Cost of Capital When Discounting Residual Profit A Case · PDF fileCost of Capital When...

Cost of Capital When Discounting Residual Profit

A Case Study

Economics Partners, LLC

White Paper

Tim Reichert, Ph.D., Erin Hutchinson, and David Suhler

White Paper 2012-1

www.econpartners.com

Table of Contents

I. Introduction ................................................................................................................................... 1

A. The Importance of the Discount Rate .................................................................................. 1

B. Transactional Measures and Model-based Estimates ....................................................... 1

1.Model-based Methods .................................................................................................................... 1

2.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 .......................................................................................... 4

1.Premia Added to Enhance CAPM’s Predictive Power .............................................................. 5

2.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 ........................................................... 8

1.Statement of Facts ........................................................................................................................... 8

2.Analysis Date ................................................................................................................................... 9

3.Risk Free Rate of Return ................................................................................................................ 9

4.Equity Risk Premium ..................................................................................................................... 9

5.Beta Coefficient.............................................................................................................................. 14

6.Size Premium ................................................................................................................................. 30

D. Capital Market Conditions as of the Transaction Date ................................................... 32

E. Concluded Model-based Estimate of the Cost of Capital ............................................... 33

III. Transaction-based Cost of Capital Estimate............................................................................ 35

IV. Concluded Cost of Capital Estimate ........................................................................................ 39

V. Consistency With Court Guidance ........................................................................................... 40

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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

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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.

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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 cross-

sectional 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).

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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).

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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.

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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. 131-155. 7 SBBI, Valuation Edition 2007 Yearbook, Morningstar, 2007, p. 129, 134. Quoted in: Pratt, Shannon, and Grabowski, Roger, Cost of Capital: Applications and Examples, 3rd Edition, John Wiley and Sons, 2008, p. 83. 8 The two most widely-accepted size premium studies are published by Morningstar and Duff & Phelps.

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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 three-

factor 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, 10th Edition, South-Western Cengage Learning, 2010, p. 96-98.

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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.

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2. Analysis Date

IPCO’s claim to residual profit is being discounted as of April 30, 2009. 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 short-

term 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, 3rd Edition, John Wiley and Sons, 2008, p. 71-72.

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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

1926-1955 and 1956-2006. 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 1926-2008.14

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.15

13 Pratt, Shannon, and Grabowski, Roger, Cost of Capital: Applications and Examples, 3rd Edition, John Wiley and Sons, 2008, p. 98-100. 14 Ibbotson Associates. 2009 Ibbotson® SBBI® Valuation Yearbook. Quoted in: Morningstar, “International Equity Risk Premium Report 2009,” Morningstar, Inc. (2009), p. 5.

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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

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, 3rd Edition, John Wiley and Sons, 2008, p. 106. 16 Damodaran, Aswath, “Equity Risk Premiums (ERP): Determinants, Estimation and Implications – The 2011 Edition,” (February 2011).

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Exhibit 1: Implied ERP Calculation

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 2011. 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.

Line Description Value Notes / Sources

1 Index Level 873.00 S&P 500

2 Trailing 12 Months Cash Flow on S&P 500 51.55 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 1 2 3 4 5 Terminal

8 Expected Dividends (See Footnote 1) 53.6 55.8 58.0 60.3 62.7 1,024.4

9 Present Value of Cash Flows (See Footnote 2) 49.0 46.5 44.2 42.0 39.9 651.4

10 Intrinsic Value of Index (See Footnote 3) 873.0

11 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.

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Exhibit 2: Implied ERP Data

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.

Monthly Implied Equity Risk Premium: 2008-Present

Implied ERP

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Exhibit 3: Concluded Equity Risk Premium

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, 309-327). 18 Pratt, Shannon, and Grabowski, Roger, Cost of Capital: Applications and Examples, 3rd Edition, John Wiley and Sons, 2008, p. 131-2. 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.

Line Source Value Notes / Comments

A Ibbotson 1926 to 2009 6.5% 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

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 beta20 for a sample of comparable software companies to ABC

Software as of April 30, 2009. 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. 132. 20 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).

Page | 16

Exhibit 4: Comparable Company Unadjusted (Levered) Beta Coefficients

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 de-

levering 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;

Line Comparable Company Unadjusted Beta Source

1 BMC Software Inc. 0.56 CapitalIQ and Economics Partners Calculations

2 Citrix Systems, Inc. 0.93 CapitalIQ and Economics Partners Calculations

3 Compuware Corporation 1.65 CapitalIQ and Economics Partners Calculations

4 Open Text Corp. 0.76 CapitalIQ and Economics Partners Calculations

5 Parametric Technology Corporation1.40 CapitalIQ and Economics Partners Calculations

6 Quest Software Inc. 0.89 CapitalIQ and Economics Partners Calculations

7 TIBCO Software Inc. 1.34 CapitalIQ and Economics Partners Calculations

8 VMware, Inc. 2.06 CapitalIQ and Economics Partners Calculations

Average Unadjusted Beta 1.20

Median Unadjusted Beta 1.13

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. 145-6.

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 4/30/2009

1 Preferred Stock -

2 Interest Bearing Debt 335.20

3 Market Value of Debt 335.2 Line 1 + Line 2

4 Share Price 31.04 60-Day

5 Shares Outstanding 184.79 60-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 317.10

10 Accounts Payable 48.90

11 Excess Cash 1,023.30 If payables exceed receivables, difference is required cash.

12 Operating Assets 2,582.10

13 Non-operating Assets 1,023.30

Page | 19

Exhibit 6: Summary Financials for Citrix Systems

Exhibit 7: Summary Financials for Compuware Corporation

1 Preferred Stock -

2 Interest Bearing Debt -

3 Market Value of Debt - Line 1 + Line 2

11 Excess Cash 326.12 If payables exceed receivables, difference is required cash.

13 Non-operating Assets 326.12

1 Preferred Stock -

Page | 20

Exhibit 8: Summary Financials for Open Text Corp.

Exhibit 9: Summary Financials for Parametric Technology Corporation

1 Preferred Stock -

7 Minority Interest 8.67

1 Preferred Stock -

Page | 21

Exhibit 10: Summary Financials for Quest Software Inc.

Exhibit 11: Summary Financials for Tibco Software Inc.

1 Preferred Stock -

6 Market Capitalization 960 Line 4 * Line 5

7 Minority Interest 0.36

8 Market Value of Equity 961 Line 6 + Line 7

12 Operating Assets 834.17

Page | 22

Exhibit 12: Summary of Financials for VMware, Inc.

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

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.

1 Preferred Stock -

11 Excess Cash 1,840.81 If payables exceed receivables, difference is required cash.

13 Non-operating Assets 1,840.81

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. 0.56 5736.01 335.20 8.24% 0.65 35% 0.54 0.57 0.56

2 Citrix Systems, Inc. 0.93 4237.24 0.00 8.24% 0.65 9.5% 0.93 0.93 0.93

3 Compuware Corporation 1.65 1575.14 0.00 8.24% 0.65 34.4% 1.65 1.65 1.65

4 Open Text Corp. 0.76 1747.15 307.79 8.24% 0.65 30.3% 0.68 0.75 0.71

5 Parametric Technology Corporation 1.40 1104.88 88.51 8.24% 0.65 33.0% 1.33 1.34 1.33

6 Quest Software Inc. 0.89 1178.67 0.00 8.24% 0.65 17.4% 0.89 0.89 0.89

7 TIBCO Software Inc. 1.34 960.66 44.56 8.24% 0.65 25.9% 1.30 1.31 1.31

8 VMware, Inc. 2.06 9752.66 450.00 8.24% 0.65 9.1% 1.98 2.00 1.99

9 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 1.17

11 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))))

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. 129-130. 23 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.

Page | 24

Exhibit 14: Operating Asset Betas

(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 2nd Edition, McGraw Hill/Irwin, 2011, pp.222-223. 26 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).

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. 0.56 2582.10 1023.30 0 0.78

2 Citrix Systems, Inc. 0.93 2368.19 326.12 0 1.05

3 Compuware Corporation 1.65 1596.74 278.11 0 1.94

4 Open Text Corp. 0.71 1179.76 254.92 0 0.87

5 Parametric Technology Corporation 1.33 1076.33 256.94 0 1.65

6 Quest Software Inc. 0.89 1127.34 215.90 0 1.06

7 TIBCO Software Inc. 1.31 834.17 254.40 0 1.70

8 VMware, Inc. 1.99 1998.39 1840.81 0 3.82

9 Source / Calculation Exhibit 13 S&P: CapitalIQ S&P: CapitalIQ Assumed E = A*((B+C)/B)-D*(C/B)

10 Average Operating Beta 1.61

11 Median Operating Beta 1.36

Page | 25

Mandelker and Rhee show that a company’s operating asset beta, which is the beta coefficient

for the entire enterprise, can be decomposed as follows.

(Formula 11) Bj = (DOL)*Bj0,

Where Bj is the beta for company j, and Bj0 is the company’s “intrinsic systematic risk.” Intrinsic

systematic risk is the systematic risk of the company’s operating assets, assuming no operating

leverage (that is, assuming that all costs are variable).

Formula 11 is both very simple, and very general. Mandelker and Rhee’s formula can be used

to compare different operating leverage positions, and their effect on beta, for a company. In

other words, the formula can be used to examine the impact on beta of increasing the operating

leverage of a company – or a specific cash flow stream.

Formally, this is expressed as:

(Formula 12) %ΔBl = (%ΔDOL)*Bl0,

where %ΔBl is the incremental increase in beta given the increase in operating leverage, and Bl0

is the beta at the base (pre-increase) level of operating leverage. This formula provides us with

the starting point for our analysis. That is, we can use this formula as the starting point for

deriving the cost of capital for ABC Software’s residual profit, given that residual profit faces

higher operating leverage than total operating profit due to the priority of the routine capital’s

claim over operating profit.

We can assume that routine invested capital claims a constant markup on total costs. We

assume that routine profits equal total cost times a markup factor. Therefore, the net residual

profit function can be written as:

(Formula 13) ,

where S is revenue, v is variable cost, C is fixed cost, and m is the routine markup on total cost.

Recall that DOL is defined as the elasticity of operating profit with respect to sales. The

elasticity of any variable Y, with respect to another variable X is always defined as

. In this

case, then, we are concerned with the elasticity of net residual profit with respect to changes in

revenue, or

. This can be expressed as follows.

(Formula 14)

where is the degree of operating leverage of net residual profit.

Page | 26

The DOL for all operating profit is derived exactly the same way as the DOL for net residual

profit. That is, we derive the elasticity of operating profit with respect to changes in revenue, or

. This can be expressed as follows.

(Formula 15)

where is the degree of operating leverage of total operating profit.

This means that we have the two components necessary to form our estimate of the beta

adjustment. The adjustment is given in Formula 16, below.

(Formula 16)

This, finally, implies that the cost of capital applicable to net residual profit, the case wherein

the return to routine invested capital is computed as a markup on total cost, is:

(Formula 17) (

(b) Application of Operating Leverage Adjustment

The preceding section outlines the theoretical relationship between operating leverage and the

cost of capital and provides a methodology for adjusting an unlevered equity beta (the

“operating beta”) for the additional risk of a residual profit flow given that routine invested

capital is a prior claimant on the cash flow stream. We next apply this method to adjust the

operating betas of the comparable companies for the additional operating leverage associated

with a residual profit flow.

As discussed above, the operating leverage beta adjustment is simply the ratio of the degree of

operating leverage for the residual profit flow divided by the degree of operating leverage for

the operating profit flow. Therefore, we can determine the operating leverage adjustment for a

company’s beta given its fixed and variable cost structure and a routine return on these costs.27

The former are readily identifiable from a company’s financial statements, and the latter can be

obtained from a sample of routine software distribution companies.28

In order to apply Formula 16, we first computed the fixed and variable cost bases for each of the

comparable companies. For ease of comparison, we have normalized the revenue to 100,

computed variable cost as a percent of revenue, and normalized the fixed cost level. The exhibit

below summarizes these calculations for the comparable companies.

27 Refer to Formula VI-15. 28 For the purpose of calculating the beta adjustment, we have used the same 3.8 percent operating margin return that was used in the previous valuation.

Page | 27

Exhibit 15: Cost Calculations for Comparable Companies

Line Description FY FY-1 FY-2 Average

BMC Software Inc. NasdaqGS:BMC

1 Revenue 1,871.9 1,731.6 1,580.4

2 Cost of Goods Sold (Variable Cost) 425.0 394.4 370.3

3 Operating Expenses (Fixed Cost) 995.3 961.0 958.2

4 Normalized Revenue 100.0 100.0 100.0

5 Normalized Fixed Cost (Line 3 * (Line 4 / Line 1) 53.2 55.5 60.6 56.4

6 Variable Cost as a % of Revenue (Line 2 / Line 1) 22.7% 22.8% 23.4% 23.0%

Citrix Systems, Inc. NasdaqGS:CTXS

7 Revenue 1,583.4 1,391.9 1,134.3

9 Operating Expenses (Fixed Cost) 1,285.1 1,071.7 850.5

Compuware Corporation NasdaqGS:CPWR

13 Revenue 1,090.5 1,229.6 1,213.0

Open Text Corp. NasdaqGS:OTEX

19 Revenue 725.5 595.7 409.6

Parametric Technology Corporation NasdaqGS:PMTC

25 Revenue 1,070.3 941.3 848.0

Page | 28

We next converted the routine operating margin for ABC Software (the guaranteed operating

margin paid by IPCO to its distributors) of 3.8 percent into an equivalent markup on total cost.

The exhibit below summarizes this calculation.

Exhibit 16: Conversion of Routine Operating Margin to Markup on Total Cost

As shown in the exhibit above, the equivalent routine markup on total cost is 3.95 percent. We

then applied this markup as outlined in Formula 16 to the appropriate fixed and variable cost

bases of the comparable companies. The exhibit below provides a calculation of the operating

leverage adjustment to each comparable company’s operating beta.

Line Description FY FY-1 FY-2 Average

Quest Software Inc. NasdaqGS:QSFT

31 Revenue 735.4 631.0 561.6

TIBCO Software Inc. NasdaqGS:TIBX

37 Revenue 644.5 577.4 517.3

VMware, Inc. NYSE:VMW

43 Revenue 1,881.0 1,325.8 703.9

45 Operating Expenses (Fixed Cost) 1,264.4 871.8 456.2

Line Description Value Source / Calculation

1 Routine Operating Margin 3.80% See Footnote 1

Conversion to Markup on Total Cost

2 Revenue 100 Assumption

3 Operating Profit 3.8 Routine profit at 3.8 % OM.

4 Markup on Total Cost 3.95% Line 3 / (Line 2 - Line 3)

/1/ The 2009 valuation determined a routine operating margin of 3.8 % for software

distribution.

Page | 29

Exhibit 17: Operating Betas Adjusted for Operating Leverage Differences (Residual Profit Betas)

As shown in the exhibit above, fully adjusted betas (the betas applicable to residual profit) for

the comparable companies range from 0.90 to 4.67. It bears noting once again that our result

does not change if we eliminate the two potential “outliers” (BMC and VMware).

The exhibit below summarizes the estimation of the beta coefficient with each adjustment and

presents the fully adjusted beta estimate.

Exhibit 18: Summary of Estimation of Beta Coefficient

As shown in the above exhibit, the fully adjusted beta, taking into consideration financial

leverage, excess cash, and the additional operating leverage of a residual profit flow, is 2.1. The

non-routine nature of the cash flows associated with this transaction necessitate each of these

adjustments in order to estimate a cost of capital that appropriate reflects the risk of the subject

profit stream.

Operating Normalized Normalized Variable Cost Markup On Beta Adjusted

Beta Sales Fixed Cost Percentage of Sales Total Cost Adjustment Operating Beta

Line Comparable Company A B C D E F G

1 BMC Software Inc. 0.78 100 56.43 22.97% 3.95% 1.17 0.90

2 Citrix Systems, Inc. 1.05 100 77.71 7.60% 3.95% 1.29 1.36

3 Compuware Corporation 1.94 100 45.23 39.96% 3.95% 1.26 2.44

4 Open Text Corp. 0.87 100 60.49 28.13% 3.95% 1.42 1.23

5 Parametric Technology Corporation1.65 100 57.28 31.20% 3.95% 1.41 2.33

6 Quest Software Inc. 1.06 100 79.25 9.72% 3.95% 1.46 1.56

7 TIBCO Software Inc. 1.70 100 61.35 26.99% 3.95% 1.41 2.40

8 VMware, Inc. 3.82 100 65.93 16.73% 3.95% 1.22 4.67

Source / Calculation Exhibit 14 Assumed Exhibit 15 Exhibit 15 Exhibit 16 See discussion G=A*F

Average Fully Adjusted Beta 2.11

Median Fully Adjusted Beta 1.94

Concluded Fully Adjusted Beta 2.11

Line Item Value Source

1 Levered Beta 1.2 Exhibit 4

2 Unlevered Beta 1.2 Exhibit 13

3 Operating Beta 1.6 Exhibit 14

4 Concluded Fully Adjusted Beta 2.1 Exhibit 17

Page | 30

6. Size Premium

As discussed in the preceding sections, one of the key limitations of the CAPM framework is

that is does not take into account the fact that smaller firms tend to be less liquid and have

higher default risk. Furthermore, because small capitalization stocks are traded less frequently,

their beta coefficients tend to be downward biased.29 Taken together, these shortcomings imply

that the basic CAPM equation would tend to systematically underestimate the cost of equity for

small stocks.

While the use of the sum beta does address the downward bias of betas for small capitalization

companies by taking into account the lagged price reaction of small stocks to movements in the

stock market, the historical data nonetheless indicate that even when applying a sum beta to the

CAPM, the CAPM estimate does not fully account for the excess returns for small stocks.30

Therefore, even when using the sum beta, an appropriate adjustment for size is required to fully

account for the additional risk associated with small company stocks.

The Duff & Phelps Risk Premium Report Size Study (the “D&P size report”), as published by

Morningstar™, uses alternative accounting or fundamental measures (e.g., net income, total

assets, sales, number of employees, etc.) to define size. Given that several of these metrics are

available for ABC Software as of the valuation date, we employed the D&P size report to

determine the size premium over the CAPM for ABC Software.

The D&P size report ranks companies by size into 25 portfolios based on a variety of accounting

and fundamental metrics. In order to determine the appropriate size premium for ABC

Software, we compared ABC’s results and financial metrics to the size portfolios and selected

the premium over CAPM consistent with ABC Software’s value for each metric.31 We then

calculated the average of the implied size premia for each of the metrics. We had information

for the following metrics—market value of equity, net income, market value of invested

capital32, total assets, sales, and the number of employees. The exhibit below summarizes the

relevant ABC Software metrics.

29 Arzac, Enrique. Valuation for Mergers, Buyouts, and Restructurings, Second Edition, John Wiley & Sons, 2008, pp. 56. 30 Pratt, Shannon, and Grabowski, Roger, Cost of Capital: Applications and Examples, 3rd Edition, John Wiley and Sons, 2008, p. 210. 31 As we noted earlier, it is important to recognize that D&P’s size premia over CAPM employ the sum beta when determining the CAPM predicted cost of capital. This is, of course, consistent with our use of the sum beta. 32 Note that in this case market value of equity is equal to the market value of invested capital.

Page | 31

Exhibit 19: Summary of ABC Size Metrics (In millions USD, except employees)

It bears noting that both the number of employees in ABC and the total assets of ABC as of the

valuation date are taken from internal data provided by the Company.

The exhibit below summarizes the implied premium over CAPM for each of these metrics and

calculates the average implied size premium for ABC.

Exhibit 20: ABC Software Size Premium Based Upon Morningstar Size Study

As shown in the exhibit above, the average implied ABC size premium is 4.0 percent.

Line Description Value Source

1 Average Net Income 199.4 2009 ABC Software Financial Information

2 Total Assets 666.8 2009 ABC Software Financial Information

3 Number of Employees 800.0 2009 ABC Software Financial Information

4 Sales 840.6 2009 ABC Software Financial Information

5 Market Value of Equity 3,500.0 ABC Software Internal Valuation

6 Market Value of Invested Capital 3,500.0 ABC Software Internal Valuation

Market Value of Equity Net Income Market Value of Invested Capital Total Assets Sales Number of Employees

Average Smoothed Average Smoothed Average Smoothed Average Smoothed Average Smoothed Average Smoothed

Size Size Premium Size Premium Size Premium Size Premium Size Premium Size Premium

Ranking $M Over CAPM $M Over CAPM $M Over CAPM $M Over CAPM $M Over CAPM $M Over CAPM

1 109,765 -1.2% 7,341 0.4% 140,685 -0.8% 114,403 0.6% 17,770 0.6% 324,433 1.2%

2 32,309 0.3% 2,081 1.6% 40,684 0.7% 36,839 1.6% 4,983 1.8% 92,527 2.2%

3 22,008 0.8% 1,320 2.0% 28,827 1.1% 26,306 1.9% 3,311 2.2% 56,404 2.6%

4 14,717 1.3% 942 2.3% 21,566 1.4% 19,119 2.2% 2,352 2.5% 42,097 2.8%

5 11,048 1.6% 696 2.6% 15,328 1.8% 13,912 2.5% 1,775 2.7% 32,807 3.0%

6 8,579 2.0% 524 2.8% 11,861 2.1% 10,000 2.8% 1,307 3.0% 26,333 3.2%

7 6,629 2.3% 407 3.1% 9,423 2.4% 7,649 3.1% 1,005 3.3% 20,964 3.4%

8 5,104 2.6% 326 3.3% 7,453 2.6% 6,542 3.2% 841 3.4% 17,852 3.5%

9 4,250 2.8% 273 3.4% 6,066 2.9% 5,522 3.4% 696 3.6% 14,952 3.6%

10 3,730 3.0% 224 3.6% 5,293 3.0% 4,791 3.5% 601 3.7% 13,054 3.7%

11 3,319 3.2% 186 3.8% 4,706 3.2% 4,170 3.6% 520 3.9% 10,862 3.9%

12 2,844 3.3% 163 3.9% 4,025 3.3% 3,627 3.8% 464 4.0% 9,523 4.0%

13 2,394 3.6% 138 4.1% 3,434 3.5% 3,118 3.9% 403 4.1% 8,185 4.1%

14 2,072 3.7% 120 4.2% 2,891 3.7% 2,746 4.0% 341 4.2% 7,149 4.2%

15 1,786 3.9% 105 4.3% 2,486 3.9% 2,291 4.2% 290 4.4% 6,229 4.3%

16 1,520 4.1% 90 4.5% 2,094 4.1% 1,947 4.3% 252 4.5% 5,465 4.4%

17 1,325 4.3% 77 4.6% 1,784 4.3% 1,697 4.5% 217 4.6% 4,747 4.5%

18 1,132 4.5% 64 4.8% 1,579 4.4% 1,487 4.6% 186 4.8% 3,859 4.7%

19 939 4.7% 56 4.9% 1,330 4.6% 1,273 4.7% 159 4.9% 3,234 4.8%

20 782 5.0% 44 5.1% 1,102 4.9% 976 5.0% 133 5.1% 2,668 5.0%

21 656 5.2% 34 5.4% 870 5.1% 788 5.2% 109 5.3% 2,135 5.2%

22 501 5.5% 26 5.6% 664 5.4% 666 5.3% 83 5.5% 1,748 5.3%

23 358 5.9% 19 5.9% 491 5.8% 520 5.6% 64 5.8% 1,203 5.6%

24 232 6.5% 12 6.3% 330 6.2% 346 5.9% 44 6.1% 751 6.0%

25 68 8.0% 4 7.3% 94 7.7% 117 6.9% 14 7.1% 251 6.9%

Constant: 13.3% 8.6% 13.0% 11.3% 9.5% 11.3%

Slope: -2.9% -2.1% -2.7% -2.1% -2.1% -1.8%

ABC Software Value: 3,500.00$ 199.4 3,500.00$ 667$ 840.6 800.00$

Implied Premium over CAPM 3.0% 3.6% 3.3% 5.2% 3.4% 5.6%

Average Implied ABC Premium: 4.0%

Page | 32

D. Capital Market Conditions as of the Transaction Date

In the spring of 2009, global capital markets were essentially frozen, as a result of the financial

crisis that halted and reversed the global capital market expansion that had lasted nearly three

decades.33 Access to capital was severely restricted as banks stopped lending and individuals

and firms stopped investing. Capital was in short supply, and basic economic theory tells us

that this capital would have an impact on the cost of capital at that time.

Capital markets were therefore highly liquidity constrained as of the valuation date. In

economic terms, the supply of capital was constrained, and therefore the price of capital was

high. One way to quantitatively evaluate the likely effect of such conditions on the cost of

capital is to examine studies of the effects of lack of liquidity on the cost of capital.

Numerous such studies exist. One study was performed by Pratt and Grabowski, building on

research by Frazier related to the illiquidity premium for restricted stocks. 34 They found that

the return for restricted stocks is between 5.0 percent and 6.0 percent above the expected return

for the freely traded underlying stock. 35

Another relevant study analyzed returns for publicly traded bonds in Germany. Kempf and

Uhrig-Homburg examined the yields on German bonds that differ only in terms of liquidity.

Bonds issued by the German Government (BUND) are liquid, while bonds issued by state-

operated funds (BAHN, POST) are illiquid. The authors found that the cost of illiquidity for a

10-year bond was approximately 1.0 percent.

There have also been studies that examine the effect of “liquidity shocks,” or periods in which

liquidity in a certain market quickly disappears. These studies are obviously relevant to the

question of the cost of capital as of April 2009. One of these studies examined all stocks on the

NYSE between 1964 and 2004 and found that illiquid portfolios have higher unconditional

average returns that liquid portfolios. The difference in returns between an illiquid portfolio

and a liquid portfolio was 0.48 percent per month, which is 5.9 percent on an annualized basis.36

Another study examined the illiquidity premium associated with junk bonds in 1998, when the

market for these bonds suddenly became very illiquid. The junk bond premium rose 3.3

percent between June 1998 and October 1998, and this rise could not be attributed to increased

default risk.37 This liquidity shock in the junk bond market provided a rare natural experiment

to isolate and identify the cost of liquidity, and the results are clear.

33 McKinsey & Company, “Global Capital Markets: Entering a New Era” (September 2009). 34 Frazier, William, “Quantitative Analysis of the Fair Market Value of and Interest in a Family Limited Partnership,” Valuation Strategies (January/February 2005). 35 Pratt, Shannon, and Grabowski, Roger, Cost of Capital: Applications and Examples, 3rd Edition, John Wiley and Sons, 2008, p. 456. 36 Watanabe, Akiko, and Watanabe, Masahiro, “Time-Varying Liquidity Risk and the Cross Section of Stock Returns,” Eighth Annual Texas Finance Festival, January 9, 2007. 37 Kwan, S.H., “Rising Junk Bond Yield: Liquidity or Credit Concerns?” FRBSF Economic Letter (November 2001).

Page | 33

Another study by Ibbotson, Chen, and Hu separates stocks into four liquidity categories based

on annual turnover, which is defined as the number of shares traded divided by the total shares

outstanding. In their study, they find that the average annual return for low liquidity stocks is

16.2 percent, while the average return for the two moderate liquidity categories is 13.5 percent.

This implies a liquidity premium of approximately 2.7 percent when comparing low and

moderate liquidity stocks.

In the following exhibit, we display the conclusions drawn from the liquidity studies discussed

above, along with the average and median estimated premiums for illiquidity.

Exhibit 21: Illiquidity Premium

Based on the studies, we have concluded that it is appropriate to apply an illiquidity premium

of 3.3 percent to ABC’s discount rate due to very illiquid capital market conditions in 2009. This

is the median result from the various studies of illiquidity premiums.

E. Concluded Model-based Estimate of the Cost of Capital

Given a risk-free rate of 4.1 percent, an ERP of 6.4 percent, a fully adjusted beta of 2.1, and a

small stock premium of 4.0 percent, the concluded model-based estimated of the cost of capital,

exclusive of the illiquidity premium, is 21.6 percent. Including the illiquidity premium of 3.3

percent as of April 2009, the fully-adjusted CAPM cost of capital is 24.9 percent. The exhibit

below summarizes these calculations.

Study Value

Frazier (2005)/Pratt and Grabowski (2008) 5.5%

Kempf and Uhrig-Homburg (2000) 1.0%

Watanabe and Watanabe (2007) 5.9%

Kwan (2001) 3.3%

Ibbotson, Chen, and Hu (2011) 2.7%

Average 3.7%

Median 3.3%

Concluded Value 3.3%

Page | 34

Exhibit 22: Concluded Cost of Capital – CAPM Method

Line Item Value Source

A Concluded Risk Free Rate of Return 4.1% 20-Year U.S. Bond

B Concluded Equity Risk Premium 6.4% Exhibit 3

C Concluded Fully Adjusted Beta 2.1 Exhibit 18

D Concluded Size Premium 4.0% Exhibit 20

E Concluded CAPM Cost Of Capital 21.6% E=A+C*B+D

F Concluded Adjustment For Market Conditions As Of April 2009 3.3% Exhibit 21

G Concluded Cost Of Capital - CAPM Method 24.9%

Page | 35

III. Transaction-based Cost of Capital Estimate

The preceding sections present a model-based estimation of the cost of capital for ABC

Software. However, as discussed above, there are also transactional methods for determining

the cost of capital based on the market’s actual estimation of the discount rate.

As noted in Section II.C.1., above, TECHCO’s acquisition of ABC provides an observed market

transaction, or transactional enterprise value estimate, for ABC. As such, there is an implicit

discount rate implied by TECHCO’s acquisition price.

Given that the price that TECHCO paid represents its perception of the fair market value of

ABC, the implied discount rate used by TECHCO can be inferred directly from TECHCO’s

“deal model,” or the valuation model that TECHCO used to develop the acquisition price. That

is, given the acquisition price, earnings, and the long term expected growth rate, we can

determine the cost of capital implicitly used by TECHCO in its valuation of ABC.

A heuristic example of this kind of approach can be seen by rearranging Formula 1 to solve for

the discount rate, as shown below.

(Formula 18)

In words, if we know the expected profit stream, the assumed growth rate, and the value of the

asset, we can solve for the implied discount rate, r. For the ABC acquisition, we know all of

these variables. The exhibit below presents this calculation of ABC’s implied discount rate.

Exhibit 23: Implied Discount Rate from ABC Software Acquisition (In millions

As shown above, the implied discount rate used by TECHCO in its valuation of ABC in 2008

was 15.9 percent. Based upon this observed discount rate, simply by applying the CAPM, we

can determine what ABC’s implied beta was as of the acquisition date. That is, given that we

know the discount rate, 15.9 percent, and the risk-free rate, equity risk premium, and an

appropriate size premium as of the acquisition date, we can estimate ABC’s beta as of its

acquisition.38

38 It bears noting that this implied discount rate would be the cost of capital as of the acquisition date inclusive of a size premium.

Line Description Value Notes

1 ABC Acquisition Price 3,500 Purchase price per board presentation

2 Less: Excess Working Capital 901 From purchase price allocation for ABC acquisition

3 Present Value of Cash Flows (V) 2,599 Line 1 - Line 2

4 Long Term Growth Rate (g) 4.0%

5 Implied Discount Rate 15.9%

Page | 36

Mathematically, this can be seen by simply setting the CAPM equation (including the size

premium but excluding a country premium), Formula 3, equal to the Gordon growth equation

solved for r in Formula 18 above. This equation can then be solved for beta. The equations

below summarize this calculation

(Formula 19) (CAPM)

(Formula 20)

(Formula 21)

Given that we know earnings (π), the acquisition price (V), the growth rate (g), and the risk-free

rate (rf), equity risk premium (ERP), and size premium for ABC39 as of the acquisition date,

Formula 20 allows us to solve for ABC’s beta (B). The exhibit below summarizes this

calculation.

Exhibit 24: Implied Beta as of ABC Acquisition Date (In millions USD)

As shown in the exhibit above, given a risk-free rate of 4.85 percent, an ERP of 7.10 percent,40

and a size premium for that at the time was 1.02 percent (the premium as of the acquisition

date), ABC’s implied unadjusted beta was 1.41.

As noted above, this implied discount rate of 15.9 percent already takes into account the excess

working capital held by ABC as of the acquisition. Therefore, the implied beta is the operating

asset beta, and no adjustment for excess cash is necessary.

However, this implied discount rate, and by extension the beta, represent the cost of capital that

TECHCO used to value the ABC business operations as a whole. In order to determine the

appropriate beta and discount rate for the residual profit flow being valued we must apply the

same operating leverage adjustment to ABC Software’s beta that is discussed above for the

39 The size premium for ABC as of the acquisition date is based on the acquisition price paid by TECHCO. 40 While the long run equity risk premium is lower as of April 2009, the data available as of the acquisition date would have implied an equity risk premium of 7.1 percent.

1 ABC Acquisition Price 3,500 Purchase price per board presentation

2 Less: Excess Working Capital 901 From purchase price allocation for ABC acquisition

3 Present Value of Cash Flows (V) 2,599 Line 1 - Line 2

4 Long Term Growth Rate (g) 4.0%

5 Implied Discount Rate 15.9%

6 Risk-free Rate as of Acquisition Date 4.85% 20-Year Treasury bond

7 ERP as of Acquisition Date 7.10% Ibbotson's Historical ERP

8 Size Premium as of Acquisition Date 1.02%

9 Unadjusted Beta as of Acquisition Date 1.41 B = ((Line 5 - Line 6 - Line 8) / Line 7)

Page | 37

comparable companies.41 Mathematically, this adjustment is performed in exactly the same

manner as described in the sections above. The exhibit below presents the calculation of ABC’s

operating leverage-adjusted beta.

Exhibit 25: ABC Software Adjusted Implied Operating Beta

As shown above, ABC’s implied beta adjusted for operating leverage is 1.56. Given this, we can

estimate a transaction-based discount rate as of the valuation date by simply applying the same

parameters discussed above in the CAPM model. The exhibit below summarizes the concluded

transaction-based discount rate.

41 It bears noting that, given that ABC’s capital structure consisted of equity, we do not adjust its beta for financial leverage.

1 Unadjusted Implied Beta 1.41 Exhibit 24

ABC Financial Assumptions

2 ABC Software Revenue 841 ABC Financial Data

3 ABC Software Cost of Sales 12 Variable Cost

4 Variable Cost as a % of Revenue 1.4% Line 3 / Line 2

5 ABC Operating Expenses 580 Fixed Cost

6 Normalized Revenue 100 Assumed

7 Normalized Fixed Cost 68.9 Line 5 * (Line 6 / Line 2)

Adjustment for Operating Leverage

8 Markup on Total Cost 3.95% Exhibit 16

9 Beta Adjustment 1.10 See earlier discussion

10 Operating Leverage Adjusted Beta 1.56 Line 1 * Line 9

Page | 38

Exhibit 26: Concluded Cost of Capital – Transactional Method

Using the transactional method, the cost of capital as of April 2009 is 21.4 percent.42

42 Note that the parameters used in this exhibit are as of April 2009, whereas the parameters used in Exhibit 24 are as of the valuation date.

1 Risk-free Rate 4.10% 20-Year Treasury Bond as of 4/30/2009

2 Equity Risk Premium 6.4% Exhibit 3

3 Operating Leverage-Adjusted Beta 1.56 Exhibit 25

4 Small Stock Premium 4.0% Exhibit 20

5 Operating Leverage Adjusted Discount Rate 18.1% Line 1 + Line 2 * Line 3 + Line 4

6 Adjustment for Market Conditions as of April 2009 3.3% Exhibit 21

7 Concluded Cost of Capital - Transactional Method 21.4% Line 5 + Line 6

Page | 39

IV. Concluded Cost of Capital Estimate

As demonstrated in the preceding sections, the concluded model-based cost of capital, exclusive

of the illiquidity premium, is 21.6 percent. Including the illiquidity premium, the CAPM-based

cost of capital is estimated to be 24.9 percent. Similarly, using the implied discount rate

calculation, the cost of capital is 21.4 percent. Averaging these two estimates, we conclude on a

cost of capital of 23.2 percent.

Page | 40

V. Consistency With Court Guidance

Cost of capital estimates have become a central focus in disputes between taxpayers and tax

authorities, and the tax courts can provide guidance on acceptable methods of calculating

discount rates. There are several decisions that are instructive, particularly in determining

appropriate adjustments and premia when using model-based methods.

For example, in one case a judge specifically noted the importance of using an appropriate size

premium, providing the following critique:

…The relationship between firm size and return is well known. Size is not an

unsystematic risk factor, and cannot be eliminated through diversification […] it has

been found that the greater risk of small stocks is not fully reflected by the CAPM, in

that actual returns may exceed those expected based on beta […] Consequently, when

calculating a cost of capital under a CAPM on a small stock […], it is appropriate to add

a small stock premium to the equity risk premium, to reflect the greater risk associated

with an investment in a small stock in comparison to the large stocks from which the

equity risk premium is calculated.43

The tax court has also ruled in favor of using an industry risk premium. In one case, the IRS

expert used Ibbotson’s industry adjustment of 5.2 percent, and the court accepted the

calculation based on the following explanation:

…we are satisfied the 5.2 percent is within a reasonable range. In part we base our

conclusion on [the subject company’s] tendency to generally outperform the industry

and the economy, so that the 5.2 percent premium may be on the conservative side…44

Perhaps the most compelling support for our cost of capital estimate comes from the recent

ruling in Veritas Software Corporation v. Commissioner.45 The issue in Veritas was the value of

certain intangible assets that Veritas U.S. had transferred to an Irish subsidiary in conjunction

with the establishment of a cost sharing arrangement. The taxpayer used a form of DCF

analysis known as a relief from royalty method to calculate the value of the intangible assets as

the present value of expected royalty payments for the subject intangibles over their expected

useful lives. While there were several areas of disagreement in the treatment and valuation of

intangibles between the taxpayer and the tax authority, one of the key points of disagreement

was in the appropriate cost of capital used in the valuation.46

The tax authority’s expert, Hatch, concluded that the appropriate discount rate to use in the

valuation of the Veritas intangibles was 13.7 percent. Hatch arrived at this discount rate by

43 Estate of Hendrickson v. Commissioner, T.C. Memo 1999-278, 78 T.C.M. (CCH) 322 (U.S. Tax Ct. 1999) (Oct. 1999 J&L) (Oct. 1999 BVU). 44 Estate of Deputy v. Commissioner, (TCM 2003-176). 45 Veritas Software Corporation & Subsidiaries v. Commissioner, 133 T.C. No. 14 (2009). 46 In addition to disagreeing on the discount rate, the tax authority argued for a perpetual life rather than a finite life. The Court ruled in favor of the taxpayer on this issue.

Page | 41

using the CAPM with the yield on the 20-year Treasury bond as the risk-free rate, an equity risk

premium of 5.0 percent and a beta of 1.42.

However, the taxpayer argued that the tax authority’s expert had employed the wrong beta and

the wrong equity risk premium, and had therefore severely underestimated the discount rate.

Hatch used an industry beta, rather than a company specific beta, in his analysis, and used a 5.0

percent ERP that the Court concluded was based on “erroneous assumptions” regarding long-

term yields in foreign markets.

The taxpayer’s expert, Malkiel, also used the CAPM. However, he arrived at a much higher

discount rate, equal to 20.47 percent. The Court had the following to say about the difference in

results:

There are two differences between Hatch’s and Malkiel’s applications of CAPM: The

estimate of the beta and the equity risk premium. Malkiel, unlike Hatch, used reliable

data to calculate both variables.47

Rather than using an industry beta based on Vertitas’ Standard Industrial Classification (SIC)

code, Malkiel used the beta for Veritas of 1.94. Malkiel’s argument, which was accepted by the

Court, was that the industry beta was not representative of Veritas’ risk, especially since the

industry beta was skewed by the presence and size of Microsoft. Barkai similarly uses an

industry beta in his calculation of the discount rate, when it is clear that the beta that we have

calculated is more reflective of the specific risks of ABC Software Israel.

Malkiel also used an ERP of 8.1 percent, which was significantly higher than the ERP employed

by the tax authority’s expert. The Court concluded that Hatch did not rely on reasonable

assumptions when he concluded that 5.0 percent was an appropriate ERP, and therefore the

Court determined that the taxpayer’s estimate, which was based on data from Ibbotson

Associates, was more reliable.

The Court soundly rejected the tax authority’s estimate of a 13.7 percent discount rate, and

accepted the taxpayer’s discount rate of 20.47 percent for use in the valuation of intangible

assets of Veritas. This case is particularly relevant since it highlights the importance of using a

discount rate that carefully considers all of the risks related to an asset, and appropriately

adjusts the inputs in a discount rate estimation model to accurately reflect those risks.

47 Veritas Software Corporation & Subsidiaries v. Commissioner, 133 T.C. No. 14 (2009), p. 70.

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