers are being honest. If this is the case, the information that is not available to investors has an equal chance of being good news and bad news. Thus, for every complex company that uncovers information that reduces its value, there should be another complex company where the information that comes out will increase value. In a diversified portfolio, these effects should average out to zero. 5. The concerns about accounting practices were global. Post-Enron, European firms with opaque financial statements such as Siemens found themselves confronted with demands for more openness from their stockholders as did Asian companies like Samsung. 6. Adjusting cashflows for risk can be dangerous because of the double counting that can occur when discount rates are also adjusted for risk. 7. This will occur only if there is a link between the negative returns associated with opacity and market returns. History suggests that there should be such a link. In fact, the problems with opaque companies seem to come to the surface in down markets and not bullish ones. 8. Note that this is a far weaker test than issuing sell recommendations. Analysts are reluctant to lower firms from a strong buy to a weak buy.

References Berger, P.G. and Ofek, E. (1995), ‘‘Diversification’s effect on firm value’’, Journal of Financial Economics, Vol. 37, pp. 39-65. Lang, L.H.P. and Stulz, R.M. (1994), ‘‘Tobin’s q, corporate diversification, and firm performance’’, Journal of Political Economy, Vol. 102, pp. 1248-80. Villalonga, B. (1999), ‘‘Does diversification cause the diversification discount?’’, working paper, University of California, Los Angeles, CA. Wernerfelt, B. and Montgomery, C.A. (1988), ‘‘Tobin’s q and the importance of focus in firm performance’’, American Economic Review, Vol. 78, pp. 246-50. Corresponding author Aswath Damodaran can be contacted at: [email protected]

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Tax rate

Cost of capital

2. 1.

Expected growth rate

2. 3. 4. 5.

Operations in emerging markets Is the debt market traded? Does the company have a rating? Does the company have off-balancesheet debt?

1. Multiple businesses

2. 3. 4.

1.

Working capital

Capital expenditures

2. One-time income and expenses 3. Income from unspecified sources 4. Items in income statement that are volatile 1. Income from multiple locales Different tax and reporting books Headquarters in tax havens Volatile effective tax rate Volatile capital expenditures Frequent and large acquisitions Stock payment for acquisitions and investments Unspecified current assets and current liabilities Volatile working capital items Off-balance-sheet assets and liabilities (operating leases and R&D) Substantial stock buybacks Changing return on capital over time Unsustainably high return

1. Multiple businesses

Operating income

2. 3. 4. 1. 2. 3.

Factors

Table AI. Measuring complexity: a complexity score

Item

Complexity score

Yes or No Is your return on capital volatile? Is your firm’s ROC much higher than industry average? Number of businesses (more than 10% of revenues) Percent of revenues Yes or No Yes or No Yes or No

Yes or No Yes or No

Yes or No

Percent of revenues from non-domestic locales Yes or No Yes or No Yes or No Yes or No Yes or No Yes or No

Number of businesses (with more than 10% of revenues) Percent of operating income Percent of operating income Percent of operating income

Follow-up question

30% Yes Yes No

2

Yes Yes Yes

Yes Yes

Yes

Yes Yes Yes Yes Yes Yes

100%

20% 15% 5%

2

Answer

51.5

1.5 0 0 0

2

3 5 5

2 3

3

3 3 2 2 4 4

3

1 0.75 0.25

4

Complexity score

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Strategic options and firm value

Strategic options and firm value

Lihui Lin and Nalin Kulatilaka School of Management, Boston University, Boston, Massachusetts, USA Abstract Purpose – This paper aims to discuss how firms make investment decisions and the impact of these decisions on firm value, considering the strategic impacts of such investments. Design/methodology/approach – Built on real options and game-theoretic models, simulations are used to find out how investment decisions and firm values change in face of network effects and potential competition. Findings – It is found that high intensity of network effects lowers the investment threshold as well as the expected value of the firm at the investment threshold. It is also found that potential competition makes an innovating firm less likely to invest. Moreover, in a more competitive environment, the value of the firm when it is indifferent between investing and waiting tends to be high. Practical implications – It is shown that overestimating and failure to capture the network values may lead to poor investment decisions, resulting in firms or projects with little value. The research also has important implications for the management of R&D. When an innovation is likely to face fierce competition, the owner may invest more aggressively under high uncertainty. However, if competitors are likely to provide substitutes, firms should be cautious making upfront investments under high uncertainty. Originality/value – This paper discusses the implications of new developments in the field of real options to firms’ strategic investment decisions and the valuation of firms. Keywords Innovation, Research and development, Corporate investments Paper type Research paper

1. Introduction The most significant economic growth engines can be attributed to technology innovations. Realizing the value of such innovations requires substantial follow-on investments in product development and commercialization. Nevertheless, these investments must be made in the face of tremendous uncertainty about the demand for the product in which the innovation is embodied. Innovators face the question of whether to commit the development efforts immediately or to postpone them until some of the uncertainty is resolved. This choice has been recognized as an option, which leads to postponement and a higher hurdle for investment. These insights are now well established in a literature that has come to be known as real options (McDonald and Siegel, 1986; Dixit and Pindyck, 1994; Amram and Kulatilaka, 1999). Although it is a substantial improvement on the traditional discounted cash flow approach, this analysis assumes that firms are strictly reacting to commonly observed market conditions, as market uncertainty is resolved. We call this approach tactical real options analysis. Recent research has relaxed the above the assumption about the passive role of investments, adding a strategic dimension to the analysis of investment decisions (Grenadier, 1996, 2002; Kulatilaka and Perotti, 1998; Kulatilaka and Lin, 2006). Although postponement can avoid regret about having invested into a market with low demand, early commitment to development can bring several strategic benefits. These strategic benefits arise from convincing potential customers of products, pre-empting competitors, and proprietary learning. By making investments, firms may either change market conditions, or learn proprietary information about the market conditions. In both cases, firms gain competitive advantage through investment.

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This paper discusses how firms make investment decisions, considering the strategic impacts of such investments on user adoption, competitor behavior, and intellectual property management. The impact of such investment decisions on the value of firms is also discussed. Innovations that may lead to new technology standards are often met with doubts in the market. In such a situation, committing irreversible investment to the innovation while uncertainty is still high can be an effective way to convince the market and stimulate adoption. When Qualcomm pitched its innovative technology, code-division multiple access (CDMA), to the mobile communications industry in 1988, people considered the technology inapplicable and impossible to implement for commercial use. This means that Qualcomm not only faced the technical challenge of developing its technology for commercial communications, but also had to convince the world that its approach was practical and had real potential (Mock, 2005). Qualcomm committed significant upfront investments to production of CDMA gear, including phones, infrastructure, and equipment for testing. Such investments helped Qualcomm convince more and more operators to adopt its CDMA technology. A firm with a disruptive innovation often faces the potential danger of competitors entering the market with alternative innovations. Committing to the development of an innovation confers two types of strategic benefits to the innovating firm. First, such investment may deter entry from any potential competitors. This may happen when the market turns out to be profitable only for the market leader, or when the development costs for competitors become prohibitively high. Second, even if the market attracts many competitors after the firm has developed its technology, the leading firm is able to dissuade competitors from developing their own technologies. Such dissuasion is most often achieved via licensing agreements on intellectual property rights. By licensing its innovation to potential entrants, the firm with the innovation is able to not only discourage other development efforts, but also appropriate value via licensing revenues (Kulatilaka and Lin, 2006). Examples of licensing strategies are observed in a wide range of industries. Chemical companies are well known for using licensing and cross licensing to share innovations. In the market for videocassette recorders, Sony failed to license its Betamax technology to Matsushita and JVC early in the 1970s. Subsequently, Matsushita and JVC successfully licensed their own VHS technology to other manufacturers, which became one of the key reasons that VHS won the VCR standards war. In the automobile industry, General Motors is attempting to forge a worldwide standard for automobile telematics by selling its OnStar system to other automobile manufacturers. OnStar provides a wide range of in-vehicle safety, communication, and information services. Manufacturers of Acura, Audi, Volkswagen, and Subaru have abandoned their own development efforts for automobile telematics and adopted OnStar. In the wireless industry, Research in Motion (RIM) licensed its software to Nokia in 2002, allowing Nokia’s customers to receive email on their cell phones using RIM’s software (Frankel, 2005). While the announcement shocked many observers at that time, BlackBerry became the de facto standard in the wireless email market in a few years despite the company’s small size. RIM’s ownership to the technology, however, was challenged in court by a patent holding company NTP, and litigations caused significant damage to RIM’s market value. The strategic effects of developing new technologies for the purpose of licensing have led to a new trend in the use of intellectual property. In the past, innovators used patents to gain legal protection to their intellectual property and ward off competitors.

Recently, however, more and more firms seek to capture the value of their innovations by licensing the intellectual property to other firms including competitors. Worldwide, revenues from patent licensing have soared from $15 billion in 1990 to $100 billion in 2000. A pioneer in intellectual property management, Qualcomm licensed its CDMA technology in late 1980s, and today it has a portfolio of more one thousand patents for the implementation of CDMA with nearly $1 billion dollars of royalty revenues each year. Similarly, IBM generated over $1 billion of annual revenues from technology licenses, amounting to nearly one-ninth of its pre-tax profits in 1999. Our research helps explain these phenomena and provide new insights to managers facing investment and licensing decisions. We find that the presence of strategic effects on stimulating user adoption and pre-empting competition would dampen or even reverse the tendency to postpone investments. We also pay close attention to licensing mechanisms that bring about strategic advantages and study a variety of licensing possibilities in different setups. Licenses can take many forms: a fixed fee, a running royalty, or a combination of the two. The pre-emption effect of investments depends crucially on the structure of the license. The optimal licensing structure, however, depends on the nature of the market, including the investment needed to replicate the innovation, the size of the potential market, and the potential value from establishing a standard. While royalty-based licenses should be used for most innovations, fee-based licenses may become optimal when the benefits from establishing a standard are very high (Lin and Kulatilaka, 2006). In addition, under uncertainty, a two-part license consisting of an up-front fee and a capped licensing schedule can also serve as a source of financing. 2. Strategic effects of investments on users in network industries We live in a networked economy. Information and communications technologies (ICT) connect large populations of people, machines, and devices to form various networks. Such connectivity coupled with digitized content has reshaped many industries, ranging from manufacturing and retailing to financial services, travel, and music industries. A proliferating strand of literature called the economics of networks studies the economic impact of networks (for surveys of this literature, see Katz and Shapiro, 1994; Economides, 1996; Shapiro and Varian, 1999; Farrell and Klemperer, 2006). For users of a network good or service such as cell phones and Internet social networks, they value the network because they reap utility from the ability to connect and interact with other users. In the literature, this is called direct network effects. Networks are also formed around systems of complementary goods or services (e.g. cars, gas stations, and repair shops, video game consoles and games). The literature characterizes such effects as indirect network effects. The mechanism of indirect network effects works as follows: the more users of a platform, the greater the incentives for other firms to create more complementary goods, and the increased variety enhances the value users gain from the complementary systems. Network effects mean that the value of a network to each user increases with the number of other users in the network. The tremendous value potential of networks can present very attractive investment opportunities to firms. However, firms that set out to establish a network must cope with adoption externalities that can prevent the capture of the value added from network effects. In the early stages of a network’s evolution, it will have few users and each user will realize only low levels of network benefits. When a new user joins the network, each existing user also stands to gain increased utility. But the producer is not

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always able to reflect this effect in the price to pre-existing users. So, higher network value does not necessarily translate into higher prices for network goods or higher profits to owners of networks. This is referred to as network externalities in the literature, because neither the firm that builds a network nor the new users of a network can internalize the network effects. Therefore, it is crucial for firms that invest in a network to internalize the network value of its product or service, which amounts to finding mechanisms to convey the equilibrium size of the network to its potential users. Lin and Kulatilaka (2007) show that investment under demand uncertainty may act to internalize the network externality. Building a network often requires the commitment of large and irreversible investments well ahead of widespread customer adoption of unproven goods and services. By investing in a network before uncertainty is resolved, a monopolistic firm can effectively communicate its network size to potential users, and thus alleviate the network externality. When a firm invests in a market characterized by network effects and uncertain demand, it trades off the costs and benefits of immediate commitment of an irreversible investment. On the one hand, demand uncertainty makes waiting valuable, which is referred to as the waiting-to-invest option in conventional real options analysis. This is because by waiting, the firm avoids regrets when the realized market demand is low. On the other hand, however, the immediate commitment to a network investment can raise users’ expectations about the size of the market. This allows the firm to charge a higher price and earn higher profits. In other words, the prospect of establishing a network is a growth option for the investing firm. This is called a strategic growth option, because it takes into account the strategic interaction between the firm and the users. The investment decision of a monopolist firm is based on a comparison of the two value functions: the expected value of immediate investment (V I) and the expected value of waiting until the next period (V NI). Lin and Kulatilaka (2007) show that this is equivalent to comparing the waiting-to-invest option and the strategic growth option. The paper also shows that the higher the intensity of network effects, the stronger the propensity to invest immediately. This is because an increase in network intensity raises the value of both options, but the value of the strategic growth option increases more than the waiting-to-invest option, making the firm more likely to invest. The paper also shows that the impact of uncertainty on the investment decision depends on the network effect. When the intensity of network effects is low, increased uncertainty tends to discourage investment if the uncertainty remains at a low level; however, when the uncertainty is extremely high, this trend is reversed: higher uncertainty makes the firm more likely to invest. When the intensity of network effects is very high, increased uncertainty always makes the firm more likely to invest. These strategic effects of investing in networks play a vital role in firm valuation. This is because the timing of the investments, the intensity of the network effect, and the level of uncertainty affect the production levels, prices, and profitability. Whether one uses a conventional discounted cash flow (DCF) model or real-options based valuation model, the valuations hinge critically on the forecasted profits and risk levels[1]. Our valuation approach recognizes the option value of waiting. Unlike conventional real options models, however, we incorporate the impact of investment timing on the resulting consumer behavior by influencing expectations. Lin and Kulatilaka (2007) show that at a given level of uncertainty, increasing network intensity lowers the investment threshold, and the value of the firm at the investment

threshold declines[2]. This is because as the network effect intensifies, firms start to make investment at a lower threshold of expected demand, and therefore the value of the firm at the threshold is lower. The value of the firm at the investment threshold, however, always increases with uncertainty, for any level of network intensity. The reason is that higher uncertainty changes the prospect of market demand, and the firm must have a higher value to justify the investment in a more uncertain environment. Results also show that when the saturation of networks is considered, investments require a higher threshold and have higher values at the threshold. These results have interesting implications. Suppose the expected demand is difficult for people outside the firm to estimate and they only observe firms’ investment decisions. For a given uncertainty level, a firm is more likely to invest when the network effect is intense. However, the firm is also likely to have very low expected value. Overall, high intensity of network effects lowers the investment threshold as well as the expected value of the firm at the investment threshold. Therefore, high propensity to invest with low returns is more likely to be seen in network industries. This tends to happen when firms overestimate the intensity of network effects. Ignoring the possibility of network saturation may also lead to over-investments. 3. Strategic effects of investments on competitors Firms investing in innovations often also need to consider the strategic effects of investments on potential competitors. 3.1 Strategic investment in incremental innovations A firm may invest in an incremental innovation that leads to a cost advantage vis-a`-vis its competitor. Kulatilaka and Perotti (1998) show that such an investment has strategic effects on competitors: first, competitors are less likely to enter the market because of their higher unit costs – this is the entry-dissuasion effect; second, if competitors do enter the market, they produce less than the innovating firm – this is the post-entry dissuasion. Results show that when the investment lowers the unit production cost dramatically, leading to strong pre-emptive effects on competitors, higher uncertainty encourages investment; when the pre-emptive effects of the investment are weak, however, higher uncertainty tends to discourage investment. The intuition of the results is as follows. The investment in a cost-saving innovation provides the firm with a growth option, and its value increases with uncertainty. The firm makes an investment decision by comparing the value of this growth option with the value of the waiting-to-invest option, which is also increasing in uncertainty. When the cost advantage is significant, the pre-emptive effects are strong and the innovating firm has a much bigger market share than its competitors. In this environment, the growth option increases with uncertainty at a higher rate than the waiting-to-invest option, thus higher uncertainty increases the firm’s propensity to invest. When the innovation reduces the cost only slightly, the innovating firm has much less market power. In this case, uncertainty increases the waiting-to-investing option more than it does the growth option, and therefore an increase in uncertainty discourages the firm from investing. 3.2 Strategic investments in developing new products Firms investing in new technologies that lead to new products and services may also have potential competitors. A new product developed around an innovation may fail to

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generate sufficient demand, which means the firm may not be able to recoup its investment. But, if demand does turn out to be high, other firms may enter the market by investing in alternative technologies and provide substitutes for the innovating firm’s product, significantly reducing the innovating firm’s profits. One mechanism through which to deter competitors from developing their own substitutable technologies is to grant potential competitors access to one’s innovation through contracts. While this may seem counterintuitive at first, there is ample empirical evidence of firms attempting to use licensing contracts to share technologies with competitors and reap licensing revenues. Teece (1986) provides details of several licensing cases in industries such as petrochemical, manufacturing, computer, and electronics. Recent case studies in biotechnology (Lerner and Merges, 1998), information technology (Cusumano and Selby, 1995), and chemical industries (Davis and Harrison, 2001) describe both successful and failed intellectual property licensing. Kulatilaka and Lin (2006) develop a game-theoretical model and find that for a firm that has invested in the R&D of an innovation, if it has a competitor that is able and willing to invest in a substitutable innovation, it is optimal for the firm to licensing its technology to this competitor via a royalty contract. The paper further examines the impact of licensing on the financing and investment decisions of the innovating firm. In particular, it studies how uncertainty influences the firm’s propensity to invest. Similar to the discussion in the previous section, the firm’s investment decision involves the evaluation of two options. Early commitment of an investment in development lets the firm capture the upside in the potential market via licensing an innovation. Therefore, the strategic value of the innovation can be interpreted as a growth option, whose value increases with uncertainty. However, the value of this growth option must be offset against the value of the waiting-to-invest option, which also increases with uncertainty. When the innovating firm is more likely to face competition, the firm cannot operate as a monopolist and its ability to collect royalties is also limited by the competitor’s ex post entry threat, therefore the value of the growth option generally increases with uncertainty at a lower rate than the waiting-to-invest option. This implies that higher uncertainty about the market condition often discourages the innovating firm from investing immediately when the market is likely to be competitive. To further discuss the impact of the investment decisions on the value of the firm, we use the model in Kulatilaka and Lin (2006) and simulate the investment decisions and the firm’s value under a set of lognormal distributions. A lognormal distribution of demand  can be characterized by the expected demand 0 and the shape parameter , which represents uncertainty in our simulations. Table I provides the simulation results. In the table, I is the leading firm’s investment required at time 0 to develop an innovation; J is the investment that a competitor can make at time 1 to develop a substitutable innovation; 
0 is the investment threshold a.k.a. the threshold level of expected demand above which the leading firm makes an investment at time 0; V is the value of the leading firm (which has this investment opportunity only) at the investment threshold. From Table I, first we notice that for any given level of uncertainty, as the investment required of the leading firm, I, increases, the investment threshold rises. This simply means that as the investment becomes more costly, the expected demand should be higher for the firm to invest immediately. Note that the value of the firm at the threshold is also increasing with I. Even though the investment costs more, because the firm is more cautious and invests immediately only when the expected demand

 !0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1


0 1.414 1.407 1.386 1.354 1.318 1.289 1.270 1.262 1.266 1.282 1.311

I ¼ 0.5 V


0

0 0 0 0.0005 0.0044 0.0150 0.0348 0.0668 0.1156 0.1883 0.2967

2.000 1.990 1.965 1.952 1.964 2.003 2.069 2.163 2.287 2.445 2.643

I¼1 V


0

0 0 0.0021 0.0187 0.0585 0.1279 0.2372 0.4039 0.6577 1.0492 1.6659

2.449 2.440 2.461 2.544 2.681 2.872 3.121 3.437 3.830 4.319 4.925

I ¼ 1.5 V


0

0 0.0013 0.0338 0.1201 0.2708 0.5105 0.8851 1.4753 2.4244 3.9918 6.6597

2.828 2.894 3.128 3.481 3.955 4.568 5.354 6.358 7.645 9.303 11.451

I¼2 V 0 0.0508 0.2425 0.5847 1.1507 2.0884 3.6756 6.4424 11.4271 20.7275 38.7182

clears a much higher hurdle a.k.a. the investment threshold, the value of the firm at the threshold is higher. Table I also allows us to see how uncertainty influences the investment threshold and the value of the firm. When the investment cost of the leading firm is approximately comparable to or lower than that of the potential competitor (when I is equal to or less than 1.5 times J), the investment threshold first decreases but then increases with the level of the uncertainty. In particular, when the investment is much less costly for the leading firm than for the follower firm (I ¼ 0.5J ), the investment threshold decreases over a wide range of uncertainty levels. Because investment is less costly for the leading firm, the firm is less likely to face the potential entry threat from its competitor, thus its behavior resembles that of a monopolist. We know that the more uncertain the market is, the more valuable the growth option for a monopolist. Thus, the investment threshold decreases with the level of uncertainty for moderate uncertainty. As the market becomes extremely uncertain, however, the competitor also finds it worthwhile to enter the market, making the investment opportunity less attractive to the leading firm. Thus, the investment threshold increases with uncertainty when uncertainty is extremely high. Note that the value of the leading firm at the investment threshold, V, keeps increasing with uncertainty. In the regime where the investment threshold decreases with uncertainty, the value increase is due to the increasing value of the growth option; in the regime where the threshold increases with uncertainty, the higher value is because the firm now only invests when the market has higher expected demand. The case where the investment required of the leading firm is lower than that of the followers may occur when the development of an innovation needs a scarce resource, such as raw material or human capital, which can be secured by the leading firm. The leading firm’s demand for such resources tends to increase the price of these resources, making any subsequent efforts to develop a substitutable innovation much more expensive. In sum, such a case implies a less competitive market, where the leading firm is more likely to operate as a monopolist. When the investment cost of the leading firm is much higher than that of the potential competitor (I ¼ 2J ), both the investment threshold and the value of the leading firm increase with the level of the uncertainty. This is the case where there is technology spillover, which means that the investment by the leading firm makes any follower’s investment less costly. In this case, the leading firm is much more likely to

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face competition. While the leading firm can partially compensate the loss of its monopolistic profits by licensing its technology to and collecting royalties from a potential entrant, the overall profitability is still eroded by the entry threat. The leading firm’s immediate investment buys itself a growth option, but the potential competition, as we have shown, limits the value of this growth option. We also know that the value of a growth option increases with uncertainty. In this case, because a higher uncertainty makes entry more attractive to potential competitors, higher uncertainty tends to increase the value of this growth option by a small magnitude. Recall that the leading firm makes the investment decision by comparing the values of the growth option and the waiting-to-invest option. In this case, the value of the growth option increases with uncertainty at a lower rate than the waiting-to-invest option, and as a result, the investment threshold increases with uncertainty. Note that the value of the leading firm at the investment threshold is also increasing in uncertainty, which is primarily due to the higher threshold at which an immediate investment is made. The above results suggest that when an innovating firm takes into account potential competition when investing in the development efforts of innovations, it is more cautious about investments. When it is highly likely that other firms may enter the market in the future, the innovating firm invests immediately only if the market is very promising. Furthermore, higher uncertainty tends to discourage the firm from investing immediately. This is because in face of competition, the effect of the growth option on investment decisions is limited and the effect of the waiting-to-invest option dominates. The innovating firm is more aggressive about the investment if future entrants face much higher investment costs. In this case, the cost of investment acts as an entry barrier and the innovating firm is more likely to be a monopolist. When competition is less likely, the effect of the growth option dominates the effect of the waiting-to-invest option, which implies that the firm’s propensity to invest increases with uncertainty. Overall, potential competition makes an innovating firm less likely to invest. Interestingly, the value of the firm when it is indifferent between investing and waiting tends to be high. This is because future competition forces the innovating firm to make an immediate investment only when the market is highly promising. Note that in Table I the lowest value of the innovating firm occurs when the uncertainty is low or when it has a significant advantage in the investment cost against the potential entrant – these are cases where competition is less likely. Licensing can also play a key role in the financing of R&D investments for start-up firms that are often financially constrained (Goldscheider, 1995; Gompers and Lerner, 1999; Hall, 2002). They may enter into licensing contracts with established firms in exchange for an upfront payment, which serves as a means of financing (Kulatilaka and Lin, 2006). The established firms that provide such financing to startups are often industry incumbents, suppliers, and distributors (Teece, 1986; Gans et al., 2002). How does the investment threshold for a financially constrained firm compare with that for a non-constrained firm? Kulatilaka and Lin (2006) prove that financing via a carefully devised licensing contract restricts the firm’s ability to capture value through a license, eroding the value of a developed innovation. This translates into a higher cost of capital, which leads to a higher threshold of expected demand for immediate investment. Therefore, the investment threshold is higher for a firm with a financial constraint (provided that investment is still feasible for the constrained firm) than for one without. As a result, the value of the financially constrained firm at the threshold

for an immediate investment[3] is higher than the value of an unconstrained firm at its investment threshold. In sum, the strategic value of developing and licensing an innovation may justify very high upfront investment when the market is promising. While this investment opportunity represents a growth option for the innovating firm, the entry threat by competitors limits the growth opportunity. Therefore, higher uncertainty makes the investment less attractive (relative to waiting). In addition, financial constraints also restrict the innovating firm’s ability to capture value by licensing, requiring much higher expectations on market demand to make immediate investment optimal or just feasible. Nevertheless, because the entry threat makes the innovating firm less likely to invest, especially when it is financially constrained, if the innovating firm does decide to invest immediately, it tends to have a high value. In other words, to some extent potential competition prevents low-value investments. 4. Concluding remarks Firms investing in R&D should consider the strategic effects of their investment. First, an investment before market uncertainty is resolved may have an impact on users’ expectation of the firm’s success. In network industries, an early investment may serve as a mechanism to credibly announce the size of the network, allowing the firm to internalize the network benefits as profits. However, firms should be aware that overestimating the intensity of network effects might lead to unprofitable investments. Since networks usually require very tremendous amount of upfront investments, the costs of poor investment decisions are often very high. One case in point is the burst of the dotcom bubble earlier this decade. Many dotcoms were investing large amounts of funds into a variety of new electronic businesses, trying to build their brand and to convince users that they would be the standard in their market segments. In practice, customers often found that they could not get the promised network values from these companies, and thus left or did not join their networks. In other cases, the companies did generate network values for users but could not turn the values into profits. The investment decisions, however, were made based on the assumption that the network values would be realized and captured by the firm. Not surprisingly, the poor investment decisions led to the failure of these companies. In contrast, one can look at the successful electronic commerce companies such as eBay, and Amazon.com. While the success of these companies can be attributed to many factors, one thing they have in common is that they provide significant network values to users and they are able to internalize such values. It should also be noted that network effects not only are related to the nature of the business, but also can be influenced by business decisions. By offering more features or services to users, the owner of a network may increase the intensity of network effects. For example, for an online bookstore, one additional buyer does not necessarily benefit existent buyers. Amazon.com, however, developed a system such that buyers can get recommendations on books, CDs, and other goods based on what other customers have purchased. This system thus created network values for users: the more other people make their purchases at Amazon.com, the more relevant recommendations one can expect to get. This means that the recommendation system increases the intensity of the network effects, and the investment decision regarding such a system should take into account the increased network intensity. In sum, assessing, influencing, and capturing the network effects are crucial for firms that invest in networks. Overestimating and failure to capture the network

Strategic options and firm value

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values often lead to poor investment decisions, resulting in firms or projects with little value. Investments have strategic effects on not only users, but also potential competitors. An investment may confer a cost advantage onto the firm, and as a result have preemptive effects on competitors. Investing in an innovation that leads to a new product or service also allows the innovating firm to pre-empt potential entrants. The firm can dissuade potential competitors from developing alternative technologies using a licensing contract: potential competitors, instead of investing in their own technologies, can access the leading firm’s technology by paying royalties. Investing in innovations before uncertainty is resolved and before others provides the firm with a growth option. How this growth option fares against the waiting-toinvest option depends critically on the effects of the investment on the competitive environment. If the investment provides the firm with a significant advantage over competitors, making the environment less competitive, the investment rule for the leading firm resembles that of a firm with monopoly rights in the market. Specifically, a more uncertain market condition encourages the innovating firm to invest. If, however, the investment only gives the firm a slight competitive advantage, the leading firm makes investment decisions similarly to firms in a competitive environment: higher uncertainty makes the firm less likely to invest. Notes 1. For extensive surveys of firm valuation, see Brealey et al. (2005) and Copeland et al. (2000). 2. The investment threshold is the expected demand that must be exceeded for the firm to invest immediately. 3. Because investment may not be feasible for a financially constrained firm, the threshold for an immediate investment is the maximum of the following two thresholds: the investment threshold a.k.a. the expected demand at which immediate investment and postponement have the same expected value, and the feasibility threshold a.k.a. the expected demand above which immediate investment is feasible for the firm. References Amram, M. and Kulatilaka, N. (1999), Real Options: Managing Strategic Investment in an Uncertain World, Harvard Business School Press, Boston, MA. Brealey, R.A., Myers, S.C. and Allen, F. (2005), Principles of Corporate Finance, 8th ed., McGrawHill College, Blacklick, OH. Copeland, T., Koller, T. and Murrin, J. (2000), Valuation: Measuring and Managing the Value of Companies, 3rd ed., John Wiley & Sons, New York, NY. Cusumano, M.A. and Selby, R.W. (1995), Microsoft Secrets, Free Press, New York, NY. Davis, J.L. and Harrison, S.S. (2001), Edison in the Boardroom: How Leading Companies Realize Value from Their Intellectual Assets, Wiley, Hoboken, NJ. Dixit, A. and Pindyck, R.S. (1994), Investment under Uncertainty, Princeton University Press, Princeton, NJ. Economides, N. (1996), ‘‘The economics of networks’’, International Journal of Industrial Organization, Vol. 14 No. 6, pp. 673-99. Farrell, J. and Klemperer, P. (2007), ‘‘Coordination and lock-in: competition with switching costs and network effects’’, in Armstrong, M. and Porter, R.H. (Eds), Handbook of Industrial Organization, Vol. 3, Elsevier, Amsterdam (forthcoming).

Frankel, A. (2005), ‘‘The willing partner’’, Technology Review, Vol. 108 No. 7, pp. 36-8. Gans, J.S., Hsu, D.H. and Stern, S. (2002), ‘‘When does start-up innovation spur the gale of creative destruction?’’, RAND Journal of Economics, Vol. 33 No. 4, pp. 571-86. Goldscheider, R. (1995), ‘‘The negotiation of royalties and other sources of income from licensing’’, IDEA: Journal of Law and Technology, Vol. 36, pp. 1-17. Gompers, P.A. and Lerner, J. (1999), The Venture Capital Cycle, MIT Press, Cambridge, MA. Grenadier, S.R. (1996), ‘‘The strategic exercise of options: development cascades and overbuilding in real estate markets’’, Journal of Finance, Vol. 51 No. 5, pp. 1653-79. Grenadier, S.R. (2002), ‘‘Option exercise games: an application to the equilibrium investment strategies of firms’’, Review of Financial Studies, Vol. 15 No. 3, pp. 691-721. Hall, B.H. (2002), ‘‘The financing of research and development’’, NBER working paper no. 8773, NBER, Cambridge, MA. Katz, M.L. and Shapiro, C. (1994), ‘‘Systems competition and network effects’’, The Journal of Economic Perspectives, Vol. 8 No. 2, pp. 93-115. Kulatilaka, N. and Lin, L. (2006), ‘‘Impact of licensing on investment and financing of technology development’’, Management Science, Vol. 52 No. 12, pp. 1824-37. Kulatilaka, N. and Perotti, E. (1998), ‘‘Strategic growth options’’, Management Science, Vol. 44 No. 8, pp. 1021-31. Lerner, J. and Merges, R. (1998), ‘‘The control of technology alliances: an empirical analysis of the biotechnology industry’’, Journal of Industrial Economics, Vol. 46 No. 2, pp. 121-56. Lin, L. and Kulatilaka, N. (2006), ‘‘Network effects and technology licensing with fixed fee, royalty, and hybrid contracts’’, Journal of Management Information Systems, Vol. 23 No. 2, pp. 91-118. Lin, L. and Kulatilaka, N. (2007), ‘‘Strategic growth options in network industries’’, Advances in Strategic Management: Real Options Theory, Vol. 24, Elsevier, Amsterdam, pp. 177-98. McDonald, R. and Siegel, D. (1986), ‘‘The value of waiting to invest’’, The Quarterly Journal of Economics, Vol. 101 No. 4, November, pp. 707-28. Mock, D. (2005), The Qualcomm Equation, American Management Association, New York, NY. Shapiro, C. and Varian, H. (1999), Information Rules: A Strategic Guide to the Network Economy, Harvard Business School Press, Boston, MA. Teece, D.J. (1986), ‘‘Profiting from technological innovation: implications for integration, collaboration, licensing and public policy’’, Research Policy, Vol. 15, pp. 285-305. Further reading D’Aspremont, C. and Jacquemin, A. (1988), ‘‘Cooperative and non-cooperative R&D in duopoly with spillovers’’, American Economic Review, Vol. 78 No. 5, pp. 1133-7. Corresponding author Lihui Lin can be contacted at: [email protected]

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Strategic options and firm value

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Determinants of market reactions to goodwill write-off after SFAS 142 Mauro Bini

904

Universita` Commerciale L. Bocconi, Milano, Italy, and

Chiara Della Bella Universita` di Modena e Reggio Emilia, Modena, Italy Abstract Purpose – The paper aims to analyze the reasons for the unremarkable increase in value relevance of new impairment testing of goodwill following the introduction of new accounting standards SFAS 141 and 142. Design/methodology/approach – After surveying main research about market reactions to announcements of goodwill write-off before and after the introduction of the new SFAS the paper shows why the two-step procedure of impairment testing risks undermining the very economic substance of the test. Findings – The analysis shows the inadequacy of the impairment test to measure the destruction of wealth experienced by acquiring firms’ shareholders and to supply value-relevant information owing to the lack of disclosure of information after the first stage of the test. It also shows the consequences of management’s discretionary power in setting forth projections. Originality/value – The paper lays the groundwork for interpreting the empirical evidence on the limited information content of goodwill write-offs. Keywords Goodwill accounting, Accounting procedures Paper type Technical paper

Managerial Finance Vol. 33 No. 11, 2007 pp. 904-914 # Emerald Group Publishing Limited 0307-4358 DOI 10.1108/03074350710823854

1. Background In June 2001, the US Financial Accounting Standard Board (FASB) issued SFAS 141 and 142, introducing new rules on business combinations and the impairment test for intangible assets acquired. The new standards required that business combinations be accounted for under the purchase method and replaced the straight-line amortization of goodwill with an impairment test (whereby the value of goodwill incorporated in the acquisition price is assessed at least once a year, based on discounted cash flow). These standards had a significant impact on corporate earnings. Fortune magazine noted that, in the first year they were applied, the Fortune 500 saw their aggregate net income fall from $206 billion in 2001 to just $69.6 billion in 2002, after impairment losses of $235 billion. Gross of such impairment, the aggregate net income of the Fortune 500 would have been $304.6 billion. Considering that the new accounting standards did not allow the recognition of amortization for $45 billion, aggregate net income for fiscal year 2002 would have amounted to $250 billion, if measured in accordance with pre-SFAS 142 accounting standards. Thus, the impairment concept downsized the Fortune 500’s reported income by more than 70 per cent. On the other hand, market reactions to impairment announcements have not been equally noticeable, as the declines in stock prices over the months (or years) preceding any such announcement largely reflected investors’ expectations. The marked discrepancy between the extent of the write-down and market reactions would seem to indicate a limited value relevance of the new accounting standards.

In this paper, we intend to explain the reasons for the unremarkable reaction of the stock market to impairment announcements. In our opinion this is due to the inadequacy of the impairment test to measure the destruction of wealth experienced by the acquiring firm’s shareholders. In fact, the acquiring firm might have destroyed wealth for its shareholders without recording any impairment loss, but simply by constantly failing to fulfill the projections made at the time of the acquisition. The result is that often, in the presence of the conditions to write off goodwill, the market has already discounted such event and, ultimately, the impairment test rubberstamps what the market already knows. Against this backdrop, the impairment test would be a tool to mark-to-market the firm’s intangibles, instead of encouraging the markto-expectation approach intended by the standard setters (fair value accounting). This paper maintains that the value relevance of impairment losses can be enhanced by having a disclosure accompany impairment tests and by eliminating the two-step mechanism to determine any impairment. 2. The reduced signaling value of write-offs before SFAS 121, between SFAS 121 and SFAS 142 and after SFAS 142 The first US accounting standard that dealt systematically with the impairment of long-lived assets was SFAS 121[1], which was issued in March 1995. Before SFAS 121, writing off long-term assets was largely arbitrary and almost exclusively related to the expectations of operating losses of the specific assets written down. In analyzing the write-offs occurred in the 1989-1992 four-year period (contained in the 674 announcements made by public non-financial corporations between 1 January 1989 and 31 December 1992), Francis et al. (1996) noted that the lack of precise accounting rules in this area left wide scope for management opportunism in terms of whether, when and by how much should long-lived assets be written down. The need to adjust the carrying value to reflect the impairment of assets seemed to take a back seat, at least in part, in the management’s decision to clear the deck of impaired assets in order to improve the investors’ perception of the firm’s future performance. The authors support their conclusion by showing that, in write-off decisions, the proxies measuring management incentives to manipulate earnings have the same weight as the proxies signaling actual triggering events. The authors explain this with the lack of authoritative guidance (which would eventually be introduced by SFAS 121) setting forth specific rules for treating the impairment of long-lived assets. They pointed also to the absence of ‘‘significant (investors) reaction to write-offs of either goodwill or PP&E’’. The same conclusion was reached by Bunsis (1997), who indicated that writeoffs had no significant informative value for the stock market in the pre-SFAS 121 period. In an effort to curb such excessive discretionary power, the FASB introduced the concept of triggering event via the SFAS 121. This involved the obligation to determine the recoverability of the carrying value of long-lived assets through undiscounted cash flows. However, this was not enough to reduce management’s discretionary power over goodwill write-offs. Riedl (2004) found that post-SFAS 121 write-offs have a weaker connection with the economic factors that prompt them, thus inferring that management had an even stronger opportunistic discretion in determining whether, when and by how much should long-lived assets be written down. This on the basis of an impairment test founded on undiscounted cash flows that translates into a quasi fair value estimate that can be easily manipulated by management.

Goodwill write-off after SFAS 142 905

MF 33,11

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In 2001, the FASB introduced the SFAS 142, which removed the assumption that intangibles have a definite life and mandated an impairment test based on discounted cash flows. Unfortunately, this standard did not have better luck. Bens and Heltzer (2004) said that ‘‘there is no statistical difference between the short-window abnormal returns in the pre- and post-SFAS 142 samples, suggesting that changes in fair value accounting of SFAS 142 do not impact the information content of accounting data’’. The FASB responded to this evidence of the feeble value relevance of the impairment test by publishing an exposure draft, ‘‘Fair Value Measurement’’ (FASB, 2004), which constitutes a further attempt to limit management’s discretionary power in recognizing the impairment of assets. In this paper, the FASB emphasized the role of market prices to define the so-called fair value hierarchy to be followed in impairment tests. However, this had the effect of shifting the focus of fair value accounting from mark-to-expectations to mark-to-market. In a fair value accounting systems, commodity-like assets are entered at their current market price while for such strategic assets as goodwill and acquired intangibles the search for a current market price is an exercise in futility, as there is no active market for these assets and their substitutes. The market for strategic assets is necessarily a seller’s market, where price is a function of the buyer’s special capabilities. Hence the need for a meaningful impairment test conducted on strategic assets to rely on the recoverable value determined through expected cash flow streams. Li et al. (2004), for their part, make a case for a cause–effect relationship between the decision of certain companies to write off their goodwill between January 2002 and March 2003 and the decrease of their stock prices in the two years before the write-off. This evidence leaves SFAS 141 (Business Combinations) open to criticism, in that the obligation to use purchase accounting would cause the acquiring firm in a paperfor-paper deal to be subject to the risk of recording carrying values of purchased assets linked to the market price of the acquiree’s stock. Such market price might even be significantly higher than the fair value of the underlying net assets. In this case, the impairment test driven by the fall of the acquiror’s stock price not only signals poor management performance but it is also indicative of the inefficiency of the stock market, thus enhancing the volatility risk to which companies are exposed. Our thesis is that, to increase the informative content of the fair value accounting regime introduced by SFAS 142, the impairment test should be stricter, dispensing with the two-step mechanism and private periodic disclosures should be the same in the cases in which there are no impairment losses. This approach is very different from that of the FASB and more similar to that of the IASB. 3. The impairment test according to SFAS 142 SFAS 142 requires companies to test their intangibles for impairment through a twostep procedure to be implemented for each reporting unit to which goodwill and indefinite-lived intangibles are allocated after the acquisition. The first step is intended to test the existence of an impairment loss. At this stage, the fair value is compared against the carrying value of each reporting unit, inclusive of goodwill. If the reporting unit’s fair value exceeds its book value, the goodwill is not deemed impaired. If the reporting unit’s fair value is lower than its book value, the goodwill is deemed impaired. This is the pre-condition for the second step of the impairment test. The second step of the impairment test is designed to measure the loss associated with the alleged impairment detected in the first. This is done by determining the

implied goodwill via the analytical estimate of the fair value of each of the reported and unreported assets and liabilities, including newly formed unrecognized intangible assets, following the same process as that utilized to calculate goodwill in the initial recognition phase. The described two-steps mechanism is the result of a trade-off between the frequency of the impairment test and the accuracy of the goodwill’s estimated value. When it issued the standard, the Board clarified that the elimination of the amortization process should not result in an unduly long preservation of the value of the goodwill in the balance sheet or in excessively substantial and infrequent writedowns. Furthermore, the Board feared the risks arising from the possibility to allow management ample discretionary power over the decision, or lack thereof, to perform the impairment test. Therefore, the introduction of the obligation to carry out the impairment test at pre-established intervals, i.e. on a yearly basis, has been necessary to ensure that the recognition of impairment losses would be separate from management’s subjective interpretation of the performance indicators for the reporting units. However, considering the efforts involved in the residual process to estimate the value of the goodwill, a decision was adopted to have a less burdensome process in place to screen any loss (phase one of the impairment test, based on a comparison between fair and carrying value) prior to the estimation process. 4. The first step of the test as an ineffective way to determine the loss of goodwill value The first step of the test rests on the assumption that the impairment of goodwill (which is not amortized under the new regime) goes hand in hand with the impairment of all the other intangibles, both acquired and internally generated. If this relationship holds, in cases of goodwill impairment there has to be also a loss of value of the reporting unit as a whole. Given the comparison that takes place in the first step, it is reasonable to suppose than when the carrying value exceeds the fair value of the reporting unit goodwill has been impaired. Thus, the outcome of the first step is a supposition based on an assumption. This is a very tortuous process that risks undermining the very economic substance of the impairment test. Let us see why. The assumption underlying the first step of the impairment process is that there is a strong positive correlation between changes in the value of goodwill and changes in the value of the other intangibles. This assumption does not hold necessarily true. Suffice it to think of the case of an acquiring firm that incorporated in the acquisition price of a business entity a goodwill value based on projections that fail to materialize, as the post-acquisition scenario varies. To protect its investment management has no choice but to invest in new internally generated intangibles to maintain unaltered the company’s earning-generating capabilities under the new circumstances. In this case, the deterioration of the goodwill value would be offset by an increase in the value of the internally generated intangibles as a result of the proactive stance by the management to adapt to the changed conditions. At the foundation of SFAS 142 there is the idea of a reporting unit that stands idly by, without reacting to the deteriorating scenario. This is highly unlikely, and it is the more so the greater the goodwill value at risk. Thus, it can be inferred that the greater the goodwill value the greater the management’s effort to protect it through strategies to react or to adapt to the new scenario. These strategies often involve the internal generation of intangibles.

Goodwill write-off after SFAS 142 907

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An example will clarify. Following a business combination, the acquiror allocates the purchase price (¼80) to the assets listed in the first column in Table I on the basis of their fair values which, as of this moment, are the same as their carrying values. After one year the carrying values of the finite-lived intangible and tangible assets decrease (as shown in column 2) by an amount equivalent to their annual amortization and depreciation. For simplicity’s sake, the firm is assumed to be profitable and that the EBITDA (the firm does not have a net working capital) has been utilized to repay in full the debt obtained to finance the acquisition. Finite-lived tangibles are fully depreciated over an estimated useful life of three years, while finite-lived intangibles are amortized over an estimated useful life of 30 years. Annual depreciation is 5 while annual amortization is 1. Therefore, the carrying value of the assets of the reporting unit is 74 (¼80
5
1). The carrying value of the goodwill is unchanged, but it is necessary to run an impairment test. Suppose that at the end of the fiscal year the fair value of the reporting unit has been estimated to amount to 74. This makes it possible to avoid step two of the test and keep the carrying value of the goodwill unchanged. On the other hand, this does not mean that the goodwill has not lost part of its value. In fact, if part of the costs incurred by the firm during the fiscal year resulted in the internal generation of intangibles for a total value of 7, and the fair value of the amortizable and depreciable assets is equivalent to their carrying value, then the goodwill value must have decreased by the same amount (7). This calculation is shown in column 4 of Table I. The example shows that SFAS 142 does not involve so much the recognition of goodwill at fair value as a confirmation that the fair value and the carrying value of the reporting unit are aligned. For this reason, SFAS 142 might be termed as a quasi fair value accounting treatment, as far as goodwill is concerned. If the impairment of goodwill is due to failed projections, the amount attributed to the intangible assets generated internally to make up for the decrease in the value of goodwill in the first phase of the impairment test might also be due to an excessively aggressive estimate of the reporting unit’s fair value. In fact, if on the one hand the change in the projected scenario erodes the heretofore ability of the firm to generate extra-returns, on the other it directs the firm to acquire new competitive advantages only in the future. The trade-off between the existing ability to generate extra-returns and future competitive advantages might be an important tool available to management to change its projections, making them more aggressive, without modifying adequately the rates at which future earnings are discounted to estimate the fair value of the reporting unit.

Balance sheet items

Table I. First step impairment test: the cushion effect

Tangible assets Finite-lived intangible assets Goodwill Internally generated intangible assets (IPR&D) Reporting unit Fair value of the reporting unit Carrying value of the reporting unit

Carrying values Initial Final (Column 1) (Column 2)

Carrying values (Column 3)

Fair values (Column 4) 10 29 28

15 30 35

10 29 35


5
1

80

74


6

7 74 74 74

The rationale for applying a quasi fair value mechanism to goodwill can be explained with the intent of the standard setters to minimize the costs associated with the impairment test. This would be fair enough, if the idea were to maximize the relevance value of the information necessary to complete the first phase of the impairment test. By contrast, the intention to minimize costs without a disclosure requirement on the key input variables utilized for the test results in a distortion of the fair value of goodwill, thereby reducing the information content of the first phase of the impairment test. It is on the basis of these considerations that the IASB mandated firms to conform to high disclosure standards for the input variables utilized to run the impairment test, regardless of the outcome. 5. Absence of impairment and destruction of shareholders’ value The previous example showed that the impairment test as is can be manipulated. Suppose that the goodwill value (¼35) was unchanged during the fiscal year and that there were no internally-generated intangibles. In this case, the fair value of the reporting unit would be equivalent to the sum of the fair values of the three asset classes acquired initially (tangible assets, finite-lived intangibles and goodwill). Yet, net income for the year was zero and the shareholders of the acquiring firm did not achieve a return on their investment. The total shareholder return on the investment is nil, as there have been no dividends and the amount of the initial equity investment is unchanged (¼80
6 ¼ purchase price minus the debt obtained to finance the acquisition and fully repaid with the cash flow generated in the first year). Assuming a cost of equity of 10 per cent for this investment, investors would have lost the return on their investment. A nil return vis-a`-vis a 10 per cent cost of equity translates into a negative 10 per cent extra-return for the shareholder. Thus, it is clear that the preservation of the reporting unit’s carrying value is not indicative of the management’s ability to fulfill the projections underpinning the purchase price. To the extent that a departure from the projected amounts results in the erosion of the return on the initially invested capital there is no impairment of goodwill, despite the destruction of value for the acquiring firm’s shareholders. The following notes illustrate these considerations by comparing the case of a perfect execution of the post-acquisition plan compared with a poor execution where, however, the fair value of the acquired reporting unit is kept in line with the historical purchase price. Let the firm carry out an acquisition at time t0 and recognize the assets taken over, at a total purchase price of 205.7, by allocating them to a reporting unit. For simplicity’s sake let us assume that these assets consist solely of infinite-lived intangible assets and goodwill, so that they are tested for impairment and no amortization charges are taken. In the meantime, post-acquisition plans have been made and the firm prepared medium-term projections for the reporting unit, as shown in Table II. The present value of expected cash flows (205.7) equals the amount recognized initially, as the price at which the assets were purchased is equivalent to their value in use. The carrying value of the assets does not change over the years, barring any impairment. Let us now follow the change in fair value of the reporting unit under two different sets of circumstances: (1) the reporting unit fulfills the projections; and (2) the management reviews the projected results for the year every year, aligning them with those for the previous period (0 growth), postponing by one year the

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five-year projections without changing them. In this case, we are dealing with a firm that cannot fulfill its projections but whose growth expectations are the same as those of the previous year: .

910

Table II. Post-acquisition projections of the reporting unit (at t0)

In case of a perfect execution of the post-acquisition plan (Table III), the firm recognizes every year an improvement in the reporting unit’s fair value, as

Projection years UFCF TV PVIF at coe NPV Fair value of the reporting unit at t0

1

2

10 0.926 9.3

3

4

5

6-8 18 225 0.681 153.1

12

14

15

16

0.857 10.3

0.794 11.1

0.735 11.0

0.681 10.9

205.7

Note: Terminal value reflects a growth rate ‘‘g’’ equal to 0

Projection years

1

2

Case (1) Good execution of the plain (projections are met) UFCF 12 14 TV PVIF 0.926 0.857 PV UFCF and TV 11.1 12.0

3

4

5

6-8

18 225 0.681 153.1

15

16

18

0.794 11.9

0.735 11.8

0.681 12.3

Fair value of the reporting unit at t1 UFCF TV PVIF PV UFCF and TV

212.2 14

15

16

18

18

0.926 13.0

0.857 12.9

0.794 12.7

0.735 13.2

0.681 12.3

Fair value of the reporting unit at t2 UFCF TV PVIF PV UFCF and TV

UFCF TV PVIF PV UFCF and TV

15

16

18

18

18

0.926 13.9

0.857 13.7

0.794 14.3

0.735 13.2

0.681 12.3

18 225 0.681 153.1 220.5

16

18

18

18

18

0.926 14.8

0.857 15.4

0.794 14.3

0.735 13.2

0.681 12.3

Fair value of the reporting unit at t4

18 225 0.681 153.1 223.1

UFCF TV PVIF

18

PV UFCF and TV

16.7

Fair value of the reporting unit at t5

18 225 0.681 153.1 217.1

Fair value of the reporting unit at t3

Table III. Five-year projection workout

NPV

0.926

18 0.857 15.4

18 0.794 14.3

18 0.735 13.2

18 0.681 12.3

18 225 0.681 153.1 225.7

time progresses and the firm generates increasingly substantial cash flows, in keeping with projections. The capital gain equates the expected total shareholder return (cost of capital times initial fair value) minus the net income for the year, that is assumed to be fully distributed. The impairment test does not reveal any loss of goodwill value, considering also that the reporting unit’s fair value at the end of each year is greater than its carrying value. Also from the shareholders’ point of view there are no losses, taking into account that the capital invested for the acquisition yields an ex post return in line with the cost of capital (e.g. 8 per cent) In fact, in every projection year the shareholders achieve an 8 per cent return, consisting of investment income (i.e. the fully distributed net income) and capital gain (higher fair value of the reporting unit) (Table IV). .

Goodwill write-off after SFAS 142 911

In case of poor execution of the post-acquisition plan, shown in Table V, the reporting unit fails to achieve the planned growth, postponing by 12 months, year after year, the expected results of the subsequent five-year period. Obviously, at the end of every fiscal year the reporting unit’s fair value (calculated as the present value of the cash flows for the next five years) is unchanged and is never lower than its carrying value. For this reason the impairment test does not reveal any loss of goodwill value. However, would it not be natural to expect a negative reaction of the stock market as early as the first year after the acquisition, once it is clear that the management fails to deliver on its promises? This shows that the firm can destroy value for its shareholders, via a decline in the share price, without recognizing any goodwill impairment.

Table VI shows that, in case the management postpones five times the projections for the subsequent five-year period, the loss of shareholders’ value, as reflected at the date of acquisition (t0), amounts to 25.8 (nearly 12 per cent of the purchase price of 205.7). This indicates that the shareholder wealth, which can be destroyed by postponing the fulfillment of projections without impairing goodwill, is: .

negatively correlated with shareholder returns in the shape of dividend yields; and

.

positively correlated with the reporting unit’s own cost of capital.

This means that the degree of looseness of the impairment test is closely related to the extent to which it concerns money-losing target firms at the time of acquisition but with a significant growth potential. Dividend
in Fair value yield Dividend yield Total Projection of reporting unit absolute
in % terms terms (capital gain) (absolute terms) (in % terms) return (%) (year end) year 0 1 2 3 4 5

205.7 212.2 217.1 220.5 223.1 225.0

6.5 5.0 3.4 2.6 1.9

3 2 2 1 1

10 12 14 15 16

5 6 6 7 7

8 8 8 8 8

Table IV. Annual shareholder return

MF 33,11

912

Projection years

1

2

Case (2) Poor execution (projection revised downward) UFCF 10 12 TV PVIF 0.926 0.857 PV UFCF and TV 9.3 10.3

3

4

5

6-8

18 225 0.681 153.1

14

15

16

0.794 11.1

0.735 11.0

0.681 10.9

Fair value of the reporting unit at t1 UFCF TV PVIF PV UFCF and TV

205.7 10 0.926 9.3

12

14

15

16

0.857 10.3

0.794 11.1

0.735 11.0

0.681 10.9

Fair value of the reporting unit at t2 UFCF TV PVIF PV UFCF and TV

205.7 10 0.926 9.3

12

14

15

16

0.857 10.3

0.794 11.1

0.735 11.0

0.681 10.9

Fair value of the reporting unit at t3 UFCF TV PVIF PV UFCF and TV

Table V. Five-year projection workout

Fair value of the reporting unit at t5

18 225 0.681 153.1 205.7

10 0.926 9.3

12

14

15

16

0.857 10.3

0.794 11.1

0.735 11.0

0.681 10.9

Fair value of the reporting unit at t4 UFCF TV PVIF PV UFCF and TV

18 225 0.681 153.1

18 225 0.681 153.1 205.7

10 0.926 9.3

12

14

15

16

0.857 10.3

0.794 11.1

0.735 11.0

0.681 10.9

18 225 0.681 153.1 205.7

6. Closing remarks The impairment test required by US accounting standards has become stricter over time but has failed to give evidence of enhanced value relevance. This unsatisfactory performance of the US accounting standards on goodwill and infinite-lived intangible impairment led the FASB to craft a solution that would not be too costly for firms . However, this solution did not make it possible, with few exceptions, to go past the stage of quasi fair value accounting for goodwill. Our analysis shows that the adoption of full fair value accounting for goodwill requires the removal of the two-step mechanism for the impairment test and the disclosure of more information after the first stage of the test, whichever the result. Our analysis shows also that the management’s discretionary power in setting forth projections also in the presence of its inability to meet the targets set at the time the business combination was announced leaves scope to opportunistic behavior intended to avoid impairment losses. Another tool that management has at its disposal to mitigate the impact of the poor execution of its plans on the carrying value of goodwill

at at at at at

t0 t1 t2 t3 t4

TV PVIF PV UFCF Wealth destroyed as expressed at t0

Projections Projections Projections Projections Projections

Projection years

0.926 9.3

0.794 7.9

12 10

10

0.857 8.6

2

1

0.735 7.4

14 12 10

3

0.681 6.8

15 14 12 10

4

0.630 6.3

16 15 14 12 10

5

0.583 7.0

18 16 15 14 12

6-8

0.540 7.6

18 16 15 14 0.500 7.5

18 16 15

0.463 7.4

18 16

225 0.463 104.2

18

P

179.9 (b)
25.8 (b)
(a)

205.7 (a) 205.7 205.7 205.7 205.7

PV ufcf

Goodwill write-off after SFAS 142 913

Calculation of the implied loss as a result of the projections revised downward

Table VI.

MF 33,11

914

involves the reduction of dividends extracted from the reporting unit, thus fostering a misallocation of capital among reporting units in a diversified group. Overall, this lays the groundwork for interpreting the empirical evidence on the limited information content of goodwill and intangible write-offs. All too often these write-offs fail to signal significant information to the market, constituting instead the final act of the wealth destruction suffered by the shareholders in preceding years. Note 1. This was eventually superseded by SFAS 144, in August 2001. References Bens, D.A. and Heltzer, W. (2004), ‘‘The information content and timeliness of fair value accounting: an examination of goodwill write-offs before, during and after implementation of SFAS 142’’, working paper, University of Chicago, Chicago, IL. Bunsis, H. (1997), ‘‘A description and market analysis of write-off announcements’’, Journal of Business Finance and Accounting, Vol. 24, pp. 1385-1400. FASB (2004), ‘‘Fair value measurement’’, Exposure Draft, 23 June. Francis, J., Hanna, J.D. and Vincent, L. (1996), ‘‘Causes and effects of discretionary asset writeoffs’’, Journal of Accounting Research, Vol. 34, pp. 117-34. Li, Z., Shroff, P.K. and Venkataraman, R. (2004), ‘‘Goodwill impairment loss: causes and consequences’’, working paper, University of Minnesota, Minneapolis, MN. Riedl, E.J. (2004), ‘‘An examination of long-lived asset impairments’’, The Accounting Review, Vol. 79, pp. 823-54. Further reading Penman, S. (2004), ‘‘The quality of financial statements: perspectives from the recent stock market bubble’’, working paper, Columbia University, New York, NY. Corresponding author Mauro Bini can be contacted at: [email protected] or [email protected]

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