Fairness Opinions: Common Errors and Omissions

Professional Chapter Reprint

Fairness Opinions: Common Errors and Omissions Gilbert E. Matthews

The McGraw·Hill Compames

Reprinted with permission from Robert F. Reilly & Robert P. Schweihs, The Handbook of Business Valuation and Intellectual Property Analysis (ISBN 0-07-142967-0); copyright© 2004 by The McGraw-Hill Companies, Inc. Visit us at httD://wWW.accessmedbooks.com

Chapter 8 Fairness Opinions: Common Errors and Omissions Gilbert E. Matthews

Introduction Calculation and Miscalculation of Aggregate Market Value Diluted Shares Long-Term and Short-Term Debt Preferred Stock and Minority Interests Cash Selection and Use of Guideline Companies and Guideline Acquisitions Acquisition Price Premiums Overstating Averages by Using the Arithmetic Mean Irrational Pricing Multiples Limitations of the Application of the Discounted Cash Flow Method Unreliability of Financial Projections Sensitivity to the Present Value Discount Rate Sensitivity to Terminal Value Depreciation and Capital Expenditures Asset Value Proper Standards of Value Stock-for-Stock Consideration to Other Class Members High-Vote versus Low-Vote Shares Structural Fairness Presentation of Fairness Opinions Updating Fairness Opinions Conclusion

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II I Business Valuation Special Applications

Introduction Fairness opinions almost always involve an assessment of the value of a company. The question in most fairness opinions is whether a merger or acquisition offer is within an objectively determined range of values for the company or for its shares. In evaluating the fairness of an offer, the analyst is required by law to use valuation methods that are generally accepted. The analyst providing a fairness opinion must expect that the opinion will be scrutinized by the parties to whom it is addressed and will perhaps even be tested in the crucible of litigation. This chapter discusses numerous issues and problems in fairness opinions and valuations, which the author has observed in more than 40 years as an investment banker. The issues range from simple mathematical errors to methodological flaws to broad conceptual issues. Errors that can be laid at the door of the analyst include (I) misinterpretation or misuse of data, (2) failure to recognize mathematical inconsistencies in the data used, and (3) misapplication of generally accepted methods. Some errors, however, derive from flaws in methodologies that have been generally accepted by investment bankers and valuation practitioners. Since analytical methods continue to evolve, it is necessary to be aware of current thinking, to recognize the strengths and weaknesses of various approaches, and to understand when traditional methods need to be reexamined. When an approach is flawed, these flaws should be recognized and corrected. When a concept or method is demonstrably incorrect, either statistically or conceptually, it should be rejected. This chapter points out several areas in which widely used approaches to valuation and to determining fairness should be subjected to critical examination. Some of the broader issues that this chapter will examine include the scope of fairness opinions, the updating of fairness opinions, and the relationship between fairness opinions and the fiduciary duties of directors and control parties. Fairness opinions are normally rendered to assist corporate directors in performing their duties. The increased focus on the duties and responsibilities of corporate directors is likely to engender greater scrutiny of the quality and scope of fairness opinions. Corporate directors should examine not only the financial aspects of fairness, but also the nonfinancial aspects. In addition, both corporate directors and analysts should also give greater attention to the question of when it is appropriate to update fairness opinions.

Calculation and Miscalculation of Aggregate Market Value An approach to valuing companies is to use pricing multiples of EBIT (earnings before interest and taxes) and EBITDA (earnings before interest, taxes, depreciation, and amortization). For computing multiples of EBIT and EBITDA, the numerator is the aggregate value of the company's capital structure. This numerator can be described in numerous ways, including aggregate market value (AMY), market capitalization, total value of invested capital (TVIC), enterprise value, and market value of invested capital (MVIC). Regardless of the name used for this level of corporate value, the concept is the same.

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AMY is defined as follows: Market price of common stock times: plus: plus: plus: plus: less: equals:

Number of diluted shares Long-term debt Short-term debt Preferred stock (if any) Minority interest (if any) Cash and cash equivalents (excluding any restricted cash) Aggregate market value

In a fairness opinion analysis, each of these components of AMY should be carefully considered. These components are discussed below.

Diluted Shares Public companies report the number of diluted shares using the "treasury stock" method. This method assumes the exercise of"in-the-money" options and warrants and also assumes that the proceeds from exercise are used to buy shares in the market. If the market price of the stock has changed materially since the latest available quarterly financial statement, it may be necessary to recalculate the number of diluted shares outstanding. Furthermore, the prospective transaction price for the subject company, not the stock market price, should be used in this calculation. Also, the analyst should consider if it is appropriate to use (I) the treasury stock method (assuming repurchase of shares in the market) or (2) the maximum dilutive effect (assuming that additional shares are added to outstanding shares with no repurchase). If the maximum dilutive effect is used, the incremental cash to be received upon the stock option exercise must be added to cash, thereby reducing net debt. An occasional error in computing AMY is double-counting "in-the-money" convertible securities. The calculation of diluted earnings per share assumes conversion of these securities. To the extent that diluted shares assume conversion of debt or preferred stock, the convertible senior securities should be excluded in the AMY calculation.

Long-Term and Short-Term Debt Conceptually, debt should be valued at its current market value. However, unless the debt pays interest at a rate materially different from the current market level for comparable quality debt, debt is usually valued at par value in the AMY computation. Zero coupon debt normally should be included at its accreted value, because the accreted value is the present value of the commitment to pay the principal at maturity. Capitalized lease obligations should be included as debt, because they are functionally equivalent to debt. Analysts sometimes calculate AMY of leveraged companies by using the market price of debt that is selling below par. This procedure often results in an overvaluation of the equity. To the extent that debt is selling in the market at substantially below par value because of a below-market coupon, the low market value of the debt does accrue to the value of the equity. Alternatively, if the low price of the debt retlects an issuer's poor credit standing rather than simply a below-market coupon,


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the issuer is nonetheless obligated to pay the debt in full when due, and it is unlikely that the issuer would be able to repurchase the debt without paying a premium above the market price. The corporation's shareholders, as residual owners of the company, do not fully benefit from the low market price of its debt in this circumstance. In calculating AMY, it is reasonable to exclude debt that reflects seasonal borrowings for a company with seasonal financing peaks. For example, the temporary financings of a toy company prior to the Christmas season or of an agricultural company prior to harvesting are not part of permanent capital. The analyst should consider whether or not the incremental debt is effectively part of permanent capital. If the seasonal debt is excluded from the AMY calculation, the exclusion should be appropriately noted.

Preferred Stock and Minority Interests A common error in the AMY calculation is to include preferred stock at the nominal value shown on a company's balance sheet. The analyst should value preferred stock at its economic market value, reflecting its repurchase value, liquidation value, or call value, as appropriate. In theory, a minority interest should be valued at its economic or fair market value. However, this information is rarely available. Since minority interests are normally a very small percentage of AMY, a minority interest is usually included in the AMY calculation at book value. In the rare situation where a minority interest is material, the analyst should, if possible, obtain data to enable him or her to value the investment.

Cash A point on which some analysts disagree is whether or not cash should be deducted in computing AMY. The argument against deducting cash from debt is based on the fact that some or all of the cash is needed for operations. The problem with including cash in the analysis is the difficulty of determining the amount of cash needed (1) for the operations of the subject company and (2) for the operations of each of the guideline companies. To the extent that companies are treated in a similar manner and their balance sheet dates are reasonably close, some analysts conclude that it does not matter if cash is deducted. The procedure of not deducting cash does not stand up to scrutiny, however. The necessity of deducting cash becomes clear when one considers the impact on AMY of a large debt financing. For example, consider a company with an equity market value of $100 million, debt of $75 million, and cash of $50 million. Assume that its AMY would be $125 million if cash were deducted from debt and $175 million if cash were not deducted. If we then assume that this company uses half its cash to repay debt, its AMY would still be $125 million if cash were deducted from debt. However, the AMY would decrease to $150 million if cash were not deducted. Alternatively, if we assume that the company borrowed an additional $50 million, its AMY would still be $125 million if cash were deducted. However, the AMY would increase to $225 million if cash were not deducted. The experienced analyst will recognize that a company does not reduce its value simply by paying off debt or increase its value by borrowing.

8 I Fairness Opinions: Common Errors and Omissions

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Generally, the more logical analytical result is reached by deducting cash from debt rather than including cash in the computation of AMV.

Selection and Use of Guideline Companies and Guideline Acquisitions In selecting guideline companies (sometimes called comparable companies), the objective is to find publicly traded companies with market multiples that can provide the analyst with guidance in valuing the subject business. Guideline companies, of course, will never be twins of the subject company. There are a few situations where numerous guideline companies are available, such as regional banks or supermarkets. Usually, however, the choice of guideline companies is limited. It is not uncommon for the analyst to be faced with situations in which there are no adequate guideline companies. When choices are limited, companies that have similar secondary characteristics should be considered. Companies that (I) supply the same end-markets or (2) produce dissimilar products but use similar manufacturing processes may be useful as guideline companies to the extent that they are subject to similar market forces. For example, there are important similarities between manufacturers of different products that are supplied to the automobile industry, because the prospects of the various manufacturers are all dependent on the prospects for the automobile industry. The fact that companies are in the same general industry category or have the same SIC code does not necessarily make them relevant guideline companies. If possible, guideline companies should have characteristics that make them similar from the perspective of investors. Companies in the electronics, computer, and semiconductor sectors include innovative, fast-growing companies with strong intellectual property and market positions. However, these sectors also include manufacturers of commodity-type products, such as electrical connectors and memory chips. Stock market pricing multiples are greatly influenced by a company's growth prospects. It is preferable to have a reasonably large sample of guideline companies. However, there are occasions where one or two entities may clearly provide the best available guideline companies. However, even when one or two appear to be the best, it is also helpful to consider companies that have secondary characteristics that are similar to the subject company. It would be appropriate, then, to accord lesser weight in the guideline publicly traded company value analysis to the companies with the similar secondary characteristics. The selection of the guideline company pricing multiples is as much an art as a science. This selection necessarily depends on the judgment and experience of the analyst. Simply applying an average of the guideline company multiples in the valuation fails to reflect whether the subject company's characteristics merit a higher or lower multiple than the average, which is typically the case. Smaller companies may have greater growth prospects than their larger competitors. However, it is not unusual to find such smaller companies valued at lower multiples. This may be because of the greater risks perceived by market participants for companies with (I) less financial strength and (2) thin management. For example, Exhibit 8.1 presents the relationship between the number of subscribers of cable television businesses and the multiple of operating cash at which they were acquired.

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Exhibit 8.1

Cable Acquisitions October 1998-March 1999 15.0x

I 14.0x

~

•

13.0x

•

ii: 12.0x

..

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~

i

•

11.0x

.·

10.0x

a. 9.0x

0

•

•

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v

• •

.

•

.,..

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•

./" • , .... :....7.. • • • ~·: •• •

al

-

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!• i I

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! I

S.Ox

··-

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4.0x 100

1,000

10,000

100,000 1,000,000 Basic Subscribers

10,000,000

100,000,000

Generally, cable companies with fewer subscribers received lower multiples of operating cash flow. A guideline (or comparable) merged or acquired company transaction takes place as of a given date and the terms of the deal reflect economic and industry conditions as of that date. A common error is the failure of the analyst to take into consideration, either quantitatively or qualitatively, any changes in market conditions, economic conditions, and/or industry conditions that occurred between the date of the guideline transaction and the date of the fairness analysis. For example, AMY multiples paid in the Internet industry in the euphoria of 1999 would have limited applicability to transactions in the Internet industry in the bear market of 2002. The selection process for public and private guideline transactions is similar to the selection process for publicly traded guideline companies. However, data on most acquisitions of private companies, as well as on many acquisitions of divisions of public companies, are often quite limited. Even when data are available, it is usually in much less detail than the data for companies that file U.S. Securities and Exchange Commission (SEC) annual and quarterly reports.

Acquisition Price Premiums The term "control premium" is used inconsistently among valuation practitioners. Many analysts, in describing "levels of value," define a "control premium" as the difference between (I) the value of a company as a stand-alone business and (2) the value of that company to an acquirer.

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However, the same term is also frequently applied to the price premium over market price paid by an acquirer. This price premium is the difference between the price paid for control and the market price of publicly traded shares. The price premium over the publicly traded market price is more accurately called an "acquisition premium." The acquisition premium is commonly used by analysts in reviewing transactions. A comparison of the acquisition price premium in the subject transaction to the average historical acquisition price premium is sometimes used as a test of a transaction's fairness. This approach is flawed, however, because the average price premium paid in acquisitions is upwardly biased. It only includes the prices paid for companies that buyers viewed as being undervalued and, therefore, as attractive targets. The average price premium in acquisitions necessarily excludes companies that acquirers considered overpriced or fairly priced in the marketplace. In any given year, only a small percentage of public companies are acquired. Moreover, market prices fluctuate regularly. For example, one company's share price may increase only because a competitor was acquired. A rational buyer does not simply determine a price premium and apply it to a fluctuating market price. A premium depends on the specific factors of each transaction. Assume there are two virtually identical companies trading in the market at a price of $50 per share, and that one is acquired at a price of $80 per share, a price premium of 60 percent. In this case, the stock price of the second company could react by rising to $60 or more. It would be illogical to argue that fairness would require a $96 price, a 60 percent price premium over a $60 price per share, for the second company. The price premium in a prior transaction does not determine fairness in a subsequent transaction. Relative pricing multiples are the appropriate measure of the price premium paid in acquisitions. If the multiples paid in acquisitions are higher than the multiples in the market, this becomes a reasonable approach for determining a fair acquisition premium. Exhibit 8.2 presents the multiples calculated for a study of supermarket chains as of late 1997. Faced with evidence like this, which shows that the acquisition multiples in contemporaneous transactions are at the same level as the market multiples, it makes sense for the analyst to conclude that no acquisition price premium is warranted.

Exhibit 8.2

Multiples of Comparable Companies, Supermarket Chain Example Price/Earnings Ratio

RatioofAMV LTM Sales

LTM EBITDA

LTM EDIT

LTM EPS

Estimated EPS

Estimated EPS-Year 2

0.35x 0.45x

6.7x 7.6x

ll.7x 11.9x

20.5x 20.2x

17.7x 19.0x

l4.6x 17.lx

0.36x 0.36x

7.5x 7.9x

12.6x 12.9x

22.3x 20.lx

19.0x 18.5x

l6.3x 16.9x

Multiples of Comparable Companies Harmonic mean Median

Multiples of Comparable Acquisitions Harmonic mean Median

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Many companies are already fully priced in the market and do not merit acquisition price premiums. In a situation where there had been no acquisitions in the previous 3 years, despite a large number of public companies in the industry, an expert witness appropriately testified that no acquisition premium was applicable. In the late 1990s, shares of most "dot-com" companies were selling in the market at far higher prices than any acquirer would be expected to pay in cash for the entire company, although some acquisitions were made using shares of similar companies. It is also erroneous to apply a price premium for control to a discounted cash flow (DCF) calculation that is based on estimated cash flow of the target corporation after its acquisition. 1 A typical DCF calculation values the cash flow of an entire company. If the present value of the future cash flows of a company is worth $50 million, why would any rational buyer pay a price premium above $50 million? A buyer may pay more for the potential incremental cash tiow from synergistic or similar benefits. However, an acquirer will rarely pay for benefits that are unique to a specific buyer and that cannot be obtained by another buyer. The incremental value stems from the higher potential cash flow embedded in the projected cash flow, not from an arbitrary control price premium based on other transactions.

Overstating Averages by Using the Arithmetic Mean Everyone is familiar with the calculation of the arithmetic mean: the arithmetic mean of 2, 4, 6 and 8 is 5. The student of statistics learns, however, that there are other methods of averaging numbers. These methods include the geometric mean (the nth root of the product of the numbers) and the harmonic mean (the reciprocal of the arithmetic mean of the reciprocals of the numbers). The geometric mean of 2, 4, 6 and 8 is 4.45, and the harmonic mean is 3.84. 2 The customary (but incorrect) manner in which analysts calculate central tendency for pricing multiples such as AMV IEBITDA and P/E is to calculate the arithmetic mean. The median is also widely used and is useful if the sample is sufficiently large. Using the arithmetic mean as a measure of the average pricing multiple is statistically incorrect, because it results in an incorrectly weighted average. The fact is that the arithmetic mean of any ratio with price in the numerator, such as AMV/EBITDA and P/E, always gives greater weight to higher multiples in the sample and lesser weight to lower multiples. The median-the midpoint of the group--is a better measure of central tendency. However, the median effectively eliminates the information in the remaining multiples. 3 Statistically, the harmonic mean is a superior measure, because it does not suffer from the flaw of misweighting the data points. The arithmetic mean weights the multiples in proportion to the

1 See Lippe v. Bairnco, 288 B.R. 678 (S.D.N.Y 2003), which stated that "the addition of a control premium to a DCF analysis is not consistent with proper and usual valuation practice." The decision criticized (and disqualified) two expert witnesses who had arbitrarily applied control premiums to their valuations based on guideline companies as well. As a result of the disqualifications of its experts, the plaintiff was unable to support its claims of undervaluation, and the defendants were granted summary judgment. Lippe v. Bairnco, 249 F.Supp.2d 357 (S.D.N.Y. 2003). . 2 The geometric mean is always lower than the arithmetic mean and higher than the harmonic mean. 3 The medians of large samples of multiples are normally close to the harmonic mean and are almost always lower than the arithmetic mean.


217

magnitude of each multiple. The harmonic mean gives equal weight to an equal dollar investment in each comparable company. Thereby, the arithmetic mean gives a multiple of 30x a weight three times higher than the weight given to a multiple of lOx. The effective weighting can be demonstrated by taking the means of the multiples of two hypothetical companies selling at $40 per share. In this example, we assume that Company A has earnings of $1.00 per share, and Company B has earnings of $4.00 per share. The PIE multiples of the two companies are 40x and I Ox, respectively, so that the arithmetic mean multiple is 25x. The harmonic mean is calculated by taking the reciprocals of 40x and lOx (0.025 and 0.1), averaging the reciprocals (0.0625), and then taking the reciprocal of 0.0625 to get a harmonic mean P/E multiple of l6x. Why is the harmonic mean a preferable measure? Assume that an investor buys 100 shares of each stock at $40, for a total investment of $8000. What would the PIE multiple of the portfolio be? The lOO shares of Company A would have aggregate earnings of $100, and the I 00 shares of Company B would have aggregate earnings of $400. With a purchase price of $8000 and $500 in total earnings, the P/E multiple of the investor's portfolio would be 16x, the same as the harmonic mean. If, instead, the investor wished to purchase $400 of earnings of each company, he or she would still buy I 00 shares of Company B for $4000. However, the investor would have to spend $16,000 to buy 400 shares of Company B. The total cost of the portfolio would be $20,000 for $800 in earnings. The PIE multiple of this portfolio would be 25x, the same as the arithmetic mean. This demonstrates the greater weight given to stocks with higher PIE multiples by the arithmetic mean. In fact, it would be a rare (and irrational) investor who would build a portfolio using the arithmetic mean. Although analysts commonly use arithmetic means, they are upwardly biased. The harmonic mean is a statistically preferable measure of averaging multiples.

Irrational Pricing Multiples There should be a rational connection between the numerator and the denominator when applying market-derived pricing multiples. Sometimes, analysts apply multiples without having given adequate consideration to the appropriate relationship between the variables in a market approach analysis. Some analysts calculate EBITDA per share and then compare it to the market price per share. This is an example of an irrational pricing multiple. The "I" in EBITDA represents the company's interest expense. Accordingly, it is inappropriate to use EBITDA in the denominator without including the company's debt in the numerator. The same criticism applies to such multiples as (I) price/revenues per share and (2) price/EBIT per share. These multiples typically overvalue companies with substantial leverage and undervalue companies with little leverage. If a company doubles its level of EBIT (for example) by making an acquisition with borrowed money, the incremental earnings that are used to make interest payments on the new debt are not available to shareholders. In the application of multiples of revenues, multiples of EBITDA, or multiples of EBIT, the appropriate numerator is not equity value alone. The numerator for these multiples should be AMY-the capitalization of the entire business. If a company incurs substantial debt to finance an acquisition, its revenues per share increase. This transaction directly reduces the equity price/revenues multiple. The equity

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price/revenues multiple does not take into account the impact on earning power of the financing cost. Normally, the equity of the company will not increase in value in proportion to the incremental revenues. However, there is a rational relationship between AMV as the numerator and either EBITDA or EBIT as the denominator, because EBITDA and EBIT include interest expense and AMV includes the amount of debt on which that interest expense is paid. A pricing multiple that is used by some analysts for companies with high rental payments (such as airlines), is AMV/EBITDAR (EBITDA plus rent expense). This approach is intended to level the playing field for comparisons of ( 1) companies that own most of their assets with (2) companies that rely primarily on leased assets. Analysts usually calculate the AMV/EBITDAR multiple by adding rent expense to EBITDA, but without a corresponding adjustment to AMV. However, this procedure is conceptually incorrect. Rent expense, in many situations, is similar to capitalized lease payments. Accordingly, rent expense is composed of an interest component and a principal payment component. The denominator-EBITDAR-should include only the portion of the annual rent expense payments that is substantively equivalent to interest-and not to the entire rent expense payment. The numerator-AMY-should be increased by the present value of the portion of future rent expense payments that are substantively equivalent to. the principal payments. 4

Limitations of the Application of the Discounted Cash Flow Method The DCF method is conceptually useful, but it has significant application limitations. The method is based on the premise that the value of a business is the present value of its future net cash flow. Projected net cash flow is discounted to present value using a cost of capital that is intended to reflect the risks of the business. Because cash flow projections are made for only a limited period, the value of a business at the end of the discrete projection period is calculated. This value at the end of a discrete projection period is typically called the "terminal value." The terminal value is typically estimated ( l) by capitalizing the projected cash flow for the final year of the projection, (2) by discounting the terminal value to its present value, and (3) by adding the present value of the terminal value to the present value of the discrete period net cash flows. The theory of a DCF analysis assumes the validity of the financial projections, but financial projection accuracy is a simplifying assumption that does not often comport with the real world. Moreover, a DCF analysis is also highly dependent on the selected discount rate, as well as the methodology used for estimating the terminal value. Often, the terminal value is based on the projected financial results for the year after the discrete projection period. Terminal value is based on the final year of a projection, which is necessarily far less predictable than projections for earlier years. The driving factor in a calculated DCF value is terminal value, so that the final year of the forecast is by far the dominant factor in the result. 4 For a method of determining the value of scheduled future principal and interest payments embedded in rentals, see Sidney Cottle, Roger F. Murray, and Frank E. Block, Graham & Dodd's Security Analysis, 5th ed. (New York: McGraw-Hill, 1988), pp. 305-310.


219

Unreliability of Financial Projections The quality of financial projections and the likelihood that a company will achieve those projections are factors that affect the reliability of a valuation calculated using the DCF method. Accordingly, the DCF method is most useful for companies with revenues that can be reasonably projected based on an existing nucleus of continuing customers, such as regulated utilities and cable television companies. For most businesses, projecting financial performance several years into the future is a difficult, if not impossible, task. Rapidly changing economic conditions and competitive pressures often make it difficult even to project next year's earnings with confidence. How far into the future can a high-tech company make a supportable financial projection? This question is difficult to answer when the company often does not even know what products it will be producing in 2 years. Changes in the competitive condition within some traditional industries have made earnings projections more speculative than they were in the past. Moreover, even in cyclical industries with volatile earnings, company managements seldom include significant downturns in their projections of future revenues and earnings. The analyst preparing a fairness opinion rarely has sufficient knowledge of the company to prepare reliable independent projections. Financial projections prepared by company management should be provided to the analyst, because management is most familiar with the company and with its prospects. Furthermore, when financial projections are used in a fairness opinion analysis, projections that have been developed in the ordinary course of business are preferable to projections prepared specifically solely for the transaction itself. When possible, the analyst should consider several sets of financial projections for the subject company. Typically, alternative financial projections will take into account alternative economic scenarios regarding both the company and its industry. With this information, the analyst could then (I) compute a DCF value estimate for each scenario, (2) consider the relative probability of each alternative, and (3) calculate value using a weighted average based on the relative probabilities.

Sensitivity to the Present Value Discount Rate It is intuitively obvious that the selected discount rate can greatly affect a DCF

method valuation. However, many analysts underestimate the impact that small changes in the discount rate have on calculated values. Exhibit 8.3 presents the range of calculated AMVs and equity values of a hypothetical company, using the following assumptions: • • • • • • • •

Revenues of $100 million Depreciation expense of $5 million Net debt of $50 million Capital expenditures of $6 million in the first year of a 5-year forecast A 20 percent EBITDA margin A I 0 percent annual long-term growth rate A 40 percent income tax rate A terminal value estimated using a multiple of 8x EBITDA


220

Exhibit 8.3

Range of Calculated AMVs and Equity Values for Hypothetical Company Discount Rate(%)

10 12 14 16 18

AMV ($million)

Equity Value ($million)

187 172 159 148 137

137 122 109 98 87

Exhibit 8.3 shows that the calculated equity value, after net debt of $50 million, is $137 million using a 10 percent discount rate, 57 percent higher than the $87 million calculated using an 18 percent discount rate. It should be noted that the impact of the selected discount rate is far more pronounced if the terminal value is computed using the Gordon growth model. The Gordon growth model computes a terminal value by (1) projecting a constant growth in long-term future net cash flow and (2) using the cash flow in the final year of the projection period as a base. The capitalization rate used to calculate terminal value is a function of the difference between the present value discount rate being applied in the computation and the company's expected long-term growth rate. Exhibit 8.4 is based on the same assumptions as presented above. However, in Exhibit 8.4, the terminal value is computed using the Gordon growth model, assuming a 5 percent expected long-term growth rate. Exhibit 8.4 shows that the AMY of $83 million calculated using a 10 percent discount rate is more than I 60 percent higher than the AMY of $218 million calculated using an 18 percent discount rate. To emphasize the sensitivity of the Gordon growth model to both the assumed discount rate and the assumed growth rate, the equity value of $168 million computed using a 10 percent discount rate is more than 400 percent higher than the equity value of $33 million computed using an 18 percent discount rate. The method most commonly taught in business schools to estimate the cost of equity capital is the capital asset pricing model (CAPM). The CAPM is typically used as a component in the calculation of the weighted average cost of capital (WACC). The standard WAIT methodology used is to determine a company's after-tax costs of debt capital and equity capital and then to weight these costs based on an appropriate Exhibit 8.4

Range of Calculated AMV s and Equity Values Using Gordon Growth Model for Hypothetical Company Discount Rate(%)

10 12 14 16 18

AMV ($million)

Equity Value {$million)

218 155 120 98 83

168 lOS

70 48 33


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debt/equity capital structure mix. Ultimately, the calculated discount rate (i.e., the after-tax WACC) is applied to the company's projected net (after-tax) cash flow in order to arrive at a value estimate. Under the CAPM, a company's cost of equity is determined by adding the riskfree rate of return (typiqllly, the yield on 20-year U.S. Treasury bonds) to a measure of the equity risk premium. 5 A company's equity risk premium is calculated by multiplying the equity risk premium for the market as a whole by a factor called beta (/3). Beta is a measure of the volatility of an individual security's return relative to the total market return. Where appropriate, a company's cost of equity may be increased (1) by a company-specific equity risk premium and/or (2) by a small stock (or size adjustment) premium. The CAPM is widely accepted for financial analysis, portfolio management, corporate planning, and other applications. However, its reliability in calculating the appropriate discount rate for an individual company is subject to question. Many of the factors used in estimating the discount rate, such as beta, the company-specific risk premium, and the small company/size adjustment risk premium, are subject to the judgment of the analyst. Ideally, valuation analysts should use a forward-looking beta. In practice, though, historical betas are commonly used because projected betas are not readily available. However, it can sometimes be difficult to determine a specific company's historical beta. Several financial reporting sources can be used to estimate the beta for a company's publicly traded stock, but these sources rarely report the same beta for the same company. In addition, a company's beta can vary widely at different points in time. A company's beta, therefore, can fluctuate depending on when it is calculated. Moreover, there is significant disagreement in the academic community over the relevance of beta in the cost of capital estimation. 6 The estimation of the company-specific equity risk premium is a matter of professional judgment in many situations. Although the company-specific equity risk premium does not lend itself to mathematical determination, it is important for analysts to consider this factor when estimating the cost of equity capital. The estimation of the small company (size adjustment) equity risk premium also requires judgment on the part of the analyst. The general practice, at least in academic theory, is to apply the small company equity risk premium based solely upon the equity value of the subject company, with no regard to the size of its industry. However, the small company equity risk premium should be influenced, at least in part, on the company's size relative to the size of other entities in its industry. The relative performance of small companies in the recent bull market has caused some analysts to question whether a small company equity risk premium should be applied at all. However, the subsequent decline in the prices of Nasdaq equities (typically smaller companies) has helped to rebut this position. 7 Another factor that affects the estimation of a discount rate is the impact of leverage on the company's capital structure. When a corporation increases its leverage, its cost of equity typically increases, because the corporation's equity risk increases as its amount of outstanding debt increases. However, this leverage-related

5 The standard source for the equity risk premium for the general stock market is Stocks. Bonds. Bills, and Inflation, published annually by Ibbotson Associates, www.ibbotson.com. Also, see Chap. I of this book. 6 For example, see Eugene F. Fama and Kenneth R. French, Industry Cost of Equity, Journal