Cost of Capital When Discounting Residual Profit A Case Study

Transcription

1 Cost of Capital When Discounting Residual Profit A Case Study White Paper Tim Reichert, Ph.D., Erin Hutchinson, and David Suhler White Paper

2 Table of Contents I. Introduction... 1 A. The Importance of the Discount Rate... 1 B. Transactional Measures and Model-based Estimates Model-based Methods Transactional Methods... 2 II. Model-based Cost of Capital The Capital Asset Pricing Model... 4 A. The CAPM Framework: Price Quantity of Risk... 4 B. Standard Adjustments to CAPM Premia Added to Enhance CAPM s Predictive Power Beta Adjustments to Accurately Price the Systematic Risk of the Assets Being Valued... 7 C. Example Estimation of CAPM Components in the Hypothetical Case of Discounting a Software Company s Residual Profit Stream Statement of Facts Analysis Date Risk Free Rate of Return Equity Risk Premium Beta Coefficient Size Premium D. Capital Market Conditions as of the Transaction Date E. Concluded Model-based Estimate of the Cost of Capital III. Transaction-based Cost of Capital Estimate IV. Concluded Cost of Capital Estimate V. Consistency With Court Guidance... 40

3 Page 1 I. Introduction A. The Importance of the Discount Rate The terms cost of capital, discount rate, and required rate of return all mean the same thing. The basic idea is simple a capital investment of any kind, including intangible capital, represents foregone consumption today in return for the likelihood of more consumption tomorrow. The required rate of return to a capital investment is just that the rate of return, r, on $1 of today s foregone consumption (i.e., investment) at which one would be indifferent between consuming $1 today and consuming $1 times (1+r) tomorrow. The discount rate is among the most important determinants of the value of an asset whether that asset is an intangible asset, or an entire enterprise. The reason for this is obvious upon inspection of the present value formula for a cash flow stream that extends into perpetuity, given below. (Formula 1). Here, V is the value of a cash flow stream that grows at a constant rate into perpetuity, π is cash flow, and r and g are the discount rate and growth rate, respectively. If we assume that π is equal to $1, and that the r-g is equal to 8 percent, then V is equal to $12.5. Under these assumptions, a one percentage point increase in r will decrease V by approximately $1.39, or 11.1 percent. Thus, small changes to the discount rate produce large swings in the present value of cash flows. Indeed, it is not an overstatement to say that the discount rate and the growth rate are generally the most important determinants of an asset s value. B. Transactional Measures and Model-based Estimates There are a variety of methods that can be used for discount rate estimation, but these methods can be classified into two distinct categories: transactional and model-based. Transactional methods determine a discount rate based upon required rates of return observed in the market, while model-based methods generally start with a risk-free rate and then add a series of upward adjustments based on the risk characteristics of the asset (cash flow stream) that is being valued. 1. Model-based Methods There are several model-based methods that are widely used in the estimation of discount rates. These include the capital asset pricing model ( CAPM ), the arbitrage pricing model, and the Fama-French Three-Factor model. While each model is unique in certain ways, each one approaches the estimation of a discount rate using the same basic approach. That is, each one starts with a risk-free rate, and then adds one or more premia to the risk-free rate to arrive at a

4 Page 2 total discount rate that incorporates a return for the various risk characteristics of the cash flow stream being discounted. The most common model-based method for discount rate estimation is the CAPM, which will be discussed in greater detail in the following subsections. It is critical to understand the fundamental logic behind model-based cost of capital methods. These methods rely on the idea that capital markets (asset markets) are perfectly competitive, or efficient. This assumption is tantamount to the assumption that, on the average, realized returns in capital markets will be equal to required (expected) returns. Therefore, under the assumption that capital markets are efficient, model-based methods attempt to fit the data, or predict the returns earned in capital markets. Models that predict returns are, under the assumption of efficient markets, also models that capture the required rate of return. While the CAPM is undoubtedly the most commonly used cost of capital model, a large body of literature demonstrates that its ability to predict capital market returns is limited in systematic ways. In particular, CAPM systematically underestimates the effect of company size on the returns realized (and required) by investors. For this reason, CAPM is routinely augmented by a size premium. This adjustment, among others, is discussed in greater detail later in this appendix. 2. Transactional Methods In contrast to model-based methods, transactional methods rely on actual rates used by investors to discount cash flows. While transactional methods do sometimes rely on assumptions (and could therefore be thought of as relying on a model of sorts), these assumptions are generally about cash flows being discounted, rather than assumptions about the way in which investors define and price risk. In other words, whereas model-based discount rate estimates make numerous assumptions about the nature of capital markets and the ways in which investors frame risk, transactional methods rely, at most, on assumptions about cash flows. There are two basic types of transactional discount rate measures hurdle rates and implied discount rates. Hurdle rates are discount rates that companies actually use internally for capital budgeting purposes (including assessing a target company in the context of an acquisition). The hurdle rate for a specific investment is the minimum rate of return that a company would require, in expectation, in order for it to make that capital investment. Correspondingly, an implied discount rate is the rate of return that equates an asset s market price to the present value of its expected future cash flows. For example, a public company s implied cost of equity capital can be estimated by using a discounted cash flow ( DCF ) analysis to solve for the rate that the market must be using to discount expected future cash flows to shareholders, given estimates of the company s cash flows and the company s known market capitalization.

5 Page 3 A large body of literature related to transactional discount rates has emerged, due in large part to the failures of the standard model-based discount rate estimates. 1 Studies have used crosssectional survey data to examine company investment decisions, finding that, on average, the hurdle rates upon which firms actually base their investment decisions exceed the discount rate implied by the CAPM by approximately five percentage points. 2 The use of implied discount rates in finance has also increased due to the advantages that the method offers, including the fact that, unlike common applications of model-based methods, implied discount rates do not rely on ex post realized returns as a proxy for expected returns. Implied discount rates have proven to be more intuitive, and consistent with theoretical predictions, than their model-based counterparts. 3 Further, the computation of an implied discount rate is also simpler and more direct than model-based methods. 1 Problems with various model-based methods are well documented. Even Fama and French, the developers of one of the widely used model-based methods, concede that Estimates of the cost of equity are distressingly imprecise (O)ur message is that the task is beset with massive uncertainty whatever the formal approach two of the ubiquitous tools in capital budgeting are a wing and a prayer, and serendipity is an important force in outcomes. (Fama, Eugene, and French, Kenneth, Industry Costs of Equity, Journal of Financial Economics (February 1997). 2 Meier, Iwan and Tarhan, Vefa, Corporate Investment Decision Practices and the Hurdle Rate Premium Puzzle (January 28, 2007). 3 Lee, Charles M.C., So, Eric C. and Wang, Charles C. Y., Evaluating Implied Cost of Capital Estimates (April 8, 2010).

6 Page 4 II. Model-based Cost of Capital The Capital Asset Pricing Model A. The CAPM Framework: Price Quantity of Risk The CAPM is the most widely accepted predictive model for estimating a company s required return on equity capital. 4 In applying the CAPM, the rate of return on equity capital is estimated, or predicted, by starting with the current risk-free rate of return appropriate for the asset(s) under review. To this is added the product of a market risk premium expected over the risk-free rate of return and the beta for the asset of interest. The intuition behind the CAPM is simple. The CAPM says that the cost of capital for any asset (or, equivalently, for any cash flow) is equal to the risk free rate of return, plus a return that is equal to the price of risk (the market risk premium) times the quantity of risk (the beta coefficient). Thus, the CAPM can be thought of as saying that the required rate of return is equal to the risk free rate plus a term equal to Price x Quantity of risk. Formally, the rate of return on equity capital using the CAPM is calculated as follows: (Formula 2) [ ( )], where: = Rate of return on equity capital; = Risk-free rate of return; = Beta for equity investment; and ( ) = Market Risk Premium, or Equity Risk Premium (MRP or ERP), which is calculated as the expected return on a broad portfolio of stocks in the market ( ) less the risk free rate ( ). Thus, the basic CAPM is, again, the risk free rate plus the cost (price x quantity) of risk. B. Standard Adjustments to CAPM There are two kinds of standard adjustments to CAPM. Both of these are made in order to increase the model s predictive power. First, certain premia are added directly to CAPM. These are added based upon empirical studies of the degree to which CAPM underestimates the cost of capital. For example, as noted earlier, it is widely known that CAPM does not properly account for the risk (and required return) for small firms. 4 Investments, W.F. Sharpe, Prentice Hall: Englewood Cliffs, New Jersey (1985).

7 Page 5 Second, certain adjustments are typically made to the beta coefficient in order to ensure that it is properly measuring the quantity of risk that is inherent in the cash flow stream being discounted (i.e., the assets being valued). That is, since observed beta coefficients (for example, those available from Bloomberg, or Yahoo!Finance) measure the quantity of risk inherent in the equity of an entire firm, betas are measuring the combined effect of financial leverage, operating leverage, and the firm s holdings of non-operating zero risk assets such as cash. It is therefore important to ensure that adjustments are made for differences in these items, as between the firm or cash flow stream being examined and the comparables (benchmarks) that are used to estimate beta. 1. Premia Added to Enhance CAPM s Predictive Power In general, two kinds of premia are added to CAPM: 1) the size premium, and 2) the country risk premium. Formula 3, below, shows the CAPM given these adjustments. (Formula 3) [ ( )], where all variables are defined as before, and = Small Company Premium, if warranted; and CRP = Country Risk Premium, if warranted. In our view, it is rarely appropriate to add a country risk premium to the CAPM for purposes of estimating the discount rate in a transfer pricing context. The reason for this is straightforward. Most firms that are used as comparables (i.e., firms that are used to estimate the beta for a given cash flow) are multinationals that operate in countries all over the world. Thus, their beta coefficients already represent the quantity of systematic risk inherent in a global set of cash flows. Unless one can reliably discern the weightings of the comparables cash flows by region or country, and from these determine the way in which the market places premia (or discounts) on cash flows from a certain region, the application of country risk premia may not be reliable. On the other hand, estimation and addition of a size premium (or discount for very large companies / cash flow streams) is nearly always warranted, in our view. The size premium, defined as the excess returns over those predicted by CAPM demanded by market for small firms, is one of the most robust results in finance, and is not dependent upon geography. ABC Software, while not a micro-cap firm, is certainly a small firm relative to most publicly traded companies. Technically, the CAPM s beta coefficient measures the risk of a security by measuring the covariance between the security s observed market price and the observed value of the market as a whole. 5 Equities whose prices move in tandem with the market, but that move more than the market in percentage terms, are clearly riskier than equities whose prices move in tandem 5 The beta coefficient will be discussed in greater detail in the sections that follow.

8 Page 6 with the market but that tend to increase or decrease by a lower percentage than the market s value. However, the empirical literature on CAPM is clear that beta does not tell the whole story. Specifically, investors clearly demand a higher return than CAPM predicts they should when investments are made in small firms. One of the earliest studies of this phenomenon is the contribution of Eugene Fama and Kenneth French (1995), 6 both extremely distinguished figures in economics. Fama and French found that CAPM tends to under-predict returns for small firms as well as firms that have low market values relative to book values of equity. Numerous other empirical studies have found that small companies have tended to realize greater returns over those predicted by the CAPM. Morningstar summarizes the research as follows: One of the most remarkable discoveries of modern finance is that of the relationship between firm size and return. The relationship cuts across the entire size spectrum but is most evident among smaller companies which have higher returns on average than larger ones The firm size phenomenon is remarkable in several ways. First, the greater risk of small stocks does not, in the context of the [CAPM], fully account for their higher returns over the long term. In the CAPM, only systematic or beta risk is rewarded; small company stocks have had returns in excess of those implied by their betas. 7 Because small stocks tend to be less liquid, traded less frequently, and have higher default risk, investors will tend to require an additional return for investing in small stocks. Several methods have been developed in order to address this key limitation of the basic CAPM approach. First, empirical studies have been performed by financial economists and practitioners in order to estimate these excess returns and develop appropriate adjustments ( size premia ) to apply directly to the CAPM framework. 8 Second, alternative cost of capital models have been proposed that take into consideration multiple risk factors that seem to matter in real life to investors (in contrast to the CAPM which assumes that only one factor, beta, measures the quantity of risk). The most common proposed alternative to the CAPM is the arbitrage pricing theory ( APT ) model, and its extension, the Fama-French three-factor model. In contrast to the CAPM, both the APT and Fama-French models allow for multiple factors to explain the relationship between risk and 6 Fama, Eugene, and French, Kenneth. Size and Book-to-Market Factors in Earnings and Returns, Journal of Finance 50 (1995), p SBBI, Valuation Edition 2007 Yearbook, Morningstar, 2007, p. 129, 134. Quoted in: Pratt, Shannon, and Grabowski, Roger, Cost of Capital: Applications and Examples, 3 rd Edition, John Wiley and Sons, 2008, p The two most widely-accepted size premium studies are published by Morningstar and Duff & Phelps.

9 Page 7 return. That is, they allow for other firm or economic characteristics to explain the variation in the return of the stock, rather than only the market s realized return. The APT provides a general multi-factor model specification wherein the return of a security can be expressed as a function of several economic factors (e.g., GDP, inflation, taxes, etc.). The Fama-French threefactor model extends the APT and specifies a three factor model based on observed above average returns for small stocks and high book to market firms. 9 The Fama-French model specification thus seeks to address the key limitation of the CAPM that is tends to systematically underestimate the returns to excess returns to small stocks. 2. Beta Adjustments to Accurately Price the Systematic Risk of the Assets Being Valued As noted earlier, the beta coefficient for a firm is influenced by the following. The presence (or absence) of zero beta assets. Cash has, by definition, a zero beta. In other words, the value of cash does not change, which means that it does not co-vary in value with the market. Therefore, if a firm holds excess cash (as many firms do), its beta will be the weighted average of zero (the beta for the firm s cash) and the beta for the firm s operating assets. The presence (or absence) of debt. Debt, or financial leverage, increases the riskiness of equity. This occurs simply because debt is the first claimant over the firm s operating profit, and its presence makes equity returns more volatile during upswings and downswings in the firm s performance. Thus, two identical firms (firms with identical assets) will have different equity betas if their financial structure differs. The presence (or absence) of operating leverage. Fixed costs, also known as operating leverage have a similar effect on a firm s beta coefficient to that of financial leverage. As a firm s fixed cost structure rises, the volatility of its cash flows (including the cash flows to equity) also rises. When discounting a cash flow stream to present value, one is arriving at the market value of the operating assets that give rise to that cash flow stream. It is therefore critical that the beta coefficient used in the CAPM is not influenced by the presence non-operating assets that are not being valued (i.e., non-operating assets such as excess cash that do not generate the cash flows of interest), or by risk characteristics that are not present in the operating assets that generate the cash flows being discounted (i.e., differences between the operating leverage or financial leverage that influences the betas of comparable firms and the operating or financial leverage of the assets of interest). Therefore, in order to properly apply the CAPM framework, it is necessary to make the following adjustments to beta. 9 Brigham, Eugene, and Daves, Phillip. Intermediate Financial Management, 10 th Edition, South-Western Cengage Learning, 2010, p

10 Page 8 First, one must de-lever the beta coefficients derived from comparable firms, in order to ensure that the beta coefficients obtained are reflective of the natural risk of the assets themselves, rather than the risks of leveraged assets. The resulting beta coefficients are referred to as asset betas. Second, one must eliminate the effect of excess cash on the discount rate that is used to discount a firm s operating cash flow (i.e., on the asset beta). Without removing the influence of excess cash on beta, the resulting present value of a firm s operating cash flow (i.e., the value of its operating assets) will be overstated due to the influence of a zero beta asset (cash) on the discount rate. Third, the influence of operating leverage on the riskiness of the firm s operating assets, known as the degree of operating leverage, must be measured and made comparable as between the benchmark assets (comparables) and the assets of interest. In particular, if the operating profit flow being discounted is residual profit (for example, operating profit less a fixed or nearly fixed routine return paid to sales companies), then this residual profit faces more operating leverage, by definition, than the asset betas of comparable companies. 10 The procedure for making these beta adjustments when one begins with betas from publicly traded firms, and then uses these betas to discount the cash flow associated with specific operating assets, is as follows. First, de-lever the beta coefficients taken from the comparable companies to arrive at estimates of the comparables asset betas. Second, adjust the asset betas for the presence of cash assets, to arrive at operating betas or operating asset betas. Finally, adjust these operating betas to reflect the degree of operating leverage associated with the profit stream being discounted for example residual profit, if it is residual profit being discounted. C. Example Estimation of CAPM Components in the Hypothetical Case of Discounting a Software Company s Residual Profit Stream 1. Statement of Facts The cash flows being discounted in this case consist of the residual profit stream associated with the intangible property holding company of ABC Software, Inc. ( ABC Software, or ABC ). ABC Software s intangible property holding company ( IPCO ) is based in Switzerland, and is the principal and residual claimant within the related party system. The intangible property owned and developed by IPCO consists of software that assists companies in managing their IT infrastructure. IPCO pays its related distributors a guaranteed operating margin of 3.8 percent. IPCO also pays related contract R&D affiliates a guaranteed cost plus markup of 7 percent. ABC Software operates as a division of TECHCO. Prior to 2008, ABC was an independent, publicly-traded, firm. 10 The reason that this is true is that the asset betas of comparable companies are the betas of these companies full operating profit, rather than their residual profit.

11 Page 9 2. Analysis Date IPCO s claim to residual profit is being discounted as of April 30, We refer to this interchangeably as the analysis date and the valuation date. 3. Risk Free Rate of Return There are a number of options available to practitioners when choosing the risk free rate of return. These include the US government s three month, one year, five year, 10 year, 20 year, and 30 year bonds. At a technical level, the choice among these should be determined by matching the duration of the cash flows being discounted with the duration of one of the government bonds. 11 However, in practice, for purposes of valuing long term investments, practitioners generally select the long-term U.S. government bond as the risk-free rate of return for the CAPM and for the estimation of the equity risk premium. In short, a long-term government bond is typically appropriate given that business investments face similar duration and reinvestment risk to that of a long-term government bond. Among business valuation practitioners, the consensus risk-free rate for use in the CAPM seems to be the 20-year U.S. government bond, for several reasons. First, the 20-year bond most closely matches the assumption of a perpetual time horizon on an equity investment. Second, long-term government bonds, such as the 20-year, tend to fluctuate considerably less than shortterm rates, reducing the chances of introducing inappropriate short-term distortions into the cost of capital. Third, practitioners generally recognize that maturity risk is embedded in this rate. Finally, the 20-year U.S. bond matches the longest-term bond over which the equity risk premium is generally measured. 12 In light of these considerations, we have used the yield on the 20-year U.S. government bond of 4.1 percent, as of the valuation date, for our risk-free rate estimate. 4. Equity Risk Premium Quantification of the equity risk premium has been the subject of much research by securities analysts. Since the expectations of the average investor are not directly observable, the equity risk premium must be inferred. 11 Duration is defined as the weighted average time period over which cash flows arrive, using present values in each period of the forecast horizon as weights. This is known as Macauley Duration. Finance practitioners will immediately note that one doesn t know the duration unless one knows the discount rate, and yet we need duration to pick the risk free rate that is an input into the discount rate. Generally, this problem can be solved by assuming a range of reasonable discount rates, resulting in a range of duration results. 12 Pratt, Shannon, and Grabowski, Roger, Cost of Capital: Applications and Examples, 3 rd Edition, John Wiley and Sons, 2008, p

12 Page 10 There are two basic measures of the ERP: historical and forward looking. Many practitioners will use historical data to estimate the ERP, under the view that the past behavior of the equity risk premium provides a reasonable indicator of how the ERP will behave going forward. Alternatively, the forward-looking ERP can be estimated at a specific point in time by identifying the implied expected return for the stock market. Each of these approaches is discussed below. a) Historical ERP The premium obtained using the historical approach is sensitive to the time period over which one calculates the average, and it is important to select the appropriate period to measure the historical ERP. While the recent past may be of particular interest to an investor, there are important reasons for using a long-term history to estimate the ERP. Long-term historical returns have been remarkably stable, and a reliance on short-term observations may bias the estimate upward or downward, thereby leading to inappropriate forecasts. Moreover, all else equal, more observations will lead to a more accurate estimate of the ERP than will fewer observations. 13 That is, a longer run time series is simply provides a larger sample size than a short run time series. It bears noting in this regard that one of the key determinants of the historical ERP is the relationship between bond and equity volatility. That is, the difference between stock yields and bond yields (and therefore, the equity risk premium) appears to be strongly positively correlated with the difference in volatility between the two types of securities. This relationship is clear when one compares the bond and equity volatility to realized ERPs during the periods and The arithmetic average ERPs were 10.5 percent and 5.1 percent, respectively, for these two periods. By comparison, the ratio of equity to bond return volatility was 5.4 and 1.5, respectively. In other words, in periods of high relative equity volatility, the equity risk premium is, quite rationally, higher. In light of the fact that equity volatility has been extreme over the past decade, it is sensible to examine the ERP from the perspective of the long run. This allows us to capture periods in which the relative volatility of stocks was high. Given this, we have used the arithmetic average historical equity risk premium calculated by Ibbotson Associates. This value was 6.5 percent for the period b) Forward Looking ERP An obvious problem with the use of the historical market risk premium is that it is backward looking. Forward looking (ex ante) approaches estimate the equity risk premium by subtracting the current risk-free rate from the implied expected return of the stock market Pratt, Shannon, and Grabowski, Roger, Cost of Capital: Applications and Examples, 3 rd Edition, John Wiley and Sons, 2008, p Ibbotson Associates Ibbotson SBBI Valuation Yearbook. Quoted in: Morningstar, International Equity Risk Premium Report 2009, Morningstar, Inc. (2009), p. 5.

13 Page 11 One approach to calculating a forward-looking equity risk premium uses a dividend discount model ( DDM ) to solve for the required return on equity. The DDM calculates the value of equity as the present value of expected dividends from an investment. Damodaran developed a more general model based on the DDM to calculate implied ERP. His model considers not only dividends but total expected cash flow to equity by including dividends and stock buybacks. 16 Damodaran estimates the implied ERP for the market using data from the S&P 500 index and consensus estimates regarding growth for stocks in the index. Damodaran s model solves for the implied ERP as the rate that makes the intrinsic value of the index (the present value of expected cash flow to the S&P 500) equal to the current market value of the index. For the expected cash flow to the S&P 500, Damodaran uses the trailing 12-month dividend/buyback yield, multiplied by the consensus S&P 500 growth estimates for the first five forecast years and then calculates a terminal value using a long term Treasury bond rate as the terminal growth rate. Using Damodaran s method, the implied forward-looking equity risk premium calculation for April 30, 2009 is approximately 6.3 percent. A summary of the calculation is provided below. 15 Pratt, Shannon, and Grabowski, Roger, Cost of Capital: Applications and Examples, 3 rd Edition, John Wiley and Sons, 2008, p Damodaran, Aswath, Equity Risk Premiums (ERP): Determinants, Estimation and Implications The 2011 Edition, (February 2011).

14 Page 12 Exhibit 1: Implied ERP Calculation Line Description Value Notes / Sources 1 Index Level S&P Trailing 12 Months Cash Flow on S&P Damodaran 3 Current Dividend Yield 5.9% Line 2 / Line 1 4 Expected Earnings Growth Rate next 5 Years 4.00% Damodaran 5 Current Long Term Bond Rate 3.2% 6 Expected Long Term Growth Rate 3.2% Line 5 = Line 6 Year (t) 7 Calculation of Implied Equity Risk Premium Terminal 8 Expected Dividends (See Footnote 1) , Present Value of Cash Flows (See Footnote 2) Intrinsic Value of Index (See Footnote 3) Implied Equity Risk Premium (See Footnote 4) 6.32% Notes: /1/ Line 3 * Line 1 * (1 + Line 4)^t where t is the year. /2/ Line 8/(1 + Line 5 + Line 11)^t /3/ Sum of Line 9. The intrinsic value of the index equals the current value of the index. /4/ The implied equity risk premium is the ERP such that the intrinsic value of the index equals the current value. The use of a historical premium assumes that the equity risk premium does not change much over short periods and, over time, reverts back to historical averages. This assumption was called into question during the recent financial crisis. In a one-month period between September 12, 2008 and October 12, 2008, the implied equity risk premium rose from 4.2 percent to 6.4 percent. This demonstrates that there can be large swings in the ERP in a short period of time, and highlights the danger of blindly using a fixed premium that ignores structural shifts in the market, such as the shifts that occurred during the financial crisis. The following chart shows the monthly implied equity risk premium between January 2008 and September Note the dramatic rise in the ERP that occurred in late 2008, with the ERP remaining above 6.0 percent through the spring of 2009.

15 Page 13 Exhibit 2: Implied ERP Data 9.00% Monthly Implied Equity Risk Premium: 2008-Present 8.00% 7.00% 6.00% 5.00% 4.00% Implied ERP 3.00% 2.00% 1.00% 0.00% c) Concluded ERP Given that the ERP can be estimated using both historical stock market returns and the forward looking premium implied by the current market value, and given that there are advantages to each approach, we have taken both these measures into consideration to determine the appropriate ERP as of the valuation date. The exhibit below summarizes the historical and forward looking ERP.

16 Page 14 Exhibit 3: Concluded Equity Risk Premium Line Source Value Notes / Comments A Ibbotson 1926 to % Morningstar International Equity Risk Premia Report 2009, pg. 5. B Forward Looking Market Risk Premium 6.32% Professor Damodaran Research, Economics Partners Calculation C Average 6.4% Average D Concluded Market Risk Premium 6.4% D=C As indicated by the exhibit above, the historical and forward looking ERP as of 4/30/2009 fall with a very tight range of 6.32 percent to 6.50 percent. The fact that these two measures produce similar results corroborates the conclusion that the true ERP falls somewhere within this tight range. We have therefore concluded on the average ERP of 6.4 percent. 5. Beta Coefficient Beta is generally estimated by regressing the excess returns (i.e., total return over the return on a risk-free investment) of an asset against the excess returns earned by the market. The regression formula for is presented in the formula below. (Formula 4) ( ) Research indicates that this regression formula tends to underestimate beta, as it assumes that stocks immediately adjust to changes in market conditions. In fact, all but the largest stocks tend to lag slightly in their adjustment to the overall market. 17 The commonly employed sum beta technique therefore provides a much more robust means of estimating beta that adjusts for this short lag. a) Sum Beta For all but the largest companies, an individual stock s price tends to react to movements in the overall market with a lag. In fact, the smaller the company is, the greater the lag in the price reaction to movements in the overall market. Consequently, due to this lag effect, the traditional measure of beta shown in formula VI-3 tends to understate systematic risk for all but the largest companies. In fact, this understatement of systematic risk by traditional beta measurements may partially, but certainly not fully, account for the excess returns over the CAPM for small stocks. 18 In order to address the lag effect, finance practitioners and researchers have developed the sum beta as an alternative estimation of the CAPM beta by incorporating a lagged term into 17 Myron Scholes and Joseph Williams, "Estimating Betas from Nonsynchronous Data," Journal of Financial Economics, vol 5, 1977, ). 18 Pratt, Shannon, and Grabowski, Roger, Cost of Capital: Applications and Examples, 3rd Edition, John Wiley and Sons, 2008, p It is very important to note that the empirical work on the small stock premium, particularly that of Morningstar, uses the premium earned by small stocks over the CAPM using the sum beta. In part for this reason, in our own application of CAPM, we also use the sum beta.

17 Page 15 the regression equation above. That is, a sum beta is calculated using a multiple regression of a stock s current month excess return on the market s current month s excess return and the market s previous month s excess return. Mathematically, the equation for the sum beta is as follows: (Formula 5) ( ) ( ) ( ) where: ( ) = Stock excess return in current month; = Estimated market coefficient for current month; ( ) = Market excess return in current month; = Estimated lagged market coefficient; ( ) = Excess return on the market in previous month; = Regression constant; and = Regression error term. The sum beta is thus the sum of the and coefficients. By incorporating the lagged effect of market movements on company returns for all but the largest companies, the sum beta estimate provides a superior estimation of the CAPM beta. In fact, researchers have observed that the use of sum betas produces much lower returns in excess of CAPM than the use of traditional OLS betas. 19 Put differently, sum beta sharply improves the predictive power of CAPM. We have calculated the sum beta 20 for a sample of comparable software companies to ABC Software as of April 30, The exhibit below summarizes the five year sum beta for each of the comparable companies. 19 Pratt, Shannon, and Grabowski, Roger, Cost of Capital: Applications and Examples, 3rd Edition, John Wiley and Sons, 2008, p We have calculated a five-year sum beta using monthly returns for the preceding 60 months. The 60 month look-back period is the most commonly used time horizon for estimating betas according to Pratt and Grabowski (2008).

18 Page 16 Exhibit 4: Comparable Company Unadjusted (Levered) Beta Coefficients Line Comparable Company Unadjusted Beta Source 1 BMC Software Inc CapitalIQ and Economics Partners Calculations 2 Citrix Systems, Inc CapitalIQ and Economics Partners Calculations 3 Compuware Corporation 1.65 CapitalIQ and Economics Partners Calculations 4 Open Text Corp CapitalIQ and Economics Partners Calculations 5 Parametric Technology Corp 1.40 CapitalIQ and Economics Partners Calculations 6 Quest Software Inc CapitalIQ and Economics Partners Calculations 7 TIBCO Software Inc CapitalIQ and Economics Partners Calculations 8 VMware, Inc CapitalIQ and Economics Partners Calculations Average Unadjusted Beta 1.20 Median Unadjusted Beta 1.13 As shown, the average and median sum betas from our sample are 1.2 and 1.13, respectively. It bears noting that deletion of the two seeming outliers from our sample (BMC Software Inc. and VMware, Inc.) barely changes our results, as the average and median given such deletion are 1.16 and 1.14, respectively. We conclude, therefore, that beta should lie within the range given in Exhibit 4. b) Beta Adjustments (1) Financial Leverage Adjustments The finance literature proposes several methods for determining the unlevered beta. The two most commonly employed adjustments are embodied in the Hamada equation and the Miles- Ezzell equation. These two formulas differ in their underlying assumptions. Specifically, Hamada assumes an expected constant level of debt over time, whereas Miles-Ezzell assumes a constant proportion of debt within the capital structure. Further, Hamada assumes that the beta coefficient of debt is zero, whereas Miles-Ezzell does not. Therefore, Hamada and Miles-Ezzell provide two formulaic ends of the spectrum when delevering beta. The application of each of these methods is discussed in turn below. The Hamada equation for the unlevered beta is as follows: (Formula 6) ( ) where: = Beta unlevered;

19 Page 17 = Beta levered; t = Company tax rate; = Debt percent of capital structure; and = Equity percent of capital structure. While the Hamada equation is by far the most commonly employed formula for unlevering beta, financial economists have proposed alternative formulas for unlevering and relevering equity betas. Perhaps the second most common alternative to Hamada is the Miles-Ezzell equation. The Miles-Ezzell equation computes the unlevered beta based on the assumptions that: 1) the risk of the tax shield after the first year is comparable to the risk of operating cash flows; 2) the variability of operating cash flows affect the risk of debt capital (i.e., the beta of debt may be greater than zero); and 3) the market value of debt remains constant as a percentage of equity capital. 21 Based on these assumptions the formula for the Miles-Ezzell unlevered beta is as follows: (Formula 7) where: = Beta unlevered = Beta levered = Market value of equity capital = Market value of debt capital = Beta of debt capital T = Company tax rate = Pre-tax cost of debt capital Importantly, unlike the Hamada equation, the Miles-Ezzell equation does not assume that the beta of debt is zero. As such, in order to apply the Miles-Ezzell equation, the debt beta must first be calculated. In order to do so, we calculate the implied debt beta using a CAPM framework. That is, given the risk-free rate, the equity risk premium, and the debt discount rate 21 Pratt, Shannon, and Grabowski, Roger, Cost of Capital: Applications and Examples, 3rd Edition, John Wiley and Sons, 2008, p

20 Page 18 (the pre-tax cost of debt capital), the beta of debt can be estimated by rearranging the CAPM to solve for beta. This formula is presented below. (Formula 8) Given the debt beta, the Miles-Ezzell equation can then be applied to calculate unlevered beta. In order to determine the unlevered beta for each of the comparable companies, we compute their unlevered beta using both the Hamada equation and the Miles-Ezzell equation. Before turning to the adjustment of each comparable company s beta for financial leverage, we first examined each company s capital structure and non-operating assets as of the valuation date. The exhibits below present these financial data for each company. Exhibit 5: Summary Financials for BMC Software Line Description Value Notes / Calculation Capital Structure as of 4/30/ Preferred Stock - 2 Interest Bearing Debt Market Value of Debt Line 1 + Line 2 4 Share Price Day 5 Shares Outstanding Day 6 Market Capitalization 5,736 Line 4 * Line 5 7 Minority Interest - 8 Market Value of Equity 5,736 Line 6 + Line 7 Excess Cash Calculation 9 Accounts Receivable Accounts Payable Excess Cash 1, If payables exceed receivables, difference is required cash. 12 Operating Assets 2, Non-operating Assets 1,023.30

21 Page 19 Exhibit 6: Summary Financials for Citrix Systems Line Description Value Notes / Calculation Capital Structure as of 4/30/ Preferred Stock - 2 Interest Bearing Debt - 3 Market Value of Debt - Line 1 + Line 2 4 Share Price Day 5 Shares Outstanding Day 6 Market Capitalization 4,237 Line 4 * Line 5 7 Minority Interest - 8 Market Value of Equity 4,237 Line 6 + Line 7 9 Accounts Receivable Accounts Payable Excess Cash If payables exceed receivables, difference is required cash. 12 Operating Assets 2, Non-operating Assets Exhibit 7: Summary Financials for Compuware Corporation Line Description Value Notes / Calculation Capital Structure as of 4/30/ Preferred Stock - 2 Interest Bearing Debt - 3 Market Value of Debt - Line 1 + Line 2 4 Share Price Day 5 Shares Outstanding Day 6 Market Capitalization 1,575 Line 4 * Line 5 7 Minority Interest - 8 Market Value of Equity 1,575 Line 6 + Line 7 Excess Cash Calculation 9 Accounts Receivable Accounts Payable Excess Cash If payables exceed receivables, difference is required cash. 12 Operating Assets 1, Non-operating Assets

22 Page 20 Exhibit 8: Summary Financials for Open Text Corp. Line Description Value Notes / Calculation Capital Structure as of 4/30/ Preferred Stock - 2 Interest Bearing Debt Market Value of Debt Line 1 + Line 2 4 Share Price Day 5 Shares Outstanding Day 6 Market Capitalization 1,738 Line 4 * Line 5 7 Minority Interest Market Value of Equity 1,747 Line 6 + Line 7 Excess Cash Calculation 9 Accounts Receivable Accounts Payable Excess Cash If payables exceed receivables, difference is required cash. 12 Operating Assets 1, Non-operating Assets Exhibit 9: Summary Financials for Parametric Technology Corporation Line Description Value Notes / Calculation Capital Structure as of 4/30/ Preferred Stock - 2 Interest Bearing Debt Market Value of Debt 88.5 Line 1 + Line 2 4 Share Price Day 5 Shares Outstanding Day 6 Market Capitalization 1,105 Line 4 * Line 5 7 Minority Interest - 8 Market Value of Equity 1,105 Line 6 + Line 7 Excess Cash Calculation 9 Accounts Receivable Accounts Payable Excess Cash If payables exceed receivables, difference is required cash. 12 Operating Assets 1, Non-operating Assets

23 Page 21 Exhibit 10: Summary Financials for Quest Software Inc. Line Description Value Notes / Calculation Capital Structure as of 4/30/ Preferred Stock - 2 Interest Bearing Debt - 3 Market Value of Debt - Line 1 + Line 2 4 Share Price Day 5 Shares Outstanding Day 6 Market Capitalization 1,179 Line 4 * Line 5 7 Minority Interest - 8 Market Value of Equity 1,179 Line 6 + Line 7 Excess Cash Calculation 9 Accounts Receivable Accounts Payable Excess Cash If payables exceed receivables, difference is required cash. 12 Operating Assets 1, Non-operating Assets Exhibit 11: Summary Financials for Tibco Software Inc. Line Description Value Notes / Calculation Capital Structure as of 4/30/ Preferred Stock - 2 Interest Bearing Debt Market Value of Debt 44.6 Line 1 + Line 2 4 Share Price Day 5 Shares Outstanding Day 6 Market Capitalization 960 Line 4 * Line 5 7 Minority Interest Market Value of Equity 961 Line 6 + Line 7 Excess Cash Calculation 9 Accounts Receivable Accounts Payable Excess Cash If payables exceed receivables, difference is required cash. 12 Operating Assets Non-operating Assets

24 Page 22 Exhibit 12: Summary of Financials for VMware, Inc. Line Description Value Notes / Calculation Capital Structure as of 4/30/ Preferred Stock - 2 Interest Bearing Debt Market Value of Debt Line 1 + Line 2 4 Share Price Day 5 Shares Outstanding Day 6 Market Capitalization 9,753 Line 4 * Line 5 7 Minority Interest - 8 Market Value of Equity 9,753 Line 6 + Line 7 Excess Cash Calculation 9 Accounts Receivable Accounts Payable Excess Cash 1, If payables exceed receivables, difference is required cash. 12 Operating Assets 1, Non-operating Assets 1, Exhibits 5 through 12 summarizes the financial information needed to perform both the financial leverage and excess cash adjustments. The exhibit below then uses these data to calculate the unlevered equity betas for each of the comparable companies using both the Hamada and Miles-Ezzell equations discussed above. Exhibit 13: Comparable Company Beta Coefficients Adjusted for Debt Leverage Unadjusted Market Value Market Value Pre-Tax Cost Implied Company Hamada Miles-Ezzell Concluded Beta Of Equity Of Debt Of Debt Capital Debt Beta Tax Rate Unlevered Beta Unlevered Beta Unlevered Beta Line Comparable Company A B C D E F G H I 1 BMC Software Inc % % Citrix Systems, Inc % % Compuware Corporation % % Open Text Corp % % Parametric Technology Corp % % Quest Software Inc % % TIBCO Software Inc % % VMware, Inc % % Source / Calculation Exhibit 4 S&P: CapitalIQ S&P: CapitalIQ Moody's Baa See Footnote 1 S&P: CapitalIQ See Footnote 2 See Footnote 3 I = (G+H)/2 10 Average Unlevered Beta Median Unlevered Beta 1.12 Notes: /1/ Implied debt beta is solved for using the CAPM framework. E=(D-4.10%)/6.41%, where 4.10% is the risk free rate of return and 6.41% is the market risk premium. /2/ F=A/(1+((1-E)*(C/(B+C))/(B/(B+C))) /3/ G=(B*A+C*E*(1-((F*D)/(1+D))))/(B+C*((1-((F*D)/(1+D)))) As is clear from Exhibit 13, our concluded unlevered betas are quite similar to the levered betas given in Exhibit 4. This is not surprising, given that software companies tend to have little in the way of financial leverage.

25 Page 23 (2) Non-operating Asset (Excess Cash) Adjustment As discussed above, the adjustment for financial leverage results in the equity (or asset) beta that reflects the firm s weighted average risk across all of its assets. However, in order to determine an operating beta that is, the beta appropriate for discounting the operating cash flow that results from the firm s operating assets it is necessary to also adjust beta for the effects of any excess cash. By definition, cash has a beta of zero. Therefore, the adjustment for excess cash is based on the fact that the company s beta is the weighted average of the company s assets, including excess cash. Given that cash has a beta of zero, the operating asset beta must be the beta such that the value-weighted average of the operating asset beta and the non-operating asset beta equals the unlevered equity beta derived above. 22 Mathematically, the adjustment for excess cash is shown below. (Formula 9) where: = Operating asset beta; and = Non-operating asset beta. We then applied this equation to the excess cash of each comparable company. 23 As shown in exhibits 5 through 12 above, we defined the cash required for business operations by comparing the payables and receivables on the company s balance sheet. If payables exceed receivables, the difference is the cash required for business operations. 24 The exhibit below summarizes the excess cash adjustment and computes the operating beta for each of the comparable companies. 22 Pratt, Shannon, and Grabowski, Roger, Cost of Capital: Applications and Examples, 3rd Edition, John Wiley and Sons, 2008, p It bears noting that we did not include marketable securities or other possible non-operating assets in our definition of cash because these assets would be expected to have a non-zero beta. 24 This is the standard definition of excess cash.

26 Page 24 Exhibit 14: Operating Asset Betas Unlevered Operating Non-Operating Non-Operating Implied Operating Beta Assets Assets Asset Beta Asset Beta Line Comparable Company A B C D E 1 BMC Software Inc Citrix Systems, Inc Compuware Corporation Open Text Corp Parametric Technology Co Quest Software Inc TIBCO Software Inc VMware, Inc Source / Calculation Exhibit 13 S&P: CapitalIQ S&P: CapitalIQ Assumed E = A*((B+C)/B)-D*(C/B) 10 Average Operating Beta Median Operating Beta 1.36 (3) Operating Leverage Adjustment (a) Theoretical Framework Operating leverage has been studied extensively by finance practitioners, and accepted models exist for determining its effect on the discount rate. Firms with high fixed costs, relative to variable costs, have high operating leverage. 25 High operating leverage is associated with increased systematic risk, which impacts the discount rate (through beta). To address the impact of operating leverage on systematic risk, Mandelker and Rhee propose a method that adjusts beta (the measure of systematic risk in the CAPM) for the degree of operating leverage. 26 The application of this method is straightforward. Mandelker and Rhee define a measure called the degree of operating leverage, or DOL. DOL is simply the elasticity of operating profit with respect to changes in sales. The more sensitive, in percentage terms, is operating profit to changes in sales, the higher is the degree of operating leverage. This makes sense, since firms with high fixed costs relative to variable costs will generally see larger movements in operating profit when sales spike upward or downward. Formally, the DOL is defined as follows: (Formula 10). 25 Brealey, Richard, Myers, Stuart, and Allen, Franklin, Principles of Corporate Finance, Concise 2 nd Edition, McGraw Hill/Irwin, 2011, pp Mandelker, Gershon, and Rhee, S. Ghon, The Impact of the Degrees of Operating and Financial Leverage on Systematic Risk of Common Stock, The Journal of Financial and Quantitative Analysis (March 1984).