Assignment 4 controllership

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Learning Objectives

Chapter 11

Risk-Adjusted Expected Rates of Return and the Dividends

Valuation Approach

1 Estimate risk-adjusted expected rates of return on equity capital, as well as weighted average costs of capital, which you will use to discount future payoffs to present value.

2 Understand the dividends valuation approach and its conceptual and practical strengths and weaknesses.

3 Develop practical valuation techniques to deal with the many difficult issues involved in estimating firm value: (a) dividends versus cash flows versus earnings, (b) cash flows to the investor versus cash flows reinvested in the firm, (c) the forecast horizon, and (d) continuing value.

4 Apply the dividends valuation techniques to estimate firm value using the present value of future dividends.

5 Develop techniques to assess the sensitivity of firm value estimates to key valuation parameters, such as discount rates and expected long-term growth rates.

INTRODUCTION AND OVERVIEW Economic theory teaches that the value of an investment equals the present value of the pro- jected future payoffs from the investment discounted at a rate that reflects the time value of money and the risk inherent in those expected payoffs. A general model for the present value of a security at time t�0 (denoted as V

0 ) with an expected life of n future periods is as

follows:1

n V

0 � ∑

Projected Future Payoffs t

t =1 (1 � Discount Rate)t

1 Throughout this chapter, t refers to accounting periods. The valuation process determines an estimate of firm value, denoted V 0 ,

in present value as of today, when t�0. The period t�1 refers to the first accounting period being discounted to present value.

Period t�n is the period of the expected final, or liquidating, payoff.

In securities markets that are less than perfectly efficient, price does not necessarily equal value for every security at all times. Therefore, it can be very fruitful to search for and ana- lyze securities that may have prices that have deviated temporarily from their fundamental

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Introduction and Overview 885

values. When buying a security, the investor pays the security’s price and receives the secu- rity’s value. When selling a security, the investor receives the selling price and gives up the security’s value. Price is observable, but value is not; value must be estimated. Therefore, estimating the value of a security to make intelligent investment decisions is a common objective of financial statement analysis. Investors, analysts, investment bankers, corporate managers, and others engage in financial statement analysis and valuation to determine a reliable appraisal of the value of shares of common equity or the value of whole firms. The questions they typically address include the following:

• What value do I think a share of common stock in a particular company is worth? • Comparing my estimate of value to the current price in the market, should I buy, sell,

or hold a particular firm’s common shares? • What price should I assign to the initial public offering of a firm’s common shares? • What is a reasonable price to accept (or ask) as a seller or pay (or bid) as a buyer for

the shares of a firm in a corporate merger or acquisition?

Equity valuation models based on dividends, cash flows, and earnings have been the topic of many theoretical and empirical research studies in recent years. These studies pro- vide many insights into valuation, but two very compelling general conclusions emerge and motivate the discussion and application of valuation models in this text: (1) share prices in the capital markets generally correlate closely with share value, but (2) share prices do not always equal share values, and temporary deviations of price from value occur. First, many empirical studies demonstrate that dividends, cash flows, and earnings-based valuation models generally provide significant explanatory power for share prices observed in the capital markets.2 The results show that share value estimates determined from these valu - ation models exhibit high positive correlations with the stock prices observed in the capital markets. These correlations hold across different types of firms, during different periods of time, and across different countries. In the same vein, many empirical research studies also have shown that unexpected changes in earnings, dividends, and cash flows correlate closely with changes in stock prices.

Second, a number of empirical research studies show that valuation models also help iden- tify when share prices in the capital markets temporarily deviate from fundamental share val- ues. Research results show that dividends, cash flows, and earnings-based valuation models help identify when shares are temporarily overpriced or underpriced, representing potentially prof- itable investment opportunities. For example, Exhibit 11.1 is a graphic depiction of results from a study by Frankel and Lee (1998) in which they sorted their sample of firms each year into five portfolios based on quintiles of their estimate of value (V) to share price (P).3

Their findings show striking differences in the average 36-month stock returns earned by their portfolios. The highest value-to-price quintile portfolio generated significantly greater average returns than the lowest value-to-price portfolio. These results and similar results from a number of related studies should be very encouraging for those interested in developing fundamental forecasting and valuation skills for investment purposes.

The six-step analysis and valuation framework that forms the structure of this book (Exhibit 1.1 in Chapter 1) is a logical sequence of steps for understanding the fundamen- tals of a business and for determining intelligent estimates of its value. First, we analyze the

2 For examples, see Stephen Penman and Theodore Sougiannis, “A Comparison of Dividend, Cash Flow, and Earnings Approaches

to Equity Valuation,” Contemporary Accounting Research 15, no. 3 (Fall 1998), pp. 343–383, and Jennifer Francis, Per Olsson, and

Dennis Oswald, “Comparing the Accuracy and Explainability of Dividend, Free Cash Flow, and Abnormal Earnings Equity Value

Estimates,” Journal of Accounting Research 38 (Spring 2000), pp. 45–70.

3 Richard Frankel and Charles Lee, “Accounting Valuation, Market Expectation, and Cross-Sectional Stock Returns,” Journal of

Accounting and Economics 25, Issue 3 (1998), pp. 283–319.

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886 Chapter 11 Risk-Adjusted Expected Rates of Return and the Dividends Valuation Approach

economics and competitive conditions of the industry. Second, we analyze the particular firm’s strategy in light of the competitive dynamics of the industry. Third, we assess the quality of the firm’s accounting and financial reporting. Fourth, we analyze the firm’s prof- itability and risk with a set of financial ratios. Fifth, we use all of this information to project the firm’s future financial statements. Finally, we derive from the projected finan- cial statements our forecasts of future earnings, cash flows, and dividends as measures of projected future payoffs for the firm. We use these projected future payoffs as inputs to valu - ation models to determine the value of the firm. Reliable projections of future payoffs to the firm (the numerator in the general valuation model presented earlier) depend on unbi- ased and thorough forecasts of future income statements, balance sheets, and statements of cash flows, all of which depend on reliable projections of the firm’s future operating, invest- ing, and financing activities. Assessing an appropriate risk-adjusted discount rate (the denominator in the general valuation model) requires an assessment of the inherent risk in the set of expected future payoffs. Therefore, reliable estimates of firm value depend on unbiased estimates of expected future payoffs and an appropriate risk-adjusted discount rate, all of which depend on all six steps of the framework.

This chapter begins the discussion of the sixth and final step of the analytical framework of this text: valuation. The first portion of this chapter describes and demonstrates com- puting risk-adjusted expected rates of return on equity capital and weighted average costs of capital, which we use as discount rates in the valuation models. The latter portion of this chapter describes and applies the dividends-based valuation model. Throughout the chap- ter, we demonstrate these techniques using PepsiCo.

Looking further ahead, Chapter 12 presents and applies cash-flow-based valuation approaches. Chapter 13 describes and applies earnings-based valuation approaches. Chapters 11–13 discuss and illustrate the important issues that determine the conceptual and practical strengths and weaknesses of each approach. All three chapters illustrate the

E X H I B I T 1 1 . 1

Empirical Evidence on Portfolio Stock Returns Associated with Share Value Relative to Share Price ( V/P)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

1 2 3 4 5

V/P Quintile

V /P

10%

20%

30%

40%

50%

60%

70%

3 6

-m o

n th

b u

y- an

d -h

o ld

s to

ck r

et u

V/P Stock return

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Equivalence Among Dividends, Cash Flows, and Earnings Valuation 887

equivalence of these valuation approaches using the theoretical development of the mod- els and applying these approaches to the projected dividends, cash flows, and earnings derived from the financial statements forecasts developed for PepsiCo in Chapter 10. Chapter 14 describes and applies market multiples such as price-earnings ratios and mar- ket-to-book ratios that analysts use in some instances to value firms.

EQUIVALENCE AMONG DIVIDENDS, CASH FLOWS, AND EARNINGS VALUATION As noted earlier, equity valuation models based on dividends, cash flows, and earnings have been the topic of many theoretical and empirical research studies in recent years, which show that, in general, share value estimates determined from these models correlate closely with stock prices observed in the capital markets. However, the valuation models also help identify when stock prices deviate temporarily from share values. Therefore, it is no sur- prise that analysts, investors, and capital market participants commonly use dividends, cash flows, and earnings to estimate share values. When the analyst derives internally consistent forecasts of future earnings, cash flows, and dividends from a set of financial statement forecasts and uses the same discount rate to compute the present values of those expected future earnings, cash flows, and dividends, the valuation models yield identical estimates of value for a firm. That is, these three valuation models are complementary approaches to valuation that produce equivalent value estimates.

The primary difference between the dividends-, cash-flows-, and earnings-based approaches to valuation are differences in perspective. The dividends-based valuation approach focuses on wealth distribution to shareholders. Essentially, share value is deter- mined by the present value of dividends the shareholder will receive. Cash-flow-based valu - ation takes an alternative perspective because the analyst forecasts and values the cash flows the firm will generate and use to pay dividends. The cash-flow-based valuation approach measures and values the free cash flows that are available for distribution to share- holders after cash is used for necessary investments in operating assets and required pay- ments to debtholders. Free cash flows can be used instead of dividends as the expected future payoffs to the investor in the numerator of the general valuation model. Both approaches, if implemented with consistent assumptions, will lead to identical estimates of value. This equivalence occurs because over the life of the firm, the free cash flows into the firm will be equivalent to the cash flows paid out of the firm in dividends to shareholders.

The earnings-based valuation approach is another alternative valuation perspective, equiva lent to both dividends-based and free-cash-flows-based valuation. The earnings- based valu ation approach takes the perspective that earnings measures the capital that firms create (or destroy) for common shareholders each period that will ultimately be real- ized in cash flows and distributed as dividends to shareholders. Thus, the earnings-based valuation approach focuses on the firm’s wealth creation for shareholders, the cash-flows- based approach focuses on dividend-paying ability, and the dividends approach focuses on wealth distribution to shareholders. Exhibit 11.2 provides a conceptual illustration of these three approaches to firm valuation.

Analysts who apply these different valuation approaches gain better insights about the value of a firm than analysts who rely on only one approach in all cases. Analysts understand valu - ation more deeply and thoroughly across a wider array of situations when they can triangulate valuation across the dividends, cash flows, and earnings valu ation approaches.

All four valuation chapters (Chapters 11–14) emphasize that the objective of the valu - ation process is not a single point estimate of value per se; instead, the objective is to deter- mine a reliable distribution of value estimates across the relevant ranges of critical forecast

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888 Chapter 11 Risk-Adjusted Expected Rates of Return and the Dividends Valuation Approach

assumptions and valuation parameters. By estimating share value using cash flows, earnings, and dividends and by assessing the sensitivity of these value estimates across a distribution of relevant forecast assumptions and valuation parameters, the goal is to determine the most likely range of values for a share, which are then compared to the share’s price in the capital market for an intelligent investment decision.

RISK-ADJUSTED EXPECTED RATES OF RETURN We base all of the valuation approaches we describe and demonstrate in Chapters 11–14 on the general valuation model set forth at the beginning of this chapter, in which we deter- mine firm value by discounting projected future payoffs to present value. Therefore, for all of the valuation approaches we need a discount rate to compute the present value of all projected future payoffs. To compensate for the time value of money and risk, the discount rate should equal the required rate of return that capital providers demand from the firm to induce them to commit capital. When the analyst computes the present value of payoffs (dividends, free cash flows, or earnings) to common equity shareholders, he or she should

E X H I B I T 1 1 . 2

Conceptual Illustration of Equivalent Approaches to Valuation Using Dividends, Cash Flows, and Earnings

Forecasts of Income Statements, Balance Sheets, and Statements of Cash Flows

Dividends Free Cash Flows Earnings

Dividends-Based Valuation Models

Free-Cash-Flows-Based Valuation Models

Earnings-Based Valuation Models

From these forecasts, derive expected future:

Perspective: Distributed Wealth

Perspective: Distributable Wealth

Perspective: Wealth Creation

Firm Value

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Risk-Adjusted Expected Rates of Return 889

use a discount rate that reflects the risk-adjusted required rate of return on common equity capital.

The discount rate should be a forecast of the required rate of return on the investment and, therefore, should be conditional on the expected future riskiness of the firm and expected future interest rates over the period during which the payoffs will be generated. The historical discount rate of the firm may be a good indicator of the appropriate discount rate to apply to the firm in the future, but only if the following three conditions hold:

• The current risk of the firm is the same as the expected future risk of the firm. • Expected future interest rates are likely to equal current interest rates. • The existing capital structure of the firm (that is, the current mix of debt and equity

financing) is the same as the expected future capital structure of the firm.

If one or more of these conditions does not hold, the analyst will need to project discount rates that appropriately capture the future risk and capital structure of the firm and future interest rates in the economy over the forecast horizon.

As a starting point to estimate expected rates of return on capital, analysts often com- pute the prevailing after-tax cost of each type of capital (debt, preferred, and common equity) invested in the firm. Existing costs of capital reflect the required rates of return for the firm’s existing capital structure, and they are appropriate discount rates for valuing future payoffs for the firm only if the three preceding conditions hold.

Developing discount rates using costs of capital assumes that the capital markets price capital to reflect the risk-free time value of money plus a premium for risk. The following sections describe and demonstrate techniques to estimate the firm’s cost of equity, debt, and preferred stock capital. After these descriptions, the chapter describes and illustrates how to compute a weighted average cost of capital for the firm.

Cost of Common Equity Capital Analysts commonly estimate the cost of equity capital using the CAPM (capital asset pric- ing model). The CAPM assumes that the market comprises risk-averse investors holding diversified portfolios of assets. The CAPM assumes that for a given level of expected return, risk-averse investors will seek to bear as little risk as possible and will mitigate risk by diver- sifying across the types of assets they hold in a portfolio. Therefore, the CAPM hypothe- sizes that in equilibrium, investors should expect to earn a rate of return on a firm’s common equity capital that equals the rate of return the market requires to hold that firm’s stock in a diversified portfolio of assets. In theory, the market comprises risk-averse investors who demand a rate of return that (1) compensates them for forgoing the con- sumption of capital (the time value of money) and (2) compensates them with a risk pre- mium for bearing systematic, marketwide risk that cannot be diversified. Systematic risk arises from economy-wide factors (such as economic growth or recession, unemployment, unexpected inflation, unexpected changes in prices for natural resources such as oil and gas, unexpected changes in exchange rates, and population growth) that affect all firms to varying degrees and therefore cannot be fully diversified. Therefore, the market’s required rate of return on equity capital is a function of prevailing risk-free rates of interest in the economy plus a risk premium for bearing risk, all conditional on the level of nondiversifi- able risk inherent in the firm’s common stock.

Note that the CAPM views nonsystematic risk as factors that are diversifiable by the investor holding a broad portfolio of stocks. Nonsystematic risk factors are industry- and firm-specific, including factors such as the level of competition in an industry, the product portfolio of a particular firm, the sustainability of the firm’s strategy, and the firm’s ability

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890 Chapter 11 Risk-Adjusted Expected Rates of Return and the Dividends Valuation Approach

to generate revenue growth and control expenses. A competitive equilibrium capital mar- ket, according to CAPM, does not expect a return for a firm’s nonsystematic risk because such risk can be diversified away in a portfolio of stocks.

Analysts measure nondiversifiable or systematic risk as the degree of covariation between a firm’s stock returns and a marketwide index of stock returns. Analysts commonly measure systematic risk using the firm’s market beta, which is estimated as the slope coef- ficient from regressing the firm’s stock returns on an index of returns reflecting a mar- ketwide portfolio of stocks over a relevant period of time.4 If a firm’s market beta from such a regression is equal to 1, it indicates that, on average, the firm’s stock returns covary iden- tically with returns to a marketwide portfolio, indicating that the firm has the same degree of systematic risk as the market as a whole. If a firm’s market beta is greater than 1, the firm has a greater degree of systematic risk than the market as a whole, whereas a firm with a market beta less than 1 has less systematic risk than the market as a whole.

Exhibit 11.3 reports industry median market betas for a sample of 42 industries over the years 1999–2007. These data depict wide variation in systematic risk across industries during

E X H I B I T 1 1 . 3

Relation between Industry and Systematic Risk over 1999–2007

Industry Median Beta during 1999–2007

Forestry 0.17 Utilities 0.32 Depository Institutions 0.39 Tobacco 0.39 Real Estate 0.43 Food Processors 0.47 Grocery Stores 0.50 Insurers 0.55 Restaurants 0.61 Metal Products 0.64 Petroleum Refining 0.65 Printing and Publishing 0.66 Wholesalers—Nondurables 0.66 Personal Services 0.68 Textiles 0.69 Rubber and Plastics 0.70 Hotels 0.74 Health Services 0.75 Amusements and Recreation 0.76 Non-Depository Financial Institutions 0.78 Metal Mining 0.80 Paper 0.81

4 Researchers and analysts have developed a variety of approaches to estimate market betas. For example, one common approach

estimates a firm’s market beta by regressing the firm’s monthly stock returns on a marketwide index of returns (such as the S&P

500 index) over the last 60 months.

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this nine-year period, with industry median market betas ranging from a low of 0.17 (Forestry) to a high of 1.64 (Electronic and Electrical Equipment). Various financial reference sources and websites regularly publish market betas for common equity in publicly traded firms. It is not uncommon to find considerable variation in market betas among the various sources. This occurs in part because of differences in the period and methodology used to estimate betas.5

The CAPM projects the expected return on common equity capital for Firm j as follows:

E[R Ej

] � E[R F ] � ß

j � {E[RM] � E[RF]}

where E denotes that the related variable is an expectation; R Ej

denotes required return on common equity in firm j; R

F denotes the risk-free rate of return; ß

j denotes the market beta

E X H I B I T 1 1 . 3 ( C o n t i n u e d )

Industry Median Beta during 1999–2007

Miscellaneous Manufacturing 0.85 Oil and Gas Extraction 0.87 Transportation Equipment 0.89 Retailers—General Merchandise 0.92 Engineering Management 0.95 Lumber 0.96 Motion Pictures 0.97 Wholesalers—Durables 0.97 Miscellaneous Retail 1.01 Instruments and Related Products 1.06 Retailing—Apparel 1.08 Chemicals 1.10 Transportation by Air 1.11 Primary Metals 1.18 Retailing—Home Furniture, Furnishings, and

Equipment 1.21 Security and Commodity Brokers 1.24 Industrial and Commercial Machinery and

Computer Equipment 1.24 Communications 1.30 Business Services 1.51 Electronic and Electrical Equipment 1.64

5 Eugene Fama and Kenneth French developed an empirical model that explains realized stock returns using three factors they found

to be correlated with returns during their study period. Their model and results indicate that during their sample period (1963–1990),

firms’ stock returns were related to firms’ market betas, market capitalizations (size), and market-to-book ratios [see Eugene F. Fama

and Kenneth R. French, “The Cross Section of Expected Stock Returns,” Journal of Finance (June 1992), pp. 427–465]. Data to imple-

ment their model can be obtained from French’s website (http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html).

Although the model deserves and has received a great deal of attention in academics and practice, more research is necessary to

determine the theoretical basis for the model and the risk factors and risk premia that constitute the model. In addition, more

research is needed to assess the empirical applicability of the model as a predictor of expected stock returns in periods following

their sample period.

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892 Chapter 11 Risk-Adjusted Expected Rates of Return and the Dividends Valuation Approach

for firm j; and R M

denotes the required return on a diversified, marketwide portfolio of stocks (such as the S&P 500). According to the CAPM, a common equity security with no system- atic risk (that is, a stock with ß

j � 0) should be expected to earn a return equal to the expected

rate of return on risk-free securities. Of course, most equity securities are not risk-free. An equity security with systematic risk equal to the average amount of systematic risk of all equity securities in the market has a market beta equal to 1. The subtraction term in brackets in the preceding equation represents the average market risk premium, which is equal to the amount of return above the risk-free rate that equity investors in the capital markets require for bearing the average amount of systematic risk in the market as a whole. Therefore, the cost of common equity capital for a firm with an average level of systematic risk should be equal to the required return on the market portfolio. A firm with a market beta greater than 1 has higher than average systematic risk and faces a higher cost of equity capital because the capi - tal markets expect the firm to yield a commensurately higher return to compensate investors for bearing greater risk. A firm with a market beta less than 1 faces a lower cost of equity capi - tal because the capital markets expect the firm to yield a commensurately lower return to investors for bearing less risk. Exhibit 11.4 depicts the CAPM graphically.

The analyst should use the market return on securities with zero systematic risk as the risk- free interest rate in the CAPM. Returns on such systematic risk-free securities (for example, U. S. Treasury securities) should exhibit no correlation with returns on a diversified mar- ketwide portfolio of stocks. Given that equity securities have indefinitely long lives, it might seem appropriate to use the yield on long-term U.S. Treasury securities as a proxy for a risk- free rate. However, yields on long-term U.S. government securities tend to exhibit greater sen- sitivity to changes in inflation and interest rates; therefore, they have a greater degree of systematic risk (although the systematic risk is still quite low) compared to short-term U.S. government securities. Common practice uses the yield on short- or intermediate-term U.S. government securities (for example, yields on three-, five-, or ten-year U.S. Treasury securities) as the risk-free rate. Historically, these yields have averaged around 6 percent over the long run, although in recent years, they have averaged roughly 3–4 percent.

The average realized rate of return on the market portfolio depends on the period stud- ied. Historically, the realized rate of return on the market portfolio has varied between 9 and 13 percent. Thus, the excess return of the market portfolio over the risk-free rate has

E X H I B I T 1 1 . 4

Relation between Cost of Equity Capital and Systematic Risk

Cost of Equity Capital

Average Return on Market Portfolio

Risk-Free Rate

0 1.0 Systematic Risk (Beta)

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varied between 3 and 7 percent. Some financial economists argue that the market risk pre- mium varies over time with investors’ demand for incremental consumption. The econo- mists argue that, on the margin, when the economy is healthy and growing (with low unemployment and high consumer confidence), investors’ demand for additional con- sumption is relatively low; therefore, investors demand relatively low rates of return for postponing incremental consumption and bearing risk. Thus, risk premia tend to be lower (perhaps 3–4 percent) when economic conditions are strong. Conversely, when the econ- omy is weak and investors face a higher degree of uncertainty, investors’ demand for addi- tional consumption is relatively high; therefore, they demand relatively high rates of return for postponing consumption and bearing risk. Thus, risk premia tend to be higher (perhaps 6–7 percent) when economic conditions are weak. The theories asserting that risk premia are time-varying (and vary inversely with investors’ marginal demand for consumption) seem intuitive and appear to explain risk premia observed in the capital markets quite well, but they require more empirical research.

Example 1: Using the CAPM to Compute Expected Rates of Return Suppose Firm A has a market beta of 0.60 and Firm B has a market beta of 1.40. Assume that the prevailing yields on three- to five-year U.S. Treasury bonds are roughly 4.0 percent and that the capital markets require a 5.0 percent risk premium for bearing an average amount of systematic risk. Applying the CAPM, we would compute the following expected rates of return for Firm A and Firm B:

Firm A: E[R A ] � 4.0 � (0.60 � 5.0) � 7.0

Firm B: E[R B ] � 4.0 � (1.40 � 5.0) � 11.0

Thus, the CAPM implies that investors require a 7.0 percent rate of return on capital invested in the equity of Firm A and an 11.0 percent rate of return on capital invested in the equity of Firm B. Firm B faces a higher cost of equity capital than Firm A because Firm B has a higher degree of systematic risk. In determining the share values of Firm A and Firm B, investors should discount to present value the expected future payoffs using a 7.0 percent discount rate for Firm A and an 11.0 percent discount rate for Firm B. If investors expect Firm A and Firm B to generate equivalent payoffs (although Firm B’s payoffs will be riskier), investors will assign a lower value to (and pay a lower price for) the common shares of Firm B than Firm A. The difference between the value of Firm B’s shares and those of Firm A reflects the additional compensation that shareholders demand for holding the riskier Firm B shares relative to shares of Firm A. Shareholders will realize this compensa- tion in the form of the equivalent payoffs, for which shareholders in Firm B paid a lower price than did shareholders in Firm A.

Computing the Required Rate of Return on Equity Capital for PepsiCo At the end of 2008, different sources provided different estimates of market beta for PepsiCo common stock, ranging from 0.50 to roughly 1.00. Historically, PepsiCo’s mar- ket beta has varied around 0.75 over time, so we will assume that PepsiCo common stock has a market beta of roughly 0.75 as of the end of 2008. At that time, U.S. Treasury bills with ten years to maturity traded with a yield of just below 4.0 percent, which we use as the risk-free rate. Additionally, economic conditions were in recession, stock mar- ket indexes had experienced substantial declines, and investors were more risk-averse than normal; so we will assume investors demanded a 6.0 percent market risk premium. Therefore, the CAPM indicates that PepsiCo has a cost of common equity capital of 8.50 percent [� 4.0 � (0.75 � 6.0)]. At the end of 2008, PepsiCo had 1,553 million shares

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894 Chapter 11 Risk-Adjusted Expected Rates of Return and the Dividends Valuation Approach

outstanding and a share price of $54.77, for a total market capital of common equity of $85,058 million.

Adjusting Market Equity Beta to Reflect a New Capital Structure Recall from the discussion in Chapter 5 that market beta reflects operating leverage, finan- cial leverage, variability of sales and earnings, and other firm characteristics. In some set- tings, such as a leveraged buyout, firms plan to make significant changes in the financial capital structure. The market beta computed using historical market price data reflects the firm’s existing capital structure. The analyst can project what market beta is likely to be after the firm changes the capital structure. The analyst can “unlever” the current market beta by adjusting it to remove the effects of leverage and then “relever” it by adjusting it to reflect leverage under the new capital structure. The following formula estimates an unlevered market beta (sometimes referred to as an asset beta):

Current Levered Market Beta � Unlevered Market Beta �

1 + (1 � Income Tax Rate) � Current Market Value of Debt

Current Market Value of Equity ⎡ ⎣

⎤ ⎦)

)

The intuition behind this formula is that current market beta reflects two components: (1) the systematic risk of the operations and assets of the firm (the unlevered beta), compounded by (2) the financial leverage of the firm (the debt-equity ratio), net of the tax benefit from using leverage (that is, tax savings from interest expense deductions.) Estimating the new levered beta requires two steps. The first step is to solve for the unlevered beta by rearranging the pre- ceding equation to divide the current levered market beta by the term in square brackets on the right-hand side of the equation, as follows:

Unlevered Market Beta � Current Levered Market Beta/[1� (1 � Income Tax Rate) � (Current Market Value of Debt/Current Market Value of Equity)]

The second step is to project the new levered market beta by multiplying the unlevered beta by the term in square brackets on the right-hand side of the equation after substituting the projected new ratio of the market value of debt to the market value of equity in place of the current ratio of the market value of debt to the market value of equity, as follows:6

New Levered Market Beta � Unlevered Market Beta � [1� (1 � Income Tax Rate) � (New Market Value of Debt/New Market Value of Equity)]

Example 2: The Effects of Leverage on Beta and Expected Rates of Return Suppose a firm has a market beta of 0.9, is subject to an income tax rate of 35 percent, and has a market value of debt to market value of equity ratio of 60 percent. If the risk-free rate is 6 percent and the market risk premium is 7 percent, then according to the CAPM, the

6 Note that the debt-to-equity ratios used in these computations are based on market values of debt and shareholders’ equity. These

market-value-based ratios will likely differ from the debt to shareholders’ equity ratios discussed in Chapter 5 for assessing long-term

solvency risk because the ratios in Chapter 5 are based on book values of debt and shareholders’ equity. As more firms choose the fair

value option for recognizing outstanding debt, as discussed in Chapter 6, book and fair values for debt will begin to converge.

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market expects this firm to generate equity returns of 12.3 percent [� 6.0 � (0.9 � 7.0)]. The firm intends to adopt a new capital structure that will increase the debt-to-equity ratio to 140 percent. To project the firm’s levered beta under the new capital structure, the first step is to solve for the unlevered beta, denoted X, as follows:

0.9 � X � [1 � (1 � 0.35) � (0.60/1.00)] X � 0.9/[1 � (1 � 0.35) � (0.60/1.00)] X � 0.65

Because financial leverage is positively related to market beta, removing the effect of finan- cial leverage reduces market beta. The unlevered beta should reflect the effects of the firm’s operating risk, sales volatility, and other operating factors, but not risk related to financial leverage. The new market beta is projected to reflect the new debt-to-equity ratio as follows:

Y � 0.65 � [1 � (1 � 0.35) � (1.40/1.00)] � 1.24

The new capital structure will increase the leverage and therefore the systematic risk of the firm. According to the CAPM, this firm will face an equity cost of capital of 14.68 percent [� 6.0 � (1.24 � 7.0)] under the new capital structure.

Evaluating the Use of the CAPM to Measure the Cost of Equity Capital The use of the CAPM to calculate the cost of equity capital has been subject to various criti - cisms, as follows:

• Market betas for a firm should vary over time as the systematic risk of the firm changes; however, market beta estimates are quite sensitive to the time period and methodology used in their computation.

• In theory, the CAPM measures required returns based on the stock’s risk relative to a diversified portfolio of assets across the economy, but a return index for a diversified portfolio of assets that spans the entire economy does not exist. Measuring a stock’s systematic risk relative to a stock market return index such as the S&P 500 Index fails to consider covariation between the stock’s returns and returns on assets outside the stock market, including other financial investments (for example, U.S. government and corporate debt securities and privately held equity), real estate, and human capital.

• The market risk premium is not stable over time and is likewise sensitive to the time period used in its calculation. Considerable uncertainty surrounds the appropriate adjustment for the market risk premium. It is not clear whether the appropriate adjust- ment should be on the order of 3 percent, 7 percent, or somewhere in between.7 As noted earlier, some financial economists now argue that the risk premium is lower in periods of economic health and growth and higher in periods of economic weakness and uncertainty, which seems plausible and consistent with observable variation in marketwide stock returns over time. However, this approach requires more research to develop practical models for measuring firm-specific time-varying risk premia.

7 See, for example, James Claus and Jacob Thomas, “Equity Premia as Low as Three Percent? Empirical Evidence from Analysts’

Earnings Forecasts for Domestic and International Stock Markets,” Journal of Finance 56 (October 2001), pp. 1629–1666. Also see

Peter Easton, Gary Taylor, Pervin Shroff, and Theodore Sougiannis, “Using Forecasts of Earnings to Simultaneously Estimate

Growth and the Rate of Return on Equity Investment,” Journal of Accounting Research 40 (June 2000), pp. 657–676.

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In light of these criticisms of the CAPM and considering the crucial role of the risk- adjusted discount rate for common equity valuation, it is important to analyze the sensitiv- ity of share value estimates across different discount rates for common equity. For example, the analyst should estimate values for a share of common equity in a particular firm across a relevant range of discount rates for common equity by varying the market risk premium from 3 to 7 percent.

Chapter 14 describes techniques to reverse-engineer the implicit expected rate of return on common equity securities. Chapter 14 also describes an approach to estimate the implicit discount in share price for risk by using risk-free discount rates. These techniques do not require the assumption of an asset pricing model such as the CAPM.

Cost of Debt Capital The analyst computes the after-tax cost of each component of debt capital, including short- term and long-term notes payable, mortgages, bonds, and capital lease obligations, as the yield to maturity on each type of debt times one minus the statutory tax rate applicable to income tax deductions for interest. The yield to maturity is the rate that discounts the con- tractual cash flows on the debt to the debt’s current fair value. If the fair value of the debt is equal to face value (for example, a $1,000 debenture trades on an exchange for $1,000), the yield to maturity equals the stated interest rate on the debt. If the fair value of the debt exceeds the face value of the debt, yield to maturity is lower than the stated rate. This can occur after interest rates fall; previously issued fixed-rate debt will have a stated rate that exceeds current market yields for debt with comparable credit quality and terms. On the other hand, after interest rates rise, existing fixed-rate debt may have a stated rate that is lower than prevailing market rates for comparable debt, in which case the debt will have a fair value that is less than face value and the yield to maturity will be greater than the stated rate.

Firms disclose in notes to their financial statements the stated interest rates on their existing interest-bearing debt capital. Firms also disclose in notes the estimated fair values of their interest-bearing debt, which should reflect the present value of the debt using pre- vailing market yields to maturity on the debt. Together, these disclosures allow the analyst to estimate prevailing market yields to maturity on the firm’s outstanding debt.

In computing costs of debt capital, analysts typically exclude operating liability accounts (such as accounts payable, accrued expenses, deferred income tax liability, and retirement benefit obligations). Instead, analysts typically treat these items as part of the firm’s operating activities rather than as part of the firm’s financial capital structure.

A capitalized lease obligation will generally have an implicit after-tax cost of capital equal to the after-tax yield to maturity on collateralized borrowing with equivalent risk and maturity. Firms recognize capital lease obligations on the balance sheet as financial liabili- ties; however, as described in Chapter 6, firms also may have significant off-balance-sheet commitments to make future payments under operating leases. If the firm has significant commitments under operating leases, the analyst may believe it necessary to include them in the computation of the cost of debt capital. If the analyst elects to adjust the firm’s bal- ance sheet to capitalize operating lease commitments as debt (as illustrated in Chapter 6), the analyst should make three sets of adjustments to include the effects of operating leases on the total cost of debt capital. First, the analyst should include the present value of oper- ating lease commitments in calculating the fair value of various components of outstand- ing debt. Second, the analyst should include the discount rate used to compute the present value of the operating lease commitments as the after-tax interest rate on operating leases in the computation of the cost of debt capital. The lessor bears more risk in an operating lease than in a capital lease, so the cost of capital represented by operating leases is likely to

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be higher than for capital leases. Third, if the analyst treats operating leases as part of debt financing, the cash outflow for rent payments under operating leases should be reclassified as interest and principal payments of debt when computing free cash flows. Chapter 6 dis- cusses techniques for the required adjustments to convert operating leases to capital leases, as well as techniques to adjust for other less common forms of off-balance-sheet financing, including contingent liabilities for receivables sold with recourse and product financing arrangements.

The income tax rate used to compute the tax effects of interest should be the firm’s tax rate applicable to interest expense deductions. For most firms, the tax rate applicable to interest expense deductions is the statutory federal tax rate, which is 35 percent in the United States in 2009. However, state and foreign taxes or other special tax factors may increase or decrease the combined statutory tax rate depending on where the firm raises its debt capital. Firms generally do not separately disclose statutory state or foreign tax rates, but do summarize the effect of these taxes in the income tax reconciliation found in the income tax note. To achieve greater precision, the analyst could approximate the combined statutory tax rate applicable to interest expense deductions using the effective tax rate dis- closed in the income tax footnote.

Cost of Preferred Equity Capital The cost of preferred stock capital depends on the preference conditions. Preferred stock that has preference over common shares with respect to dividends and priority in liquida- tion generally sells near its par value. Therefore, its cost of capital is the dividend rate on the preferred stock. Depending on the attributes of the preferred stock, dividends on pre- ferred stock may give rise to a tax deduction, in which case the after-tax cost of capital will be lower than the pretax cost. Preferred stock that is convertible into common stock has both preferred and common equity attributes. Its cost is a blending of the cost of noncon- vertible preferred stock and common equity.

Computing the Weighted Average Cost of Capital In some circumstances, the analyst may want to determine the present value of payoffs to investment in all of the assets of a firm, not just the equity capital of the firm. Such circum- stances might arise, for example, if the analyst is considering acquiring all of the assets of a firm or if the analyst is considering acquiring control of a firm by acquiring all of the finan- cial claims (common equity shares, preferred shares, and debt) on the assets of a firm. If the analyst needs to determine the present value of the payoffs from investing in the total assets of the firm, or, equivalently, acquiring all of the debt, preferred, and common equity claims on the firm, the analyst should use a discount rate that reflects the weighted average required rate of return that encompasses the debt, preferred, and common equity capital used to finance the net operating assets of the firm.

A formula for the weighted average cost of capital (denoted as R A ) is given here:

R A

� [w D

� R D

� (1 � tax rate)] � [w P

� R P ] � [w

E � R

E ]

In this formula, w denotes the weight on each type of capital (D denotes debt capital, P denotes preferred stock capital, and E denotes common equity capital), R denotes the cost of each type of capital, and tax rate denotes the tax rate applicable to debt capital costs. The weights used to compute the weighted average cost of capital should be the market values of each type of capital in proportion to the total market value of the financial capital structure

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898 Chapter 11 Risk-Adjusted Expected Rates of Return and the Dividends Valuation Approach

of the firm (that is, w D

� w P

� w E

� 1.0). On the right-hand side of the equation, the first term in brackets measures the weighted after-tax cost of debt capital, the second term mea - sures the weighted cost of preferred stock capital, and the third term measures the weighted cost of common equity capital.

Example 3: Computing the Weighted Average Cost of Capital A firm has the following capital structure on its balance sheet:

Book Value

Long-term bonds, 10 percent annual coupon, issued at par $20,000,000 Preferred stock, 4 percent dividend, issued at par 5,000,000 Common equity 25,000,000

Total $50,000,000

The market values of the securities are as follows: bonds, $22,000,000; preferred equity, $5,000,000; common equity, $33,000,000. The market has priced the bonds to yield 8.0 per- cent. (That is, the interest rate that discounts the annuity of contractual $2,000,000 inter- est payments and the $20,000,000 maturity value to the bonds’ $22,000,000 fair value is 8 percent.) The firm’s income tax rate is 35 percent, so the after-tax cost of debt is 5.2 per- cent [� (1 � 0.35) � 8.0 percent]. Note that this rate is less than the coupon rate of 10 per- cent and that the market value of the debt is greater than its par value. Use of coupon rates and book values in this case would result in a higher cost of debt capital (6.5 percent � 0.65 � 10.0 percent) but a smaller weight for debt in the weighted average. Assuming that the divi - dend on the preferred stock is not tax deductible, its cost is the dividend rate of 4.0 percent because it is selling for par value. The equity capital has a market beta of 0.9. Assuming a risk-free interest rate of 6.0 percent and a market premium of 7.0 percent, the cost of equity capital is 12.3 percent [� 6.0 percent � (0.9 � 7.0 percent)]. The calculation of the weighted average cost of capital is as follows:

After-Tax Weighted Security Market Value Weight Cost Average

Long-Term Debt $22,000,000 37% 5.2% 1.92% Preferred Equity 5,000,000 8% 4.0% 0.32% Common Equity 33,000,000 55% 12.3% 6.77%

Total $60,000,000 100% 9.01%

Over time, the weights for debt, preferred, and equity capital may change if the analyst expects the firm’s capital structure to change over the forecast horizon. In addition, the ana- lyst may expect yields to maturity on debt capital and required rates of return on equity capital to change as interest rates in the economy change, the risk of the firm changes, or the firm’s tax status changes. Thus, to capture these changes in the weighted average cost of capital, the analyst may need to project a weighted average cost of capital for each period over the forecast horizon.

To determine the appropriate weights to use in the weighted average cost of capital, the analyst must determine the market values of the debt, preferred, and common equity capital. Market values for debt will be observable only for firms that have issued publicly traded debt; however, U.S. GAAP and IFRS require firms to disclose the fair value of their outstanding debt capital in notes to the financial statements each year. Fair value disclosures may not be

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available, however, if the firm is privately owned, the firm is not required to follow U.S. GAAP or IFRS, or the firm is a division and does not publish its own financial statements. If market values are not observable and fair values for the firm’s debt are not disclosed, the analyst can (1) estimate the fair value of the firm’s debt if sufficient data are available about the firm’s credit quality and the maturity and terms of the debt or (2) rely on the book value of debt. The book value of debt can be a reliable estimate of fair value if the debt is recently issued, if the debt bears a variable rate of interest, or if the debt bears a fixed rate of interest but inter- est rates and the firm’s credit quality have been stable since the debt was issued. Because the yield to maturity on debt is inversely related to its market value, analysts sometimes approxi - mate the cost of debt by simply using the coupon rate and the book value of debt when com- puting the weighted average cost of capital, particularly when interest rates are stable and the market value of debt is likely to be close to book value.

If available, market prices for equity securities provide the amounts for determining the market value of equity. Market prices for equity may not be available, however, if the firm is privately owned or if it is a division of a firm. The analyst can then use the book value of equity as a starting point to compute the weight of equity in the capital structure for pur- poses of estimating a weighted average cost of capital.

The preceding discussion reveals circular reasoning in computing weighted average costs of capital for valuation purposes. Analysts use the market values of debt and equity to compute the weighted average cost of capital, which is used in turn to compute the value of the debt and equity in the firm. This is circular reasoning because the analyst needs to know the market values to determine the weights but needs to know the weights to deter- mine the weighted average cost of capital to use in estimating firm value. In practice, ana- lysts can use two approaches to avoid this circularity. One approach assumes that the firm will maintain a target debt-to-equity structure in the future based on benchmarks such as the firm’s past debt-to-equity ratios, the firm’s stated strategy with respect to financial leverage, or industry averages. The other approach computes iteratively the weighted aver- age cost of capital and the value of debt and equity capital until the weights and the values converge. Example 4 illustrates this iterative approach.

Example 4: Computing the Weighted Average Cost of Capital Iteratively Suppose that someone wants to compute the weighted average cost of capital and the mar- ket value of equity for a firm for which no market or fair value data are available. Also sup- pose that the firm has outstanding debt with a book value of $40 million. The firm recently issued this debt, and it carries a stated rate of 8.0 percent; so the analyst can assume that this is a reliable measure of the cost of debt capital. The firm faces a 35 percent tax rate. The book value of equity is $60 million. Similar firms in the same industry with comparable risks have a market beta of 1.2. Using the same risk-free rate and market risk premium as in Example 3, the cost of equity capital is 14.4 percent [� 6.0 percent � (1.2 � 7.0 per- cent)]. The first estimate of the weighted average cost of capital is as follows:

After-Tax Weighted Security Amount Weight Cost Average

Debt $ 40,000,000 40% 5.2% 2.08% Common Equity 60,000,000 60% 14.4% 8.64%

Total $100,000,000 100% 10.72%

After using the 10.72 percent weighted average cost of capital to discount the free cash flows to present value, the analyst determines that the firm’s equity value is roughly

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900 Chapter 11 Risk-Adjusted Expected Rates of Return and the Dividends Valuation Approach

$120 million (calculations not shown). Therefore, the values and weights used to compute the weighted average cost of capital are inconsistent with value estimates for equity. The first-iteration estimates placed too much weight on debt and too little weight on equity. The analyst should use the revised estimate of the value of equity to recompute the weighted average cost of capital and then recompute the value of the firm. Using the revised estimates produces a weighted average cost of capital estimate as follows:

After-Tax Weighted Security Amount Weight Cost Average

Debt $ 40,000,000 25% 5.2% 1.30% Common Equity 120,000,000 75% 14.4% 10.80%

Total $160,000,000 100% 12.10%

The analyst should then use the revised estimate of the weighted average cost of capital of 12.10 percent to recompute the value of equity once again and then iterate this process until the values of debt and equity converge with the weights of debt and equity.

Computing the Weighted Average Cost of Capital for PepsiCo PepsiCo’s balance sheet at the end of 2008 shows interest-bearing debt from short-term obli- gations and long-term debt obligations totaling $8,227 million (� $369 � $7,858, as reported in Appendix A). Recall that Chapter 10 used information disclosed in Note 9, “Debt Obligations and Commitments” (Appendix A), to assess stated interest rates on PepsiCo’s interest-bearing debt. In 2008, PepsiCo’s outstanding debt carries a weighted average inter- est rate of approximately 5.8 percent. In Note 10, “Financial Instruments” (Appendix A), PepsiCo discloses that the fair value of outstanding debt obligations at the end of 2008 is $8,800 million. Thus, PepsiCo has experienced an unrealized (and unrecognized) loss of $573 million (� $8,227 million � $8,800 million) on its debt capital. This unrealized loss is surprising because more than half of PepsiCo’s outstanding debt obligations were newly issued in 2008 at prevailing market rates. The unrealized loss implies that the firm’s out- standing debt carries stated rates of interest that now exceed prevailing market yields, which at the end of 2008 are at relatively low levels given the recession in the U.S. economy. Based on the fact that most of PepsiCo’s outstanding debt obligations were recently issued in 2008 and the expectation that prevailing yields to maturity are temporarily low, Chapter 10 pro- jected that PepsiCo’s cost of debt capital will continue to approximate 5.8 percent in Year �1 and beyond. We use the current book value (as a proxy for market value) of PepsiCo’s debt for weighting purposes. In Note 5, “Income Taxes” (Appendix A), PepsiCo discloses that the combined average federal, state, and foreign tax rate is approximately 26.8 percent in 2008. Chapter 10 projected that PepsiCo will continue to face average tax rates of roughly 26.8 per- cent in Year �1 and beyond. Therefore, we will assume the tax rate applicable to PepsiCo’s interest expense deductions will be the effective 26.8 percent rate rather than the statutory federal rate of 35 percent. Long-run projections imply that PepsiCo faces an after-tax cost of debt capital of 4.25 percent [4.25 � 5.8 � (1 � 0.268)].

PepsiCo also has a net negative balance of $97 million in preferred stock on the 2008 bal- ance sheet. Chapter 10 projected that PepsiCo will retire the remaining outstanding pre- ferred stock during Year �1 and that that PepsiCo will not issue any additional preferred stock capital in future years. Therefore, we include no preferred stock in the computation of PepsiCo’s weighted average cost of capital.

Recall that earlier in this chapter we used the CAPM to determine that PepsiCo faces an 8.50 percent cost of equity capital. We also computed that at the end of 2008, PepsiCo had

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1,553 million shares outstanding and a share price of $54.77, for a total market capital of common equity of $85,058 million.

Bringing these costs of debt and equity capital together, we compute PepsiCo’s weighted average cost of capital to be 8.12 percent as follows:

After-Tax Weighted- Value Cost Average

Capital Basis Amount Weight of Capital Component

Debt Book $ 8,227 8.82% 4.25% 0.37% Common Market 85,058 91.18% 8.50% 7.75%

Total $93,285 100.00% 8.12%

This is just an initial estimate of PepsiCo’s weighted average cost of capital. As described earlier, the weighted average cost of capital must be computed iteratively until the weights used are consistent with the present values of debt and equity capital.

RATIONALE FOR DIVIDENDS-BASED VALUATION In theory, the value of a share of common equity is the present value of the expected future dividends the shareholder will receive.8 Dividends are the most fundamental value-relevant measure of expected future payoffs to use to value shares because they represent the distri- bution of wealth from the firm to the shareholders. The equity shareholder invests cash to purchase the share and then receives cash in the form of dividends as the payoffs from hold- ing the share, including the final “liquidating” dividend when the investor sells the share. In dividends-based valuation, we define dividends broadly to include all cash flows between the firm and the common equity shareholders. Therefore, in valuation, “dividends” encompass all cash flows from the firm to shareholders through periodic dividend payments, stock buy- backs, and the liquidating dividend, as well as cash flows from the shareholders to the firm when the firm issues shares (in a sense, negative dividends).

The rationale for using expected dividends in valuation is twofold:

1. Cash is the primary medium of exchange for consumption, which is the ultimate source of value. When individuals and firms invest in an economic resource, they forgo current consumption in favor of future consumption. Cash is the medium of exchange that will permit them to consume various goods and services in the future. An investment has value because of its ability to provide future cash flows. Dividends measure the cash that investors ultimately receive from investing in an equity share.

2. Dividends are paid in cash, and cash serves as a measurable common denominator for comparing the future benefits of alternative investment opportunities. One might compare investment opportunities involving the holding of a bond, a stock, or an office building, but comparing these alternatives requires a common measur- ing unit of their future benefits. The future cash flows derived from their future ser - vices serve such a function.

As a practical matter, however, quarterly or annual dividend payment amounts are arbitrary, established by a dividend policy set by the firm’s managers and board of directors. Periodic dividend payments do not vary closely with firm performance from one period to the next. Some firms do not pay any regular periodic dividends, particularly young, high-growth firms. For most firms, the final liquidating dividend plays an important role,

8 John Burr Williams, The Theory of Investment and Value (Cambridge, Mass.: Harvard University Press), 1938.

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902 Chapter 11 Risk-Adjusted Expected Rates of Return and the Dividends Valuation Approach

usually representing a large proportion of firm value in a dividends-based valuation. The final liquidating dividend arises when the firm liquidates its assets and returns all of the capital to shareholders, when all of the outstanding shares of the firm are acquired by another firm in a merger or an acquisition transaction, or when shareholders elect to liq- uidate their investment by selling shares. Therefore, to value a firm’s shares using divi- dends, one must forecast dividends over the life of the firm (or the expected length of time the share will be held), including the final liquidating dividend (that is, the future price at which shares will be retired, acquired, or sold). Thus, the analyst faces the challenge of needing to forecast the value of shares in the future at the time of the liquidating dividend in order to value the shares today.

Dividends-Based Valuation Concepts This section describes and illustrates key concepts in dividends-based valuation, first pre- senting simple examples involving a single project and then confronting conceptual mea - surement issues regarding dividends to the investor versus cash flows to the firm and nominal versus real dividends. Later in the chapter, we illustrate this approach with a more complex and realistic example involving the valuation of PepsiCo using dividends derived from the projected financial statements developed in Chapter 10.

Dividends Valuation for a Single-Asset Firm For the following examples, make these assumptions:

• The firm consists of a single asset that will generate pretax net cash flows of $2 million per year forever.

• The income tax rate is 40 percent. • After making debt service payments and paying taxes, the firm pays dividends to dis-

tribute any remaining cash flows to the equity shareholders each year.

Example 5: Value of Common Equity in an All-Equity Firm For this example, make the following additional assumptions:

• Equity shareholders have financed the asset entirely with $10 million of equity capital. • The cost of equity capital is 10 percent. The value of the common equity investment to the shareholders can be determined

using the present value of dividends for common equity shareholders. The dividends to common equity shareholders each year will be as follows:

Net Pretax Cash Flow for All Debt and Equity Capital $2,000,000 Interest Paid on Debt (0) Income Taxes: 0.40 � $2,000,000 (800,000)

Dividends for Common Equity Shareholders $1,200,000

The value to the shareholders of the common equity in the firm is $12,000,000 (� $1,200,000/0.10). Dividing by the discount rate is appropriate because the $1,200,000 annual dividend for common equity is a perpetuity. This investment is worth $12,000,000 to those shareholders (a gain of $2,000,000 over their initial $10,000,000 investment) because of the present value of the dividends the investment will pay to the shareholders.

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Example 6: Value of Common Equity in a Firm with Debt Financing Assume the same original facts, but now make the following additional assumptions:

• The equity shareholders finance a portion of the investment in the asset with $4 million of equity capital.

• The firm finances the remainder of the asset using $6 million of debt capital. • This amount of debt in the firm’s capital structure does not alter substantially the risk of

the firm to the equity investors, so they continue to require a 10 percent rate of return. • The debt is issued at par, and it is less risky than equity; so the debtholders demand

interest of only 6 percent each year, payable at the end of each year. • Interest expense is deductible for income tax purposes. Again the value of the common equity investment can be determined using the present

value of dividends for common equity shareholders. The dividend to common equity is as follows:

Net Pretax Cash Flow for All Debt and Equity Capital $2,000,000 Interest Paid on Debt: 0.06 � $6,000,000 (360,000) Income Taxes: 0.40 � ($2,000,000 � $360,000) (656,000)

Dividends for Common Equity Shareholders $ 984,000

Assuming that the firm will pay this amount of dividend each year in perpetuity, the value of the common equity to the shareholders in the firm is $9,840,000 (� $984,000/0.10). Note that in this example, the present value of the gain to the common equity shareholders in excess of their initial investment is $5,840,000 (� $9,840,000 � $4,000,000). In this example, the gain to the shareholders is $3,840,000 (� $5,840,000 � $2,000,000) larger than in the previous example because (1) the debt capital is less expensive than the equity capital (6 percent rather than 10 percent on $6,000,000 of financing), creating $2,400,000 of value for equity sharehold- ers from capital structure leverage [� ($6,000,000 � {0.10 � 0.06})/0.10], and (2) the net tax savings from interest expense creates $1,440,000 of value for equity shareholders [� ($800,000 � $656,000)/0.10, or, alternatively, (� $360,000 interest deduction � 0.40 tax rate)/0.10].

Dividends to the Investor versus Cash Flows to the Firm The beginning of this chapter asserted that the analyst can use dividends expected to be paid to the investor or the free cash flows expected to be generated by the firm (that will ultimately be paid to the investor) as equivalent approaches to measure value-relevant expected payoffs to shareholders. Will using net cash flows into the firm result in the same estimate of value as using dividends paid out of the firm? Cash flows paid to the investor via dividends and free cash flows to the firm that are available for common equity share- holders will differ each period to the extent that the firm reinvests a portion (or all) of the cash flows generated. However, if the firm generates a rate of return on reinvested free cash flow equal to the discount rate used by the investor (that is, the cost of equity capital), either set of payoffs (dividends or free cash flows) will yield the same valuation of a firm’s shares at a point in time. To demonstrate this equivalence, consider the following scenarios.

Example 7: Dividend Policy Irrelevance with 100 Percent Payout A firm expects to generate free cash flows of 15 percent annually on invested equity capital for the rest of its life, which is likely to continue for an indefinitely long period of time into the future (until t�n). Equity investors in this firm require a 15 percent return each year, considering the riskiness of the firm. Assume that the firm pays out 100 percent of the free

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904 Chapter 11 Risk-Adjusted Expected Rates of Return and the Dividends Valuation Approach

cash flows each year as dividends to the shareholders. Thus, the free cash flows generated by the firm equal the cash dividends received by the investors each period. Each dollar of capital committed by the investors has a present value of future cash flows equal to one dol- lar. That is, over an indefinitely long period of time into the future,

Example 8: Dividend Policy Irrelevance with Zero Payout Assume the same facts as Example 7 except that the firm pays out none of the free cash flows as a dividend. The firm retains the $0.15 free cash flow on each dollar of capital and rein- vests it in projects expected to earn 15 percent return per year. In this case, the investor receives no periodic dividends and receives cash only when the investor sells the shares or the firm liquidates at date t�n. By the terminal date, n periods in the future, each dollar of capital invested in the firm today will have earned a compound rate of return of 15 percent, equal to the required rate of return. In this case also, each dollar of invested capital has a present value of future cash flows equal to one dollar, exactly the same as in the full payout dividend discount example above. That is,

Example 9: Dividend Policy Irrelevance with Partial Payout Assume the same facts as Example 8 except that the firm pays out 25 percent of the free cash flow each period as a dividend and reinvests the other 75 percent in projects expected to generate a return of 15 percent. In this case also, each dollar of invested capital has a pres- ent value of future cash flows equal to one dollar, the same as in the two preceding exam- ples. That is,

$1 � ($1.15) n

(1.15)n

n $1 � ∑ $0.15

t =1 (1.15)t

These three examples illustrate the relevance of dividends as payoffs that are sufficient for valuation for equity shareholders and the irrelevance of the firm’s dividend policy in valu- ation, assuming the firm reinvests cash flows to earn the investors’ required rate of return.9

The same valuation should arise whether the analyst discounts (1) the expected dividends to the investor or (2) the expected free cash flows to the firm that are available to pay future dividends to equity shareholders. Further, the same valuation should arise whether the firm pays all of its cash flows as a dividend, reinvests all cash flows to earn the investors’ required rate of return, or pays a portion of cash flows in dividends each period and reinvests the remaining cash flows to earn the investors’ required rate of return.

Nominal versus Real Dividends Changes in general price levels (that is, inflation or deflation) cause the purchasing power of the monetary unit to change over time. Should the valuation use projected nominal dividends,

9 Merton Miller and Franco Modigliani, “Dividend Policy, Growth and the Valuation of Shares,” Journal of Business (October 1961),

pp. 411–433. Penman and Sougiannis test empirically the replacement property of dividends for future earnings and find support

for the irrelevance of dividend policy in valuation. See Stephen H. Penman and Theodore Sougiannis, “The Dividend

Displacement Property and the Substitution of Anticipated Earnings for Dividends in Equity Valuation,” The Accounting Review

(January 1997), pp. 1–21.

n V

0 � ∑

(0.25)($0.15) (0.75)($1.15)n

t =1 (1.15)t �

(1.15)n

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The Dividends Valuation Model 905

which include the effects of inflation or deflation, or real dividends, which filter out the effects of changes in general purchasing power?10 The valuation of an investment in an economic resource should be the same whether nominal or real dividend amounts are used as long as the discount rate used is the nominal or real rate of return that is consistent with the dividend measure. That is, if projected dividends are nominal and include the effects of changes in gen- eral purchasing power of the monetary unit, the discount rate should be nominal and include an inflation component. If projected dividends are real amounts that filter out the effects of general price changes, the discount rate should be a real rate of return, excluding the inflation component.

Example 10: Nominal versus Real Dividends A firm owns an asset that it expects to sell one year from today for $115.5 million. The firm expects the general price level to increase 10 percent during this period. The real interest rate is 5 percent. The nominal discount rate should be 15.5 percent to measure the com- pound effects of the real rate of interest and inflation [0.155 � (1.10 � 1.05) � 1]. Discounting nominal or real dividends, the value of the asset to the firm today is $100 mil- lion, as shown:

Discount Rate Including Nominal Dividends � Expected Inflation � Value

$115.5 million � 1/(1.05 � 1.10) � $100 million

Discount Rate Excluding Real Dividends � Expected Inflation � Value

$115.5 million/1.10 � 1/1.05 � $100 million

Both examples derived the value of the equity of the firm by computing the present value of the dividends to common equity shareholders. As a practical matter, costs of capi - tal and expected returns are typically quoted in nominal terms, so analysts usually find it more straightforward to discount nominal dividends using nominal discount rates than to first adjust nominal dividends to real dividends and then discount real dividends using real interest rates.

THE DIVIDENDS VALUATION MODEL This section presents the dividends valuation model that determines the value of common shareholders’ equity in the firm. The sections following the model demonstrate how to implement the model using PepsiCo.

The dividends valuation model determines the value of common shareholders’ equity in the firm (denoted as V

0 ) as the sum of the present value of all future dividends to share-

holders over the life of the firm, which is indefinite. The dividends valuation model includes all-inclusive dividends (denoted as D) that encompass all of the net cash flows

10 Note that the issue here is not with specific price changes of a firm’s particular assets, liabilities, revenues, and expenses. These

specific price changes affect projections of the firm’s dividends, cash flows, and earnings and should enter into the valuation of the

firm. The issue is whether some portion, all, or more than all of the specific price changes represent simply an economy-wide

change in the purchasing power of the monetary unit, which should not affect the value of a firm.

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906 Chapter 11 Risk-Adjusted Expected Rates of Return and the Dividends Valuation Approach

from the firm to shareholders through periodic dividend payments and stock buybacks and subtracts cash flows from the shareholders to the firm when the firm issues shares. The next section demonstrates how to measure dividends (D). We discount the stream of future dividends to present value using the required return on common equity capital in the firm (denoted as R

E ). The following general model expresses the dividends valuation

approach:

∞ V

0 � ∑

D t

D 1

D 2

D 3

t =1 (1+RE) t

� (1+R

E )1

� (1+R

E )2

� (1+R

E )3

�. . .

∞ V

T � ∑

D T�1

t = 1 (1+RE) t

∞ V

0 � ∑

D t

D 1

D 2

D 3

D T

V T

t =1 (1+RE) t

� (1+R

E )1

� (1+R

E )2

� (1+R

E )3

� . . . � (1+R

E )T

� (1+R

E )T

Suppose dividend amounts can be reliably forecasted through Year T. At the end of Year T, assume that the continuing value of the common equity of the firm (denoted as V

T ) will

equal the present value of all expected future continuing dividends in Year T�1 and beyond (a perpetuity of D

T+1 in every year), which can be expressed as follows:

Thus, the value of the firm today can be expressed using periodic dividends over a finite hori- zon to Year T plus continuing value based on dividends in Year T�1 and beyond as follows:

This equation reveals that the estimate of value today (V 0 ) depends on the estimate of value

in the future (V T ).

As described in more detail in an upcoming section, we project the continuing dividends in the continuing value period beyond Year T using the expected, long-run steady state growth of the firm, which we specify as (1 � g). We project the Year T�1 dividend by assuming that each line item on the Year T income statement and balance sheet will grow at rate (1 � g) and then deriving the Year T�1 dividend. As described in an upcoming sec- tion, to derive dividends, assume that accounting for the book value of the shareholders’ equity (BV) follows the general principle of adding net income (NI) and subtracting divi- dends to common shareholders each period (that is, BV

t � BV

t�1 � NI

t � D

t ). Therefore,

the Year T�1 dividend can be derived as follows:

D T�1

� NI T�1

� BV T

� BV T�1

The assumption is that growth in net income and book value in Year T�1 equals (1 � g); therefore, NI

T�1 � NI

T � (1 � g) and BV

T�1 � BV

T � (1 � g). These terms can be substi-

tuted, and the D T�1

equation can be rewritten as follows:

D T�1

� [NI T

� (1 � g)] � BV T

� [BV T

� (1 � g)]

Assuming that D T�1

will grow in perpetuity at rate g, the firm can be valued at the end of Year T using the perpetuity-with-growth model as follows:

∞ V

T � ∑

D T�1

[NI T

� (1 + g)] � BV T

� [BV T

� (1 + g)]

t =1 (1+RE) t

� (R

E �g)

� (R

E �g)

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Implementing the Dividends Valuation Model 907

IMPLEMENTING THE DIVIDENDS VALUATION MODEL Implementing the dividends valuation model to determine the value of the common share- holders’ equity in a firm involves measuring the following three elements:

1. The discount rate (denoted as R E

in the valuation model) used to compute the pres- ent value of the future dividends

2. The expected future dividends over the forecast horizon (denoted as D t in periods 1

through T in the valuation model) 3. The expected dividend at the final period of the forecast horizon, which we refer to

as the continuing dividend (denoted as D T�1

in the valuation model) and a forecast of the long-run growth rate (denoted as g in the model) in the continuing dividend beyond the forecast horizon

The first part of this chapter discussed the first element, computing the appropriate discount rate. The following sections discuss measuring the second and third of these elements.

Measuring Dividends Dividends-based valuation values the common equity in a firm by measuring the present value of all net cash flows from the firm to the equity shareholders. Therefore, the objective in divi- dends valuation is to measure the present value of total dividends for common equity share- holders, including all of the cash flows the shareholders will receive from holding the share.

Total dividends encompass cash flows from the firm to common equity shareholders through periodic dividend payments such as quarterly or annual dividends paid to sharehold- ers each period based on the firm’s dividend payout policy. Total dividends also include cash flows to common equity shareholders through stock buybacks. Further, cash flows from the shareholders to the firm when the firm issues shares are negative dividends. Thus, to measure total value-relevant dividends that encompass all of the cash flows from the firm to common equity shareholders each period, the analyst should include the following three components:

� Quarterly or annual ordinary dividend payments to common equity shareholders � Net cash flows to shareholders from common equity share repurchases � Net cash flows from shareholders through common equity issues

� Total dividends to common equity shareholders.

Alternatively, accounting for shareholders’ equity is a reliable framework for measuring total dividends for valuation. To begin, assume that the accounting for shareholders’ equity

Therefore, the present value of common equity today can be expressed using dividends as follows:

[NI T

� (1 + g)] � BV T

� [BV T

� (1 + g)] �

(R E

� g) � (1 + R E )T

∞ V

0 � ∑

D t

t =1 (1 + RE) t

D 1

D 2

D 3

D T

V T

� (1+R

E )1

� (1+R

E )2

� (1+R

E )3

� . . .� (1+R

E )T

� (1+R

E )T

D 1

D 2

D 3

D T

� (1+R

E )1

� (1+R

E )2

� (1+R

E )3

� . . . � (1+R

E )T

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908 Chapter 11 Risk-Adjusted Expected Rates of Return and the Dividends Valuation Approach

follows clean surplus accounting. Under clean surplus accounting, income must include all of the elements of income (all revenues and expenses, all gains and losses) generated by the firm for common equity shareholders. Under U.S. GAAP and IFRS, clean surplus income is measured by comprehensive income (that is, net income plus all of the unrealized gains and losses included in other comprehensive income). Also assume that the effects of all of the direct capital transactions between the firm and the common equity shareholders, such as periodic dividend payments, share issues, and share repurchases, are included in the book value of common shareholders’ equity.11

Under these simple and general principles of clean surplus accounting, the accounting for common equity is represented as follows:

BV t � BV

t�1 � I

t � D

where BV t

denotes the book value of equity at the end of year t, I denotes clean surplus income for year t, and D denotes net direct capital transactions between the firm and com- mon shareholders (dividend payments, stock issues, and stock repurchases) during year t. To isolate all of the net cash flows between the firm and the shareholders during year t, sim- ply rearrange the equation as follows:

D t � I

t � BV

t�1 � BV

Therefore, total dividends used in dividends valuation should equal clean surplus income each year, adjusted for the change in the book value of common equity as a result of direct capital transactions.

Measuring Dividends for PepsiCo This section illustrates the dividends measurement approach using PepsiCo. We derive our dividends expectations from our projected financial statements for PepsiCo in Chapter 10.

In development of the financial statement forecasts for PepsiCo for Year �1, for exam- ple, we projected that PepsiCo would pay common equity dividends equal to 50 percent of lagged net income from continuing operations, amounting to $2,571.0 million [� 0.50 � ($5,142.0 � $0)]. We also assumed that PepsiCo would use implied dividends as the flexible financial account to balance the balance sheet, so an additional $444.3 million in capital would be distributed to common equity shareholders through additional divi - dends or share repurchases. Therefore, we projected that net dividends would amount to $3,015.3 million (� $2,571.0 � $444.3) in Year �1.

We also projected that common stock and additional paid-in capital would remain roughly 1.1 percent of total assets. Because the projections expect total assets to grow by 7.0 per- cent in Year �1, common stock and additional paid-in capital would also grow by 7.0 percent from $381.0 million to $407.5 million by the end of Year �1, implying new stock issues (in effect, negative dividends) of �$26.5 million. Further, we projected that PepsiCo would engage in direct capital transactions with common equity shareholders through the treasury stock account. We projected that PepsiCo would pay $2,500.0 million to repur- chase common shares, net of any shares reissued for stock options exercises. Together, these capital transactions would result in a net cash outflow of $2,473.5 million (� $2,500.0 � $26.5) from PepsiCo to common shareholders.

11 Also assume that direct capital transactions between the firm and common equity shareholders are value-neutral (that is, zero

net present value projects) to the existing common shareholders.

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Bringing these components together, we projected that total value-relevant dividends to common equity shareholders in Year �1 will be as follows (in millions):

Periodic dividend payments $3,015.3 Net purchases of treasury stock 2,500.0 Common stock issues (26.5)

Total dividends to common equity shareholders $5,488.8

This computation can be reconciled with the clean surplus accounting approach as fol- lows: The Year �1 forecast of comprehensive income is $6,110.9 million. After deducting the forecast of the liquidating dividend to retire the preferred shares, the projected amount of comprehensive income available to common shareholders is as follows (in millions):

$6,110.9 � $169.0 � $5,941.9

Total book value of common shareholders’ equity is $12,203.0 million at the beginning of Year �1 and $12,656.1 million at the end of Year �1. Using the clean surplus accounting approach, dividends in Year �1 are as follows (in millions):

D t � I

t � BV

t�1 � BV

t � $5,941.9 � $12,203.0 � $12,656.1 � $5,488.8

Exhibit 11.5 demonstrates these computations for Years �1 through �5.

Selecting a Forecast Horizon For how many future years should the analyst project future payoffs from an investment? The correct answer is the expected life of the investment being valued. This life is a finite number of years for a resource such as a machine, a building, or any resource with limits to its physical existence or a financial instrument with a finite stated maturity (such as a bond, mortgage, or lease). In equity valuation, however, the resource to be valued is an ownership claim on the firm, a resource that has an expected life that is typically indefinite. Therefore, in the case of an equity security, the analyst must project future dividends that, in theory, extend indefinitely.

Of course, as a practical matter, the analyst cannot precisely predict a firm’s dividends very many years into the future. Therefore, analysts commonly develop specific projections of all of the elements of the income statements and balance sheets for the firm and use those ele- ments to derive forecasts of dividends over an explicit forecast horizon (for example, five or ten years) depending on the industry, the maturity of the firm, and the expected growth and predictability of the firm’s business activities. After the explicit forecast horizon, analysts then typically use general steady-state growth assumptions to project the future income statements and balance sheets and use them to derive the dividends that will persist each period to infin- ity. Therefore, the analyst will find it desirable to develop specific forecasts of income state- ments, balance sheets, and cash flows over an explicit forecast horizon that extends until the point at which a firm’s growth pattern is expected to settle into steady-state equilibrium, dur- ing which time dividends might be expected to grow at a steady, predictable rate.

Selecting a forecast horizon involves trade-offs. Reasonably reliable projections can be developed over longer forecast horizons for stable and mature firms. Projections for such firms, as in the case of PepsiCo demonstrated in Chapter 10, capture relatively steady-state operations. On the other hand, it is more difficult to develop reliable projections over long

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910 Chapter 11 Risk-Adjusted Expected Rates of Return and the Dividends Valuation Approach

forecast horizons for young high-growth firms because their future operating performance is relatively more uncertain. This difficulty is exacerbated by the fact that a much higher proportion of the value of young growth firms will be achieved in distant future years, after they reach their potential steady-state profitability. Thus, the analyst faces the dilemma of depending most heavily on long-run forecasts for young growth firms for which long-run projections are most uncertain and most difficult to project. The forecasting and valuation process is particularly difficult for growth firms when the near-term dividends are pro- jected to be zero or negative, as is common for rapidly growing firms that finance growth by issuing common stock. In this case, most of the firm’s value depends on dividends to be generated in years far into the future.

Unfortunately, there is no way to avoid this dilemma. The predictive accuracy of dividends forecasts many years into the future is likely to be questionable for even the most stable and predictable firms. The analyst must recognize that forecasts and value estimates for all firms,

E X H I B I T 1 1 . 5

Computation of PepsiCo’s Total Dividends for the Dividends Valuation Approach

Computing Total Dividends Using Components

Year �1 Year �2 Year �3 Year �4 Year �5

Dividends Paid to Common Shareholders $ 3,015.3 $ 3,324.5 $ 3,818.5 $ 4,398.5 $ 4,848.3

Less: Common Stock Issues (26.5) (33.8) (43.7) (30.2) (51.2) Plus: Common Stock Repurchases 2,500.0 2,500.0 2,500.0 2,500.0 2,500.0

Total Dividends to Common Equity $ 5,488.8 $ 5,790.7 $ 6,274.8 $ 6,868.3 $ 7,297.1

Computing Total Dividends Using Clean Surplus Accounting

Year �1 Year �2 Year �3 Year �4 Year �5

Comprehensive Income $ 6,110.9 $ 6,602.1 $ 7,272.7 $ 7,726.4 $ 8,427.3 Less: Preferred Dividends (169.0) (0.0) (0.0) (0.0) (0.0) Comprehensive Income

Available for Common Equity $ 5,941.9 $ 6,602.1 $ 7,272.7 $ 7,726.4 $ 8,427.3 Plus: Beginning Book

Value of Common Equity 12,203.0 12,656.1 13,467.4 14,465.3 15,323.5 Less: Ending Book Value

of Common Equity (12,656.1) (13,467.4) (14,465.3) (15,323.5) (16,453.6)

Total Dividends to Common Equity $ 5,488.8 $ 5,790.7 $ 6,274.8 $ 6,868.3 $ 7,297.1

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but especially growth firms, have a high degree of uncertainty and estimation risk. To miti- gate this uncertainty and estimation risk, the analyst should adhere to the following points:

• Diligently and comprehensively follow all six steps of the analysis framework. By thor- oughly analyzing the firm’s industry and strategy, the firm’s accounting quality, and the firm’s financial performance and risk ratios, the analyst will have more information to use to develop long-term forecasts that are as reliable as possible.

• To the extent possible, confront directly the problem of long-term uncertainty by developing specific projections of dividends derived from projected income statements and balance sheets that extend five or ten years into the future, at which point the firm may be projected to reach steady-state growth.

• Assess the sensitivity of the forecast projections and value estimates across the reasonable range of growth assumptions.

Continuing Value of Future Dividends The previous section described measuring periodic dividends over an explicit forecast hori- zon. This section describes techniques to project continuing dividends using a steady-state growth rate continuing beyond the explicit forecast horizon and to measure the present value of continuing dividends. We refer to them as continuing dividends because they reflect the cash flows from the firm to the common equity shareholders continuing into the long- run future.

In some circumstances, however, the analyst may not find it necessary to forecast divi- dends continuing beyond the explicit forecast horizon if he or she can reliably predict that the share will receive a future liquidating dividend. In such circumstances, the liquidating dividend is the final cash flow to the shareholder. The liquidating dividend might arise when the firm liquidates its assets at the end of its business life and distributes the proceeds to shareholders to retire their shares. Alternatively, the liquidating dividend might arise when a firm’s shares are acquired by another firm in a merger or an acquisition transaction. The liquidating dividend also can arise when the shareholder elects to sell the share, thereby creating a liquidating dividend from the selling price.

Projecting Continuing Dividends In most circumstances, the analyst will not be able to reliably predict whether or when the share will receive a liquidating dividend. Therefore, analysts commonly forecast dividends over an explicit forecast horizon until the point at which the analyst expects a firm to mature into a steady-state growth pattern, during which time dividends are assumed to grow at a constant steady-state rate. The long-run sustainable growth rate (denoted as g) in future continuing dividends could be positive, negative, or zero. Sustainable growth in divi - dends could be driven by long-run expectations for inflation, the industry’s sales, the econ- omy in general, or the population. The analyst should select a growth rate that captures realistic long-run expectations for Year T�1 and beyond.

Unfortunately, a shortcut analysts sometimes use (and a common error analysts make) in computing the continuing dividends for Year T�1 is to multiply the dividends for Year T by (1 � g) instead of deriving the Year T�1 dividends from the projected Year T�1 income statement and balance sheet. If the analyst wants to compute internally consistent and iden- tical estimates of firm value using dividends, free cash flows, and earnings, he or she should not project dividends for Year T�1 by simply multiplying dividends for Year T by (1 � g). Doing so ignores the necessary growth in all of the elements of the balance sheet and the income statement, which can introduce inconsistent forecast assumptions for dividends, cash flows, and earnings. Even if the analyst simply projects Year T�1 dividends, cash flows,

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912 Chapter 11 Risk-Adjusted Expected Rates of Return and the Dividends Valuation Approach

and earnings to grow at an identical rate (1 � g), doing so may impound inconsistent assumptions and lead to inconsistent value estimates if Year T dividends, cash flows, and earnings are not consistent with their long-run continuing amounts.

Example 11: Projecting Continuing Dividends Suppose the analyst develops the following forecasts for the firm in Year T�1 and Year T:

Shareholders’ Assets � Liabilities � Equity

Year T�1 Balances $100 � $60 � $40 � Net Income �20 �20 � New Borrowing �6 �6 � Dividends Paid �10 �10 Year T Balances $116 � $66 � $50

Suppose the analyst projects that the firm will grow at a steady-state rate of 10 percent in Year T�1 and thereafter. If the analyst simply (and erroneously) projects Year T dividends to grow by 10 percent, the Year T�1 projections will be only $11 (� $10 Year T dividends � 1.10), which is not correct because it relies on implicit inconsistent assumptions. This error would force the estimated value of the firm using dividends to be lower than the value estimates using cash flows or earnings.

To project continuing dividends in Year T�1 correctly, the analyst should derive the continuing dividends from the projected Year T�1 income statement and balance sheet. To do so correctly, the analyst should use the expected long-run growth rate (g) to project all of the items of the Year T�1 income statement and balance sheet. That is, the analyst should project each item on the Year T�1 income statement and balance sheet by multi- plying each item for Year T times (1 � g). The analyst can then derive Year T�1 dividends using clean surplus accounting as follows:

D T�1

� NI T�1

� BV T

� BV T�1

� [NI T

� (1 � g)] � BV T

� [BV T

� (1 � g)]

The analyst must impose the long-run growth rate assumption (1 � g) uniformly on the Year T�1 income statement and balance sheet projections to derive the dividends for Year T�1 correctly. In the long run, assuming that the firm itself will grow at a steady-state rate, all of the elements of the firm (dividends, revenues, expenses, income, assets, liabilities, sharehold- ers’ equity, and cash flows) will grow at the same rate. By applying a uniform growth rate across all of the items of the income statement and balance sheet, the analyst achieves inter- nally consistent steady-state growth across all of the projections of the firm, keeping the bal- ance sheet in balance throughout the continuing forecast horizon and keeping growth in dividends, cash flows, and earnings internally consistent with the long-run growth rate.

Returning to Example 11, to compute continuing dividends in Year T�1 correctly, the analyst should project Year T�1 net income, assets, liabilities, and shareholders’ equity to grow by 10 percent each and then compute Year T�1 continuing dividends as follows:

Shareholders’ Assets � Liabilities � Equity

Year T Balances $ 116 � $ 66 � $50 Growth �1.10 �1.10 �1.10 Year T�1 Balances $127.6 � $72.6 � $55

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The projected net income would be $22 (� $20 � 1.10). The Year T�1 dividends pro- jection would be $17 (� $22 net income � $50 beginning shareholders’ equity � $55 end- ing shareholders’ equity). Note that the correct projected Year T�1 dividend amount of $17 is substantially larger than the erroneous $11 dividend projection. Also note that the $17 Year T�1 dividend is substantially larger than the $10 dividend amount for Year T. The rea- son the firm can begin to pay larger dividends in Year T�1 and beyond is that the firm’s long-run growth rate of 10 percent is lower than the Year T growth rate in assets (16 per- cent) and shareholders’ equity (25 percent); thus, this firm will not need to reinvest as much of its earnings to fund growth and will be able to pay larger dividend amounts in Year T�1 and beyond.

In projecting continuing dividends in Year T�1 and beyond, analysts assume that the firm will settle into a long-run sustainable growth rate. Often analysts assume that the firm’s long-run sustainable growth rate will be consistent with long-run growth in the economy, on the order of 3–5 percent. For firms that have been growing faster than that in the years leading up to Year T�1, the long-run sustainable growth rate implies that the firm will maintain a lower growth rate in assets and equity and thus will be able to pay out substantially larger dividends. By projecting Year T�1 net income, assets, and equity using the long-run sustainable growth rate, it is possible to solve for the long-run sustainable dividends the firm can pay. The continuing dividend amount derived for Year T�1 may be significantly larger than the amounts the firm actually paid during its higher- growth-rate years. The Year T�1 dividend amount reflects the firm’s transition from a high rate of reinvestment to finance high growth in assets to lower reinvestment for lower growth.

Computing Continuing Value As was demonstrated earlier in the dividends valuation model, once the analyst has com- puted continuing dividends for Year T�1, he or she can compute continuing value (some- times called residual value or terminal value) of continuing dividends in Year T�1 and beyond using the perpetuity-with-growth valuation model, as follows:12

∞ V

T � ∑

D T�1

[NI T

� (1 + g)] � BV T

� [BV T

� (1 + g)]

t =1 (1+RE) t

� (R

E �g)

� (R

E �g)

Example 12: Valuing Continuing Dividends An analyst forecasts that the dividends of a firm in Year �5 will be $30 million and that Year �5 earnings and cash flows also will be $30 million. For simplicity in this example, assume the analyst expects that the firm’s income statements and balance sheets will grow uni- formly over the long run and, therefore, that cash flows, earnings, and dividends will grow uniformly over the long run. But the analyst is uncertain about the steady-state long-run growth rate in Year �6 and beyond. The analyst believes that the growth rate will most likely be zero but could reasonably fall in the range between �6 and �6 percent per year; so the analyst derived the range of Year �6 dividends shown in the following table. Assuming a 15 percent cost of capital, the table shows the range of possible continuing val- ues (in millions) for the firm in present value at the beginning of the continuing value period (that is, the beginning of Year �6) and in present value as of today; that is, the con- tinuing value is discounted to today using a factor of 1/(1.15)5:

12 This formula is simply the algebraic simplification for the present value of a growing perpetuity.

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914 Chapter 11 Risk-Adjusted Expected Rates of Return and the Dividends Valuation Approach

Continuing Value in Present Value as of:

Long-Run Perpetuity Dividends in Growth Dividends in with Growth Beginning of

Year T Assumption Year T�1 Factor Year T�1 Today

$30.00 0% $30.00 1/(0.15 � 0.0) � 6.67 $200.00 $ 99.44

$30.00 �6% $31.80 1/(0.15 � 0.06) � 11.11 $353.30 $175.65

$30.00 �6% $28.20 1/(0.15 � 0.06) � 4.76 $134.23 $ 66.74

Analysts also can estimate continuing value using a multiple of dividends in the first year of the continuing value period. The following table shows the continuing value multiples using 1/(R � g) for various costs of equity capital and growth rates. The multiples increase with growth for a given cost of capital, and they decrease as the cost of capital increases for a given level of growth.

Continuing Value Multiples

Long-Run Growth Rates

Cost of Equity Capital 0% 2% 3% 4% 5% 6%

6% 16.67 25.00 33.33 50.00 100.00 na 8% 12.50 16.67 20.00 25.00 33.33 50.00

10% 10.00 12.50 14.29 16.67 20.00 25.00 12% 8.33 10.00 11.11 12.50 14.29 16.67 15% 6.67 7.69 8.33 9.09 10.00 11.11 18% 5.56 6.25 6.67 7.14 7.69 8.33 20% 5.00 5.56 5.88 6.25 6.67 7.14

The continuing value computation using the perpetuity-with-growth valuation model does not work when the growth rate equals or exceeds the discount rate (that is, when g ≥ R) because the denominator in the computation is zero or negative and the resulting contin- uing value estimate is meaningless. In this case, the analyst cannot use the perpetuity com- putation illustrated here. Instead, the analyst must forecast dividend amounts for each year beyond the forecast horizon using the terminal period growth rate and then discount each year’s dividends to present value using the discount rate. The analyst also should reconsider whether it is realistic to expect the firm’s dividends growth rate to exceed the discount rate (the expected rate of return) in perpetuity. This scenario can exist for some years, but is not likely to be sustainable indefinitely. Competition, technological change, new entrants into an industry, and similar dynamic factors eventually reduce growth rates.

An alternative approach for estimating the continuing value is to use the dividends mul- tiples for comparable firms that currently trade in the market. The analyst identifies com- parable companies by studying characteristics such as industry, firm size and age, past growth rates in dividends, profitability, risk, and similar factors. Chapter 14 discusses valu- ation multiples in more depth.

Because of the uncertainty inherent in long-run growth rate forecasts and because con- tinuing value amounts are commonly large proportions of value estimates, analysts should

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conduct sensitivity analysis to assess how sensitive the firm value estimate is to variations in the long-run growth assumption. For example, suppose an analyst is valuing a young high-growth company and can reliably forecast dividends five years into the future. After that horizon, the analyst expects the firm to grow at 6 percent per year, although this is highly uncertain, and long-run growth could range from �3 percent per year to as much as 9 percent per year. The analyst should conduct sensitivity analysis on the projections and valuation, varying long-run growth across the range from �3 to 9 percent per year.

Using the Dividends Valuation Model to Value PepsiCo At the end of 2008, trading in PepsiCo shares on the New York Stock Exchange closed at $54.77 per share, which is the price at which an investor can buy or sell PepsiCo shares. But what is the value of these shares? The valuation of PepsiCo shares uses the techniques described in this chapter and the forecasts developed in Chapter 10. The forecasts and valu - ation estimates are developed using the Forecast and Valuation spreadsheets in FSAP.

We estimate the present value of a share of common equity in PepsiCo at the end of 2008 (equivalently, the start of Year �1) using the risk-adjusted rate of return on PepsiCo’s equity capital as the appropriate discount rate. A prior section of this chapter computed the PepsiCo equity cost of capital to be 8.5 percent. Exhibit 11.5 summarizes the computations of PepsiCo’s dividends in Years �1 to �5. Discounting these future dividends using a dis- count rate of 8.50 percent yields a present value estimate of $24,699.3 million. Exhibit 11.6 illustrates these computations, and Exhibit 11.7 (see page 917) presents the dividend valu- ation model from FSAP.

To compute the present value of continuing value of PepsiCo’s dividends in Year �6 and beyond, we project that continuing dividends will grow at a 3 percent rate in perpetuity, consistent with long-run average growth in the economy. We forecast Year �6 dividends as follows:

D 6

� [NI 5 � (1 � g)] � BV

5 � [BV

5 � (1 � g)]

� [$8,427.3 million � 1.03] � $16,453.6 million � [$16,453.6 million � 1.03]

� $8,680.1 million � $16,453.6 million � $16,947.2 million

� $8,186.5 million

We use the perpetuity-with-growth model to discount dividends in the continuing value period to present value as of the beginning of Year �6 (the beginning of the continuing value period) using PepsiCo’s 8.50 percent cost of equity capital, as follows (allowing for rounding):

Continuing Value 0

� [D 6 � (1/{R

E �g})]

� $8,186.5 million � [1/(0.085 � 0.030)]

� $8,186.5 million � 18.18182

� $148,845.45 million

We then discount the continuing value as of the beginning of Year �6 to present value, as follows (allow for rounding):

Present Value of Continuing Value 0

� $148,845.45 million � [1/{1 � R E }5]

� $148,845.45 million � [1/{1 � 0.085}5]

� $148,845.45 million � 0.665

� $98,988.9 million

Implementing the Dividends Valuation Model 915

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916 Chapter 11 Risk-Adjusted Expected Rates of Return and the Dividends Valuation Approach

The total present value of PepsiCo’s free cash flows to common equity shareholders is the sum of these two parts:

Present Value of Dividends through Year �5 $ 24,699.3 million Present Value of Continuing Value 98,988.9 million Present Value of Common Equity $123,688.2 million

E X H I B I T 1 1 . 6

Valuation of PepsiCo Present Value of Dividends to Common Equity

Year �1 through Year �5 and Beyond

Valuation of Dividends in Year �1 through Year �5

Year �1 Year �2 Year �3 Year �4 Year �5

Total Dividends to Common Equity (from Exhibit 11.5) $ 5,488.8 $5,790.7 $6,274.8 $6,868.3 $7,297.1

Present Value Factors (R E

= 8.50%) 0.922 0.849 0.783 0.722 0.665

Present Value of Dividends $ 5,058.8 $4,919.0 $4,912.6 $4,956.0 $4,852.9

Sum of Present Value Dividends, Years �1 through �5 $24,699.3

Continuing Value Based on Dividends in Year � 6 and Beyond

Project Year �6 Dividends: D

6 = [NI

5 × (1 � g)] � BV

5 – [BV

5 × (1 � g)]

= [$8,427.3 million × 1.03] � $16,453.6 million – [$16,453.6 million × 1.03] = $8,680.1 million � $16,453.6 million – $16,947.2 million = $8,186.5 million

Present Value of Continuing Value (R E

= 8.50% and g = 3.0%):

Present Value of Continuing Value 0

= D 6

× [1 / (R E

– g)] × [1 / (1 � R E )5]

= $8,186.5 million × [1 / (0.085 – 0.030)] × [1 / (1 � 0.085)5] = $8,186.5 million × 18.18182 × 0.665 = $98,988.9 million

Total Value of PepsiCo’s Dividends

Present Value of Dividends through Year �5 $ 24,699.3 million � Present Value of Continuing Value � 98,988.9 million

Present Value of Common Equity $123,688.2 million Adjust for Midyear Discounting (multiply by 1 � [R

E /2]) × 1.0425

Total Present Value of Common Equity $128,945.0 million Divide by Number of Shares Outstanding / 1,553 million

Value per Share of PepsiCo Common Equity = $ 83.03

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Implementing the Dividends Valuation Model 917

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918 Chapter 11 Risk-Adjusted Expected Rates of Return and the Dividends Valuation Approach

Midyear Discounting Present value calculations like those illustrated earlier discount amounts for full periods. Thus, the valuation computations include Year �1 dividends discounted for a full year, Year �2 dividends discounted for two full years, and so on, which is appropriate if the divi - dends being discounted occur at the end of each year. Dividends often occur throughout the period. If this is the case, present value computations with full-year discounting will overdiscount these flows. To avoid overdiscounting, the analyst can compute the present value discount factors as of the midpoint of each year, thereby effectively discounting the dividends as if they occur, on average, in the middle of each year. Suppose the analyst uses a discount rate of 10 percent (R � 0.10). The Year �1 dividends would be discounted from the middle of Year �1 using a factor of 1/(1 � R)0.5 � 1/(1.10)0.5 � 0.9535; the Year �2 dividends would be discounted from the middle of Year �2 using a factor of 1/(1 � R)1.5 � 1/(1.10)1.5 � 0.8668; and so on. The analyst also can use a shortcut approach to this correc- tion by adjusting the total present value to a midyear approximation by adding back one- half year of discounting. To make this midyear adjustment, the analyst multiplies the total present value of the discounted dividends by a factor of 1 � (R/2). For example, if R � 0.10, the midyear adjustment is 1.05 [� 1 � (0.10/2)]. The Valuation spreadsheet computations in FSAP use this shortcut adjustment.13

Applying the midyear discounting adjustment to the computation of the present value of PepsiCo dividends results in the following:

Present Value of Common Equity $123,688.2 million Midyear Adjustment Factor [� 1 � (0.085/2)] � 1.0425 Total Present Value of Common Equity $128,945.0 million

Computing Common Equity Value per Share Dividing the total present value of common equity of $128,945.0 million by 1,553 million shares outstanding indicates that PepsiCo’s common equity shares have a value of $83.03 per share. We will obtain identical value estimates for PepsiCo when we apply the free cash flows to equity valuation model in Chapter 12 and the residual income valuation model in Chapter 13.

Sensitivity Analysis and Investment Decision Making One should not place too much confidence in the precision of firm value estimates using these (or any) forecasts over the remaining life of any firm, even a mature firm such as PepsiCo. Although we have constructed these forecasts and value estimates with care, the forecasting and valuation process has an inherently high degree of uncertainty and estima- tion error. Therefore, the analyst should not rely too heavily on any one point estimate of the value of a firm’s shares and instead should describe a reasonable range of values for a firm’s shares.

13 The valuation models described in this chapter estimate the present value of the firm as of the first day of the first year of the

forecast horizon; for example, January 1 of Year +1 for a firm with an accounting period that matches the calendar year. However,

analysts estimate valuations every day of the year. Suppose the analyst values a firm as of June 17 and compares the value estimate

to that day’s market price. A present value calculation that determines the value of the firm as of January 1 will ignore the value

accumulation between January 1 and June 17 of that year. To refine the calculation, the analyst can adjust the present value as of

January 1 to a present value as of June 17 by multiplying V 0

by a future value factor that reflects value accumulation for the appro-

priate number of days (in this case, 168 days). For example, if the valuation date is June 17 and if R � 0.10, the analyst can update

the January 1 value estimate by multiplying V 0

by (1 + R)(168/365) � (1 + 0.10)(168/365) � 1.0448.

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Two critical forecasting and valuation parameters in most valuations are the long-run growth rate assumption and the cost of equity capital assumption. Analysts should con- duct sensitivity analysis to test the effects of these and other key valuation parameters and forecast assumptions on the share value estimate. Sensitivity analysis tests should allow the analyst to vary these valuation parameters individually and jointly for addi- tional insights into the correlation between share values, growth rates, and discount rate assumptions.

For PepsiCo, the base case assumptions indicate PepsiCo’s share value to be roughly $83. The base case valuation assumes a long-run growth rate of 3.0 percent and a cost of equity capital of 8.50 percent. The sensitivity of the estimates of PepsiCo’s share value can be assessed by varying these two parameters (or any other key parameters in the valuation) across reasonable ranges. Exhibit 11.8 contains the results of sensitivity analysis varying the long-run growth rate from 0–10 percent and the cost of equity capital from 5–20 percent. The data in Exhibit 11.8 show that as the discount rate increases, holding growth constant, share value estimates of PepsiCo fall. Likewise, value estimates fall as growth rates decrease, holding discount rates constant. Note that we omit value estimates from this analysis when the assumed growth rate equals or exceeds the assumed discount rate because the continu- ing value computation is meaningless.

Considering the downside possibilities first, sensitivity analysis should consider how sensitive the share value estimate for PepsiCo is to adverse changes in long-run growth and discount rates. For example, by reducing the long-run growth assumption from 3.0 percent to 2.0 percent while holding the discount rate constant at 8.50 percent, PepsiCo share value falls to $73.36, still well above current market price. In fact, reducing the long-run growth assumption to zero, while holding the discount rate constant at 8.50 percent, PepsiCo’s

Implementing the Dividends Valuation Model 919

E X H I B I T 1 1 . 8

Valuation of PepsiCo Sensitivity Analysis of Value to Growth and Equity Cost of Capital

Long-Run Growth Assumptions

0% 2% 3% 4% 5% 6% 8% 10%

Discount 5% 105.16 160.50 229.67 437.20 Rates: 6% 87.18 120.00 152.81 218.45 415.34

7% 74.37 95.73 114.41 145.56 207.85 394.72 8.50% 60.84 73.36 83.03 97.00 118.95 158.47 711.69

9% 57.34 68.04 76.06 87.30 104.14 132.22 356.87 10% 51.41 59.41 65.13 72.75 83.42 99.42 179.45 11% 46.57 52.71 56.94 62.37 69.61 79.75 120.30 323.07 12% 42.55 47.37 50.58 54.59 59.76 66.64 90.73 163.00 13% 39.16 43.00 45.50 48.55 52.37 57.28 72.98 109.63 14% 36.26 39.37 41.35 43.73 46.63 50.26 61.15 82.93 15% 33.76 36.30 37.90 39.78 42.04 44.80 52.70 66.90 16% 31.57 33.68 34.98 36.50 38.29 40.44 46.35 56.21 18% 27.95 29.44 30.33 31.35 32.53 33.90 37.47 42.83 20% 25.08 26.16 26.79 27.51 28.31 29.24 31.55 34.79

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920 Chapter 11 Risk-Adjusted Expected Rates of Return and the Dividends Valuation Approach

share value estimate falls to $60.84, still above current market price. Similarly, increasing the discount rate from 8.5 percent to 9.0 or 10.0 percent while holding constant the long- run growth assumption at 3.0 percent, PepsiCo shares have a value of roughly $76 or $65, respectively, above current market price. If we revise both assumptions at once, and reduce the long-run growth assumption to 2.0 percent and increase the discount rate assumption to 10.0 percent, PepsiCo’s share value falls to roughly $59.

On the upside, reducing the discount rate to 7.0 percent while holding growth constant at 3.0 percent or increasing the long-run growth assumption from 3.0 to 4.0 percent while holding the discount rate constant at 8.50 percent, the value estimates jump to roughly $114 per share or $97 per share, respectively. If we reduce the discount rate assumption fur- ther, or increase the long-run growth rate further, the share value estimates for PepsiCo jump dramatically higher. For example, increasing the growth rate assumption to 4.0 per- cent and decreasing the discount rate assumption to 7.0 percent moves the share value esti- mate to more than $145.

These data suggest that the value estimate is sensitive to slight variations in the baseline assumptions of 3.0 percent long-run growth and an 8.50 percent discount rate, which yield a share value estimate of $83. Adverse variations in valuation parameters could reduce PepsiCo’s share value estimates to $55 or lower, whereas favorable variations could increase PepsiCo’s share value to over $100.

If the forecast and valuation assumptions are realistic, the baseline value estimate for PepsiCo is $83 per share at the end of 2008. At that time, the market price of $54.77 per share indicates that PepsiCo shares were underpriced by about 52 percent. Under the fore- cast assumptions, PepsiCo’s share value could vary within a range of a low of $51 per share to a high of $114 per share with only minor perturbations in the growth rate and discount rate assumptions. Given PepsiCo’s $54.77 share price, these value estimates would have supported a buy recommendation or perhaps a strong buy recommendation at the end of 2008 because the valuation sensitivity analysis reveals limited downside potential but sub- stantial upside potential for the value of PepsiCo shares.

Evaluation of the Dividends Valuation Method The principal advantages of the dividends valuation method include the following:

• This valuation method focuses on dividends. Economists argue that dividends provide the classical approach to valuing shares. Dividends reflect the payoffs that sharehold- ers can consume.

• Projected amounts of dividends result from projecting expected amounts of revenues, expenses, assets, liabilities, and shareholders’ equity. Therefore, they reflect the impli- cations of the analyst’s expectations for the future operating, investing, and financing decisions of a firm.

The principal disadvantages of the dividends valuation method include the following:

• The continuing value (terminal value) tends to dominate the total value in many cases. For firms that do not pay periodic dividends or repurchase shares, the continuing value can comprise the total value of the firm, which requires the analyst to forecast the future value of the firm in order to compute the present value of the firm. Continuing value estimates are sensitive to assumptions made about growth rates after the forecast horizon and discount rates.

• The projection of dividends can be time-consuming for the analyst, making it costly when the analyst follows many companies and must regularly identify under- and overvalued firms.

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Questions, Exercises, Problems, and Cases 921

SUMMARY This chapter illustrated the computation of risk-adjusted required rates of return on equity and the weighted average cost of capital, which analysts use as discount rates in valuation models. In valuation, analysts use these discount rates to compute the present value of future dividends, cash flows, or earnings. This chapter also described the dividends valu - ation model and applied it to value PepsiCo at the end of 2008. As with the preparation of projected financial statements in Chapter 10, the reasonableness of the valuations depends on the reasonableness of the forecast assumptions and the valuation parameters. The ana- lyst should assess the sensitivity of the valuation to alternative long-run growth and dis- count rate parameters and to other key drivers of value. To validate value estimates using the dividends valuation approach, the analyst also should compute the value of the firm using other approaches, such as the free-cash-flows-based approaches discussed in Chapter 12, the earnings-based approaches discussed in Chapter 13, and the valuation multiples approaches described in Chapter 14.

QUESTIONS, EXERCISES, PROBLEMS, AND CASES

Questions and Exercises 11.1 THE RISK-RETURN TRADE-OFF. Explain why analysts and investors use risk-adjusted expected rates of return as discount rates in valuation. Why do risk-adjusted expected rates of return increase with risk?

11.2 THE COMPONENTS OF THE CAPM. The CAPM computes expected rates of return using the following model (described in the chapter):

E[R Ej

] � E[R F ] � ß

j � {E[R

M ] � E[R

F ]}

Explain the role of each of the three components of this model.

11.3 NONDIVERSIFIABLE AND DIVERSIFIABLE RISK FACTORS. Identify the types of firm-specific factors that increase a firm’s nondiversifiable risk (sys- tematic risk). Identify the types of firm-specific factors that increase a firm’s diversifiable risk (idiosyncratic risk or nonsystematic risk). Why do models of risk-adjusted expected returns include no expected return premia for diversifiable risk?

11.4 DEBT AND THE WEIGHTED AVERAGE COST OF CAPITAL. Why do investors typically accept a lower risk-adjusted rate of return on debt capital than equity capital? Suppose a stable, financially healthy, profitable, tax-paying firm that has been financed with all equity and no debt decides to add a reasonable amount of debt to its capi - tal structure. What effect will that change in capital structure likely have on the firm’s weighted average cost of capital?

11.5 THE DIVIDENDS VALUATION APPROACH. Explain the theory behind the dividends valuation approach. Why are dividends value-relevant to common equity shareholders?

11.6 MEASURING VALUE-RELEVANT DIVIDENDS. The chapter describes how the dividends valuation approach measures value-relevant dividends to encompass

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922 Chapter 11 Risk-Adjusted Expected Rates of Return and the Dividends Valuation Approach

various transactions between the firm and the common shareholders. What transactions should the analyst include in value-relevant dividends for purposes of implementing the dividends valuation model? Why?

11.7 FIRMS THAT DO NOT PAY PERIODIC DIVIDENDS. Why is the divi - dends valuation approach applicable to firms that do not pay periodic (quarterly or annual) dividends?

11.8 VALUATION APPROACH EQUIVALENCE. Conceptually, why should an analyst expect the dividends valuation approach to yield equivalent value estimates to the valuation approach that is based on free cash flows available to be distributed to common equity shareholders?

11.9 DIVIDEND POLICY IRRELEVANCE. The chapter asserts that dividends are value-relevant even though the firm’s dividend policy is irrelevant. How can that be true? What is the key assumption in the theory of dividend policy irrelevance?

Problems and Cases 11.10 CALCULATING REQUIRED RATES OF RETURN ON EQUITY CAPITAL ACROSS DIFFERENT INDUSTRIES. The data in Exhibit 11.3 on industry median betas suggest that firms in the following three sets of related industries have different degrees of systematic risk.

Median Beta during 1999–2007

Utilities versus Petroleum Refining 0.32 versus 0.65 Grocery Stores versus Retailing—Apparel 0.50 versus 1.08 Depository Institutions (such as Banks) versus

Security and Commodity Brokers 0.39 versus 1.24

Required a. For each matched pair of industries, describe factors that characterize a typical firm’s

business model in each industry. Describe how such factors would contribute to dif- ferences in systematic risk.

b. For each matched pair of industries, use the CAPM to compute the required rate of return on equity capital for the median firm in each industry. Assume that the risk- free rate of return is 4.0 percent and the market risk premium is 5.0 percent.

c. For each matched pair of industries, compute the present value of a stream of $1 divi - dends for the median firm in each industry. Use the perpetuity-with-growth model and assume 3.0 percent long-run growth for each industry. What effect does the dif- ference in systematic risk across industries have on the per dollar dividend valuation of the median firm in each industry?

11.11 CALCULATING THE COST OF CAPITAL. Whirlpool manufactures and sells home appliances under various brand names. IBM develops and manufactures com- puter hardware and offers related technology services. Target Stores operates a chain of gen- eral merchandise discount retail stores. Selected data for these companies appear in the following table (dollar amounts in millions). For each firm, assume that the market value of the debt equals its book value.

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Whirlpool IBM Target Stores

Total Assets $13,532 $109,524 $44,106 Interest-Bearing Debt $ 2,597 $ 33,925 $18,752 Average Pretax Borrowing Cost 6.1% 4.3% 4.9% Common Equity:

Book Value $ 3,006 $ 13,465 $13,712 Market Value $ 2,959 $110,984 $22,521

Income Tax Rate 35.0% 35.0% 35.0% Market Equity Beta 2.27 0.78 1.20

Required a. Assume that the intermediate-term yields on U.S. government Treasury securities

are roughly 3.5 percent. Assume that the market risk premium is 5.0 percent. Compute the cost of equity capital for each of the three companies.

b. Compute the weighted average cost of capital for each of the three companies. c. Compute the unlevered market (asset) beta for each of the three companies. d. Assume for this part that each company is a candidate for a potential leveraged buy-

out. The buyers intend to implement a capital structure that has 75 percent debt (with a pretax borrowing cost of 8.0 percent) and 25 percent common equity. Project the weighted average cost of capital for each company based on the new capi - tal structure. To what extent do these revised weighted average costs of capital differ from those computed in Part b?

11.12 CALCULATION OF DIVIDENDS-BASED VALUE. Royal Dutch Shell is a petroleum and petrochemicals company. It engages primarily in the exploration, pro- duction, and sale of crude oil and natural gas and the manufacture, transportation, and sale of petroleum and petrochemical products. The company operates in approximately 200 countries worldwide—in countries in North America, Europe, Asia-Pacific, Africa, South America, and the Middle East. During 2006–2008, Royal Dutch Shell generated the follow- ing total dividends to common equity shareholders (in USD millions):

2006 2007 2008

Common Dividend Payments $ 8,142 $ 9,001 $ 9,516 Stock Repurchases 8,047 4,387 3,573

Total Dividends $16,189 $13,388 $13,089

Analysts project 5 percent growth in earnings over the next five years. Assuming concur- rent 5 percent growth in dividends, the following table provides the amounts that analysts project for Royal Dutch Shell’s total dividends for each of the next five years. In Year �6, total dividends are projected for Royal Dutch Shell assuming that its income statement and balance sheet will grow at a long-term growth rate of 3 percent.

Year �1 Year �2 Year �3 Year �4 Year �5 Year �6

Projected Growth 5% 5% 5% 5% 5% 3% Projected Total Dividends

to Common Equity $13,743 $14,431 $15,152 $15,910 $16,705 $17,206

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924 Chapter 11 Risk-Adjusted Expected Rates of Return and the Dividends Valuation Approach

At the end of 2008, Royal Dutch Shell had a market beta of 0.71. At that time, yields on intermediate-term U.S. Treasuries were roughly 3.5 percent. Assume that the market required a 5.0 percent risk premium. Royal Dutch Shell had 6,241 million shares outstand- ing at the end of 2008 that traded at a share price of $24.87.

Required a. Calculate the required rate of return on equity for Royal Dutch Shell as of the begin-

ning of Year �1. b. Calculate the sum of the present value of total dividends for Year �1 through �5. c. Calculate the continuing value of Royal Dutch Shell at the start of Year �6 using the

perpetuity-with-growth model with Year �6 total dividends. Also compute the pres- ent value of continuing value as of the beginning of Year �1.

d. Compute the total present value of dividends for Royal Dutch Shell as of the begin- ning of Year �1. Remember to adjust the present value for midyear discounting.

e. Compute the value per share of Royal Dutch Shell as of the beginning of Year �1. f. Given the share price at the start of Year �1, do Royal Dutch Shell shares appear

underpriced, overpriced, or correctly priced?

11.13 VALUING THE EQUITY OF A PRIVATELY HELD FIRM. Refer to the financial statement forecasts for Massachusetts Stove Company (MSC) prepared for Case 10.2. The management of MSC wants to know the equity valuation implications of adding gas stoves under the best, most likely, and worst case scenarios. Under the three scenarios from Case 10.2, the actual amounts of net income and common shareholders’ equity for Year 7 and the projected amounts for Year 8–Year 12 are as follows:

Actual Projected

Year 7 Year 8 Year 9 Year 10 Year 11 Year 12

Best-Case Scenario:

Net Income $154,601 $148,422 $123,226 $173,336 $ 271,725 $ 390,639 Common Equity $552,080 $700,502 $823,728 $997,064 $1,268,789 $1,659,429

Most Likely Scenario:

Net Income $154,601 $135,343 $ 74,437 $ 72,899 $ 109,357 $ 149,977 Common Equity $552,080 $687,423 $761,860 $834,759 $ 944,116 $1,094,093

Worst-Case Scenario:

Net Income $154,601 $128,263 $ 18,796 $(39,902) $ (58,316) $ (77,156) Common Equity $552,080 $680,343 $699,139 $659,238 $ 600,921 $ 523,766

MSC is not publicly traded and therefore does not have a market equity beta. Using the market equity beta of the only publicly traded woodstove and gas stove manufacturing firm and adjusting it for differences in the debt-to-equity ratio, income tax rate, and privately owned status of MSC yields a cost of equity capital for MSC of 13.55 percent.

Required a. Use the clean surplus accounting approach to derive the projected total amount of

MSC’s dividends to common equity shareholders in Years 8 through 12. b. Given that MSC is a privately held company, assume that ending book value of com-

mon equity at the end of Year 12 is a reasonable estimate of the value at which the

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common shareholders’ equity could be liquidated. Calculate the value of the equity of MSC as of the end of Year 7 under each of the three scenarios. Ignore the midyear discounting adjustment.

c. How do these valuations affect your advice to the management of MSC about adding gas stoves to its woodstove line?

11.14 DIVIDENDS-BASED VALUATION OF COMMON EQUITY. Problem 10.16 projected financial statements for Walmart for Years �1 through �5. The following data for Walmart include the actual amounts for 2008 and the projected amounts for Year �1 to Year �5 for comprehensive income and common shareholders’ equity (assuming Walmart will use implied dividends as the financial flexible account to balance the balance sheet; amounts in millions).

Actual Projected

2008 Year �1 Year �2 Year �3 Year �4 Year �5

Comprehensive Income $ 6,848 $ 13,995 $ 15,024 $ 16,126 $ 17,306 $ 18,569

Common Shareholders’ Equity:

Paid-In Capital $ 4,313 $ 4,744 $ 5,219 $ 5,741 $ 6,315 $ 6,946 Retained Earnings 63,660 68,692 77,018 80,957 93,955 97,024 Accumulated Other

Comprehensive Income (2,688) (2,688) (2,688) (2,688) (2,688) (2,688)

Total Common Equity $ 65,285 $ 70,749 $ 79,549 $ 84,010 $ 97,582 $101,282

The market equity beta for Walmart at the end of 2008 was 0.80. Assume that the risk- free interest rate was 3.5 percent and the market risk premium was 5.0 percent. Walmart had 3,925 million shares outstanding at the end of 2008, and share price was $46.06.

Required a. Use the CAPM to compute the required rate of return on common equity capital for

Walmart. b. Compute the weighted average cost of capital for Walmart as of the start of Year �1.

At the end of 2008, Walmart had $42,218 million in outstanding interest-bearing debt on the balance sheet and no preferred stock. Assume that the balance sheet value of Walmart’s debt is approximately equal to the market value of the debt. Assume that at the start of Year �1, Walmart will incur interest expense of 5.0 per- cent on debt capital and that Walmart’s average tax rate is 34.2 percent.

c. Use the clean surplus accounting approach to derive the projected dividends for Walmart for Years �1 through �5 based on the projected comprehensive income and shareholders’ equity amounts.

d. Use the clean surplus accounting approach to project the continuing dividend in Year �6. Assume that the steady-state long-run growth rate will be 3 percent in Year �6 and beyond.

e. Using the required rate of return on common equity from Part a as a discount rate, compute the sum of the present value of dividends for Walmart for Years �1 through �5.

f. Using the required rate of return on common equity from Part a as a discount rate and the long-run growth rate from Part d, compute the continuing value of Walmart as of the beginning of Year �6 based on Walmart’s continuing dividends in Years �6

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926 Chapter 11 Risk-Adjusted Expected Rates of Return and the Dividends Valuation Approach

and beyond. After computing continuing value, bring continuing value back to pres- ent value at the start of Year �1.

g. Compute the value of a share of Walmart common stock. (i) Compute the sum of the present value of dividends including the present value of continuing value. (ii) Adjust the sum of the present value using the midyear discounting adjust- ment factor. (iii) Compute the per-share value estimate.

h. Using the same set of forecast assumptions as before, recompute the value of Walmart shares under two alternative scenarios. Scenario 1: Assume that Walmart’s long-run growth will be 2 percent, not 3 percent as before, and assume that Walmart’s required rate of return on equity is 1 percentage point higher than the rate you computed using the CAPM in Part a. Scenario 2: Assume that Walmart’s long- run growth will be 4 percent, not 3 percent as before, and assume that Walmart’s required rate of return on equity is 1 percentage point lower than the rate you com- puted using the CAPM in Part a. To quantify the sensitivity of your share value esti- mate for Walmart to these variations in growth and discount rates, compare (in percentage terms) your value estimates under these two scenarios with your value estimate from Part g.

i. What reasonable range of share values would you expect for Walmart common stock? Where is the current price for Walmart shares relative to this range? What do you recommend?

INTEGRATIVE CASE 11.1

STARBUCKS

Dividends-Based Valuation of Starbucks’ Common Equity Integrative Case 10.1 projected financial statements for Starbucks for Years �1 through �5. This portion of the Starbucks Integrative Case applies the techniques in Chapter 11 to com- pute Starbucks’ required rate of return on equity and share value based on the dividends valuation model. This case also compares the value estimate to Starbucks’ share price at the time of the case development to provide an investment recommendation.

The market equity beta for Starbucks at the end of 2008 was 0.58. Assume that the risk- free interest rate was 4.0 percent and the market risk premium was 6.0 percent. Starbucks had 735.5 million shares outstanding at the end of 2008, and share price was $14.17.

Required a. Use the CAPM to compute the required rate of return on equity capital for

Starbucks. b. Compute the weighted average cost of capital for Starbucks as of the start of Year

�1. At the start of Year �1, Starbucks had $1,263 million in outstanding interest- bearing debt on the balance sheet and no preferred stock. Assume that the balance sheet value of Starbucks’ debt is approximately equal to the market value of the debt. Assume that at the start of Year �1, Starbucks will incur interest expense of 6.25 per- cent on debt capital and that Starbucks’ average tax rate is 36.0 percent.

c. From your forecasts of Starbucks’ financial statements for Years �1 through �5, derive the projected dividends using the projected amounts for the plug to dividends less the net amounts of common stock issued each year (if any). Then compute pro- jected dividends for Starbucks for Years �1 through �5 using the clean surplus accounting approach based on projected amounts for comprehensive income and

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Starbucks 927

common shareholders’ equity. The projected amounts of dividends under the two approaches should be identical.

d. Use the clean surplus accounting approach to project the continuing dividend in Year �6. Assume that the steady-state long-run growth rate will be 3 percent in Year �6 and beyond.

e. Using the required rate of return on common equity capital from Part a as a dis- count rate, compute the sum of the present value of dividends for Starbucks for Years �1 through �5.

f. Using the required rate of return on common equity capital from Part a as a dis- count rate and a 3.0 percent long-run growth rate, compute the continuing value of Starbucks as of the beginning of Year �6 based on Starbucks’ continuing dividends in Year �6 and beyond. After computing continuing value, bring continuing value back to present value at the start of Year �1.

g. Compute the value of a share of Starbucks’ common stock. (i) Compute the sum of the present value of dividends including the present value of continuing value. (ii) Adjust the sum of the present value using the midyear discounting adjustment factor. (iii) Compute the per-share value estimate.

h. Using the same set of forecast assumptions as before, recompute the value of Starbucks shares under two alternative scenarios. Scenario 1: Assume that Starbucks’ long-run growth will be 2 percent, not 3 percent as before, and assume that Starbucks’ required rate of return on equity is 1 percentage point higher than the rate you computed using the CAPM in Part a. Scenario 2: Assume that Starbucks’ long-run growth will be 4 percent, not 3 percent as before, and assume that Starbucks’ required rate of return on equity is 1 percentage point lower than the rate you computed using the CAPM in Part a. To quantify the sensitivity of your estimate of share value for Starbucks to variations in long-run growth and discount rates, compare (in percentage terms) your value estimates under these two scenarios with your value estimate from Part f.

i. What reasonable range of share values would you expect for Starbucks’ common stock? Where is the current price for Starbucks’ shares relative to this range? What do you recommend?

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Learning Objectives

Chapter 12

Valuation: Cash-Flow-Based Approaches

1 Understand cash-flow-based valuation models and their conceptual and practical strengths and weaknesses.

2 Apply practical techniques to deal with many of the difficult issues involved in estimating firm value using the present value of expected future free cash flows:

a. Risk, discount rates, and the cost of capital

b. Cash flows to the investor versus cash flows to the firm

c. Nominal versus real cash flows

d. Pretax versus after-tax cash flows

e. The forecast horizon

f. Computation of continuing value

3 Measure free cash flows for all debt and equity capital stakeholders as well as free cash flows for common equity shareholders and understand when each measure is appropriate.

4 Understand the reasons for discounting free cash flows for common equity shareholders using a required rate of return on equity capital and discounting free cash flows for all debt and equity capital stakeholders using a weighted average cost of capital.

5 Apply all of these techniques to estimate firm value using the present value of future free cash flows for common equity shareholders and the present value of future free cash flows for all debt and equity capital stakeholders.

6 Assess the sensitivity of firm value estimates to key valuation parameters such as discount rates and expected long-term growth rates.

INTRODUCTION AND OVERVIEW This chapter relies heavily on the financial statement forecasts developed for PepsiCo in Chapter 10, as well as the valuation concepts and techniques introduced and applied in Chapter 11. This chapter extends valuation methodology to encompass free-cash-flows- based valuation approaches and applies these valuation approaches to PepsiCo.

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Introduction and Overview 929

As introduced in Chapter 11, economic theory teaches that the value of an investment equals the present value of the expected future payoffs from the investment, discounted at a rate that reflects the risk inherent in those expected payoffs. The general model for esti- mating the present value of a security (denoted as V

0 with present value denoted at time

t�0) with an expected life of n future periods is as follows:1

n Expected Future Payoffs

tV 0

� ∑ t=1 (1 � Discount Rate)

Valuation methods such as the dividends-based valuation methods demonstrated in the previous chapter, the free-cash-flows-based methods demonstrated in this chapter, and the earnings-based methods demonstrated in the next chapter are all designed to produce reli- able estimates of the value of the firm’s equity shares. The value estimates that these approaches produce provide the basis for intelligent investment decisions because even in relatively efficient securities markets, price does not necessarily equal value for every secu- rity at all times. Price is observable, but value is not; value must be estimated. Therefore, estimating the value of a security is a common objective of financial statement analysis. The financial statement analysis and valuation process enables investors, analysts, portfolio managers, investment bankers, and corporate managers to determine a reliable appraisal of the value of shares of common equity. Comparing value to price then yields a reliable basis to assess whether a firm’s equity shares are underpriced, overpriced, or fairly priced in the capital markets.

Whether an analyst will produce reliable estimates of share value as a result of the finan- cial statement analysis and valuation process depends entirely on whether the analyst care- fully and thoughtfully applies each step of the process. The six-step analysis framework that forms the structure of this book (Exhibit 1.2 in Chapter 1) is a logical set of steps that enables the analyst to determine reliable estimates of value. Following the first three steps, the analyst should first understand the economics of the industry, then assess the particu- lar firm’s strategy, and then carefully evaluate the quality of the firm’s accounting, making adjustments if necessary. In the fourth step, the analyst should evaluate the firm’s profitabil- ity and risk with a set of financial ratios. All of this information should provide the analyst with a solid foundation of information to use in the fifth step, projecting the firm’s future financial statements. The analyst can then use those financial statement forecasts to derive expectations of future earnings, cash flows, and dividends, which are the fundamental pay- off measures used in valuation. In the sixth and final step, the analyst applies valuation models to these expectations to estimate the value of the firm. Forecasts of expected future payoffs (the numerator in the valuation model) depend on forecasts of future earnings, cash flows, or dividends. Assessing an appropriate risk-adjusted discount rate (the denomi - nator in the valuation model) requires an unbiased assessment of the inherent riskiness in the set of expected future payoffs. Therefore, reliable estimates of firm value depend on unbiased expectations of future payoffs and an appropriate risk-adjusted discount rate, all of which depend on all six steps of the framework.

As explained in the previous chapter, when the analyst derives forecasts of future earn- ings, cash flows, and dividends from a set of internally consistent financial statement fore- casts for a firm and uses the same discount rate in correctly specified models to compute

1 In this chapter, as in the previous chapter, t refers to accounting periods. The valuation process determines an estimate of firm

value, denoted as V 0 , in present value as of today, when t�0. The period t�1 refers to the first accounting period being discounted

to present value. Period t�n is the period of the expected final payoff.

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930 Chapter 12 Valuation: Cash-Flow-Based Approaches

present values, the expected earnings, cash flows, and dividends valuation models will yield identical estimates of value for a firm. We applied the dividends-based valuation approach to PepsiCo and estimated that, given our forecast assumptions and valuation parameters, PepsiCo’s share value should be within a fairly narrow range of around $83 at the time of our analysis. This chapter illustrates the equivalence of the dividends and free cash flows valuation approaches, both in the theoretical development of the models and in their appli- cation to the valuation of PepsiCo. The next chapter will describe and apply the earnings- based valuation approach and demonstrate its theoretical and practical equivalence with both the dividends and free cash flows approaches.2

It is important that analysts understand the similarities and differences in the dividends, cash flows, and earnings valuation approaches and see their theoretical and practical equiva - lence. Our experience strongly suggests that applying several different valuation approaches yields better insights about the value of a firm than relying on one approach in all cases. In addition, it is our experience that an analyst is better equipped to work successfully with clients, managers, colleagues, and subordinates in the financial statement analysis and valuation process if the analyst thoroughly understands all three valuation approaches.

All four valuation chapters—Chapters 11–14—emphasize that the objective of the valu - ation process is not a single point estimate of value per se. Instead, the objective is to determine the distribution of value estimates across the relevant ranges of critical forecast assumptions and valuation parameters. By assessing the sensitivity of value estimates across a distribution of relevant forecast assumptions and valuation parameters, we seek to deter- mine the most likely range of values for a share, which we then compare to the share’s cur- rent price for an intelligent investment decision.

RATIONALE FOR CASH-FLOW-BASED VALUATION As we demonstrated in the previous chapter, the value of a share of common equity is the present value of the expected future dividends.3 Dividends are fundamental expected future payoffs that analysts can use to value shares because they represent the distribution of wealth to shareholders. The equity shareholder invests cash to purchase the share and then receives cash through dividends as the payoffs from holding the share, including the final “liquidating” dividend when the investor sells the share. In dividends-based valuation, we define dividends broadly to encompass all cash flows from the firm to the common equity shareholders through periodic dividend payments, stock buybacks, and the liquidating dividend, as well as cash flows from the shareholders to the firm when the firm issues shares (negative dividends).

Cash-flow-based valuation and dividends-based valuation can be considered two sides to the same coin: the analyst can value the firm based on the cash flows into the firm that will be used to pay dividends or, equivalently, value the firm using cash flows the firm pays out in dividends to common shareholders. In the cash flows approach, we focus on the cash that flows into the firm; in the dividends approach we focus on the cash that flows out of the firm. Instead of focusing on wealth distribution through dividends, the cash-flow-based

2 For examples of research on the complementarity of these approaches, see Stephen Penman and Theodore Sougiannis, “A

Comparison of Dividend, Cash Flow, and Earnings Approaches to Equity Valuation,” Contemporary Accounting Research 15, no. 3

(Fall 1998), pp. 343–383, and Jennifer Francis, Per Olsson, and Dennis Oswald, “Comparing the Accuracy and Explainability of

Dividend, Free Cash Flow, and Abnormal Earnings Equity Value Estimates,” Journal of Accounting Research 38, no. 1 (Spring 2000),

pp. 45–70.

3 John Burr Williams, The Theory of Investment and Value (Cambridge, Mass.: Harvard University Press, 1938).

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approach focuses on cash flows generated by the firm that create dividend-paying capacity. In any given period, the amount of cash flow into the firm and the amount of dividends paid out of the firm will likely differ; the equivalence of these two valuation approaches arises because over the lifetime of the firm the cash flows into and out of the firm will be equivalent.

The cash-flow-based valuation approach measures and values the cash flows that are “free” to be distributed to shareholders. That is, free cash flows are the cash flows each period that are available for distribution to shareholders, unencumbered by necessary reinvest- ments in operating assets or required payments to debtholders. Free cash flows can be used instead of dividends as the value-relevant measures of expected future payoffs to the investor in the numerator of the general value model set forth at the outset of this chapter. Both approaches, if implemented with consistent assumptions, will lead to identical estimates of value.

The rationale for using expected free cash flows in valuation is twofold and is essentially the same rationale for using dividends, as follows:

• Cash is the ultimate source of value. When individuals and firms invest in an economic resource, they delay current consumption in favor of future consumption. Cash is the medium of exchange that will permit them to consume various goods and services in the future. A resource has value because of its ability to provide future cash flows. The free cash flows approach measures value based on the cash flows that the firm gener- ates that can be distributed to investors.

• Cash is a measurable common denominator for comparing the future benefits of alter- native investment opportunities. One might compare investment opportunities involving the holding of a bond, a stock, or an office building, but comparing these alternatives requires a common measuring unit of their future benefits. The future cash flows derived from their future services serve such a function.

FREE-CASH-FLOWS-BASED VALUATION CONCEPTS The following sections describe and illustrate these key concepts in free-cash-flows-based valuation methods:

• Risk, discount rates, and the cost of capital • Cash flows to the investor versus cash flows to the firm • Nominal versus real cash flows • Pretax versus after-tax cash flows • The forecast horizon • Computation of continuing value These concepts are the same underlying concepts described in the previous chapter in pre-

senting dividends-based valuation methods. Therefore, we will briefly review those concepts here and describe how they apply to free cash flows valuation. Refer back to the previous chapter for more detailed explanations of these concepts.

We first describe computing discount rates to use in free-cash-flows-based valuation, including required rates of return on equity capital and weighted average costs of capital. We then present simple examples involving a single project. Next, we confront conceptual measurement issues regarding cash flows to the investor versus cash flows to the firm, nomi nal versus real cash flows, and pretax versus after-tax cash flows. We also address fore- cast horizons and continuing value. A later section of this chapter describes how to compute free cash flows to equity shareholders versus free cash flows to all debt and equity stake- holders. Later in the chapter, we also illustrate the free cash flow valu ation approaches by

Free-Cash-Flows-Based Valuation Concepts 931

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932 Chapter 12 Valuation: Cash-Flow-Based Approaches

valuing PepsiCo using free cash flows derived from the projected financial statements developed in Chapter 10.

Risk, Discount Rates, and the Cost of Capital The general valuation model described at the beginning of the chapter is a present value model, so the analyst must determine an appropriate discount rate to use to measure future payoffs in present value. This section briefly reviews the computation of the required rate of return on equity capital and the weighted average cost of capital.

Cost of Common Equity Capital When discounting the free cash flows available to common equity shareholders, the analyst should use a risk-adjusted required rate of return on equity capital. As described in more depth in the previous chapter, analysts commonly estimate the cost of equity capital using an expected return model such as the CAPM (capital asset pricing model). The CAPM assumes that the market is composed of risk-averse investors who demand a rate of return that (1) compensates them for forgoing the consumption of capital and (2) compensates them with a risk premium for bearing systematic (nondiversifiable) risk. Systematic risk arises from economy-wide factors (such as economic growth or recession, unemployment, unexpected inflation, unexpected changes in prices for natural resources such as oil and gas, unexpected changes in exchange rates, and population growth) that affect all firms to varying degrees and therefore cannot be fully diversified. The amount of the risk premium for a particular stock depends on the level of the firm’s systematic risk.

Analysts often measure systematic risk using the firm’s market beta, which is estimated as the slope coefficient from regressing the firm’s stock returns on an index of returns on a marketwide portfolio of stocks over a relevant period of time.4 Market beta is an estimate of systematic risk based on the degree of covariation between a firm’s stock returns and an index of stock returns for all firms in the market. If a firm’s market beta from such a regres- sion is equal to 1, it indicates the firm’s stock returns covary identically with returns to a marketwide portfolio, indicating that the firm has the same degree of systematic risk as the market as a whole. If a firm’s market beta is greater than or less than 1, the firm has a greater or lesser degree of systematic risk than the market portfolio as a whole.

The CAPM computes the expected return on common equity capital for Firm j as follows:

E[R Ej

] � E[R F ] � ß

j � {E[RM] � E[RF]}

where E denotes that the related variable is an expectation; R Ej

denotes return on common equity in Firm j; R

F denotes the risk-free rate of return; ß

j denotes the market beta for Firm

j; and R M

denotes the return on a diversified, marketwide portfolio of stocks (such as the S&P 500). According to the CAPM, a common equity security with no systematic risk (that is, a stock with ß

j � 0) should be expected to earn a return equal to the expected rate of

return on risk-free securities. The subtraction term in brackets in the preceding equation represents the average market risk premium, equal to the return that equity investors in the capital markets require for bearing the average amount of systematic risk in the market portfolio. An equity security with systematic risk equal to the average amount of systematic

4 Researchers and analysts have developed a variety of approaches to estimate market betas. For example, one common approach

estimates a firm’s market beta by regressing the firm’s monthly stock returns on a marketwide index of returns (such as the S&P

500) over the last 60 months.

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risk of all equity securities in the market has a market beta equal to 1 and should expect to earn the same rate of return as the average stock in the market portfolio.

Note that the CAPM views firm-specific nonsystematic risk as diversifiable by the investor. Nonsystematic risk factors would include, for example, the industry and product portfolio of the firm, the sustainability of the firm’s strategy, and the firm’s ability to gen- erate revenue growth and control expenses. According to CAPM, a competitive equilibrium capital market does not expect a return for a firm’s nonsystematic risk because such risk can be diversified away in a portfolio of stocks.

Computing the Weighted Average Cost of Capital In some circumstances, the analyst may want to value all of the assets of a firm rather than directly value the common equity of the firm. In such circumstances, the analyst should discount to present value the free cash flows that the assets will generate that will be avail- able to satisfy all of the debt and equity claims that finance the assets of the firm. In these circumstances, analysts commonly use a weighted average cost of capital that reflects the relative proportions of debt, preferred, and common equity capital the firm will use to finance the assets and the respective costs of each type of capital. Such circumstances might arise, for example, if the analyst is considering acquiring all of the assets of a firm or acquir- ing all of the financial claims (common equity shares, preferred shares, and debt) through a merger with the firm. Therefore, the analyst determines the present value of the future free cash flows available to satisfy all of the firm’s financing using a discount rate that reflects the weighted average cost of the debt, preferred, and common equity capital the firm uses to finance the net operating assets.

A formula for the weighted average cost of capital (denoted as R A

to indicate that the discount rate is the required rate of return applicable to the net operating assets of the firm) is given here:

R A

� [w D

� R D

� (1 � tax rate)] � [w P

� R P ] � [w

E � R

E ]

In this formula, the subscripts D, P, and E refer to different types of capital (debt, pre- ferred stock, and common equity, respectively); w denotes the weight on each type of capital; R denotes the cost of each type of capital; and tax rate denotes the tax rate appli- cable to tax deductions for debt capital costs. The weights used to compute the weighted average cost of capital should be the market values of each type of capital in proportion to the total market value of the capital structure that will be used to finance the firm (that is, w

D � w

P � w

E � 1.0). On the right-hand side of this equation, the first term in brackets

measures the weighted after-tax cost of debt capital, the second term measures the weighted cost of preferred stock capital, and the third term measures the weighted cost of equity capital. Refer to the previous chapter for more detailed discussions and exam- ples of computing the cost of debt, preferred, and common equity capital.

Free Cash Flows Valuation Examples for a Single-Asset Firm For the next three examples, make the following assumptions:

• The firm consists of a single asset that will generate net cash flows of $2 million per year forever.

• The income tax rate is 40 percent.

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934 Chapter 12 Valuation: Cash-Flow-Based Approaches

• After making debt service payments and paying taxes, the firm pays dividends to dis- tribute any remaining free cash flows to the equity shareholders each year.

• The cost of equity capital is 10 percent.

Example 1: Value of Common Equity in an All-Equity Firm Assume that the common equity shareholders have financed the asset entirely with $10 mil- lion of equity capital. We can determine the value of the common equity investment to the shareholders using the present value of free cash flows for common equity shareholders. The free cash flow to common equity shareholders each year will be as follows:

Net Cash Flow $2,000,000 Income Taxes: 0.40 � $2,000,000 (800,000)

Free Cash Flow for Common Equity Shareholders $1,200,000

The value to the shareholders of the common equity in the firm is $12,000,000 (� $1,200,000/0.10). Dividing by the discount rate is appropriate because the $1.2 million annual free cash flow for common equity is a perpetuity with no growth. This investment is worth $12 million to those shareholders (a gain of $2 million over the original invest- ment of $10 million) because of the present value of the free cash flows the investment will generate and that will in turn be paid out as dividends to the shareholders. Therefore, we would determine the same value for the investment using the dividends-based valuation model as shown in Example 5 in Chapter 11.

Example 2: Value of Common Equity in a Firm with Debt Financing For this example, we will make the same assumptions as in the preceding example, except we will now make the following additional assumptions to use both debt and equity financing:

• The equity shareholders finance a portion of the investment in the asset with $4 mil- lion of equity capital.

• The firm finances the remainder of the asset using $6 million of debt capital. • This amount of debt in the firm’s capital structure does not alter substantially the risk

of the firm to the equity investors, so they continue to require a 10 percent rate of return.

• The debt is issued at par, and it is less risky than equity; so the debtholders demand interest of only 6 percent each year, payable at the end of each year.

• Interest expense is deductible for income tax purposes. We can again determine the value of the common equity investment using the present

value of free cash flows for common equity shareholders. Note that this example is essen- tially the same as Example 6 in Chapter 11, except that the valuation focus changes from dividends to free cash flows. The free cash flow available to common equity shareholders each year is as follows:

Net Cash Flow for All Debt and Equity Capital $2,000,000 Interest Paid on Debt: 0.06 � $6,000,000 (360,000) Income Taxes: 0.40 � ($2,000,000 � $360,000) (656,000)

Free Cash Flow for Common Equity Shareholders $ 984,000

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The value of the common equity to the shareholders in the firm is $9,840,000 (� $984,000/0.10). Dividing by the discount rate is appropriate because the $984,000 annual free cash flow for common equity is a perpetuity with no growth. Note that in this example, the present value of the gain to the common equity shareholders in excess of their initial investment is $5,840,000 (� $9,840,000 � $4,000,000). The gain to the shareholders is $3,840,000 (� $5,840,000 � $2,000,000) larger in this example than in the previous example because (1) the debt capital is less expensive than the equity capital (6 percent rather than 10 percent on $6,000,000 of financing), creating $2,400,000 of value for equity shareholders from capital structure leverage [� ($6,000,000 � {0.10 � 0.06})/0.10], and (2) the net tax savings from interest expense creates $1,440,000 of value for equity shareholders [� ($800,000 � $656,000)/0.10, or, alternatively, � ($360,000 interest deduc- tion � 0.40 tax rate)/0.10].

Example 3: Value of More Risky Common Equity in a Firm with Debt Financing Now make the same assumptions as the preceding example except now assume that by chang- ing the capital structure to 60 percent debt and 40 percent equity, the firm becomes more risky to the equity investors and they demand a 15 percent rate of return rather than 10 per- cent. Under these assumptions, the value of the common equity to the investors in the firm will be $6,560,000 (� $984,000/0.15). Note that in this example, the present value of the gain to the common equity investors in excess of their initial investment falls to $2,560,000 (� $6,560,000 � $4,000,000). Because of the increased risk, the investors demand a higher rate of return; so the value for equity investors from the net tax savings from interest expense falls to $960,000 [� ($800,000 � $656,000)/0.15] and the value for equity investors from capital structure leverage falls to $1,600,000 (� $2,560,000 � $960,000).5

Cash Flows to the Investor versus Cash Flows to the Firm The analyst can use expectations of the dividends to be paid to the investor or the free cash flows to be generated by the firm (that will ultimately be paid to the investor) as equivalent approaches to measure the value-relevant expected payoffs to shareholders. Cash flows paid to the investor via dividends and free cash flows that are available for common equity share- holders will differ each period to the extent that the firm reinvests a portion (or all) of the cash flows generated. However, if the firm generates a rate of return on reinvested free cash flow equal to the discount rate used by the investor (that is, the cost of equity capital), either set of payoffs (dividends or free cash flows) will yield the same valuation of a firm’s shares. To demonstrate this equivalence, consider the following scenarios.

Example 4: Free Cash Flows with 100 Percent Payout A firm expects to generate free cash flows of $0.15 for each dollar of invested equity capi- tal for the foreseeable future (until, for example, t�n). Considering the riskiness of the

5 The lower value to equity investors from capital structure leverage is the net result of two effects. First, the increased risk of the

firm causes the equity investors to increase the discount rate from 10 percent to 15 percent, which would (if considered in isola-

tion) cause the value of the project to fall to $8,000,000 (= $1,200,000/0.15), which would imply a $2,000,000 loss on the investors’

$10,000,000 investment. Second, the debt capital is less expensive than the equity capital, creating $3,600,000 of value for equity

investors from capital structure leverage [= ($6,000,000 � {0.15 � 0.06})/0.15]. The net result is $1,600,000 of value to equity

investors from capital structure leverage, net of the incremental effects of risk.

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936 Chapter 12 Valuation: Cash-Flow-Based Approaches

firm, equity investors in this firm require a 15 percent return each year. We assume that the firm will pay out 100 percent of the free cash flows each year as a dividend. Thus, the free cash flows generated by the firm equal the cash dividends received by the investor each period. Each dollar of capital committed by the investor has a present value of future cash flows equal to one dollar. That is, over an indefinitely long period of time into the future,

Example 5: Free Cash Flows with Zero Payout Assume the same facts as in Example 4 except that the firm will pay out none of the free cash flows as a dividend. The firm will retain the $0.15 free cash flow on each dollar of capi - tal and reinvest it in projects expected to earn 15 percent return per year. In this case, the investor receives no periodic dividends and receives cash only when the investor sells the shares or the firm liquidates at date t�n. By the terminal date, n periods in the future, each dollar of capital invested in the firm today will have earned a compound rate of return of 15 percent, equal to the required rate of return. Therefore, each dollar of invested capital has a present value of future free cash flows equal to one dollar, as in the preceding exam- ple with full payout of free cash flows. That is,

Example 6: Free Cash Flows with Partial Payout Assume the same facts as in Example 5 except that the firm pays out 25 percent of the free cash flow each period as a dividend and reinvests the other 75 percent in projects expected to generate a return of 15 percent. In this case also, each dollar of invested capital has a pres- ent value of future cash flows equal to one dollar. That is,

We used these three examples in the previous chapter to illustrate the relevance of divi- dends as payoffs that are sufficient for valuation for equity shareholders and the irrelevance of the firm’s dividend policy in valuation.6 We use the same examples here to illustrate that the assumptions we make about dividend policy are the complementary assumptions we make about free cash flows reinvested in the firm. Therefore, if the firm can be expected to reinvest cash flows to earn the required rate of return, the same valuation should arise whether the analyst discounts (1) the expected dividends to the investor, or (2) the expected free cash flows to the firm that are available to pay future dividends to equity shareholders. Further, the same valuation should arise whether the firm pays all of its free cash flows as a dividend, reinvests all free cash flows to earn the investors’ required rate of return, or pays

n $1 � ∑ $0.15

t =1(1.15)t

$1 � ($1.15) n

(1.15)n

n $1 � ∑

(0.25)($0.15) (0.75)($1.15)n

t=1 (1.15)t �

(1.15)n

6 Merton Miller and Franco Modigliani, “Dividend Policy, Growth and the Valuation of Shares,” Journal of Business (October 1961),

pp. 411–433. Penman and Sougiannis test empirically the replacement property of dividends for future earnings and find support

for the irrelevance of dividend policy in valuation. See Stephen H. Penman and Theodore Sougiannis, “The Dividend

Displacement Property and the Substitution of Anticipated Earnings for Dividends in Equity Valuation,” The Accounting Review

(January 1997), pp. 1–21.

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a portion of free cash flows in dividends each period and reinvests the remainder to earn the investors’ required rate of return. Note that the crucial assumption is that capital retained in the firm will generate a rate of return exactly equal to the investors’ required rate of return.

Nominal versus Real Cash Flows Changes in general price levels (that is, inflation or deflation) cause the purchasing power of the monetary unit to change over time.7 The valuation of an investment in an economic resource should be the same whether one uses nominal or real free cash flow amounts as long as the valuation uses a consistent discount rate that is the nominal or real rate of return. That is, if projected free cash flows are nominal and include the effects of changes in general purchasing power of the monetary unit, the discount rate should be nominal and include an inflation component. If projected free cash flows are real amounts that filter out the effects of general price changes, the discount rate should be a real rate of return, exclud- ing the inflation component.

Example 7: Nominal versus Real Free Cash Flows A firm owns an asset that it expects to sell one year from today for $115.5 million. The firm expects the general price level to increase 10 percent during this period. The real interest rate is 5 percent. The nominal discount rate should be 15.5 percent to measure the com- pound effects of the real rate of interest and inflation [0.155 � (1.10 � 1.05) � 1]. Discounting nominal or real free cash flows, the present value of the asset to the firm is $100 million, as shown:

Discount Rate Including Nominal Free Cash Flows � Expected Inflation � Value

$115.5 million � 1/(1.05 � 1.10) � $100 million

Discount Rate Excluding Real Free Cash Flows � Expected Inflation � Value

$115.5 million/1.10 � 1/1.05 � $100 million

In both computations, we derived the value of the equity of the firm by computing the present value of the free cash flows to common equity shareholders. As a practical matter, analysts usually find it more straightforward to discount nominal free cash flows using nominal discount rates than to adjust nominal free cash flows to real free cash flows and then discount real free cash flows using real interest rates. Discount rates derived from the CAPM are nominal because the risk-free rate component incorporates expected inflation. Further, stated and effective interest rates on long-term debt also are nominal because they incorporate expected inflation rates. Thus, readily available or easily estimable discount

7 Note that the issue here is not with specific price changes of a firm’s particular assets, liabilities, revenues, and expenses. These

specific price changes affect our projections of the firm’s dividends, cash flows, and earnings and should enter into the valuation

of the firm. The issue is whether some portion, all, or more than all of the specific price changes simply represent an economy-

wide change in the purchasing power of the monetary unit, which should not affect the value of a firm.

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938 Chapter 12 Valuation: Cash-Flow-Based Approaches

rates relating to the cost of equity and debt capital are typically nominal rates, as are weighted average costs of capital.

Pretax versus After-Tax Free Cash Flows Will the same valuation arise if the analyst discounts pretax-free cash flows at a pretax cost of capital and after-tax free cash flows at an after-tax cost of capital? The answer is no if costs of debt and equity capital receive different tax treatments. For tax purposes, firms can typically deduct the costs of debt capital but cannot deduct the costs of equity capital.

Example 8: Tax Effects on Free Cash Flows Suppose the firm faces the following costs of capital:

Proportion Weighted Average in Capital Pretax Tax After-Tax Cost of Capital Structure Cost Effect Cost Pretax After-Tax

Debt 0.33 10% 0.40 6% 3.33% 2.00% Equity 0.67 18% — 18% 12.00% 12.00%

1.00 15.33% 14.00%

Assume that this firm expects to generate $90 million of pretax-free cash flows and $54 mil- lion of after-tax free cash flows [� (1 � 0.40) � $90 million] one year from today. This firm would be valued using pretax and after-tax amounts (assuming a one-year horizon) as follows:

Pretax: $90 million � 1/1.1533 � $78.04 million After-tax: $54 million � 1/1.14 � $47.37 million

These values are not equivalent because cash inflows from assets are taxed at 40 percent and cash outflows to service debt give rise to a tax savings of 40 percent. However, the cost of equity capital does not provide a tax benefit. The appropriate valuation in this case is $47.37 million. Thus, the analyst should use after-tax free cash flows and the after-tax cost of capital.

Selecting a Forecast Horizon The analyst will need to project periodic free cash flows over the remaining expected life of the resource to be valued. This life is a finite number of years for a resource with a finite physical life, such as a machine or a building, or a financial instrument with a finite stated maturity, such as a bond, a mortgage, or a lease. But an equity security is a resource that has an indefinite life; therefore, the analyst must project future periodic free cash flows that, in theory, could extend to infinity. As a practical matter, the analyst cannot precisely predict a firm’s free cash flows very many years into the future. Therefore, analysts develop specific projections of income statements and balance sheets for the firm and use them to derive forecasts of free cash flows over an explicit forecast horizon (for example, five or ten years) depending on the industry, the maturity of the firm, and the expected growth and pre- dictability of the firm’s cash flows. After the explicit forecast horizon, analysts then use gen- eral growth assumptions to project the future income statements and balance sheets and use them to derive the free cash flows that will persist each period to infinity. Therefore, the

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analyst will find it desirable to develop specific forecasts of income statements, balance sheets, and free cash flows over an explicit forecast horizon that extends until the point when the firm’s growth can be expected to settle into steady-state equilibrium, during which time free cash flows can be expected to grow at a steady, predictable rate.

Selecting a forecast horizon involves trade-offs. For stable and mature firms such as PepsiCo, one can develop reasonably reliable projections over longer forecast horizons, as demonstrated in Chapter 10. For young high-growth firms, it is more difficult to develop reliable projections of free cash flows over long forecast horizons because their future oper- ating performance is relatively more uncertain. This difficulty is magnified by the fact that these firms will achieve a much higher proportion of their value in distant future years, after they reach their potential steady-state profitability. Ironically, the analyst faces the dilemma of depending most heavily on long-run forecasts for young growth firms for which long-run projections are most uncertain. The forecasting and valuation process is particularly difficult for growth firms when the near-term free cash flows are likely to be negative, as is common for rapidly growing firms that finance growth by issuing common stock. Most of the value of these firms depends on free cash flows they will generate in years far into the future.

Unfortunately, this dilemma is inevitable. The analyst must recognize that forecasts and value estimates for all firms have some degree of uncertainty and estimation risk. To miti- gate this uncertainty and estimation risk, we suggest the following:

1. Apply all six steps of the analysis framework. By thoroughly analyzing the firm’s industry and strategy, the firm’s accounting quality, and the firm’s financial per- formance and risk ratios, the analyst will have more information to use to develop long-term forecasts that are as reliable as possible.

2. To the extent possible, confront directly the problem of long-term uncertainty by developing specific projections of free cash flows derived from projected income statements and balance sheets that extend five or ten years into the future, at which point the firm may be projected to reach steady-state growth.

3. Assess the sensitivity of the forecast projections and value estimates across the rea- sonable range of long-term growth parameter assumptions.

Computing Continuing Value of Future Free Cash Flows As described in the previous section, the analyst will find it desirable to forecast free cash flows over an explicit forecast horizon, until the point at which the firm’s free cash flows growth will settle into a long-run steady-state growth rate. We refer to these free cash flows as continuing free cash flows because they reflect the free cash flows continuing into the long-run future of the firm. The long-run steady-state growth rate in future continuing free cash flows could be positive, negative, or zero. Steady-state growth in free cash flows could be driven by long-run expectations for growth attributable to economy-wide infla- tion, general economic productivity, the population, or demand for the industry’s output. The analyst should select a growth rate that captures realistic expectations for the long run.

Once the analyst projects the firm’s long-run steady-state growth rate (denoted as g) continuing after the end of the explicit forecast horizon (for example, after Year T), the ana- lyst can derive the continuing free cash flows from the projected income statements and balance sheets. The same principles demonstrated in the previous chapter for projecting continuing dividends apply here in projecting continuing free cash flows. The analyst should use the expected long-run growth rate (g) to project all of the items of the Year T�1 income statement and balance sheet by multiplying each item on the Year T income state- ment and balance sheet times (1 � g). The analyst can then derive the Year T�1 statement

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940 Chapter 12 Valuation: Cash-Flow-Based Approaches

of cash flows (and thus Year T�1 free cash flows) from the Year T�1 income statement and balance sheet projections. It is necessary to impose the long-run growth rate assump- tion (1 � g) uniformly on the Year T income statement and balance sheet projections in order to derive the free cash flows for Year T�1 correctly. We assume that in steady state, the firm’s assets, liabilities, and shareholders’ equity (and therefore the firm’s earnings, cash flows, and dividends) will all grow at equivalent rates. By applying a uniform growth rate, the analyst achieves internally consistent steady-state growth across all of the projections of the firm, keeping the balance sheet in balance throughout the continuing forecast horizon and keeping the cash flows, earnings, and dividends internally consistent with the assumed long-run growth rate.

In projecting continuing free cash flows in Year T�1 and beyond, analysts often assume that the firm’s long-run sustainable growth rate will be consistent with inflation and long- run growth in the economy, on the order of 3–5 percent. For firms that have been growing more quickly than that (for example, at 10 percent) in the years leading up to Year T�1, the long-run sustainable growth rate implies that the firm will maintain a lower growth rate in assets and equity and thus generate substantially larger amounts of free cash flow. By projecting Year T�1 net income, assets, and equity using the long-run sustainable growth rate, we can solve for the long-run sustainable free cash flows the firm will generate. The continuing free cash flow amount we derive for Year T�1 may be significantly larger than the amounts the firm actually generated during its higher-growth-rate years. The Year T�1 free cash flow amount reflects the firm’s transition from a high rate of reinvestment of cash flows for growth in assets to reinvestment for a much lower rate of growth, thereby creating the need to solve for the long-run sustainable free cash flows amount.

If the analyst wants to compute internally consistent and identical estimates of firm value using free cash flows, earnings, and dividends, he or she should not simply project free cash flows for Year T�1 by multiplying free cash flows for Year T by (1 � g). Doing so ignores the necessary growth in all of the elements of the balance sheet and the income statement, which can introduce inconsistent forecast assumptions for cash flows, earnings, and dividends. Even if the analyst simply projects that Year T free cash flows, earnings, and dividends will grow at an identical rate (1 � g) in Year T�1, doing so may impound incon- sistent assumptions and lead to inconsistent value estimates if Year T cash flows, earnings, and dividends are not consistent with their long-run continuing amounts.

Example 9: Projecting Continuing Value Free Cash Flows Suppose the analyst develops the following forecasts for the firm in Year T–1 and Year T:

Shareholders’ Assets � Liabilities � Equity

Year T–1 Balances $100 � $60 � $40 � Net Income �20 �20 � New Borrowing � 6 �6 � Dividends Paid �10 �10

Year T Balances $116 � $66 � $50

Assume that the entire increase in assets involves growth in assets required for opera- tions, such as inventory and equipment. The analyst would compute Year T free cash flows for common equity shareholders to equal $10 (� $20 net income � $16 increase in assets � $6 increase in liabilities). Now suppose the analyst projects that the firm will grow at a

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steady-state rate of 10 percent in Year T�1 and thereafter. The analyst should project Year T�1 net income, assets, liabilities, and shareholders’ equity to grow by 10 percent each and then compute Year T�1 free cash flows as follows:

Shareholders’ Assets � Liabilities � Equity

Year T Balances $116.0 � $66.0 � $50.0 Growth � 1.10 � 1.10 � 1.10 Year T�1 Balances $127.6 � $72.6 � $55.0

The projected net income would be $22 (� $20 � 1.10). The Year T�1 free cash flow projection would be $17 (� $22 net income � $11.6 increase in assets � $6.6 increase in liabilities). However, if the analyst had simply projected Year T free cash flows to grow by 10 percent, the Year T�1 projections would be only $11 (� $10 Year T free cash flow � 1.10). By making this simple projection of free cash flows, the analyst is implicitly assum- ing that the $16 increase in assets in Year T will grow by 10 percent in Year T�1 (� $17.6 increase in assets). This is internally inconsistent with our long-run assumption of 10 per- cent growth in assets, liabilities, equity, and income growth. This will understate free cash flows to equity in Year T�1 by $6 (� $11.6 increase in assets � $17.6 increase in assets). This error will understate the estimated value of the firm using free cash flows, relative to the value estimate using earnings, because of the inconsistent assumptions. Note that the correct projected Year T�1 free cash flow amount of $17 is substantially larger than the $10 free cash flow amount for Year T. The reason the firm will generate larger amounts of free cash flow in Year T�1 and beyond is that the firm’s long-run growth rate is 10 per- cent, which is lower than the Year T growth rate in assets (16 percent) and shareholders’ equity (25 percent); thus, this firm will not need to reinvest as much of its cash flows to fund growth and will generate larger free cash flow amounts in Year T�1 and beyond.

As demonstrated for dividends in the previous chapter, once the analyst has com- puted free cash flows for Year T�1, he or she can compute continuing value (some- times called terminal value) of future free cash flows for Years T�1 and beyond using the perpetuity-with-growth valuation model:8

Continuing Value Continuing at End of Forecast � Free Cash Flow � 1/(R � g) Horizon (Year T) Projection for T�1

where g denotes the projected steady-state growth rate for Years T�1 and beyond and is applied uniformly to project the income statement and balance sheet in Year T�1, which are then used to project the continuing free cash flows in Year T�1; R denotes the appropriate risk-adjusted discount rate. Once the analyst has computed the continuing value at the end of the forecast horizon (Year T), the analyst must discount continuing value from that point in time to present value today by multiplying by the present value factor of 1/(1 � R)T.

Example 10: Computing Continuing Value An analyst forecasts that the free cash flow of a firm in Year �5 will be $30 million and that Year �5 earnings and dividends also will be $30 million. Assume for the simplicity of this

8 This formula is simply the algebraic simplification for the present value of a growing perpetuity.

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942 Chapter 12 Valuation: Cash-Flow-Based Approaches

example that the analyst expects that the firm’s income statements and balance sheets will grow uniformly over the long run and, therefore, that cash flows, earnings, and dividends will grow uniformly over the long run. But the analyst is uncertain about the steady-state long-run growth rate in Year �6 and beyond. He or she believes that the growth rate will most likely be zero but could reasonably fall between �6 and �6 percent per year. Assuming a 15 percent cost of capital, the following table shows the range of possible con- tinuing values (in millions) for the firm at the beginning of the continuing value period (that is, the beginning of Year �6 or, equivalently, the end of Year �5) and in present value as of today; that is, the continuing value is discounted to today using a factor of 1/(1.15)5:

Continuing Value in Present Value as of:

Free Cash Long-Run Free Cash Perpetuity Flows in Growth Flows in with Growth Beginning of

Year T Assumption Year T�1 Factor Year T�1 Today

$30 0% $30.00 1

� 6.67 $200.00 $ 99.44 (0.15 � 0.00)

$30 �6% $31.80 1

� 11.11 $353.30 $175.65 (0.15 � 0.06)

$30 �6% $28.20 1

� 4.76 $134.23 $ 66.74 (0.15 � 0.06)

Analysts also can estimate a continuing value using a multiple of free cash flow in the first year of the continuing value period to value the common stock of a firm. The follow- ing table shows the cash flow multiples using 1/(R � g) for various costs of equity capital and growth rates. The multiples increase with growth for a given cost of capital, and they decrease as cost of capital increases for a given level of growth.

Continuing Value Multiples

Long-Run Growth Rates

Cost of Equity Capital 0% 2% 3% 4% 5% 6%

6% 16.67 25.00 33.33 50.00 100.00 na 8% 12.50 16.67 20.00 25.00 33.33 50.00

10% 10.00 12.50 14.29 16.67 20.00 25.00 12% 8.33 10.00 11.11 12.50 14.29 16.67 15% 6.67 7.69 8.33 9.09 10.00 11.11 18% 5.56 6.25 6.67 7.14 7.69 8.33 20% 5.00 5.56 5.88 6.25 6.67 7.14

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Measuring Periodic Free Cash Flows 943

probably reconsider whether it is realistic to expect the firm’s free cash flow growth rate to exceed the discount rate (the expected rate of return) in perpetuity. This scenario can exist for some years, but is not likely to be sustainable indefinitely. Competition, technological change, new entrants into an industry, and similar factors eventually reduce growth rates. Thus, in applying the model, the analyst must attempt to estimate the long-term sustain- able growth rate in cash flows. (Refer to the discussion of sustainable earnings in Chapter 9.)

MEASURING PERIODIC FREE CASH FLOWS This section first presents a conceptual framework for measuring free cash flows. Then it describes specific practical steps to measure free cash flows from two different perspectives— free cash flows to all debt and equity stakeholders and free cash flows to common equity shareholders—and when to use each free cash flow measure.

A Framework for Free Cash Flows A conceptual framework for free cash flows to the firm emanates from the familiar balance sheet equation in which assets equal liabilities plus shareholders’ equity:

A = L � SE

Recall from Chapter 5 the demonstration of an alternative ROCE decomposition into oper- ating and financial leverage components. Using the same approach, separate all of the assets and liabilities into two categories: operating or financing:

OA � FA = OL � FL � SE

Operating assets (denoted as OA) and operating liabilities (denoted as OL) relate to the firm’s day-to-day operations in the normal course of business. For most firms, operating assets include cash and short-term investment securities necessary for operating liquid- ity purposes; accounts receivable; inventory; property, plant, and equipment; intangible assets (for example, licenses, patents, trademarks, and goodwill); and investments in affili - ated companies. Operating liabilities typically include accounts payable, accrued expenses, accrued taxes, deferred taxes, pension obligations, and other retirement bene- fits obligations.

Financial liabilities include interest-bearing liabilities that are part of the financial capi- tal structure of the firm. Financial liabilities (denoted as FL) include such interest-bearing items as short-term notes payable; current maturities of long-term debt; and long-term debt in the forms of mortgages, bonds, notes, and capital lease obligations. Insofar as out- standing preferred stock contains features indicating that it is economically similar to debt (features such as limited life, mandatory redemption, and guaranteed dividends), the ana- lyst should include preferred stock with financial liabilities.

In some circumstances, firms may hold financial assets (denoted as FA) such as excess cash and short-term or long-term investment securities to provide the firm with liquidity to repay debt, pay dividends, and repurchase common stock. Distinguishing financial assets that the firm will use to change its financial capital structure from cash and marketable securities the firm will use for liquidity for operating purposes requires a judgment call by the analyst. Analysts consider financial assets to be part of the financial structure of the firm if the firm is likely to use the financial assets to offset or retire debt or if the financial assets could be used to pay dividends or repurchase common equity shares. For example, such financial assets may exist if a firm is accumulating cash or investment securities for pur- poses of retiring debt, if a firm is required to hold certain amounts of restricted cash or

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944 Chapter 12 Valuation: Cash-Flow-Based Approaches

investment securities under a loan covenant (such as required compensating cash bal- ances), or if a firm is maintaining and accumulating a sinking fund for bond retirement under the terms of a bond debenture. Analysts typically do not consider financial assets to be part of the financial capital structure of a firm when the financial assets are necessary to manage the liquidity needs of the firm’s operating activities across different seasons or busi- ness cycles and the assets are held in liquid interest-earning accounts such as cash and cash equivalents, marketable securities, and short-term investment securities. Analysts also typi - cally do not consider financial assets to be part of the financial capital structure of the firm when the financial assets include investment securities that are part of the long-term strat- egy of the firm, such as investments in affiliated subsidiaries with related operating activi- ties or strategic investments in potential acquisition targets.9 Capital held in these types of accounts for purposes of operating liquidity or strategic investments in securities of affili- ated companies or potential takeover targets should be considered operating assets, not financial assets.

Once the analyst has separated the balance sheet into operating and financing compo- nents, he or she should rearrange the balance sheet equation to put operating accounts on one side and financing accounts and shareholders’ equity on the other side, as follows:

OA � OL = FL � FA � SE,

which is equivalent to

NetOA = NetFL � SE

where NetOA � OA � OL and NetFL � FL � FA. For most firms, operating assets are likely to exceed operating liabilities and financial liabilities are likely to exceed financial assets. (Financial borrowing usually exceeds financial assets because the firm uses the funds obtained from borrowing to purchase operating assets.)

This rearrangement of the balance sheet provides a useful basis from which to concep- tualize free cash flows to the firm. If we substitute for each term the present values of the expected future net cash flows associated with operating activities, financing activities, and shareholders’ equity, we can express the balance sheet in the following cash flow terms:

Present Value of Net Cash Flows from Operations � Present Value of Net Cash Flows Available for Debt Financing � Present Value of Net Cash Flows Available for Shareholders’ Equity

This expression indicates that the present value of the expected net cash flows from opera- tions of the firm determines the sum of the values of the debt and equity claims on the firm.10 Therefore, one can estimate the value of the debt and equity capital of the firm by

9 The calculation of the rate of return on assets, or ROA, in Chapter 4 assumed that all assets were operating assets and that oper-

ating income is equal to net income excluding the after-tax cost of financial liabilities. Thus, Chapter 4 made no adjustment to

eliminate interest income on financial assets from net income in the numerator of ROA and no adjustment to eliminate financial

assets in the denominator. Most manufacturing, retailing, and service firms hold only minor amounts of financial assets, so ignor-

ing adjustments for financial assets does not usually introduce a material amount of bias to the calculation of ROA. A more pre-

cise calculation of ROA for firms with a material amount of financial assets in the capital structure adjusts the numerator to

eliminate interest income and adjusts the denominator of ROA for the portions of financial assets (cash, marketable securities, and

investment securities) that are part of the financial capital structure and are not directly related to operating activities.

10 The next section explains how our use of Net Cash Flows from Operations in this section differs from Cash Flow from

Operations reported in the Statement of Cash Flows.

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projecting the net cash flows from operations that are “free” to service debt and equity claims and discounting those free cash flows to present value. We refer to this measure of free cash flows as the free cash flows for all debt and equity capital stakeholders because they reflect the cash flows that are available to the debt and equity capital stakeholders in the firm as a whole.

We can rearrange the balance sheet equation slightly further:

NetOA � NetFL = SE

Using the same present value cash flow terms as before, we can express this form of the balance sheet in terms of present values of expected future cash flows as follows:

Present Value of Net Cash Flows from Operations � Present Value of Net Cash Flows Available for Debt Financing � Present Value of Net Cash Flows Available for Shareholders’ Equity

With this expression, we can conceptualize free cash flows specifically attributable to the equity shareholders of the firm. The present value of free cash flows produced by the opera - tions of the firm minus the present value of cash flows necessary to service claims of the net debtholders yields free cash flows available for common equity shareholders. This measure captures the net free cash flows available to equity shareholders after debt claims are satisfied.

Free Cash Flows Measurement The following sections describe how to measure free cash flows from the two perspectives described above—free cash flows for all debt and equity capital stakeholders and free cash flows for common equity shareholders—and when to use each free cash flow measure. In practice, different analysts compute free cash flows from various starting points: the state- ment of cash flows, net income, EBITDA (earnings before interest, tax, depreciation, and amortization), and NOPAT (net operating profit adjusted for tax). We describe how to measure free cash flows from each starting point.

Measuring Free Cash Flows: The Statement of Cash Flows as the Starting Point Under U.S. GAAP and IFRS, firms report the statement of cash flows by decomposing the net change in cash into operating, investing, and financing activity components. These three categories do not match the operating and financing classifications we need for com- puting free cash flows. Thus, the analyst needs to reclassify some of the components of the statement of cash flows to compute free cash flows for valuation purposes. Exhibit 12.1 describes the computation of each of these two measures of free cash flows.

Cash flow from operations from the projected statement of cash flows is the most direct starting point for computing both measures of free cash flows because it requires the fewest adjustments. Recall from Chapter 3 that the statement of cash flows measures cash flow from operations by beginning with net income, adding back any non-cash expenses or losses (such as depreciation and amortization expenses), subtracting any non-cash income or gains (such as income from equity method affiliates), and then adjusting for net cash flows for operating activities (such as changes in receivables, inventory, accounts payable, and accrued expenses).

Measuring Periodic Free Cash Flows 945

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946 Chapter 12 Valuation: Cash-Flow-Based Approaches

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948 Chapter 12 Valuation: Cash-Flow-Based Approaches

Free Cash Flows for All Debt and Equity Capital Stakeholders Free cash flows for all debt and equity capital stakeholders are the cash flows available to make interest and principal payments to debtholders, redeem preferred shares or pay div- idends to preferred shareholders, and pay dividends and buy back shares from common equity shareholders. To measure these free cash flows, we begin with cash flow from opera tions from the projected statement of cash flows, as shown in the left-hand side of Exhibit 12.1. To measure cash flow from operations before the effects of the firm’s financial capital structure, the analyst must add back the interest expense on financial liabilities, net of any income tax savings from interest expense. If the analyst makes the judgment call that some or all of the firm’s financial assets (such as excess cash holdings or marketable securities) are intended to retire debt and pay dividends and are part of the financial capital structure of the firm (rather than part of the operating liquidity management of the firm), the analyst should subtract the interest income on those financial assets, net of the income taxes paid on that interest income. To adjust interest expense and interest income for tax effects, the analyst typically multiplies interest expense and interest income by one minus the firm’s marginal tax rate.11

The analyst also should add or subtract any change in the cash balance that the firm will require for operating liquidity. Cash that the firm must maintain for operating liquidity purposes is not available for distribution to debt or equity stakeholders and therefore is not part of free cash flow. For example, suppose an analyst is valuing a retail store chain and the chain must maintain the equivalent of seven days of sales in checking accounts and cash on hand at each store for purposes of conducting retail sales transactions. When the chain opens new stores, it is required to hold additional cash as part of operations (as it would need to hold additional inventory). These additional cash requirements are not available for debt and equity capital providers if the firm intends to maintain its operations. If the firm improves its cash management efficiency and reduces the amount of cash required for operating liquidity, the firm has additional free cash flow that can be distributed to debt or equity stakeholders. Procedurally, the analyst should project the required change in cash for working capital purposes each period and add or subtract that amount to determine free cash flow from operations for debt and equity stakeholders.

Next, the analyst adjusts for cash flows related to capital expenditures on long-lived assets that are a part of the firm’s productive capacity (for example, property, plant, and equipment; affiliated companies; intangible assets; and other investing activities). The ana- lyst should subtract cash outflows for purchases and add cash inflows from sales of these types of assets related to the firm’s long-term productive activities. The analyst can mea - sure the cash flows for capital expenditures and other investing activities that are part of the long-term productive activities of the firm by using the amounts reported in the investing activities section of the projected statement of cash flows.

As noted earlier, the analyst must make a judgment call about the amounts of the firm’s financial assets (for example, in cash and cash equivalents, short-term securities, or long- term investment securities) that are (1) necessary for the liquidity and operating capacity of the firm or (2) part of the financial capital structure of the firm and therefore distrib- utable to debt or equity stakeholders. For example, if the analyst projects that the firm will retain financial assets by saving some portion of its cash flows in a securities account each

11 Technically, analysts should make these adjustments using the cash amounts of interest paid and interest received rather than

the accrual amounts of interest expense and interest income. However, as a practical matter, it is reasonable to assume that fore-

casted amounts of interest expense will equal interest paid and forecasted amounts of interest income will equal interest received.

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period and that this cash can ultimately be used to repay debt, pay dividends, or buy back shares, the analyst should deem these cash flows as free cash flows for debt and equity capi - tal. For instance, the firm may be required by a bond indenture agreement to maintain a sinking fund of cash or liquid securities that will be available to repay the bond when it matures. In this case, the analyst should include the amount of cash added to the bond sinking fund as free cash flows for debt and equity capital.

This adjustment requires a judgment call by the analyst because in some circumstances, firms retain seemingly excess amounts of cash, marketable securities, or investment securi- ties accounts when these assets are in fact not free for potential distribution to capital stake- holders. For example, in some cases, firms with seasonal business need to maintain large balances in cash or securities accounts in order to provide needed liquidity during particu - lar seasons. In other cases, firms may build up large balances in investment securities accounts that represent investments in key affiliates, such as PepsiCo’s and Coca-Cola’s investments in bottling companies. In scenarios such as these, the analyst should not assess these cash flows as “free” for potential distribution to capital stakeholders, but instead should consider these cash flows necessary investments in the liquidity and productive capacity of the firm.

Together, these computations result in free cash flows for all debt and equity capital stakeholders, which are available to service debt, pay dividends to preferred and common shareholders, and buy back shares or for reinvestment. A later section describes the approach to estimate the present value of the sum of the debt and equity claims on the firm by discounting free cash flows for debt and equity capital using the weighted average cost of capital of the firm.

Free Cash Flows for Common Equity Shareholders Free cash flows for common equity shareholders are the cash flows specifically available to the common shareholders after all debt service payments have been made to lenders and dividends have been paid to preferred shareholders. Therefore, the free cash flows for com- mon equity shareholders amount to the free cash flows available to all debt and equity capi - tal less any cash flows that are attributable to debt and preferred stock claims.

To measure free cash flows for common equity shareholders, we can again begin with cash flow from operations from the projected statement of cash flows, as presented in the right-hand side of Exhibit 12.1. As in the previous section, the analyst should add or sub- tract any change in the cash balance that the firm will require for operating liquidity because this cash is not available for distribution to equity shareholders and therefore is not part of free cash flow. Procedurally, the analyst should add or subtract the projected change in cash required for liquidity purposes each period.12

Also, as in the previous section, the analyst should adjust for cash flows for capital expenditures on long-lived assets that are a part of the firm’s productive capacity (for exam- ple, property, plant, and equipment; affiliated companies; intangible assets; and other investing activities). The analyst should subtract cash outflows for purchases and add cash inflows from sales of assets related to the firm’s long-term productive activities.

The analyst should incorporate cash flows related to debt claims by adding cash inflows from new borrowing in short- and long-term debt and subtracting cash outflows for repay- ments of short- and long-term debt. In calculating free cash flows to debt and equity capital, if

12 Note that unlike the computation of free cash flows for all debt and equity stakeholders, we do not adjust for interest expense

or interest income after tax when we compute free cash flows for equity. Our measure of free cash flow for equity already reflects

net cash flows for interest payments for interest-bearing debt capital because the statement of cash flows starts with net income to

compute cash flow from operations and because net income already reflects interest expense after tax.

Measuring Periodic Free Cash Flows 949

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950 Chapter 12 Valuation: Cash-Flow-Based Approaches

the analyst made the judgment call that the firm saves financial capital beyond its immediate liquidity needs in a cash or investment securities account, these cash flows reflect financing activities. Therefore, the analyst must (1) subtract the amount of cash outflow used to purchase the securities because this cash obviously was not paid out to equity share- holders or (2) add the amount of cash inflow received from selling such securities because this cash inflow is available for distribution to equity shareholders. For example, if the firm maintains a bond sinking fund to be used for the eventual retirement of bonds when they mature, the cash invested in the sinking fund is clearly not free cash flows available for common equity shareholders. Finally, the analyst also should add cash inflows from new issues of preferred stock and subtract cash outflows from preferred-stock retirements and dividend payments.13 These computations measure free cash flows for common equity share- holders. These cash flows are available to common equity shareholders for dividends, stock buybacks, or reinvestment. As described in a later section of this chapter, free cash flows for common equity should be discounted at the cost of equity capital to determine the present value of the common equity of the firm.

Measuring Free Cash Flows: Alternative Starting Points In practice, different analysts use different starting points to compute free cash flows. The approaches described above used cash flow from operations from the projected statement of cash flows because it is the most direct starting point, requiring the fewest adjustments. However, some analysts compute free cash flows by beginning with projected net income, some start with EBITDA, and yet others start with NOPAT. Exhibit 12.2 describes the steps the analyst must take to adjust each of these starting points to determine free cash flows to all debt and equity stakeholders. Exhibit 12.3 (see page 952) describes the steps the analyst must take to adjust each of these starting points to determine free cash flows to common equity shareholders.

If the analyst starts with net income and wants to determine free cash flows for all debt and equity stakeholders, Exhibit 12.2 indicates that the analyst must add back all non-cash expenses (such as depreciation and amortization expenses), subtract all non-cash income items (such as accrued income from equity method affiliates), and adjust for cash flows related to changes in working capital accounts (such as cash flows related to changes in receivables, inventory, and payables). These adjustments bring the analyst up to our starting point, cash flow from operations. The analyst then incorporates the remaining steps by adjusting for net interest expense after tax, changes in cash requirements for liquidity, and capital expenditures.

Other analysts compute free cash flows for all debt and equity by starting with EBITDA, which already adds back non-cash income items for depreciation and amortization, inter- est expense (but usually not interest income) and all of the provision for income taxes. From this starting point, the analyst must adjust further by adding back any other non- cash expenses (apart from depreciation and amortization), adjust for non-cash income items, and adjust for cash flows related to working capital activities. In addition, because EBITDA adds back all of the provision for income taxes, the analyst must subtract cash taxes paid, net of tax saving on interest expense. These adjustments bring the analyst up

13 It might seem inappropriate to include changes in debt and preferred stock financing, which appear in the financing section of

the statement of cash flows, in the valuation of a firm. Economic theory suggests that the capital structure (that is, the proportion

of debt versus equity) should not affect the value. Changes in debt and preferred stock, however, affect the amount of cash avail-

able to the common shareholders. The analyst includes cash flows related to debt and preferred stock financing in free cash flows

for common equity shareholders but adjusts the cost of equity capital to reflect the amounts of such senior financing in the

capital structure.

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to our starting point, cash flow from operations. The analyst then incorporates the remaining steps by adjusting for changes in cash requirements for operating liquidity and capital expenditures.

Still other analysts begin the computation of free cash flows for all debt and equity stake- holders using NOPAT, which is net income with net interest expense (adjusted for tax sav- ings) added back. From this starting point, the analyst should add back all non-cash expense items (such as depreciation and amortization expenses), subtract all non-cash income items (such as accrued income from equity method affiliates), and adjust for cash flows related to working capital activities. The analyst then incorporates the remaining steps by adjusting for changes in cash requirements for liquidity and capital expenditures.

In practice, some analysts also use net income, EBITDA, and NOPAT as starting points to compute free cash flows for equity shareholders. Exhibit 12.3 shows the steps necessary to adjust each of these starting point amounts to complete measures of free cash flows for common equity. Note that many but not all of the additional adjustments are similar to those demonstrated in Exhibit 12.2. Also note that although it occurs in practice, starting with EBITDA or NOPAT to compute free cash flows for equity is inefficient because it is necessary to subtract interest expense after tax from both EBITDA and NOPAT.

The starting point of the computation of free cash flows is less important than the ending point. The analyst can begin the computation of free cash flows with cash from operating activities on the statement of cash flows, net income, EBITDA, or NOPAT, so long as he or she properly makes all of the necessary adjustments to compute a complete measure of free cash flows as described in Exhibits 12.1–12.3.

Which Free Cash Flow Measure Should Be Used? The appropriate free cash flow measure to use—free cash flows to all debt and equity stake- holders or free cash flows to equity shareholders—depends on the resource to be valued.

• If the objective is to value operating assets net of operating liabilities or, equivalently, the sum of the debt and equity capital of a firm, the free cash flow for all debt and equity capital is the appropriate cash flow measure and the appropriate discount rate is the weighted average cost of capital.

• If the objective is to value the common shareholders’ equity of a firm, the free cash flow for common equity shareholders is the appropriate cash flow measure and the appro- priate discount rate is the cost of equity capital.

The difference between these two valuations is the value of total debt financing and pre- ferred stock. To reconcile the two valuations, one could value the debt financing instru- ments by discounting all future debt service cash flows (including repayments of principal) at the after-tax cost of debt capital and all preferred-stock dividends at the cost of preferred equity. Subtracting the present value of debt financing and preferred stock from the pres- ent value of the sum of debt and equity capital yields the present value of common equity. The approach to use depends on the valuation setting.

Example 11: Valuing an Asset Acquisition One firm wants to acquire the net operating assets of a division of another firm. The acquiring firm will replace the financing structure of the division with a financing struc- ture that matches its own. The relevant cash flows for valuing the division’s net operating assets are the free operating cash flows the assets will generate minus the expected capital expenditures in operating assets or, equivalently, the free cash flows for all debt and equity capital. The acquiring firm would then discount these projected free cash flows for all debt and equity capital at the expected future weighted average cost of capital of the division to

Measuring Periodic Free Cash Flows 953

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954 Chapter 12 Valuation: Cash-Flow-Based Approaches

be acquired, which will match the weighted average cost of capital of the acquiring firm because the acquiring firm will use a similar financing structure for the division.

Example 12: Valuing Equity Shares An investor wants to value a potential investment in 1,000 shares of common stock in a firm. The relevant cash flows are the free cash flows available for distribution to common equity shareholders. These free cash flows measure the cash flows generated from using the assets of the firm minus the cash required to service the debt. Thus, free cash flows for com- mon equity shareholders should capture the cash generated by operating the assets of the firm plus any beneficial effects of financial leverage on the value of the common equity less the cash flows required to service debt capital. The investor should discount these projected free cash flows at the required return on equity capital.

Example 13: Valuing a Leveraged Buyout The managers of a firm intend to acquire a target firm through an LBO (leveraged buy- out). The managers will offer to purchase the outstanding shares of the target firm by investing their own equity (usually 20–25 percent of the total) and borrowing the remain- der from various lenders. The tendered shares serve as collateral for the loan (often called a bridge loan) during the transaction. After gaining voting control of the firm, the man- agers will have the firm engage in sufficient new borrowing to repay the bridge loan. Following an LBO, the firm will likely have a significantly higher debt level in the capital structure from the use of leverage to execute the takeover.

Determining the value of the common shares acquired follows the usual procedure for an equity investment. (See Example 12.) This value should equal the present value of free cash flows for common equity discounted at the cost of common equity capital. The valu- ation of the equity must reflect the new capital structure and the related increase in debt service costs. Also, the cost of equity capital will likely increase as a result of the higher level of debt in the capital structure; the common shareholders bear more risk as residual claimants on the assets of the firm. Therefore, the valuation must be based on the expected new cost of equity capital.

As an alternative approach that will produce the same value for the common equity, the analyst can treat an LBO as a purchase of assets (similar to Example 11). That is, compute the present value of the free cash flows for all debt and equity capital stakeholders using the expected future weighted average cost of debt and equity capital, using weights that reflect the newly leveraged capital structure of the acquired firm. This amount represents the value of net operating assets. Subtract from the present value of net operating assets the present value of debt raised to execute the LBO.14 The result is the present value of the common equity.

CASH-FLOW-BASED VALUATION MODELS Thus far, this chapter has discussed all of the elements of free-cash-flow-based valuation. To bring all of the elements together, we next present equations to describe the free-cash-flow- based valuation models. In each of these equations, all of the variables used to compute firm

14 It is irrelevant whether any debt on the books of the target firm remains outstanding after the LBO or whether the firm engages

in additional borrowing to repay existing debt, as long as the weighted average cost of capital properly includes the costs of each

financing arrangement.

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Cash-Flow-Based Valuation Models 955

value are expectations of future free cash flows, future discount rates, and future growth rates. We present the valuation equations with and without explicit terms for continuing val- ues. Recall that Exhibits 12.1–12.3 describe the computations for free cash flows for com- mon equity shareholders and free cash flows for all debt and equity capital stakeholders.

Valuation Models for Free Cash Flows for Common Equity Shareholders The following equation summarizes the computation of the present value of the com- mon equity of a firm as of time t�0 (denoted as V

0 ) using the present value of free cash

flows for common equity shareholders discounted at the required rate of return on equity capital (R

E ):

∞ V

0 � ∑ [Free Cash Flow Equity

t /(1 + R

E )t]

t = 1

This valuation approach expresses the value of the common equity of the firm as a func- tion of the present value of the free cash flows the firm will generate for the common equity shareholders after the firm has met all other cash requirements for working capital, capital expenditures, principal and interest payments on debt financing, preferred stock dividends, and so on. Given that common equity shareholders are the residual risk-bearers of the firm, this valuation approach estimates common equity value using the residual free cash flows available to them. Therefore, it is appropriate to discount these payoffs to present value using a discount rate that reflects the risk-adjusted required rate of return on common equity capital of the firm.

The following equation summarizes the computation of the present value of common equity as of time t�0, but in this equation, the analyst computes the present value of the expected future free cash flows for common equity shareholders over a finite forecast hori- zon through Year T plus the present value of continuing value of free cash flows for equity shareholders continuing in Year T�1 and beyond.15 The analyst computes continuing value based on the forecast assumption that the firm will grow indefinitely at rate g begin- ning in Year T�1 and continuing thereafter. The analyst derives free cash flows for com- mon equity shareholders in Year T�1 from the projected income statement and balance sheet for Year T�1, in which the analyst projects all of the elements of the Year T income statement and balance sheet to grow at rate g beginning in Year T�1. The equation is as follows:

V 0

� ∑ [Free Cash Flow Equity t /(1 + R

E )t]

t = 1

+ [Free Cash Flow Equity T+1

] � [1/(R E

– g)] � [1/(1 + R E )T]

Both of these free-cash-flow-based equations represent the value of the common equity of the firm. The Valuations spreadsheet in FSAP provides a template that calculates V

0 using

the present value of free cash flows for common equity shareholders, including the contin- uing value computation.

15 Note that this valuation model is essentially identical to the dividends valuation model described in Chapter 11 (see page 905).

The only difference between the two models is the payoff being valued—dividends versus free cash flows for equity shareholders.

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956 Chapter 12 Valuation: Cash-Flow-Based Approaches

Valuation Models for Free Cash Flows for All Debt and Equity Capital Stakeholders The following equation determines the present value of the net operating assets of a firm as of time t�0 (denoted as VNOA

0 ) by computing the present value of all future free cash

flows for all debt and equity capital stakeholders (denoted as Free Cash Flow All):

∞ VNOA

0 � ∑ [Free Cash Flow All

t /(1 + R

A )t]

t = 1

This equation differs from the models in the previous section in three important ways. First, this valuation approach does not compute the value of common shareholders’ equity (V

0 ); instead, it computes the value of the net operating assets of the firm or, equivalently,

the value of all of the debt, preferred, and common equity claims on the net assets of the firm. Second, this model differs from the models of the previous section because it includes the analyst’s forecasts (as of time t � 0) of future free cash flows to all debt and equity stakeholders. The prior equation focused specifically on the value of common equity capi - tal, measured as the present value of all future free cash flows to common equity share- holders. Third, this equation differs from the prior models because it discounts the free cash flows to present value using R

A , which denotes the expected future weighted average

cost of capital (which should reflect the weighted average required rate of return on the net operating assets of the firm). The prior equations relied on a discount rate using the required rate of return to equity (R

E ).

This valuation approach expresses the value of the financial claims (debt, preferred, and common equity) on the firm as a function of the present value of the free cash flows the firm’s net operating assets will generate that can ultimately be distributed to debtholders, preferred stockholders, and common shareholders. Thus, the value-relevant payoff measure in this approach is the excess cash the firm’s operations generate that will be avail- able to satisfy all capital claims. Given that these free cash flows will be distributed to debt, preferred, and common equity stakeholders, it is appropriate to discount these payoffs to present value using a discount rate that reflects the weighted average cost of capital across these different capital claims.

The next equation summarizes the same computation but uses the present value of the analyst’s forecasts of free cash flows for all debt and equity capital stakeholders over a finite forecast horizon through Year T (for example, T may be five or ten years in the future) plus the present value of continuing value. The analyst computes continuing value based on the forecast assumption that the firm will grow indefinitely at rate g beginning in Year T�1 and continuing thereafter. The analyst derives free cash flows for all debt and equity capital stakeholders in Year T�1 from the projected income statement and balance sheet for Year T�1, in which the analyst projects all elements of the Year T income statement and balance sheet to grow at rate g beginning in Year T�1. The equation is as follows:

VNOA 0

� ∑ [Free Cash Flow All t /(1 + R

A )t]

t = 1

+ [Free Cash Flow All T+1

] � [1/(R A

– g)] � [1/(1 + R A )T]

Both of the prior equations represent estimates of the value of the net operating assets of the firm, which is equivalent to the sum of the values of debt, preferred, and common equity capital. To isolate the value of common equity capital, the analyst must subtract the

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Free Cash Flows Valuation of PepsiCo 957

present value of all interest-bearing debt and preferred stock. The equation to compute the value of equity (denoted as V

0 ) is as follows:

V 0

= VNOA 0

– VDebt 0

– VPreferred 0

The Valuations spreadsheet in FSAP provides a template that calculates VNOA 0

and V 0

using the present value of free cash flows for all debt and equity capital stakeholders, including the continuing value computation.

In theory, the value of common equity using this valuation approach should be identi- cal to the value of common equity using the free cash flows to equity approach, the divi- dends valuation approach discussed in the previous chapter, and the earnings-based approaches discussed in the following chapter. As a practical matter, however, it is some- times difficult to get the equity value estimate from the free cash flows to all debt and equity stakeholders to match the other value estimates. The main reason is the added degrees of circularity in this valuation approach. In this approach, the market-value-based weights for debt, preferred stock, and common equity capital used in computing the weighted average cost of capital must agree with the value estimates for debt, preferred stock, and common equity. Thus, additional degrees of circularity arise because the value estimates depend on the weighted average cost of capital, and the weighted average cost of capital depends on the value estimates. Obtaining an internally consistent set of value estimates for each type of capital and an internally consistent weighted average cost of capital may require a num- ber of iterations until all of the weights and value estimates agree.

FREE CASH FLOWS VALUATION OF PEPSICO At the end of 2008, trading in PepsiCo shares on the New York Stock Exchange closed at $54.77 per share. Therefore, we know the price at which we can buy or sell PepsiCo shares. The free cash flows valuation methods enable us to estimate the value of these shares. This section illustrates the valuation of PepsiCo shares using the free cash flows valuation techniques described in this chapter and the forecasts developed in Chapter 10. We develop these forecasts and value estimates using the Forecast and Valuation spreadsheets in FSAP (see Appendix C).

In this section, we estimate the present value of a share of common equity in PepsiCo at the end of 2008 (equivalently, the start of forecast Year �1) two ways by estimating the present value of the following:

1. Free cash flows to common equity shareholders directly, discounted at the required rate of return to common equity

2. Free cash flows to all debt and equity capital stakeholders, discounted using PepsiCo’s weighted average cost of capital; then subtract the present value of debt claims.

To proceed with each valuation, we follow four steps:

1. Estimate the appropriate discount rates for PepsiCo. 2. Derive the free cash flows from the projected financial statements for PepsiCo

described in Chapter 10 and make assumptions about free cash flows growth in the continuing periods beyond the forecast horizon.

3. Discount the free cash flows to present value, including continuing value. 4. Make the necessary adjustments to convert the present value computation to an esti-

mate of share value for PepsiCo.

Once we have our benchmark estimate of PepsiCo’s share value, we conduct sensitivity analysis to determine the reasonable range of values for PepsiCo shares. Finally, we compare

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958 Chapter 12 Valuation: Cash-Flow-Based Approaches

this range of reasonable values to PepsiCo’s share price in the market and suggest an appro- priate investment decision indicated by our analysis.

Recall in the previous chapter that we used the dividends valuation approach to estimate the value of PepsiCo shares to be in a range around $83 per share. This section shows that we obtain equivalent estimates of value using the free cash flows valuation approaches.

PepsiCo Discount Rates To discount free cash flows to common equity shareholders, we need to compute PepsiCo’s required rate of return on equity capital. To discount free cash flows to all debt and equity capital, we need to compute PepsiCo’s weighted average cost of capital. The following sec- tions briefly describe the computations. Recall that we briefly explained these computations at the outset of this chapter, and we explained and described these computations in detail in Chapter 11.

Computing the Required Rate of Return on Equity Capital for PepsiCo At the end of 2008, different sources provided different estimates of market beta for PepsiCo common stock, ranging from 0.50 to roughly 1.00. Historically, PepsiCo’s market beta has varied around 0.75 over time, so we will assume that PepsiCo common stock has a market beta of roughly 0.75 as of the end of 2008. At that time, U.S. Treasury bills with one to five years to maturity traded with a yield of approximately 4.0 percent, which we use as the risk-free rate. Assuming a 6.0 percent market risk premium, the CAPM indicates that PepsiCo has a cost of common equity capital of 8.50 percent [8.50 � 4.0 � (0.75 � 6.0)]. At the end of 2008, PepsiCo had 1,553 million shares outstanding and a share price of $54.77 for a total market capital of common equity of $85,058 million.

Computing the Weighted Average Cost of Capital for PepsiCo PepsiCo’s balance sheet at the end of 2008 shows interest-bearing debt from short-term obligations and long-term debt obligations totaling $8,227 million (� $369 � $7,858, as reported in Appendix A). Recall that in Chapter 10, we used information disclosed in Note 9, “Debt Obligations and Commitments” (Appendix A), to assess stated interest rates on PepsiCo’s interest-bearing debt. We determined that in 2008, PepsiCo’s outstanding debt carries a weighted average interest rate of approximately 5.8 percent. In Note 10, “Financial Instruments” (Appendix A), PepsiCo discloses that the fair value of outstanding debt obli- gations at the end of 2008 is $8,800 million. Thus, PepsiCo has experienced an unrealized (and unrecognized) loss of $573 million (� $8,227 million � $8,800 million) on its debt capital. This unrealized loss is surprising because more than half of PepsiCo’s outstanding debt obligations were newly issued in 2008 at prevailing market rates. The unrealized loss implies that the firm’s outstanding debt carries stated rates of interest that now exceed pre- vailing market yields, which at the end of 2008 are at relatively low levels given the reces- sion in the U.S. economy. Given that most of PepsiCo’s outstanding debt obligations were recently issued in 2008 and that prevailing yields to maturity are expected to be temporar- ily low, we forecast in Chapter 10 that PepsiCo’s cost of debt capital will continue to approxi - mate 5.8 percent in Year �1 and beyond. We use the current book value (as a proxy for market value) of PepsiCo’s debt for weighting purposes. In Note 5, “Income Taxes” (Appendix A), PepsiCo discloses that the combined average federal, state, and foreign tax

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rate is approximately 26.8 percent in 2008. In Chapter 10, we forecast that PepsiCo will con- tinue to face average tax rates of roughly 26.8 percent in Year �1 and beyond. Therefore, we assume that the tax rate applicable to PepsiCo’s interest expense deductions will be the effective 26.8 percent rate rather than the statutory federal rate of 35 percent. Our long-run projections imply that PepsiCo faces an after-tax cost of debt capital of 4.25 percent [4.25 � 5.8 � (1 � 0.268)].

PepsiCo also has a net negative balance of $97 million in preferred stock on the 2008 bal- ance sheet. In Chapter 10, we forecast that PepsiCo will retire the remaining outstanding preferred stock during Year �1. We also forecast that PepsiCo will not issue any additional preferred stock capital in future years. Therefore, we do not include any preferred stock in the computation of PepsiCo’s weighted average cost of capital.

Bringing the costs of debt and equity capital together, we compute PepsiCo’s weighted average cost of capital to be 8.12 percent as follows:

After-Tax Weighted- Value Cost Average

Capital Basis Amount Weight of Capital Component

Debt Book $ 8,227 8.82% 4.25% 0.37% Common Market 85,058 91.18% 8.50% 7.75% Total $93,285 100.00% 8.12%

Note that this is just our initial estimate of PepsiCo’s weighted average cost of capital. As described earlier, the weighted average cost of capital must be computed iteratively until the weights used are consistent with the present values of debt and equity capital.

Computing Free Cash Flows for PepsiCo This section first describes the computations for PepsiCo’s free cash flows for all debt and equity stakeholders, then describes the computations for PepsiCo’s free cash flows for com- mon equity shareholders. Recall that Exhibits 12.1–12.3 presented the steps to compute free cash flows.

Chapter 10 described detailed projections of PepsiCo’s future statements of cash flows by making specific assumptions regarding each item in the income statement and balance sheet and then deriving the related cash flow effects using a five-year forecast horizon. We use these projections of PepsiCo’s statements of cash flows (see Exhibit 10.6) to compute projected free cash flows. We present the projections of free cash flows for all debt and equity stakeholders in Exhibit 12.4 and the projections of free cash flows for common equity shareholders in Exhibit 12.5.

PepsiCo’s Free Cash Flows to All Debt and Equity Capital Stakeholders In Exhibit 12.4, we begin our computation of free cash flows with cash flows from opera- tions from the projected statements of cash flows. In Chapter 10, we developed our projec- tions of PepsiCo’s statements of cash flows for Year �1 through Year �5. In Year �1, for example, we project that PepsiCo’s cash flows from operations will be $8,359.9 million. We then adjust for net interest, adding back interest expense after tax. Specifically, in Year �1, we add back $361.2 million in interest expense after tax [� $493 million � (1 � 0.268)]. We do not make an adjustment to subtract interest income after tax because we assume that

Free Cash Flows Valuation of PepsiCo 959

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960 Chapter 12 Valuation: Cash-Flow-Based Approaches

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Free Cash Flows Valuation of PepsiCo 961

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962 Chapter 12 Valuation: Cash-Flow-Based Approaches

all of PepsiCo’s interest income relates to financial assets (cash and short-term investments) that are used for liquidity in operating activities and strategic investments in affiliates such as bottlers and are not part of the capital structure. We also adjust cash flow from operations for required investments in operating cash. In Chapter 10, we projected that PepsiCo would need to maintain roughly 12 days of sales in cash for liquidity purposes; therefore, PepsiCo’s required cash balance varies with sales. For example, at the end of Year �1, we project that PepsiCo’s cash balance will be $1,551 million, equivalent to 12 days of sales in Year �1. Given that this balance is lower than PepsiCo’s 2008 year-end cash balance of $2,064 million, it implies that PepsiCo will reduce its cash by $512.5 million. This increment of cash is avail- able to satisfy debt and equity claims, so we add it to free cash flows. [By contrast, in Year �2, we project that the cash balance will grow by $143.7 million to $1,695 million. This additional increment of cash is required for liquidity in Year �2 and therefore is not a free cash flow; so we subtract it.] As a result of these adjustments, we project that PepsiCo’s free cash flows for all debt and equity from operations will be $9,233.6 million in Year �1.

Next, we subtract cash flows for capital expenditures using the amount of net cash flow for investing from PepsiCo’s projected statements of cash flows. For example, in Year �1, we projected that net cash flows for investing activities will be $3,874.4 million. These investing cash flows include cash outflows for purchases of property, plant, and equipment; acquisitions of goodwill and other intangible assets; and purchases of marketable securities and investment securities. We consider these to be investing activities because we assumed that these securities are for purposes of operating liquidity and are not financial assets that are part of the financing structure of PepsiCo. Also note that PepsiCo’s investing cash flows include cash outflows for long-term investments that relate primarily to affiliated bottling companies, which we deem to be part of PepsiCo’s operations and therefore not free cash flows. Therefore, we subtract the full amount of net cash flow for investing activities from the free cash flow from operations. We forecast that PepsiCo’s free cash flows for all debt and equity capital stakeholders will be $5,359.3 million (� $9,233.6 million � $3,874.4 million) in Year �1. We repeat these steps each year through Year �5.

To project PepsiCo’s free cash flows continuing in Year �6 and beyond, we forecast that PepsiCo will sustain a long-run growth rate of 3.0 percent, consistent with 3.0 percent long- term growth in the economy. To compute continuing free cash flows in Year �6, we pro ject each line item on PepsiCo’s Year �5 income statement and balance sheet to grow at 3.0 per- cent per year in Year �6. We use these Year �6 projected income statement and balance sheet amounts to derive the Year �6 free cash flows for all debt and equity capital, which we project will be $8,330.1 million. We assume that this free cash flow amount is the begin- ning of a perpetuity of continuing free cash flows that PepsiCo will generate beginning in Year �6, growing at 3 percent each year thereafter. The computations are shown in detail in the Forecast and Valuation spreadsheets in FSAP (Appendix C), which permit specific forecast assumptions to extend as far as Year �5 into the future, with continuing value assumptions thereafter.

PepsiCo’s Free Cash Flows to Common Equity Exhibit 12.5 presents estimates of PepsiCo’s free cash flows for common equity sharehold- ers through Year �6. The computations begin with the Year �1 projection of $8,359.9 mil- lion of cash flows from operations, as described earlier. As in the previous section, we adjust cash flow from operations in Year �1 by adding the increment of $512.5 million of cash no longer required for liquidity. Also as in the previous section, we subtract $3,874.4 million of projected cash outflows for capital expenditures and other investing activities in Year �1. Note that unlike the previous section, we make no adjustment for net interest expense after tax because we need to measure the free cash flows available to equity shareholders net of

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all debt-related cash flows. Because our starting point, cash flows from operations, is derived from net income and because we measure net income after interest expense, our cash flows amount is net of interest expense.

To further refine these cash flows to free cash flows available to common equity, we need to adjust them for cash flows related to debt and preferred-stock financing. We first add any cash inflows from new borrowing and subtract any cash outflows for debt repayments. For example, in Year �1, we add $562.8 million in cash flows for our projections of PepsiCo’s additional short-term and long-term borrowing. Next, we add inflows and subtract out- flows related to transactions with preferred stock and minority equity shareholders (if any). In Year �1, we subtract $72.0 million for payments to retire the outstanding preferred stock. We also subtract any cash outflows and add any cash inflows related to financial asset accounts that are part of PepsiCo’s capital structure (which we have deemed to be zero). The computations project $5,488.8 million in free cash flows for PepsiCo’s common equity shareholders in Year �1. We repeat these steps each year through Year �5.

To project PepsiCo’s free cash flows for common equity continuing in Year �6 and beyond, we again forecast that PepsiCo can sustain long-run growth of 3.0 percent. We project the Year �5 income statement and balance sheet amounts to grow at a rate of 3.0 percent in Year �6 and derive free cash flows to common equity from the projected Year �6 statements. Our computations indicate that free cash flows to common equity in Year �6 will be $8,186.5 million (shown in detail in the Forecast and Valuation spread- sheets in FSAP in Appendix C). We assume that these free cash flows will continue to grow at 3.0 percent per year thereafter.

Valuation of PepsiCo Using Free Cash Flows to Common Equity Shareholders We estimate the present value of a share of common equity in PepsiCo at the end of 2008 (equivalently, the start of Year �1) by discounting the free cash flows to equity using PepsiCo’s 8.50 percent risk-adjusted required rate of return on equity capital as the appro- priate discount rate. Exhibit 12.5 shows that PepsiCo’s free cash flows for common equity through Year �5 have a present value of $24,699.3 million. We compute the present value of PepsiCo’s continuing value as the present value of a growing perpetuity of free cash flows beginning in Year �6, which we project will be $8,186.5. We project these free cash flows to grow at 3.0 percent and discount them to present value using the 8.50 percent discount rate. The present value of these cash flows is $98,988.9 million. As shown in Exhibit 12.6, the present value of PepsiCo’s free cash flows to common equity shareholders is the sum of these two parts:

Present Value Free Cash Flows through Year �5 $ 24,699.3 million Present Value of Continuing Value in Year �6 and Beyond 98,988.9 million Present Value of Common Equity $123,688.2 million

As described in the previous chapter, we need to correct our present value calculations for overdiscounting. To make the correction, we multiply the present value sum by the midyear adjustment factor of 1.0425 [� 1 � (R

E /2) � 1 � (0.0850/2)]. The total present

value of free cash flows to common equity shareholders should be $128,945.0 million (� $123,688.2 million � 1.0425).

Dividing the total value of common equity of PepsiCo by 1,553 million shares outstand- ing indicates that PepsiCo’s common equity shares have a value of $83.03 per share. This share value estimate is identical to the share value estimate we computed using dividends

Free Cash Flows Valuation of PepsiCo 963

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964 Chapter 12 Valuation: Cash-Flow-Based Approaches

in the previous chapter. Exhibit 12.7 presents the computations to arrive at PepsiCo’s com- mon equity share value using the free cash flows to common equity shareholders approach in the Valuations spreadsheet in FSAP.

Valuation of PepsiCo Using Free Cash Flows to All Debt and Equity Capital Stakeholders We also estimate the present value of a share of common equity in PepsiCo at the end of 2008 by discounting the free cash flows to all debt and equity stakeholders using PepsiCo’s 8.12 percent weighted average cost of capital as the appropriate discount rate. Exhibit 12.4 shows that PepsiCo’s free cash flows for all debt and equity stakeholders through Year �5 have a present value of $23,582.3 million. To compute the present value of PepsiCo’s continuing value, we compute the continuing value beyond Year �5 using the perpetuity-with-growth

E X H I B I T 1 2 . 6

Valuation of PepsiCo Using Free Cash Flows to Common Equity Shareholders

Present Value of Free Cash Flows to Common Equity Shareholders in Year +1 through Year +5:

From Exhibit 12.5: $ 24,699.3 million

Present Value of Continuing Value of Free Cash Flows to Common Equity in Year +6 and Beyond:

Projected Year +6 Free Cash Flows to Common Equity (Exhibit 12.5): $8,186.5 million

Continuing Value in Present Value (R E

= 8.50% and g = 3.0%):

Continuing Value = Free Cash Flow Year+6

� [1/(R E

� g)] = $8,186.5 million � [1/(0.0850 � 0.0300)] = $8,186.5 million � 18.18182 = $148,845.4 million

Present Value of Continuing Value = Continuing Value � [1/(1 + R

E )5]

= $148,845.4 million � [1/(1 + 0.0850)5] = $148,845.4 million � 0.665 = $98,988.9 million

Total Value of PepsiCo’s Free Cash Flows to Common Equity Shareholders:

Present Value of Free Cash Flows through Year +5 $ 24,699.3 million + Present Value of Continuing Value + 98,988.9 million

Present Value of Common Equity $123,688.2 million Adjust for Midyear Discounting (multiply by 1 + [R

E /2]) � 1.0425

Total Present Value of Common Equity $128,945.0 million Divide by Number of Shares Outstanding � 1,553 million

Value per Share of PepsiCo Common Equity = $ 83.03

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Free Cash Flows Valuation of PepsiCo 965

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966 Chapter 12 Valuation: Cash-Flow-Based Approaches

model. First, as described earlier and shown in Exhibit 12.4, we project that PepsiCo will gen- erate free cash flows of $8,330.1 million in Year �6, and that these free cash flows will grow at a rate of 3.0 percent indefinitely. Exhibit 12.8 demonstrates that in present value, PepsiCo’s continuing value has a present value of $109,988.1 million.16 The present value of PepsiCo’s free cash flows to all debt and equity capital stakeholders is the sum of these two parts:

Present Value Free Cash Flows through Year �5 $ 23,582.3 million Present Value of Continuing Value Year �6 and Beyond 109,988.1 million Present Value of Free Cash Flows for All Debt and Equity Capital $133,570.4 million

E X H I B I T 1 2 . 8

Valuation of PepsiCo Using Free Cash Flows to All Debt and Equity Stakeholders

Present Value of Free Cash Flows to All Debt and Equity Stakeholders in Year +1 through Year +5:

From Exhibit 12.4: $ 23,582.3 million

Present Value of Continuing Value of Free Cash Flows to All Debt and Equity Stakeholders in Year + 6 and Beyond:

Projected Year +6 Free Cash Flows to All Debt and Equity Stakeholders (Exhibit 12.4): $8,330.1 million

Continuing Value in Present Value (R A

= 8.12% and g = 3.0%):

Continuing Value = Free Cash Flow Year+6

� [1/(R A

– g)] = $8,330.1 million � [1/(0.0812 – 0.0300)] = $8,330.1 million � 19.5312 = $162,544.5 million

Present Value of Continuing Value = Continuing Value � [1/(1 + R A )5]

= $162,544.5 million � [1/(1 + 0.0812)5] = $162,544.5 million � 0.677 = $109,988.1 million

Total Value of PepsiCo’s Free Cash Flows to All Debt and Equity Stakeholders:

Present Value of Free Cash Flows through Year +5 $ 23,582.3 million + Present Value of Continuing Value + 109,988.1 million

Present Value of All Debt and Equity $133,570.4 million Subtract Market Value of Debt – 8,227.0 million

Present Value of Common Equity $125,343.4 million Adjust for Midyear Discounting [multiply by 1 + (R

A /2)] � 1.0406

Total Present Value of Common Equity $130,435.3 million Divide by Number of Shares Outstanding � 1,553 million

Value per Share of PepsiCo Common Equity = $ 83.99

16 Because of the effects of rounding, it appears the present value of continuing value computation may be slightly in error.

But when computed with greater precision and less rounding the computation is correct, as follows: Continuing Value �

Free Cash Flow Year+6

� [1/(R A

� g)] � [1/(1 + R A )5] � $8,330.07 million � [1/(0.08125 � 0.0300)] � [1/(1 + 0.08125)5] �

$8,330.07 million � 19.51298 � 0.67666 � $109,988.1 million.

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Necessary Adjustments to Compute Common Equity Share Value To narrow this computation to the present value of common equity, we need to subtract the market value of interest-bearing debt and preferred stock and add the present value of interest-earning financial assets that are part of the firm’s financial capital structure. Relying on PepsiCo’s book values of debt, we subtract $8,227 million for outstanding debt. We assumed that PepsiCo would retire the outstanding preferred stock during Year �1, so our cash outflows already account for the payment to retire that preferred stock. We assumed that PepsiCo’s financial assets are not part of the financial capital structure, so we need no adjustments for them. After subtracting the value of debt, the present value of PepsiCo’s common equity capital is $125,343.4 million (� $133,570.4 million � $8,227.0 million).

As described earlier, our present value calculations have overdiscounted these cash flows because we have discounted each year’s cash flows for a full period when, in fact, PepsiCo generates cash flows throughout each period and we should discount them from the midpoint of the year to the present. Therefore, to make the correction, we multiply the present value sum by the midyear adjustment factor of 1.0406 [� 1 � (R

A /2) � 1 �

(0.0812/2)]. Therefore, the total present value of free cash flows to common equity capi- tal stakeholders is $130,435.3 million (� $125,343.4 million � 1.0406). Dividing by 1,553 million shares outstanding indicates that PepsiCo’s common equity shares have a value of $83.99 per share. Exhibit 12.8 summarizes all of these computations, and Exhibit 12.9 presents the computations to arrive at PepsiCo’s common equity share value using the free cash flows to all debt and equity stakeholders approach in the Valuations spread- sheet in FSAP.

Note that our calculation of an $83.99 value for PepsiCo’s common equity shares is slightly different from the value of $83.03 per share obtained from the free cash flows to common equity approach described previously and the dividends approach in the previous chapter. This is because we used the current market price per share of PepsiCo common stock ($54.77) in the initial weighted average cost of capital computation. As a conse- quence, we did not place enough weight on the market value of equity in the initial cost of capital computation. To iterate the valuation approach, we can use the share value estimate of $83.03 to determine that the total value of PepsiCo common equity in the weighted aver- age cost of capital computation. To further iterate the valuation approach, we can recom- pute the weighted average cost of equity capital each forecast year because our projections indicate that PepsiCo’s common equity in the capital structure will gradually fall in propor- tion to the debt financing in the capital structure in future years. After a number of itera- tions, the valuation computations and the weights we use to compute the weighted average cost of capital converge. The equity value estimate of $128,945.0 million, or $83.03 per share, is the internally consistent value.

Sensitivity Analysis and Investment Decision Making As we emphasized in the previous chapter, forecasts of cash flows over the remaining life of any firm, even a mature firm such as PepsiCo, contain a high degree of uncertainty; so one should not place too much confidence in the precision of firm value estimates using these forecasts. Although we have constructed these forecasts and value estimates with care, the forecasting and valuation process has an inherently high degree of uncertainty and estimation error. Therefore, the analyst should not rely too heavily on any one point esti- mate of the value of a firm’s shares; instead, the analyst should describe a reasonable range of values for a firm’s shares.

Free Cash Flows Valuation of PepsiCo 967

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968 Chapter 12 Valuation: Cash-Flow-Based Approaches

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Two critical forecasting and valuation parameters in most valuations are the long-run growth rate assumption and the cost of equity capital assumption. Analysts should conduct sensitivity analyses to test the effects of these and other key forecast assumptions and valu- ation parameters on the share value estimate. Sensitivity analysis tests should allow the ana- lyst to vary these assumptions and parameters individually and jointly for additional insights into the correlation between share value, the growth rate, and the discount rate assumptions.

For PepsiCo, our base case assumptions indicate PepsiCo’s share value to be roughly $83. Our base case valuation assumptions include a long-run growth rate of 3 percent and a cost of equity capital of 8.50 percent. We can assess the sensitivity of our estimates of PepsiCo’s share value by varying these two parameters (or any other key parameters in the valuation) across reasonable ranges. Exhibit 12.10 contains the results of sensitivity analysis varying the long-run growth rate from 0–10 percent and the cost of equity capital from 5–20 per- cent. The data in Exhibit 12.10 show that as the discount rate increases, holding growth constant, share value estimates of PepsiCo fall. Likewise, value estimates fall as growth rates decrease, holding discount rates constant.

Considering the downside possibilities first, if we reduce the long-run growth assump- tion to 2.0 percent while holding the discount rate constant at 8.50 percent, PepsiCo’s share value falls to $73.36, still well above current market price. In fact, if we drop the long-run growth assumption to zero while holding the discount rate constant at 8.50 per- cent, PepsiCo’s share value estimate falls to $60.84, still above current market price. Similarly, if we increase the discount rate to 9.0 or 10.0 percent while holding the long- run growth assumption constant at 3.0 percent, PepsiCo shares have a value of roughly $76 or $65, respectively. If we revise both assumptions at once and reduce the long-run growth assumption to 0 percent and increase the discount rate assumption to 10.0 per- cent, PepsiCo’s share value falls to roughly $51, which is slightly below market price of $54.77.

On the upside, if we reduce the discount rate to 7.0 percent while holding long-run growth constant at 3.0 percent or if we increase the long-run growth assumption from 3.0 to 4.0 percent while holding the discount rate constant at 8.50 percent, the value estimates jump to roughly $114 per share or $97 per share, respectively. If we reduce the discount rate assumption further or increase the long-run growth rate further, our share value estimates for PepsiCo jump dramatically higher.

These data suggest that our value estimate is sensitive to slight variations of our baseline assumptions of 3.0 percent long-run growth and an 8.50 percent discount rate, which yield a share value estimate of $83. Adverse variations in valuation parameters could reduce PepsiCo’s share value estimates to $55 or lower, whereas favorable variations could increase PepsiCo’s share value up to or above $100.

If our forecast and valuation assumptions are realistic, our baseline value estimate for PepsiCo is $83 per share at the end of 2008. At that time, the market price of $54.77 per share indicates that PepsiCo shares were underpriced by about 52 percent. Under our fore- cast assumptions, PepsiCo’s share value could vary within a range of a low of $51 per share to a high of $114 per share with only minor perturbations in our growth rate and discount rate assumptions. Given PepsiCo’s $54.77 share price, these value estimates would have supported a buy recommendation or perhaps a strong buy recommendation at the end of 2008 because the valuation sensitivity analysis reveals limited downside potential but sub- stantial upside potential for the value of PepsiCo shares.

Free Cash Flows Valuation of PepsiCo 969

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970 Chapter 12 Valuation: Cash-Flow-Based Approaches

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Questions, Exercises, Problems, and Cases 971

EVALUATION OF THE FREE CASH FLOWS VALUATION METHOD The principal advantages of the present value of future free cash flows valuation method include the following:

• This valuation method focuses on free cash flows, a base that economists would argue has a more basic economic meaning than earnings.

• Projected amounts of free cash flows result from projected amounts of revenues, expenses, assets, liabilities, and shareholders’ equities, thereby requiring the analyst to project the future operating, investing, and financing decisions of a firm.

• The free cash flows valuation focuses directly on net cash inflows to the entity that are available to distribute to capital providers, as opposed to focusing on dividends to common equity shareholders. This cash flow perspective is especially pertinent to acquisition decisions.

• The free cash flows valuation approaches are widely used in practice. The principal disadvantages of the present value of future free cash flows valuation

method include the following:

• The projection of free cash flows can be time-consuming for the analyst, making it costly when the analyst follows many companies and must regularly identify under- and overvalued firms.

• The continuing value (terminal value) tends to dominate the total value in many cases. This continuing value is sensitive to assumptions made about growth rates after the forecast horizon and discount rates.

• The analyst must be very careful that free cash flow computations are internally con- sistent with long-run assumptions regarding growth and payout. Failure to do so can result in unnecessary estimation errors that produce poor valuations that are inconsis- tent with those derived from expected future dividends and earnings.

SUMMARY This chapter illustrates valuation using the present value of future free cash flows. As with the preparation of financial statement forecasts in Chapter 10, the reasonableness of the valuations depends on the reasonableness of the assumptions. The analyst should assess the sensitivity of the valuation to alternative assumptions regarding growth and discount rates. To validate value estimates using the free-cash-flows-based approach, the analyst also should compute the value of the common equity of the firm using other approaches, such as the dividends approach described in Chapter 11, the earnings-based approach described in Chapter 13, and the valuation multiples approaches described in Chapter 14.

QUESTIONS, EXERCISES, PROBLEMS, AND CASES

Questions and Exercises 12.1 FREE CASH FLOWS. Explain “free” cash flows. Describe which types of cash flows are free and which are not. How do free cash flows available for debt and equity stake- holders differ from free cash flows available for common equity shareholders?

12.2 THE FREE CASH FLOWS VALUATION APPROACH. Explain the the- ory behind the free cash flows valuation approach. Why are free cash flows value-relevant

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to common equity shareholders when they are not cash flows to those shareholders, but rather are cash flows into the firm?

12.3 MEASURING VALUE-RELEVANT FREE CASH FLOWS. The chapter describes free cash flows for common equity shareholders. If the firm borrows cash by issu- ing debt, how does that transaction affect free cash flows for common equity shareholders in that period? If the firm uses cash to repay debt, how does that transaction affect free cash flows for common equity shareholders in that period?

12.4 MEASURING VALUE-RELEVANT FREE CASH FLOWS. The chapter describes free cash flows for common equity shareholders. Suppose a firm has no debt and uses marketable securities to manage operating liquidity. If the firm uses cash to purchase marketable securities, how does that transaction affect free cash flows for common equity shareholders in that period? If the firm sells marketable securities for cash, how does that transaction affect free cash flows for common equity shareholders in that period?

12.5 VALUATION APPROACH EQUIVALENCE. Conceptually, why should an analyst expect valuation based on dividends and valuation based on the free cash flows for common equity shareholders to yield identical value estimates?

12.6 FREE CASH FLOWS VALUATION WHEN FREE CASH FLOWS ARE NEGATIVE. Suppose you are valuing a healthy, growing, profitable firm and you project that the firm will generate negative free cash flows for equity shareholders in each of the next five years. Can you use the free cash flows valuation approach when cash flows are nega- tive? If so, explain how the free cash flows approach can produce positive valuations of firms when they are expected to generate negative free cash flows over the next five years.

12.7 USING DIFFERENT FREE CASH FLOWS MEASURES. The chapter describes free cash flows for all debt and equity stakeholders and free cash flows for equity shareholders. Give examples of valuation settings in which one approach or the other is appropriate.

12.8 APPROPRIATE DISCOUNT RATES. Describe valuation settings in which the appropriate discount rate to use is the required rate of return on equity capital versus settings in which it is appropriate to use a weighted average cost of capital.

12.9 FREE CASH FLOWS AND DISCOUNT RATES. Describe circum- stances and give an example of when free cash flows to equity shareholders and free cash flows to all debt and equity stakeholders will be identical. Under those circumstances, will the required rate of return on equity and the weighted average cost of capital be identi- cal too? Explain.

Problems and Cases 12.10 CALCULATING FREE CASH FLOWS. The 3M Company is a global diver- sified technology company active in the following product markets: consumer and office; display and graphics; electronics and communications; health care; industrial; safety, secu- rity, and protection services; and transportation. At the consumer level, 3M is probably most widely known for products such as Scotch® Brand transparent tape and Post-it® notes. Exhibit 12.11 presents information from the statement of cash flows and income

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statement for the 3M Company for 2006–2008. From 2006 through 2008, 3M increased cash and cash equivalents. Assume that 3M considers these increases in cash and cash equivalents to be necessary to sustain operating liquidity. The interest income reported by 3M pertains to interest earned on cash and marketable securities. 3M holds only small amounts of investments in marketable securities. 3M’s income tax rate is 35 percent.

Required a. Beginning with cash flows from operating activities, calculate the amount of free cash

flows to all debt and equity capital stakeholders for 3M for 2006, 2007, and 2008. b. Beginning with cash flows from operating activities, calculate the amount of free

cash flows 3M generated for common equity shareholders in 2006, 2007, and 2008. c. Reconcile the amounts of free cash flows 3M generated for common equity share-

holders in 2006, 2007, and 2008 from Part b with 3M’s uses of cash flow for equity shareholders, including share repurchases and dividend payments.

12.11 CALCULATING FREE CASH FLOWS. Dick’s Sporting Goods is a chain of full-line sporting goods retail stores offering a broad assortment of brand name sporting goods equipment, apparel, and footwear. Dick’s Sporting Goods had its initial public offer- ing of shares in fiscal 2003. Since then, Dick’s Sporting Goods has grown its chain of retail

Preparing Financial Statement Forecasts 973E X H I B I T 1 2 . 1 1

3M Company Selected Information from the Statement of Cash Flows

(amounts in millions) (Problem 12.10)

2008 2007 2006

Cash Flow from Operating Activities $ 4,118 $ 4,363 $ 3,896

Investing Activities: Fixed Assets Acquired, Net (1,384) (1,319) (1,119) (Acquisition) Sale of Businesses, Net (1,306) 358 321 (Purchase) Sale of Investments 291 (406) (662)

Cash Flow from Investing Activities $(2,399) $(1,367) $ (1,460)

Financing Activities: Increase (Decrease) in Short-Term Borrowing 361 (1,222) 882 Increase (Decrease) in Long-Term Debt 676 2,444 253 Increase (Decrease) in Common Stock (1,405) (2,389) (1,820) Dividends Paid (1,398) (1,380) (1,376)

Cash Flow from Financing Activities $(1,766) $(2,547) $ (2,061)

Net Increase (Decrease) in Cash & Equivalents $ (47) $ 449 $ 375 Cash at Beginning of Year $ 1,896 $ 1,447 $ 1,072

Cash at End of Year $ 1,849 $ 1,896 $ 1,447

Interest Income $ 105 $ 132 $ 51 Interest Expense $ 215 $ 210 $ 122

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stores rapidly and has acquired several other chains of retail sporting goods stores, including Golf Galaxy and Chick’s Sporting Goods in the fiscal year ending in 2008. As of the end of the fiscal year ending in 2009, Dick’s Sporting Goods operated 409 stores in 40 states of the United States. Exhibit 12.12 presents information from the statement of cash flows and income statement for Dick’s Sporting Goods for the fiscal years ending in 2007 through 2009. Dick’s Sporting Goods requires all of its cash and cash equivalents for operating li - quidity and reports no interest income on the income statement. The average income tax rate for Dick’s Sporting Goods during 2007 through 2009 is 40 percent.

Required a. Beginning with cash flows from operating activities, calculate free cash flows to all

debt and equity capital stakeholders for Dick’s Sporting Goods for fiscal years end- ing in 2009, 2008, and 2007.

b. Beginning with cash flows from operating activities, calculate free cash flows for common equity shareholders for Dick’s Sporting Goods for fiscal years ending in 2009, 2008, and 2007.

c. Reconcile the amounts of free cash flows for common equity shareholders for Dick’s Sporting Goods for fiscal years ending in 2009, 2008, and 2007 with Dick’s Sporting Goods’ sources of cash flow from equity shareholders.

d. Why do the free cash flows to all debt and equity capital stakeholders for Dick’s Sporting Goods change so much from 2007 through 2009? In each of these three years, why do the free cash flows to all debt and equity capital stakeholders differ so much from the free cash flows to common equity shareholders?

e. In each of these three years, Dick’s Sporting Goods produces negative free cash flows for common shareholders. Does that imply that Dick’s Sporting Goods is destroying the value of common equity? Explain.

12.12 VALUING A LEVERAGED BUYOUT CANDIDATE. May Department Stores (May) operates retail department store chains throughout the United States. At the end of Year 12, May reports debt of $4,658 million and common shareholders’ equity at book value of $3,923 million. The market value of its common stock is $6,705, and its mar- ket equity beta is 0.88.

An equity buyout group is considering an LBO of May as of the beginning of Year 13. The group intends to finance the buyout with 25 percent common equity and 75 percent debt carrying an interest rate of 10 percent. The group projects that the free cash flows to all debt and equity capital stakeholders of May will be as follows: Year 13, $798 million; Year 14, $861 million; Year 15, $904 million; Year 16, $850 million; Year 17, $834 million; Year 18, $884 mil- lion; Year 19, $919 million; Year 20, $947 million; Year 21, $985 million; and Year 22, $1,034 million. The group projects free cash flows to grow 3 percent annually after Year 22.

This problem sets forth the steps the analyst might follow in deciding whether to acquire May and the value to place on the firm.

Required a. Compute the unlevered market equity (asset) beta of May before consideration of

the LBO. Assume that the book value of the debt equals its market value. The income tax rate is 35 percent. [See Chapter 11.]

b. Compute the cost of equity capital with the new capital structure that results from the LBO. Assume a risk-free rate of 4.2 percent and a market risk premium of 5.0 percent.

c. Compute the weighted average cost of capital of the new capital structure.

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Preparing Financial Statement Forecasts 975E X H I B I T 1 2 . 1 2

Dick’s Sporting Goods Selected Information from the Statement of Cash Flows

(amounts in thousands) (Problem 12.11)

Fiscal year ended:

January 31, 2009 February 2, 2008 February 3, 2007

CASH FLOWS FROM OPERATING ACTIVITIES: Net (loss) income $ (35,094) $ 155,036 $ 112,611 Adjustments to reconcile net (loss) income to net

cash provided by operating activities: Depreciation and amortization 90,732 75,052 54,929 Impairment of store assets, goodwill

and other intangible assets 193,350 — — Deferred income taxes (45,906) (32,696) (1,110) Various addbacks to net income 24,709 2,462 (7,371)

Changes in assets and liabilities, net of acquired assets and liabilities:

Accounts receivable 3,090 (10,982) (2,142) Inventories 29,581 (127,027) (105,766) Prepaid expenses and other assets (10,554) (4,267) (29,039) Accounts payable (56,709) 12,337 24,444 Accrued expenses (7,575) 26,222 42,479 Income taxes payable/receivable (63,089) 114,706 4,750 Deferred construction allowances 19,452 22,256 19,264 Deferred revenue and other liabilities 17,689 29,869 26,560

Net cash provided by operating activities $ 159,676 $ 262,968 $ 139,609

CASH FLOWS USED IN INVESTING ACTIVITIES: Capital expenditures (191,423) (172,366) (162,995) Purchase of corporate aircraft (25,107) — — Proceeds from sale of corporate aircraft 27,463 — — Proceeds from sale-leaseback transactions 44,873 28,440 32,509 Payment for the purchase of Golf Galaxy,

net of $4,859 cash acquired — (222,170) — Payment for the purchase of Chick’s Sporting Goods — (69,200) —

Net cash used in investing activities $(144,194) $(435,296) $(130,486)

CASH FLOWS FROM FINANCING ACTIVITIES: Increase (Decrease) Short-term borrowing (9,927) 4,785 8,829 Long-term borrowing—Construction allowance receipts 11,874 13,282 17,902 Payments on long-term debt and capital leases (6,793) (1,058) (184) Proceeds from sale of common stock 13,894 69,684 63,708

Net cash provided by financing activities $ 9,048 $ 86,693 $ 90,255

NET INCREASE (DECREASE) IN CASH $ 24,530 $ (85,635) $ 99,378 CASH, BEGINNING OF PERIOD 50,307 135,942 36,564

CASH, END OF PERIOD $ 74,837 $ 50,307 $ 135,942

Cash paid during the year for interest $ 8,021 $ 12,314 $ 9,286

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976 Chapter 12 Valuation: Cash-Flow-Based Approaches

d. Compute the present value of the projected free cash flows to all debt and equity capital stakeholders at the weighted average cost of capital. Ignore the midyear adjustment related to the assumption that cash flows occur, on average, over the year. In computing the continuing value, apply the projected growth rate in free cash flows after Year 22 of 3 percent directly to the free cash flows of Year 22.

e. Assume that the buyout group acquires May for the value determined in Part d. Assuming that the realized free cash flows coincide with projections, will May gen- erate sufficient cash flow each year to service the interest on the debt? Explain.

12.13 VALUING A LEVERAGED BUYOUT CANDIDATE. Experian Information Solutions (Experian) is a wholly owned subsidiary of TRW, a publicly traded company. The subsidiary has (in thousands) total assets of $555,443, long-term debt of $1,839, and common equity at book value of $402,759.

An equity buyout group is planning to acquire Experian from TRW in an LBO as of the beginning of Year 6. The group plans to finance the buyout with 60 percent debt that has an interest cost of 10 percent per year and 40 percent common equity. Analysts for the buy- out group project free cash flows to all debt and equity capital stakeholders as follows (in thousands): Year 6, $52,300; Year 7, $54,915; Year 8, $57,112; Year 9, $59,396; and Year 10, $62,366. Because Experian is not a publicly traded firm, it does not have a market equity beta. The company most comparable to Experian is Equifax. Equifax has an equity beta of 0.86. The market value of Equifax’s debt is $366.5 thousand, and its common equity is $4,436.8 thousand. Assume an income tax rate of 35 percent throughout this problem.

This problem sets forth the steps the analyst might follow in valuing an LBO candidate.

Required a. Compute the unlevered market equity (asset) beta of Equifax. [See Chapter 11.] b. Assuming that the unlevered market equity beta of Equifax is appropriate for

Experian, compute the equity beta of Experian after the buyout with its new capital structure.

c. Compute the weighted average cost of capital of Experian after the buyout. Assume a risk-free interest rate of 4.2 percent and a market risk premium of 5.0 percent.

d. The analysts at the buyout firm project that free cash flows for all debt and equity capital stakeholders of Experian will increase 5.0 percent each year after Year 10. Compute the present value of the free cash flows at the weighted average cost of capi - tal. Ignore the midyear adjustment related to the assumption that cash flows occur, on average, over the year. In computing the continuing value, apply the 5.0 percent projected growth rate directly to the free cash flows of Year 10.

e. Assume that the buyout group acquires Experian for the value determined in Part d. Assuming that actual free cash flows to all debt and equity capital stakeholders coin- cide with projections, will Experian generate sufficient cash flow each year to service the debt? Explain.

12.14 APPLYING VARIOUS PRESENT VALUE APPROACHES TO VALUATION. An equity buyout group intends to acquire Wedgewood Products (Wedgewood) as of the beginning of Year 8. The buyout group intends to finance 40 per- cent of the acquisition price with 10 percent annual coupon debt and 60 percent with com- mon equity. The income tax rate is 40 percent. The cost of equity capital is 14 percent. Analysts at the buyout firm project the following free cash flows for all debt and equity capi - tal stakeholders for Wedgewood (in millions): Year 8, $2,100; Year 9, $2,268; Year 10, $2,449; Year 11, $2,645; and Year 12, $2,857. The analysts project that free cash flows for all debt and equity capital stakeholders will increase 8 percent each year after Year 12.

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Required a. Compute the weighted average cost of capital for Wedgewood based on the proposed

capital structure. b. Compute the total purchase price of Wedgewood (debt plus common equity). To do

this, discount the free cash flows for all debt and equity capital stakeholders at the weighted average cost of capital. Ignore the midyear adjustment related to the assumption that cash flows occur, on average, over the year. In computing the con- tinuing value, apply the 8 percent projected growth rate in free cash flows after Year 12 directly to the free cash flows of Year 12.

c. Given the purchase price determined in Part b, compute the total amount of debt, the annual interest cost, and the free cash flows to common equity shareholders for Year 8 to Year 12.

d. The present value of the free cash flows for common equity shareholders when dis- counted at the 14 percent cost of equity capital should equal the common equity portion of the total purchase price computed in Part b. Determine the growth rate in free cash flows for common equity shareholders after Year 12 that will result in a present value of free cash flows for common equity shareholders equal to 60 percent of the purchase price computed in Part b.

e. Why does the implied growth rate in free cash flows to common equity sharehold- ers determined in Part d differ from the 8 percent assumed growth rate in free cash flows for all debt and equity capital stakeholders?

f. The adjusted present value valuation approach separates the total value of the firm into the value of an all-equity firm and the value of the tax savings from interest deductions. Assume that the cost of unlevered equity is 11.33 percent. Compute the present value of the free cash flows to all debt and equity capital stakeholders at this unlevered equity cost. Compute the present value of the tax savings from interest expense deductions using the pretax cost of debt as the discount rate. Compare the total of these two present values to the purchase price determined in Part b.

12.15 VALUING THE EQUITY OF A PRIVATELY HELD FIRM. Refer to the projected financial statements for Massachusetts Stove Company (MSC) prepared for Case 10.2. The management of MSC wants to know the equity valuation implications of not adding gas stoves versus adding gas stoves under the best, most likely, and worst scenarios. Under the three scenarios from Case 10.2 and a fourth scenario involving not adding gas stoves, the projected free cash flows to common equity shareholders for Year 8 to Year 12, and assumed growth rates thereafter, are as follows:

Year Best Most Likely Worst No Gas

8 $ 73,967 $ 47,034 $ 3,027 $162,455 9 $ 52,143 $ (3,120) $(84,800) $132,708

10 $213,895 $135,939 $ 48,353 $106,021 11 $315,633 $178,510 $ 36,605 $ 81,840 12 $432,232 $220,010 $ 10,232 $ 60,007 13–17 20% Growth 10% Growth Zero Growth Zero Growth After Year 17 10% Growth 5% Growth Zero Growth Zero Growth

MSC is not publicly traded and therefore does not have a market equity beta. Using the market equity beta of the only publicly traded woodstove and gas stove manufacturing firm

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978 Chapter 12 Valuation: Cash-Flow-Based Approaches

and adjusting it for differences in the debt-to-equity ratio, income tax rate, and privately owned status of MSC yields a cost of equity capital for MSC of 13.55 percent.

Required a. Calculate the value of the equity of MSC as of the end of Year 7 under each of the

four scenarios. Ignore the midyear adjustment related to the assumption that cash flows occur, on average, over the year. Apply the growth rates in free cash flows to common equity shareholders after Year 12 directly to the free cash flow of the pre- ceding year. (That is, Year 13 free cash flow equals the free cash flow for Year 12 times the given growth rate; Year 18 free cash flow equals the free cash flow for Year 17 times the given growth rate.)

b. How do these valuations affect your advice to the management of MSC regarding the addition of gas stoves to its woodstove line?

12.16 FREE-CASH-FLOWS-BASED VALUATION. The Coca-Cola Company is a global soft drink beverage company (ticker symbol � KO) that is a primary and direct com- petitor with PepsiCo. The data in Exhibits 12.13–12.15 (see pages 980–983) include the actual amounts for 2006, 2007, and 2008 and projected amounts for Year �1 to Year �6 for the income statements, balance sheets, and statements of cash flows for Coca-Cola (in millions).

The market equity beta for Coca-Cola at the end of 2008 is 0.61. Assume that the risk-free interest rate is 4.0 percent and the market risk premium is 6.0 percent. Coca-Cola has 2,312 million shares outstanding at the end of 2008, when Coca-Cola’s share price was $44.42.

Required

Part I—Computing Coca-Cola’s Share Value Using Free Cash Flows to Common Equity Shareholders

a. Use the CAPM to compute the required rate of return on common equity capital for Coca-Cola.

b. Derive the projected free cash flows for common equity shareholders for Coca-Cola for Years �1 through �6 based on the projected financial statements. Assume that Coca-Cola’s changes in cash each year are necessary for operating liquidity purposes. The financial statement forecasts for Year �6 assume that Coca-Cola will experience a steady-state long-run growth rate of 3 percent in Year �6 and beyond.

c. Using the required rate of return on common equity from Part a as a discount rate, compute the sum of the present value of free cash flows for common equity share- holders for Coca-Cola for Years �1 through �5.

d. Using the required rate of return on common equity from Part a as a discount rate and the long-run growth rate from Part b, compute the continuing value of Coca- Cola as of the start of Year �6 based on Coca-Cola’s continuing free cash flows for common equity shareholders in Year �6 and beyond. After computing continuing value as of the start of Year �6, discount it to present value at the start of Year �1.

e. Compute the value of a share of Coca-Cola common stock. (1) Compute the total sum of the present value of all future free cash flows for equity shareholders (from Parts c and d). (2) Adjust the total sum of the present value using the midyear dis- counting adjustment factor. (3) Compute the per-share value estimate.

Part II—Computing Coca-Cola’s Share Value Using Free Cash Flows to All Debt and Equity Stakeholders

f. At the end of 2008, Coca-Cola had $9,312 million in outstanding interest-bear- ing short-term and long-term debt on the balance sheet and no preferred stock. Assume that the balance sheet value of Coca-Cola’s debt is approximately equal

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to the market value of the debt. The forecasts assume that Coca-Cola will face an interest rate of 4.5 percent on debt capital and that Coca-Cola’s average tax rate will be 23.2 percent (based on the past five-year average effective tax rate). Compute the weighted average cost of capital for Coca-Cola as of the start of Year �1.

g. Beginning with projected net cash flows from operations, derive the projected free cash flows for all debt and equity stakeholders for Coca-Cola for Years �1 through �6 based on the projected financial statements. Assume that the change in cash each year is related to operating liquidity needs.

h. Using the weighted average cost of capital from Part f as a discount rate, compute the sum of the present value of free cash flows for all debt and equity stakeholders for Coca-Cola for Years �1 through �5.

i. Using the weighted average cost of capital from Part f as a discount rate and the long-run growth rate from Part b, compute the continuing value of Coca-Cola as of the start of Year �6 based on Coca-Cola’s continuing free cash flows for all debt and equity stakeholders in Year �6 and beyond. After computing continuing value as of the start of Year �6, discount it to present value as of the start of Year �1.

j. Compute the value of a share of Coca-Cola common stock. (1) Compute the total value of Coca-Cola’s net operating assets using the total sum of the present value of free cash flows for all debt and equity stakeholders (from Parts h and i). (2) Subtract the value of outstanding debt to obtain the value of equity. (3) Adjust the present value of equity using the midyear discounting adjustment factor. (4) Compute the per-share value estimate of Coca-Cola’s common equity shares.

Note: Do not be alarmed if your share value estimate from Part e is slightly different from your share value estimate from Part j. The weighted average cost of capital computation in Part f used the weight of equity based on the market price of Coca-Cola’s stock at the end of 2008. The share value estimates from Parts e and j likely differ from the market price, so the weights used to compute the weighted average cost of capital are not internally consistent with the estimated share values.

Part III—Sensitivity Analysis and Recommendation

k. Using the free cash flows to common equity shareholders, recompute the value of Coca-Cola shares under two alternative scenarios. Scenario 1: Assume that Coca- Cola’s long-run growth will be 2 percent, not 3 percent as before, and assume that Coca-Cola’s required rate of return on equity is 1 percent higher than the rate you computed for Part a. Scenario 2: Assume that Coca-Cola’s long-run growth will be 4 percent, not 3 percent as before, and assume that Coca-Cola’s required rate of return on equity is 1 percent lower than the rate you computed in Part a. To quantify the sensitivity of your share value estimate for Coca-Cola to these variations in growth and discount rates, compare (in percentage terms) your value estimates under these two scenarios with your value estimate from Part e.

l. Using these data at the end of 2008, what reasonable range of share values would you have expected for Coca-Cola common stock? At that time, what was the market price for Coca-Cola shares relative to this range? What investment strategy (buy, hold, or sell) would you have recommended?

12.17 FREE-CASH-FLOWS-BASED VALUATION. In Problem 10.16, we pro- jected financial statements for Wal-Mart Stores, Inc. (Walmart) for Years �1 through �5. The data in Exhibits 12.16–12.18 (see pages 985–987) include the actual amounts for 2008 and the projected amounts for Year �1 to Year �5 for the income statements, balance sheets, and statements of cash flows for Walmart (in millions).

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980 Chapter 12 Valuation: Cash-Flow-Based Approaches

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7 3

In te

re st

e xp

en se

(2 2

0 )

(4 5

6 )

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8 )

(4 2

5 )

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2 )

(4 6

2 )

(4 8

2 )

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3 )

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8 )

In co

m e

(l o

ss )

fr o

m e

q u

it y

af fi

li at

1 0

6 6

(8 7

4 )

4 6

4 9

7 5

2 7

5 9

2 6

1 0

In co

m e

b ef

o re

T ax

6 ,5

7 8

7 ,8

7 3

7 ,4

3 9

9 ,1

7 5

9 ,6

3 1

$ 1

0 ,1

0 7

$ 1

0 ,6

0 7

$ 1

1 ,1

3 4

$ 1

1 ,4

6 8

In co

m e

ta x

ex p

en se

,4 9

8 )

(1 ,8

9 2

) (1

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(2 ,1

2 4

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,2 3

0 )

(2 ,3

4 0

) (2

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6 )

(2 ,5

7 8

) (2

,6 5

5 )

N et

I n

co m

e $

,0 8

0 $

,9 8

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,8 0

7 $

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1 $

,4 0

1 $

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7 $

,1 5

1 $

,5 5

6 $

,8 1

O th

er c

o m

p re

h en

si ve

i n

co m

e it

em s

6 6

6 1

,9 1

7 (3

,3 0

0 )

0 0

C o

m p

re h

en si

ve I

n co

m e

5 ,7

4 6

7 ,8

9 8

2 ,5

0 7

7 ,0

5 1

7 ,4

0 1

7 ,7

6 7

8 ,1

5 1

8 ,5

5 6

8 ,8

1 3

E X

H IB

IT 1

2 .1

Th e

C o ca

-C o la

C o m

p an

y In

co m

e St

at em

en ts

f o r

2 0 0 6 t

h ro

u gh

2 0 0 8 (

A ct

u al

) an

d Y

ea r

+ 1 t

h ro

u gh

+ 6 (

P ro

je ct

ed )

(a m

o u n ts

i n m

ill io

n s)

(P ro

b le

m 1

2 .1

6 )

CHE-WAHLEN-09-1211-012.qxd:. 6/30/10 3:12 PM Page 980

PR OP

ER TY

O F

CE NG

AG E

LE AR

NI NG

E X

H IB

IT 1

2 .1

Th e

C o ca

-C o la

C o m

p an

y B

al an

ce S

h ee

ts f

o r

2 0 0 6 t

h ro

u gh

2 0 0 8 (

A ct

u al

) an

d Y

ea r

+ 1 t

h ro

u gh

+ 6 (

P ro

je ct

ed )

(a m

o u n ts

i n m

ill io

n s)

(P ro

b le

m 1

2 .1

6 )

A ct

u al

s F

o re

ca st

2 0

0 6

0 0

2 0

0 8

ea r

+ 1

Y ea

r +

2 Y

ea r

+ 3

Y ea

r +

4 Y

ea r

+ 5

Y ea

r +

A S

S E

T S

C as

h a

n d

c as

h e

q u

iv al

en ts

2 ,4

4 0

4 ,0

9 3

4 ,7

0 1

,7 0

1 $

,7 0

1 $

,7 0

1 $

,7 0

1 $

,7 0

1 $

4 ,8

4 2

M ar

ke ta

b le

s ec

u ri

ti es

1 5

0 2

1 5

2 7

8 2

8 6

2 9

5 3

0 4

3 1

3 3

2 2

3 3

2 A

cc o

u n

ts r

ec ei

va b

le —

N et

2 ,5

8 7

3 ,3

1 7

3 ,0

9 0

3 ,7

1 0

3 ,4

3 0

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6 7

3 ,8

0 5

4 ,4

6 1

4 ,5

9 5

In ve

n to

ri es

1 ,6

4 1

2 ,2

2 0

2 ,1

8 7

2 ,3

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2 ,4

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2 ,5

5 6

2 ,6

6 1

2 ,8

1 7

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0 2

P re

p ai

d e

xp en

se s

an d

th er

c u

rr en

t as

se ts

1 ,6

2 3

2 ,2

6 0

1 ,9

2 0

2 ,0

1 6

2 ,1

1 7

2 ,2

2 3

2 ,3

3 4

2 ,4

5 0

2 ,5

2 4

C u

rr en

t A

ss et

s $

,4 4

1 $

1 2

,1 0

5 $

1 2

,1 7

6 $

1 3

,0 3

3 $

1 2

,9 5

5 $

1 3

,8 5

1 $

1 3

,8 1

3 $

1 4

,7 5

2 $

1 5

,1 9

L o

n g-

te rm

i n

ve st

m en

ts i

n a

ff il

ia te

s 6

,7 8

3 7

,7 7

7 5

,7 7

9 6

,1 2

6 6

,4 9

3 6

,8 8

3 7

,2 9

6 7

,7 3

4 7

,9 6

6 P

ro p

er ty

, p la

n t

& e

q u

ip m

en t—

A t

co st

1 1

,9 1

1 1

4 ,4

4 4

1 4

,4 0

0 1

6 ,1

9 1

1 8

,0 7

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0 ,0

4 5

2 2

,1 1

8 2

4 ,2

9 4

2 5

,0 2

3 (A

cc u

m u

la te

d d

ep re

ci at

io n

) (5

,0 0

8 )

(5 ,9

5 1

) (6

,0 7

4 )

(7 ,1

8 9

) (8

,4 3

3 )

(9 ,8

1 3

) (1

1 ,3

3 6

) (1

3 ,0

0 9

) (1

3 ,3

9 9

) A

m o

rt iz

ab le

i n

ta n

gi b

le a

ss et

s (n

et )

1 ,6

8 7

2 ,8

1 0

2 ,4

1 7

2 ,4

1 7

2 ,4

1 7

2 ,4

1 7

2 ,4

1 7

2 ,4

1 7

2 ,4

9 0

G o

o d

w il

l an

d n

o n

am o

rt iz

ab le

i n

ta n

gi b

le s

3 ,4

4 8

9 ,4

0 9

1 0

,0 8

8 1

0 ,5

9 2

1 1

,1 2

2 1

1 ,6

7 8

1 2

,2 6

2 1

2 ,8

7 5

1 3

,2 6

1 O

th er

n o

n -c

u rr

en t

as se

ts (

1 )

2 ,7

0 1

2 ,6

7 5

1 ,7

3 3

1 ,7

8 5

1 ,8

3 9

1 ,8

9 4

1 ,9

5 1

2 ,0

0 9

2 ,0

6 9

T o

ta l A

ss et

s $

2 9

,9 6

3 $

4 3

,2 6

9 $

4 0

,5 1

9 $

4 2

,9 5

5 $

4 4

,4 6

4 $

4 6

,9 5

4 $

4 8

,5 2

0 $

5 1

,0 7

2 $

5 2

,6 0

(C on

ti n

u ed

)

Questions, Exercises, Problems, and Cases 981

CHE-WAHLEN-09-1211-012.qxd:. 6/30/10 3:12 PM Page 981

PR OP

ER TY

O F

CE NG

AG E

LE AR

NI NG

A ct

u al

s F

o re

ca st

2 0

0 6

0 0

2 0

0 8

ea r

+ 1

Y ea

r +

2 Y

ea r

+ 3

Y ea

r +

4 Y

ea r

+ 5

Y ea

r +

L IA

B IL

IT IE

S A

cc o

u n

ts p

ay ab

le —

T ra

d e

9 2

9 $

,3 8

0 $

,3 7

0 $

,2 7

7 $

,4 9

2 $

,4 2

5 $

,6 2

8 $

,5 8

8 $

1 ,

6 3

6 C

u rr

en t

ac cr

u ed

l ia

b il

it ie

s 4

,1 2

6 5

,5 3

5 4

,8 3

5 5

,0 7

7 5

,3 3

1 5

,5 9

7 5

,8 7

7 6

,1 7

1 6

,3 5

6 N

o te

s p

ay ab

le a

n d

s h

o rt

-t er

m d

eb t

3 ,2

3 5

5 ,9

1 9

6 ,0

6 6

6 ,4

4 3

6 ,6

7 0

7 ,0

4 3

7 ,2

7 8

7 ,6

6 1

7 ,8

9 1

C u

rr en

t m

at u

ri ti

es o

f lo

n g-

te rm

d eb

t 3

3 1

3 3

4 6

5 3

0 5

3 2

2 3

3 3

3 5

1 3

6 1

3 7

2 In

co m

e ta

xe s

p ay

ab le

5 6

7 2

5 8

2 5

2 1

7 2

1 7

8 1

8 8

1 9

4 2

0 4

2 1

C u

rr en

t L

ia b

il it

ie s

8 ,8

9 0

$ 1

3 ,2

2 5

$ 1

2 ,9

8 8

$ 1

3 ,2

7 4

$ 1

3 ,9

9 2

$ 1

4 ,5

8 6

$ 1

5 ,3

2 7

$ 1

5 ,9

8 5

$ 1

6 ,4

6 5

L o

n g-

te rm

d eb

t 1

,3 1

4 3

,2 7

7 2

,7 8

1 2

,9 4

8 3

,0 5

2 3

,2 2

3 3

,3 3

0 3

,5 0

5 3

,6 1

0 D

ef er

re d

t ax

l ia

b il

it ie

s— N

o n

cu rr

en t

6 0

8 1

,8 9

0 8

7 7

9 3

0 9

6 2

1 ,0

1 6

1 ,0

5 0

1 ,1

0 5

1 ,1

3 9

O th

er n

o n

-c u

rr en

t li

ab il

it ie

s (1

) 2

,2 3

1 3

,1 3

3 3

,4 0

1 3

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1 3

,7 5

0 3

,9 3

7 4

,1 3

4 4

,3 4

1 4

,4 7

T o

ta l

L ia

b il

it ie

s $

1 3

,0 4

3 $

2 1

,5 2

5 $

2 0

,0 4

7 $

2 0

,7 2

3 $

2 1

,7 5

6 $

2 2

,7 6

2 $

2 3

,8 4

2 $

2 4

,9 3

6 $

2 5

,6 8

S H

A R

E H

O L

D E

R S

’ E Q

U IT

Y :

C o

m m

o n

s to

ck +

p ai

d -i

n c

ap it

al $

,8 6

1 $

,2 5

8 $

,8 4

6 $

,3 7

8 $

,7 0

7 $

1 0

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1 $

1 0

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3 $

1 1

,1 5

0 $

1 1

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4 R

et ai

n ed

e ar

n in

gs 3

3 ,4

6 8

3 6

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5 3

8 ,5

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3 9

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9 ,8

8 7

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3 ,0

4 9

A cc

u m

. o th

er c

o m

p re

h en

si ve

co m

e (l

o ss

) (1

,2 9

1 )

6 2

6 (2

,6 7

4 )

(2 ,6

7 4

) (2

,6 7

4 )

(2 ,6

7 4

) (2

,6 7

4 )

(2 ,6

7 4

) (2

,6 7

4 )

(T re

as u

ry s

to ck

) (2

2 ,1

1 8

) (2

3 ,3

7 5

) (2

4 ,2

1 3

) (2

4 ,2

1 3

) (2

4 ,2

1 3

) (2

4 ,2

1 3

) (2

4 ,2

1 3

) (2

4 ,2

1 3

) (2

4 ,9

3 9

)

C o

m m

o n

S h

ar eh

o ld

er s’

E q

u it

y $

1 6

,9 2

0 $

2 1

,7 4

4 $

2 0

,4 7

2 $

2 2

,2 3

2 $

2 2

,7 0

8 $

2 4

,1 9

2 $

2 4

,6 7

9 $

2 6

,1 3

5 $

2 6

,9 2

T o

ta l

L ia

b il

it ie

s an

d E

q u

it ie

s $

2 9

,9 6

$ 4

3 ,2

6 9

4 0

,5 1

9 $

4 2

,9 5

5 $

4 4

,4 6

$ 4

6 ,9

5 4

4 8

,5 2

0 $

5 1

,0 7

2 $

5 2

,6 0

982 Chapter 12 Valuation: Cash-Flow-Based Approaches

E X

H IB

IT 1

2 .1

4 (

C o

n ti

n u

e d

)

CHE-WAHLEN-09-1211-012.qxd:. 6/30/10 3:12 PM Page 982

PR OP

ER TY

O F

CE NG

AG E

LE AR

NI NG

E X

H IB

IT 1

2 .1

Th e

C o ca

-C o la

C o m

p an

y P ro

je ct

ed I

m p lie

d S

ta te

m en

ts o

f C

as h F

lo w

s fo

r Ye

ar �

1 t

h ro

u gh

� 6

(a m

o u n ts

i n m

ill io

n s)

(P ro

b le

m 1

2 .1

6 )

F o

re ca

st s

Y ea

r �

1 Y

ea r

� 2

Y ea

r �

3 Y

ea r

� 4

Y ea

r �

5 Y

ea r

� 6

IM P

L IE

D S

T A

T E

M E

N T

O F

C A

S H

F L

O W

S N

et I

n co

m e

$ 7

,0 5

1 $

7 ,4

0 1

$ 7

,7 6

7 $

8 ,1

5 1

$ 8

,5 5

6 $

8 ,8

1 3

A d

d b

ac k

d ep

re ci

at io

n e

xp en

se (

n et

) 1

,1 1

5 1

,2 4

4 1

,3 8

0 1

,5 2

3 1

,6 7

3 3

9 0

(I n

cr ea

se )

D ec

re as

e in

r ec

ei va

b le

s— N

et (6

2 0

) 2

8 0

(6 3

7 )

2 6

2 (6

5 6

) (1

3 4

) (I

n cr

ea se

) D

ec re

as e

in i

n ve

n to

ri es

(1 3

3 )

(9 3

) (1

4 4

) (1

0 4

) (1

5 6

) (8

5 )

(I n

cr ea

se )

D ec

re as

e in

p re

p ai

d e

xp en

se s

(9 6

) (1

0 1

) (1

0 6

) (1

1 1

) (1

1 7

) (7

4 )

In cr

ea se

( D

ec re

as e)

i n

a cc

o u

n ts

p ay

ab le

— T

ra d

e (9

3 )

2 1

5 (6

7 )

2 0

2 (4

0 )

4 8

In cr

ea se

( D

ec re

as e)

i n

c u

rr en

t ac

cr u

ed l

ia b

il it

ie s

2 4

2 2

5 4

2 6

7 2

8 0

2 9

4 1

8 5

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ea se

( D

ec re

as e)

i n

co m

e ta

xe s

p ay

ab le

(8 0

) 6

1 0

6 1

0 6

N et

c h

an ge

i n

d ef

er re

d t

ax a

ss et

s an

d l

ia b

il it

ie s

5 3

3 3

5 4

3 4

5 5

3 3

In cr

ea se

( D

ec re

as e)

i n

o th

er n

o n

-c u

rr en

t li

ab il

it ie

s 1

7 0

1 7

9 1

8 7

1 9

7 2

0 7

1 3

N et

C as

h F

lo w

s fr

o m

O p

er at

io n

s $

7 ,6

0 8

$ 9

,4 1

9 $

8 ,7

1 1

$ 1

0 ,4

4 0

$ 9

,8 2

6 $

9 ,3

1 3

(I n

cr ea

se )

D ec

re as

e in

p ro

p .,

p la

n t,

& e

q u

ip . a

t co

st (1

,7 9

1 )

(1 ,8

8 0

) (1

,9 7

4 )

(2 ,0

7 3

) (2

,1 7

7 )

(7 2

9 )

(I n

cr ea

se )

D ec

re as

e in

m ar

ke ta

b le

s ec

u ri

ti es

(8 )

(9 )

(1 0

) (I

n cr

ea se

) D

ec re

as e

in i

n ve

st m

en t

se cu

ri ti

es (3

4 7

) (3

6 8

) (3

9 0

) (4

1 3

) (4

3 8

) (2

3 2

) (I

n cr

ea se

) D

ec re

as e

in a

m o

rt iz

ab le

i n

ta n

gi b

le a

ss et

s (n

et )

0 0

0 (7

3 )

(I n

cr ea

se )

D ec

re as

e in

g o

o d

w il

l an

d n

o n

am o

rt . i

n ta

n g.

(5 0

4 )

(5 3

0 )

(5 5

6 )

(5 8

4 )

(6 1

3 )

(3 8

6 )

(I n

cr ea

se )

D ec

re as

e in

o th

er n

o n

-c u

rr en

t as

se ts

(5 2

) (5

4 )

(5 5

) (5

7 )

(5 9

) (6

0 )

N et

C as

h F

lo w

s fr

o m

I n

ve st

in g

$ (2

,7 0

2 )

$ (2

,8 3

9 )

$ (2

,9 8

4 )

$ (

3 ,1

3 6

) $

(3 ,2

9 5

) $

(1 ,4

9 0

)

In cr

ea se

( D

ec re

as e)

i n

s h

o rt

-t er

m d

eb t

2 1

7 2

4 3

3 8

4 2

5 2

3 9

3 2

4 1

In cr

ea se

( D

ec re

as e)

i n

l o

n g-

te rm

d eb

t 1

6 7

1 0

4 1

7 1

1 0

7 1

7 5

1 0

5 In

cr ea

se (

D ec

re as

e) i

n c

o m

m o

n s

to ck

+ p

ai d

-i n

c ap

it al

5 3

2 3

2 9

5 4

4 3

4 2

5 5

7 3

3 4

In cr

ea se

( D

ec re

as e)

i n

a cc

u m

. O C

I an

d o

th er

e q

u it

y ad

js .

0 0

In cr

ea se

( D

ec re

as e)

i n

t re

as u

ry s

to ck

0 0

0 (7

2 6

) D

iv id

en d

s (5

,8 2

2 )

(7 ,2

5 5

) (6

,8 2

6 )

(8 ,0

0 6

) (7

,6 5

6 )

(7 ,6

3 7

)

N et

C as

h F

lo w

s fr

o m

F in

an ci

n g

$ (4

,9 0

6 )

$ (6

,5 7

9 )

$ (5

,7 2

7 )

$ (

7 ,3

0 5

) $

(6 ,5

3 1

) $

(7 ,6

8 3

)

N et

C h

an ge

i n

C as

h $

— $

1 4

Questions, Exercises, Problems, and Cases 983

CHE-WAHLEN-09-1211-012.qxd:. 6/30/10 3:12 PM Page 983

PR OP

ER TY

O F

CE NG

AG E

LE AR

NI NG

984 Chapter 12 Valuation: Cash-Flow-Based Approaches

The market equity beta for Walmart at the end of Year 4 was 0.80. Assume that the risk-free inter- est rate was 3.5 percent and the market risk premium was 5.0 percent. Walmart had 3,925 million shares outstanding at the end of 2008. At the end of 2008, Walmart’s share price was $46.06.

Required

Part I—Computing Walmart’s Share Value Using Free Cash Flows to Common Equity Shareholders

a. Use the CAPM to compute the required rate of return on common equity capital for Walmart. b. Beginning with projected net cash flows from operations, derive the projected free cash flows

for common equity shareholders for Walmart for Years �1 through �5 based on the pro- jected financial statements. Assume that Walmart uses any change in cash each year for oper- ating liquidity purposes.

c. Project the continuing free cash flow for common equity shareholders in Year �6. Assume that the steady-state long-run growth rate will be 3 percent in Year �6 and beyond. Project that the Year �5 income statement and balance sheet amounts will grow by 3 percent in Year �6; then derive the projected statement of cash flows for Year �6. Derive the projected free cash flow for common equity shareholders in Year �6 from the projected statement of cash flows for Year �6.

d. Using the required rate of return on common equity from Part a as a discount rate, compute the sum of the present value of free cash flows for common equity shareholders for Walmart for Years �1 through �5.

e. Using the required rate of return on common equity from Part a as a discount rate and the long-run growth rate from Part c, compute the continuing value of Walmart as of the start of Year �6 based on Walmart’s continuing free cash flows for common equity shareholders in Year �6 and beyond. After computing continuing value as of the start of Year �6, discount it to present value at the start of Year �1.

f. Compute the value of a share of Walmart common stock. (1) Compute the total sum of the present value of all future free cash flows for equity shareholders (from Parts d and e). (2) Adjust the total sum of the present value using the midyear discounting adjustment factor. (3) Compute the per-share value estimate.

Note: If you worked Problem 11.14 in Chapter 11 and computed Walmart’s share value using the dividends valuation approach, compare your value estimate from that problem with the value esti- mate you obtain here. They should be the same.

Part II—Computing Walmart’s Share Value Using Free Cash Flows to All Debt and Equity Stakeholders

g. At the end of 2008, Walmart had $42,218 million in outstanding interest-bearing short-term and long-term debt on the balance sheet and no preferred stock. Assume that the balance sheet value of Walmart’s debt is approximately equal to the market value of the debt. During 2008, Walmart’s income statement included interest expense of $2,184 million. During 2008, Walmart faced an average interest expense of roughly 5.0 percent. Assume that at the start of Year �1, Walmart will continue to incur interest expense of 5.0 percent on debt capital and that Walmart’s average tax rate will be 34.2 percent. Compute the weighted average cost of capital for Walmart as of the start of Year �1.

h. Beginning with projected net cash flows from operations, derive the projected free cash flows for all debt and equity stakeholders for Walmart for Years �1 through �5 based on the pro- jected financial statements.

i. Project the continuing free cash flows for all debt and equity stakeholders in Year �6. Use the projected financial statements for Year �6 from Part c to derive the projected free cash flow for all debt and equity stakeholders in Year �6.

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Questions, Exercises, Problems, and Cases 985

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Questions, Exercises, Problems, and Cases 987

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988 Chapter 12 Valuation: Cash-Flow-Based Approaches

j. Using the weighted average cost of capital from Part g as a discount rate, compute the sum of the present value of free cash flows for all debt and equity stakeholders for Walmart for Years �1 through �5.

k. Using the weighted average cost of capital from Part g as a discount rate and the long-run growth rate from Part c, compute the continuing value of Walmart as of the start of Year �6 based on Walmart’s continuing free cash flows for all debt and equity stakeholders in Year �6 and beyond. After computing continuing value as of the start of Year �6, discount it to present value as of the start of Year �1.

l. Compute the value of a share of Walmart common stock. (1) Compute the total value of Walmart’s net operating assets using the total sum of the present value of free cash flows for all debt and equity stakeholders (from Parts j and k). (2) Subtract the value of outstanding debt to obtain the value of equity. (3) Adjust the present value of equity using the midyear discounting adjustment factor. (4) Compute the per-share value estimate of Walmart’s common equity shares.

Note: Do not be alarmed if your share value estimate from Part f is slightly different from your share value estimate from Part l. The weighted average cost of capital computation in Part g used the weight of equity based on the market price of Walmart’s stock at the end of 2008. The share value estimates from Parts f and l likely differ from the market price, so the weights used to compute the weighted average cost of capital are not internally consistent with the estimated share values.

Part III—Sensitivity Analysis and Recommendation

m. Using the free cash flows to common equity shareholders, recompute the value of Walmart shares under two alternative scenarios. Scenario 1: Assume that Walmart’s long-run growth will be 2 percent, not 3 percent as before, and assume that Walmart’s required rate of return on equity is 1 percentage point higher than the rate you computed using the CAPM in Part a. Scenario 2: Assume that Walmart’s long- run growth will be 4 percent, not 3 percent as before, and assume that Walmart’s required rate of return on equity is 1 percentage point lower than the rate you com- puted using the CAPM in Part a. To quantify the sensitivity of your share value esti- mate for Walmart to these variations in growth and discount rates, compare (in percentage terms) your value estimates under these two scenarios with your value estimate from Part f.

n. Using these data at the end of Year 4, what reasonable range of share values would you have expected for Walmart common stock? At that time, what was the market price for Walmart shares relative to this range? What would you have recommended?

INTEGRATIVE CASE 12.1

STARBUCKS

Free Cash Flows Valuation of Starbucks’ Common Equity In Integrative Case 10.1, we projected financial statements for Starbucks for Years �1 through �5. In this portion of the Starbucks Integrative Case, we use the projected finan- cial statements from Integrative Case 10.1 and apply the techniques in Chapter 12 to com- pute Starbucks’ required rate of return on equity and share value based on the free cash flows valuation model. We also compare our value estimate to Starbucks’ share price at the time of the case development to provide an investment recommendation.

The market equity beta for Starbucks at the end of 2008 is 0.58. Assume that the risk- free interest rate is 4.0 percent and the market risk premium is 6.0 percent. Starbucks has

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Starbucks 989

735.5 million shares outstanding at the end of 2008. At the start of Year �1, Starbucks’ share price was $14.17.

Required

Part I—Computing Starbucks’ Share Value Using Free Cash Flows to Common Equity Shareholders

a. Use the CAPM to compute the required rate of return on common equity capital for Starbucks.

b. Using your projected financial statements from Integrative Case 10.1 for Starbucks, begin with projected net cash flows from operations and derive the projected free cash flows for common equity shareholders for Starbucks for Years �1 through �5. You must determine whether your projected changes in cash are necessary for oper- ating liquidity purposes.

d. Using the required rate of return on common equity from Part a as a discount rate, compute the sum of the present value of free cash flows for common equity share- holders for Starbucks for Years �1 through �5.

e. Using the required rate of return on common equity from Part a as a discount rate and the long-run growth rate from Part c, compute the continuing value of Starbucks as of the start of Year �6 based on Starbucks’ continuing free cash flows for common equity shareholders in Year �6 and beyond. After computing continuing value as of the start of Year �6, discount it to present value at the start of Year �1.

f. Compute the value of a share of Starbucks common stock. (1) Compute the total sum of the present value of free cash flows for equity shareholders (from Parts d and e). (2) Adjust the total sum of the present value using the midyear discounting adjust- ment factor. (3) Compute the per-share value estimate.

Note: If you worked Integrative Case 11.1 from Chapter 11 and computed Starbucks’ share value using the dividends valuation approach, compare your value estimate from that case with the value estimate you obtain here. They should be the same.

Part II—Computing Starbucks’ Share Value Using Free Cash Flows to All Debt and Equity Stakeholders

g. At the end of 2008, Starbucks had $1,263 million in outstanding interest-bearing short-term and long-term debt on the balance sheet and no preferred stock. Assume that the balance sheet value of Starbucks’ debt equals the market value of the debt. Starbucks faces an interest rate of roughly 6.25 percent on its outstanding debt. Assume that Starbucks will continue to face the same interest rate on this outstand- ing debt capital over the remaining life of the debt. Using the amounts on Starbucks’ 2008 income statement in Exhibit 1.27 for Integrative Case 1.1 in Chapter 1, com- pute Starbucks’ average tax rate in 2008. Assume that Starbucks will continue to face the same income tax rate over the forecast horizon. Compute the weighted average cost of capital for Starbucks as of the start of Year �1. Compare your computation of Starbucks’ weighted average cost of capital with your estimate of Starbucks’ required return on equity from Part a. Why do the two amounts differ?

h. Based on your projections of Starbucks’ financial statements, begin with projected net cash flows from operations and derive the projected free cash flows for all debt

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990 Chapter 12 Valuation: Cash-Flow-Based Approaches

and equity stakeholders for Years �1 through �5. Compare your forecasts of Starbucks’ free cash flows for all debt and equity stakeholders Years �1 through �5 with your forecast of Starbucks’ free cash flows for equity shareholders in Part b. Why are the amounts not identical—what causes the difference each year?

i. Project the continuing free cash flows for all debt and equity stakeholders in Year �6. Use the projected financial statements for Year �6 from Part c to derive the pro- jected free cash flow for all debt and equity stakeholders in Year �6.

j. Using the weighted average cost of capital from Part g as a discount rate, compute the sum of the present value of free cash flows for all debt and equity stakeholders for Starbucks for Years �1 through �5.

k. Using the weighted average cost of capital from Part g as a discount rate and the long-run growth rate from Part c, compute the continuing value of Starbucks as of the start of Year �6 based on Starbucks’ continuing free cash flows for all debt and equity stakeholders in Year �6 and beyond. After computing continuing value as of the start of Year �6, discount it to present value at the start of Year �1.

l. Compute the value of a share of Starbucks common stock. (1) Compute the value of Starbucks’ net operating assets using the total sum of the present value of free cash flows for all debt and equity stakeholders (from Parts j and k). (2) Subtract the value of outstanding debt to obtain the value of equity. (3) Adjust the present value of equity using the midyear discounting adjustment factor. (4) Compute the per-share value estimate.

m. Compare your share value estimate from Part f with your share value estimate from Part l. These values should be similar.

Part III—Sensitivity Analysis and Recommendation

n. Using the free cash flows to common equity shareholders, recompute the value of Starbucks shares under two alternative scenarios. Scenario 1: Assume that Starbucks’ long-run growth will be 2 percent, not 3 percent as before, and assume that Starbucks’ required rate of return on equity is 1 percentage point higher than the rate you computed using the CAPM in Part a. Scenario 2: Assume that Starbucks’ long-run growth will be 4 percent, not 3 percent as before, and assume that Starbucks’ required rate of return on equity is 1 percentage point lower than the rate you computed using the CAPM in Part a. To quantify the sensitivity of your share value estimate for Starbucks to these variations in growth and discount rates, com- pare (in percentage terms) your value estimates under these two scenarios with your value estimate from Part f.

o. At the end of 2008, what reasonable range of share values would you have expected for Starbucks common stock? At that time, where was the market price for Starbucks shares relative to this range? What would you have recommended?

p. If you computed Starbucks’ common equity share value using the dividends-valua- tion approach in Integrative Case 11.1, compare the value estimate you obtained in that case with the estimate you obtained in this case. They should be identical.

CASE 12.2

HOLMES CORPORATION: LBO VALUATION Holmes Corporation is a leading designer and manufacturer of material handling and process equipment for heavy industry in the United States and abroad. Its sales have more

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Holmes Corporation: LBO Valuation 991

than doubled and its earnings have increased more than sixfold in the past five years. In material handling, Holmes is a major producer of electric overhead and gantry cranes, ranging from 5 tons in capacity to 600-ton giants, the latter used primarily in nuclear and conventional power-generating plants. It also builds underhung cranes and monorail sys- tems for general industrial use carrying loads up to 40 tons, railcar movers, railroad and mass transit shop maintenance equipment, and a broad line of advanced package convey- ors. Holmes is a world leader in evaporation and crystallization systems and furnishes dry- ers, heat exchangers, and filters to complete its line of chemical processing equipment sold internationally to the chemical, fertilizer, food, drug, and paper industries. For the metal- lurgical industry, it designs and manufactures electric arc and induction furnaces, cupolas, ladles, and hot metal distribution equipment.

The information below and on the following pages appears in the Year 15 annual report of Holmes Corporation.

Highlights

Year 15 Year 14

Net Sales $102,698,836 $109,372,718 Net Earnings 6,601,908 6,583,360 Net Earnings per Share 3.62* 3.61* Cash Dividends Paid 2,241,892 1,426,502 Cash Dividends per Share 1.22* 0.78* Shareholders’ Equity 29,333,803 24,659,214 Shareholders’ Equity per Share 16.07* 13.51* Working Capital 23,100,863 19,029,626 Orders Received 95,436,103 80,707,576 Unfilled Orders at End of Period 77,455,900 84,718,633 Average Number of Common Shares

Outstanding during Period 1,824,853* 1,824,754*

*Adjusted for June, Year 15, and June, Year 14, 5-for-4 stock distributions.

Net Sales, Net Earnings, and Net Earnings per Share by Quarter (adjusted for 5-for-4 stock distribution in June, Year 15, and June, Year 14)

Year 15 Year 14

Net Net Per Net Net Per Sales Earnings Share Sales Earnings Share

First Quarter $ 25,931,457 $1,602,837 $0.88 $ 21,768,077 $1,126,470 $0.62 Second Quarter 24,390,079 1,727,112 0.95 28,514,298 1,716,910 0.94 Third Quarter 25,327,226 1,505,118 0.82 28,798,564 1,510,958 0.82 Fourth Quarter 27,050,074 1,766,841 0.97 30,291,779 2,229,022 1.23

$102,698,836 $6,601,908 $3.62 $109,372,718 $6,583,360 $3.61

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Common Stock Prices and Cash Dividends Paid per Common Share by Quarter (adjusted for 5-for-4 stock distribution in June, Year 15, and June, Year 14)

Year 15 Year 14 Cash Cash

Stock Prices Dividends Stock Prices Dividends High Low per Share High Low per Share

First Quarter $22 1 ⁄ 2

$18 1 ⁄ 2

$0.26 $11 1 ⁄ 4

$ 9 1 ⁄ 2

$0.16 Second Quarter 25

1 ⁄ 4

19 1 ⁄ 2

0.26 12 3 ⁄ 8

8 7 ⁄ 8

0.16 Third Quarter 26

1 ⁄ 4

19 3 ⁄ 4

0.325 15 7 ⁄ 8

11 5 ⁄ 8

0.20 Fourth Quarter 28

1 ⁄ 8

23 1 ⁄ 4

0.375 20 7 ⁄ 8

15 7 ⁄ 8

0.26 $1.22 $0.78

Management’s Report to Shareholders Year 15 was a pleasant surprise for all of us at Holmes Corporation. When the year started, it looked as though Year 15 would be a good year but not up to the record performance of Year 14. However, due to the excellent performance of our employees and the benefit of a favorable acquisition, Year 15 produced both record earnings and the largest cash dividend outlay in the company’s 93-year history.

There is no doubt that some of the attractive orders received in late Year 12 and early Year 13 contributed to Year 15 profit. But of major significance was our organization’s favorable response to several new management policies instituted to emphasize higher cor- porate profitability. Year 15 showed a net profit on net sales of 6.4 percent, which not only exceeded the 6.0 percent of last year but represents the highest net margin in several decades.

Net sales for the year were $102,698,836, down 6 percent from the $109,372,718 of a year ago but still the second largest volume in our history. Net earnings, however, set a new record at $6,601,908, or $3.62 per common share, which slightly exceeded the $6,583,360, or $3.61 per common share earned last year.

Cash dividends of $2,241,892 paid in Year 15 were 57 percent above the $1,426,502 paid a year ago. The record total resulted from your Board’s approval of two increases during the year. When we implemented the 5-for-4 stock distribution in June, Year 15, we maintained the quarterly dividend rate of $0.325 on the increased number of shares for the January payment. Then, in December, Year 15, we increased the quarterly rate to $0.375 per share.

Year 15 certainly was not the most exuberant year in the capital equipment markets. Fortunately, our heavy involvement in ecology improvement, power generation, and inter- national markets continued to serve us well, with the result that new orders of $95,436,103 were 18 percent over the $80,707,576 of Year 14.

Economists have predicted a substantial capital spending upturn for well over a year, but, so far, our customers have displayed stubborn reluctance to place new orders amid the uncertainty concerning the economy. Confidence is the answer. As soon as potential buyers can see clearly the future direction of the economy, we expect the unleashing of a large latent demand for capital goods, producing a much-expanded market for Holmes’ products.

Fortunately, the accelerating pace of international markets continues to yield new busi- ness. Year 15 was an excellent year on the international front as our foreign customers continue to recognize our technological leadership in several product lines. Net sales of

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Holmes products shipped overseas and fees from foreign licensees amounted to $30,495,041, which represents a 31 percent increase over the $23,351,980 of a year ago.

Management fully recognizes and intends to take maximum advantage of our technolog- ical leadership in foreign lands. The latest manifestation of this policy was the acquisition of a controlling interest in Societé Francaise Holmes Fermont, our Swenson process equipment licensee located in Paris. Holmes and a partner started this firm 14 years ago as a sales and engineering organization to function in the Common Market. The company currently operates in the same mode. It owns no physical manufacturing assets, subcontracting all production. Its markets have expanded to include Spain and the East European countries.

Holmes Fermont is experiencing strong demand in Europe. For example, in early May, a $5.5 million order for a large potash crystallization system was received from a French engineering company representing a Russian client. Management estimates that Holmes Fermont will contribute approximately $6 to $8 million of net sales in Year 16.

Holmes’ other wholly owned subsidiaries—Holmes Equipment Limited in Canada, Ermanco Incorporated in Michigan, and Holmes International, Inc., our FSC (Foreign Sales Corporation)—again contributed substantially to the success of Year 15. Holmes Equipment Limited registered its second best year. However, capital equipment markets in Canada have virtually come to a standstill in the past two quarters. Ermanco achieved the best year in its history, while Holmes International, Inc. had a truly exceptional year because of the very high level of activity in our international markets.

The financial condition of the company showed further improvement and is now unusually strong as a result of very stringent financial controls. Working capital increased to $23,100,863 from $19,029,626, a 21 percent improvement. Inventories decreased 6 per- cent from $18,559,231 to $17,491,741. The company currently has no long-term or short- term debt, and has considerable cash in short-term instruments. Much of our cash position, however, results from customers’ advance payments which we will absorb as we make shipments on the contracts. Shareholders’ equity increased 19 percent to $29,393,803 from $24,690,214 a year ago.

Plant equipment expenditures for the year were $1,172,057, down 18 percent from $1,426,347 of Year 14. Several appropriations approved during the year did not require expenditures because of delayed deliveries beyond Year 15. The major emphasis again was on our continuing program of improving capacity and efficiency through the purchase of numerically controlled machine tools. We expanded the Ermanco plant by 50 percent, but since this is a leasehold arrangement, we made only minor direct investment. We also improved the Canadian operation by adding more manufacturing space and installing energy-saving insulation.

Labor relations were excellent throughout the year. The Harvey plant continues to be nonunion. We negotiated a new labor contract at the Canadian plant, which extends to March 1, Year 17. The Pioneer Division in Alabama has a labor contract that does not expire until April, Year 16. While the union contract at Ermanco expired June 1, Year 15, work con- tinues while negotiation proceeds on a new contract. We anticipate no difficulty in reach- ing a new agreement.

We exerted considerable effort during the year to improve Holmes’ image in the invest- ment community. Management held several informative meetings with security analyst groups to enhance the awareness of our activities and corporate performance.

The outlook for Year 16, while generally favorable, depends in part on the course of capital spending over the next several months. If the spending rate accelerates, the quickening pace of new orders, coupled with present backlogs, will provide the conditions for another fine year. On the other hand, if general industry continues the reluctant spending pattern of the last two years, Year 16 could be a year of maintaining market positions while awaiting better market conditions. Management takes an optimistic view and thus looks for a successful Year 16.

Holmes Corporation: LBO Valuation 993

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The achievement of record earnings and the highest profit margin in decades demon- strates the capability and the dedication of our employees. Management is most grateful for their efforts throughout the excellent year.

T. R. Varnum T. L. Fuller President Chairman March 15, Year 16

Review of Operations Year 15 was a very active year although the pace was not at the hectic tempo of Year 14. It was a year that showed continued strong demand in some product areas but a dampened rate in others. The product areas that had some special economic circumstances enhancing demand fared well. For example, the continuing effort toward ecological improvement fos- tered excellent activity in Swenson process equipment. Likewise, the energy concern and the need for more electrical power generation capacity boded well for large overhead cranes. On the other hand, Holmes’ products that relate to general industry and depend on the overall capital spending rate for new equipment experienced lesser demand, resulting in lower new orders and reduced backlogs. The affected products were small cranes, under- hung cranes, railcar movers, and metallurgical equipment.

Year 15 was the first full year of operations under some major policy changes instituted to improve Holmes’ profitability. The two primary revisions were the restructuring of our marketing effort along product division lines, and the conversion of the product division incentive plans to a profit-based formula. The corporate organization adapted extremely well to the new policies. The improved profit margin in Year 15, in substantial part, was a result of the changes.

International activity increased markedly during the year. Surging foreign business and the expressed objective to capitalize on Holmes’ technological leadership overseas resulted in the elevation of Mr. R. E. Foster to officer status as Vice President-International. The year involved heavy commitments of the product division staffs, engineering groups, and manu- facturing organization to such important contracts as the $14 million Swenson order for Poland, the $8 million Swenson project for Mexico, the $2 million crane order for Venezuela, and several millions of dollars of railcar movers for all areas of the world.

The acquisition of control and commencement of operating responsibility of Societé Francaise Holmes Fermont, the Swenson licensee in Paris, was a major milestone in our international strategy. This organization has the potential of becoming a very substantial contributor in the years immediately ahead. Its long-range market opportunities in Europe and Asia are excellent.

Material Handling Products Material handling equipment activities portrayed conflicting trends. During the year, when total backlog decreased, the crane division backlog increased. This was a result of several multimillion dollar contracts for power plant cranes. The small crane market, on the other hand, experienced depressed conditions during most of the year as general industry with- held appropriations for new plant and equipment. The underhung crane market experi- enced similar conditions. However, as Congressional attitudes and policies on investment unfold, we expect capital spending to show a substantial upturn.

The Transportation Equipment Division secured the second order for orbital service bridges, a new product for the containment vessels of nuclear power plants. This design is unique and allows considerable cost savings in erecting and maintaining containment shells.

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The Ermanco Conveyor Division completed its best year with the growing acceptance of the unique XenoROL design. We expanded the Grand Haven plant by 50 percent to effect further cost reduction and new concepts of marketing.

The railcar moving line continued to produce more business from international mar- kets. We installed the new 11TM unit in six domestic locations, a product showing signs of exceptional performance. We shipped the first foreign 11TM machine to Sweden.

Process Equipment Products Process equipment again accounted for slightly more than half of the year’s business.

Swenson activity reached an all-time high level with much of the division’s effort going into international projects. The large foreign orders required considerable additional work to cover the necessary documentation, metrification when required, and general liaison.

We engaged in considerably more subcontracting during the year to accommodate one- piece shipment of the huge vessels pioneered by Swenson to effect greater equipment economies. The division continued to expand the use of computerization for design work and contract administration. We developed more capability during the year to handle the many additional tasks associated with turnkey projects. Swenson research and development efforts accelerated in search of better technology and new products. We conducted pilot plant test work at our facilities and in the field to convert several sales prospects into new contracts.

The metallurgical business proceeded at a slower pace in Year 15. However, with construction activity showing early signs of improvement, and automotive and farm machinery manufacturers increasing their operating rates, we see intensified interest in metallurgical equipment.

Financial Statements The financial statements of Holmes Corporation and related notes appear in Exhibits 12.19–12.21 (see pages 996–998). Exhibit 12.22 (see page 999) presents five-year summary operating information for Holmes.

Notes to Consolidated Financial Statements Year 15 and Year 14

Note A—Summary of Significant Accounting Policies. Significant accounting policies con- sistently applied appear below to assist the reader in reviewing the company’s consolidated financial statements contained in this report.

Consolidation—The consolidated financial statements include the accounts of the com- pany and its subsidiaries after eliminating all intercompany transactions and balances.

Inventories—Inventories generally appear at the lower of cost or market, with cost determined principally on a first-in, first-out method.

Property, plant, and equipment—Property, plant, and equipment appear at acquisition cost less accumulated depreciation. When the company retires or disposes of properties, it removes the related costs and accumulated depreciation from the respective accounts and credits, or charges any gain or loss to earnings. The company expenses maintenance and repairs as incurred. It capitalizes major betterments and renewals. Depreciation results from applying the straight-line method over the estimated useful lives of the assets as follows:

Buildings 30 to 45 years Machinery and equipment 4 to 20 years Furniture and fixtures 10 years

Holmes Corporation: LBO Valuation 995

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996 Chapter 12 Valuation: Cash-Flow-Based Approaches

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E X H I B I T 1 2 . 2 0

Holmes Corporation Income Statement

(amounts in thousands) (Case 12.2)

Year 11 Year 12 Year 13 Year 14 Year 15

Sales $ 41,428 $ 53,541 $ 76,328 $109,373 $102,699 Other revenues and gains 0 41 0 0 211 Cost of goods sold (33,269) (43,142) (60,000) (85,364) (80,260) Selling and administrative expense (6,175) (7,215) (9,325) (13,416) (12,090) Other expenses and losses (2) 0 (11) (31) (1)

Operating Income $ 1,982 $ 3,225 $ 6,992 $ 10,562 $ 10,559 Interest expense (43) (21) (284) (276) (13) Income tax expense (894) (1,471) (2,992) (3,703) (3,944)

Net Income $ 1,045 $ 1,733 $ 3,716 $ 6,583 $ 6,602

Holmes Corporation: LBO Valuation 997

Intangible assets—The company has amortized the unallocated excess of cost of a sub- sidiary over net assets acquired (that is, goodwill) over a 17-year period. Beginning in Year 16, GAAP no longer requires amortization of goodwill.

Research and development costs—The company charges research and development costs to operations as incurred ($479,410 in Year 15, and $467,733 in Year 14).

Pension plans—The company and its subsidiaries have noncontributory pension plans covering substantially all of their employees. The company’s policy is to fund accrued pen- sion costs as determined by independent actuaries. Pension costs amounted to $471,826 in Year 15, and $366,802 in Year 14.

Revenue recognition—The company generally recognizes income on a percentage-of- completion basis. It records advance payments as received and reports them as a deduction from billings when earned. The company recognizes royalties, included in net sales, as income when received. Royalties total $656,043 in Year 15, and $723,930 in Year 14.

Income taxes—The company provides no income taxes on unremitted earnings of for- eign subsidiaries since it anticipates no significant tax liabilities should foreign units remit such earnings. The company makes provision for deferred income taxes applicable to tim- ing differences between financial statement and income tax accounting, principally on the earnings of a foreign sales subsidiary which existing statutes defer in part from current taxation. Note B—Foreign Operations. The consolidated financial statements in Year 15 include net assets of $2,120,648 ($1,847,534 in Year 14), undistributed earnings of $2,061,441 ($1,808,752 in Year 14), sales of $7,287,566 ($8,603,225 in Year 14), and net income of $454,999 ($641,454 in Year 14) applicable to the Canadian subsidiary.

The company translates balance sheet accounts of the Canadian subsidiary into U.S. dol- lars at the exchange rates at the end of the year, and operating results at the average of exchange rates for the year.

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998 Chapter 12 Valuation: Cash-Flow-Based Approaches

E X H I B I T 1 2 . 2 1

Holmes Corporation Statement of Cash Flows (amounts in thousands)

(Case 12.2)

Year 11 Year 12 Year 13 Year 14 Year 15

OPERATIONS Net income $ 1,045 $ 1,733 $ 3,716 $ 6,583 $ 6,602 Depreciation and amortization 491 490 513 586 643 Other addbacks 20 25 243 151 299 Other subtractions 0 0 0 0 (97) (Increase) Decrease in receivables (750) (2,424) (3,589) (5,452) 4,456 (Increase) Decrease in inventories (1,387) (4,111) (7,629) 1,867 1,068 Increase (Decrease) accounts

payable—Trade 1,228 2,374 1,393 1,496 (2,608) Increase (Decrease) in other

current liabilities 473 2,865 4,737 1,649 (1,509)

Cash Flow from Operations $ 1,120 $ 952 $ (616) $ 6,880 $ 8,854

INVESTING Fixed assets acquired, net $ (347) $ (849) $ (749) $(1,426) $(1,172) Investments acquired 0 0 0 0 (3,306) Other investing transactions 45 0 81 (64) 39

Cash Flow from Investing $ (302) $ (849) $ (668) $(1,490) $(4,439)

FINANCING Increase in short-term borrowing $ 0 $ 700 $ 2,800 $ 0 $ 0 Decrease in short-term borrowing 0 0 0 (3,500) 0 Increase in long-term borrowing 0 0 0 0 0 Decrease in long-term borrowing (170) (170) (170) (170) (170) Issue of capital stock 0 0 0 0 315 Acquisition of capital stock (27) 0 0 0 0 Dividends (614) (730) (964) (1,427) (2,243) Other financing transactions 0 0 0 0 0

Cash Flow from Financing $ (811) $ (200) $ 1,666 $(5,097) $(2,098)

Net Change in Cash $ 7 $ (97) $ 382 $ 293 $ 2,317 Cash, beginning of year 955 962 865 1,247 1,540

Cash, End of Year $ 962 $ 865 $ 1,247 $ 1,540 $ 3,857

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Holmes Corporation: LBO Valuation 999

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1000 Chapter 12 Valuation: Cash-Flow-Based Approaches

Note C—Inventories. Inventories used in determining cost of sales appear below:

Year 15 Year 14 Year 13

Raw materials and supplies $ 8,889,147 $ 9,720,581 $ 8,900,911 Work in process 8,602,594 8,838,650 11,524,805

Total inventories $17,491,741 $18,559,231 $20,425,716

Note D—Short-Term Borrowing. The company has short-term credit agreements which principally provide for loans of 90-day periods at varying interest rates. There were no bor- rowings in Year 15. In Year 14, the maximum borrowing at the end of any calendar month was $4,500,000 and the approximate average loan balance and weighted average interest rate, computed by using the days outstanding method, was $3,435,000 and 7.6 percent. There were no restrictions upon the company during the period of the loans and no com- pensating bank balance arrangements required by the lending institutions. Note E—Income Taxes. Provision for income taxes consists of:

Year 15 Year 14

Current Federal $2,931,152 $2,633,663 State 466,113 483,240 Canadian 260,306 472,450

Total current provision $3,657,571 $3,589,353

Deferred Federal $ 263,797 $ 91,524 Canadian 22,937 21,706

Total deferred $ 286,734 $ 113,230

Total provision for income taxes $3,944,305 $3,702,583

Reconciliation of the total provision for income taxes to the current federal statutory rate of 35 percent is as follows:

Year 15 Year 14

Amount % Amount %

Tax at statutory rate $3,691,000 35.0% $3,600,100 35.0% State taxes, net of U.S. tax credit 302,973 2.9 314,106 3.1 All other items (49,668) (.5) (211,623) (2.1)

Total provision for income taxes $3,944,305 37.4% $3,702,583 36.0%

Note F—Pensions. The components of pension expense appear below:

Year 15 Year 14

Service cost $476,490 $429,700 Interest cost 567,159 446,605 Expected return on pension investments (558,373) (494,083) Amortization of actuarial gains and losses (13,450) (15,420)

Pension expense $471,826 $366,802

The funded status of the pension plan appears on the next page.

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December 31:

Year 15 Year 14

Accumulated benefit obligation $5,763,450 $5,325,291 Effect of salary increases 1,031,970 976,480

Projected benefit obligation $6,795,420 $6,301,771 Pension fund assets 6,247,940 5,583,730

Excess pension obligation $ 547,480 $ 718,041

Assumptions used in accounting for pensions appear below:

Year 15 Year 14

Expected return on pension assets 10% 10% Discount rate for projected benefit obligation 9% 8% Salary increases 5% 5%

Note G—Common Stock. As of March 20, Year 15, the company increased the authorized number of shares of common stock from 1,800,000 shares to 5,000,000 shares.

On December 29, Year 15, the company increased its equity interest (from 45 percent to 85 percent) in Societé Francaise Holmes Fermont, a French affiliate, in exchange for 18,040 of its common shares in a transaction accounted for as a purchase. The company credited the excess of the fair value ($224,373) of the company’s shares issued over their par value ($90,200) to additional contributed capital. The excess of the purchase cost over the under- lying value of the assets acquired was insignificant.

The company made a 25 percent common stock distribution on June 15, Year 14, and on June 19, Year 15, resulting in increases of 291,915 shares in Year 14 and 364,433 shares in Year 15, respectively. We capitalized the par value of these additional shares by a transfer of $1,457,575 in Year 14 and $1,822,165 in Year 15 from retained earnings to the common stock account. In Year 14 and Year 15, we paid cash of $2,611 and $15,340, respectively, in lieu of fractional share interests.

In addition, the company retired 2,570 shares of treasury stock in June, Year 14. The earnings and dividends per share for Year 14 and Year 15 in the accompanying consolidated financial statements reflect the 25 percent stock distributions. Note H—Contingent Liabilities. The company has certain contingent liabilities with respect to litigation and claims arising in the ordinary course of business. The company cannot determine the ultimate disposition of these contingent liabilities but, in the opinion of management, they will not result in any material effect upon the company’s consolidated financial position or results of operations.

Note I—Quarterly Data (unaudited). Quarterly sales, gross profit, net earnings, and earnings

per share for Year 15 appear below (first quarter results restated for 25 percent stock distribution):

Net Gross Net Earnings Sales Profit Earnings per Share

First $ 25,931,457 $ 5,606,013 $1,602,837 $0.88 Second 24,390,079 6,148,725 1,727,112 0.95 Third 25,327,226 5,706,407 1,505,118 0.82 Fourth 27,050,074 4,977,774 1,766,841 0.97

Year $102,698,836 $22,438,919 $6,601,908 $3.62

Holmes Corporation: LBO Valuation 1001

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1002 Chapter 12 Valuation: Cash-Flow-Based Approaches

Auditors’ Report Board of Directors and Stockholders

Holmes Corporation We have examined the consolidated balance sheets of Holmes Corporation and Subsidiaries as of December 31, Year 15 and Year 14, and the related consolidated statements of earnings and cash flows for the years then ended. Our examination was made in accordance with gen- erally accepted auditing standards, and accordingly included such tests of the accounting records and such other auditing procedures as we considered necessary in the circumstances.

In our opinion, the financial statements referred to above present fairly the consolidated financial position of Holmes Corporation and Subsidiaries at December 31, Year 15 and Year 14, and the consolidated results of their operations and changes in cash flows for the years then ended, in conformity with generally accepted accounting principles applied on a consistent basis.

SBW, LLP Chicago, Illinois March 15, Year 16

Required A group of Holmes’ top management is interested in acquiring Holmes in an LBO.

a. Briefly describe the factors that make Holmes an attractive and, conversely, an unat- tractive LBO candidate.

b. (This question requires coverage of Chapter 10.) Prepare projected financial state- ments for Holmes Corporation for Year 16 through Year 20 excluding all financing. That is, project the amount of operating income after taxes, assets, and cash flows from operating and investing activities. State the underlying assumptions made.

c. Ascertain the value of Holmes’ common shareholders’ equity using the present value of its future cash flows valuation approach. Assume a risk-free interest rate of 4.2 percent and a market premium of 5.0 percent. Note that information in Part e may be helpful in this valuation. Assume the following financing structure for the LBO:

Interest Type Proportion Rate Term

Term debt 50% 8% 7-year amortizationa

Subordinated debt 25 12% 10-year amortizationa

Shareholders’ equity 25

100%

a Holmes must repay principal and interest in equal annual payments.

d. (This question requires coverage of Chapter 13.) Ascertain the value of Holmes’ common shareholders’ equity using the residual income approach.

e. (This question requires coverage of Chapter 14.) Ascertain the value of Holmes’ common shareholders’ equity using the residual ROCE model and the price-to- earnings ratio and the market value to book value of comparable companies’

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approaches. Selected data for similar companies for Year 15 appear in the following table (amounts in millions):

Agee GI Handling LJG Gelas Robotics Systems Industries Corp.

Conveyor Conveyor Industrial Industry: Systems Systems Cranes Furnaces

Sales $4,214 $28,998 $123,034 $75,830 Net Income $ 309 $ 2,020 $ 9,872 $ 5,117 Assets $2,634 $15,197 $ 72,518 $41,665 Long-Term Debt $ 736 $ 5,098 $ 23,745 $ 8,869 Common Shareholders’ Equity $1,551 $ 7,473 $ 38,939 $26,884 Market Value of Common Equity $6,915 $20,000 $102,667 $41,962 Market Beta 1.12 0.88 0.99 0.93

f. Would you attempt to acquire Holmes Corporation after completing the analyses in Parts a–e? If not, how would you change the analyses to make this an attractive LBO?

Holmes Corporation: LBO Valuation 1003

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Learning Objectives

Chapter 13

Valuation: Earnings-Based Approaches

1 Understand earnings-based valuation, particularly the value-relevance of earnings versus dividends versus cash flows.

2 Evaluate the conceptual and practical strengths and weaknesses of earnings-based valuation using the residual income valuation method.

3 Develop a conceptual understanding and practical techniques to deal with the impor- tant issues involved in residual income valuation:

(a) Utilizing book value of common shareholders’ equity, comprehensive income, dividends, and clean surplus accounting in valuation

(b) Measuring required (or “normal”) income by multiplying beginning-of-period book value of equity by the risk-adjusted required rate of return on equity capital

(d) Determining the value of common equity as the sum of book value of common shareholders’ equity plus the present value of expected future residual income

4 Apply the residual income valuation method by valuing the common shareholders’ equity of PepsiCo.

5 Assess the sensitivity of firm value estimates to key valuation parameters such as discount rates and expected long-term growth rates.

6 Identify potential causes of errors if the residual income, free cash flows, and dividend valuations do not determine identical value estimates.

INTRODUCTION AND OVERVIEW Reported earnings are the single most widely followed measures of firm performance. Accounting standard setters (most notably the FASB and IASB), along with the accounting profession and the community of financial statement users, have designed the accrual accounting process to measure earnings as the bottom line of the firm’s profitability each

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Introduction and Overview 1005

period. As a result, firms’ reported earnings play central roles as the primary value-relevant measures of performance used in the capital markets for share pricing and capital allocation.

Because of the demand in the capital markets for earnings information, firms usually release quarterly and annual earnings to the public as soon as accountants have prepared and verified them, often weeks before the firms release their detailed quarterly and annual income statements, balance sheets, statements of cash flows, and notes. Firms commonly announce earnings during conference calls and press conferences attended by investors, analysts, managers, board members, and the financial press. Analysts often spend enor- mous amounts of time and effort building (and when new information arrives, revising) forecasts of firms’ upcoming quarterly and annual earnings. Sell-side analysts sell their earnings forecasts to interested investors, brokers, and fund managers. Commercial firms such as I/B/E/S and First Call have built businesses on compiling and distributing daily data on analysts’ earnings forecasts. The financial media (broadcast, print, and online) provide daily coverage of firms’ earnings announcements. For example, The Wall Street Journal pro- vides a summary report of firms’ earnings announcements each day in the “Earnings Digest” section. The Wall Street Journal also reports daily data on each firm’s stock trading activity, including a daily price-earnings ratio. In fact, because of the demand for and atten- tion devoted to earnings among capital markets participants, U.S. GAAP and IFRS require firms to report earnings scaled on a per-share basis in their financial statements. (See the related discussion in Chapter 4.)1

Firms’ share prices usually react quickly to earnings announcements, and the direction and magnitude of the market’s reaction depends on the direction and magnitude of the earnings news relative to the market’s expectations. Firms that announce earnings beating the market’s expectations (“good news”) often experience significant jumps in share price during the day of and the days immediately following the announcement. Likewise, firms that announce earnings falling short of the market’s expectations (“bad news”) usually experience a decline in share price—and, in some circumstances, severe drops in share price—during the day of and the days immediately following the announcement. As noted in several prior chapters, the seminal Ball and Brown (1968) study2 and many other research studies, including the Nichols and Wahlen (2004) study described in Chapter 1 and Exhibit 1.21, have shown that firms’ stock returns are highly positively correlated with changes in earnings.

Because earnings provide such important information to investors and other external stakeholders, earnings also play key roles in decisions that firms make with regard to inter- nal capital allocation. New project proposals within firms are often evaluated based on the effects they will have on reported earnings. In addition, corporate governance processes commonly reward or punish managers with compensation and bonus plans based on whether firm performance meets certain earnings targets. Managers who meet or exceed specified earnings targets are usually rewarded with substantial bonuses. Managers who consistently fall short of earnings targets do not receive bonuses and typically need to explain why they failed to meet the targets. If the explanations are not satisfactory, they may find themselves being replaced.

The preceding observations establish the important roles of earnings:

• Earnings is the primary measure of firm performance produced by the accrual accounting system.

• Earnings has a direct impact on the capital markets and the pricing of shares.

1 Financial Accounting Standards Board, Statement of Financial Accounting Standard No. 128, “Earnings per Share” (1997); FASB

Codification Topic 260; International Accounting Standards Board, International Accounting Standard 33, “Earnings per Share”

(revised 2003).

2 Ray Ball and Philip Brown, “An Evaluation of Accounting Income Numbers,” Journal of Accounting Research (Autumn 1968),

pp. 159–178.

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1006 Chapter 13 Valuation: Earnings-Based Approaches

• Corporate managers and boards of directors use earnings for internal capital alloca- tion and for aligning the incentives of managers with shareholders.

• The financial press and the analyst community devote tremendous time and attention to reporting, analyzing, and predicting earnings.

Therefore, it is logical that accounting earnings provide a basis for valuation. This chapter describes the conceptual and practical strengths and weaknesses of the earnings- based valuation model known as the residual income valuation model. The residual income valuation model uses expected future earnings and the book value of common shareholders’ equity as the bases for valuation.

To describe, explain, and apply the residual income valuation model, this chapter takes four important steps. Exhibit 13.1 illustrates these steps and some of the key questions we will address in this chapter. First, we describe the rationale behind earnings-based valuation. Second, we explain the theoretical and conceptual foundation for residual income valuation, with a number of illustrations and examples. Third, we demonstrate the residual income

E X H I B I T 1 3 . 1

Steps to Understanding Residual Income Valuation

1. Rationale

• What is the rationale for using earnings as a basis for valuation? • What are the practical advantages and concerns associated with using earnings to

determine common shareholders’ equity value?

2. Theoretical and Conceptual Foundations for Residual Income Valuation

• What theories and concepts support residual income valuation? • How do we measure residual income? What does it represent?

3. Practical Applications

• What steps do we take to determine value using residual income valuation methods?

• What implementation issues do we need to understand in order to use the residual income model?

• What value estimate do we get from this approach for the common shareholders’ equity of PepsiCo?

4. Linking Residual Income Valuation to Dividends Valuation and Free Cash Flow Valuation

• Conceptually, why is the residual income valuation approach equivalent to the valuation approaches that rely on dividends and free cash flows?

• Practically, does the value estimate we obtain for PepsiCo using the residual income valuation approach agree with the estimate from Chapter 11 using the dividends valuation approach and from Chapter 12 using the free cash flows to equity valuation approach?

• What if the value estimates do not agree across these three models? How do we find and correct possible valuation errors?

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Rationale for Earnings-Based Valuation 1007

model by applying it to value the common shareholders’ equity of PepsiCo. As we apply the model to PepsiCo, we describe the key measurement and implementation issues. Fourth, we come full circle in valuation by demonstrating the internal consistency in dividends, free cash flows, and residual income valuation. We demonstrate that these three valuation approaches yield identical valuations if applied properly. We also help the analyst under- stand how to identify and correct valuation errors if the three valuation models do not agree.

The residual income valuation model in this chapter provides a powerful approach that is a complementary equivalent to the classical dividends-based valuation approach pre- sented in Chapter 11 and to the free-cash-flows-based valuation approach presented in Chapter 12. The residual income valuation model in this chapter forms the basis for the market-based multiples described in Chapter 14, including the market-to-book ratio and the price-earnings ratio.

RATIONALE FOR EARNINGS-BASED VALUATION Exhibit 13.1 shows that the first step toward understanding residual income valuation is to establish the theoretical and conceptual rationale for using an earnings-based valuation approach. Economic theory teaches that the value of any resource equals the present value of the expected future payoffs from the resource discounted at a rate that reflects the risk inherent in those expected future payoffs. Like Chapters 11 and 12, we again start with the same general model for the present value of a security (denoted as V

0 , with present value

denoted as of time t�0) with an expected life of n future periods, as follows:3

n Expected Future Payoffs t

V 0

� ∑ t =1 (1 � Discount Rate)t

Chapter 11 demonstrates that the value of a share of common equity should equal the pres- ent value of the expected future dividends the shareholder will receive.4 Dividends are the fundamental value-relevant payoffs because they represent the distribution of wealth from the firm to the shareholders. The equity shareholder receives dividends as the payoffs from holding a share, including the final “liquidating” dividend when the firm liquidates the share or the shareholder sells the share. Thus, to value a firm’s shares using dividends, one discounts to present value the expected future dividends over the life of the firm (or the expected length of time the share will be held), including the final liquidating dividend. This is a wealth distribution (or liquidation) approach to valuation.

Chapter 12 demonstrates that the value of a share of common equity also should equal the present value of the expected future free cash flows that the firm will create and ultimately distribute in dividends to the common equity shareholders. The free-cash- flows-based valuation approach focuses on the amounts and timing of the cash flows the firm will generate that will eventually be distributed to shareholders in future dividends. Thus, to value a firm’s shares using free cash flows, one discounts to present value the expected future free cash flows for common equity shareholders over the life of the firm

3 This chapter uses the same notation as in prior chapters, where t refers to accounting periods. The valuation process determines

an estimate of firm value, denoted as V 0 , in present value as of today, when t�0. The period t�1 refers to the first accounting

period being discounted to present value. Period t�n is the period of the expected final, or liquidating, payoff.

4 John Burr Williams, The Theory of Investment and Value, Cambridge, Mass.: Harvard University Press (1938).

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1008 Chapter 13 Valuation: Earnings-Based Approaches

(or the expected length of time the share will be held), including the final liquidating cash flows. This is a free cash flow realization approach to valuation.

The residual income valuation approach presented in this chapter parallels the dividends- based valuation approach and the cash-flow-based valuation approach, except that it uses a different measure of payoffs. The residual income valuation approach uses book value of common shareholders’ equity and expected future earnings to determine the value-relevant expected future payoffs to the investor (that is, the numerator of the general value model above) in place of future dividends or future free cash flows. The rationale for the role of book value of shareholders’ equity is straightforward: it is the starting point for valuation because it is the balance sheet measure of the common equity shareholders’ claim on the net assets of the firm. The rationale for using expected future earnings as a basis for valuation is also straightforward: future earnings measure the net profits or losses the firm will generate for the shareholders. Over the remaining life of the firm, earnings measure the total wealth to be created by the firm for the shareholders. Instead of focusing on wealth distribution through dividends payments and instead of focusing on dividend-paying capacity in free cash flows, residual income valuation focuses on earnings as a periodic measure of shareholder wealth creation. Therefore, residual income is a wealth creation approach to valuation. In Chapter 11, Exhibit 11.1 showed the differences in valuation approach perspectives between dividends as measures of value distribution, free cash flows as measures of distributable wealth, and earnings as value-relevant measures of wealth creation.

To measure wealth creation, the accrual accounting process measures income for the equity shareholders based on the net amount of economic resources generated and con- sumed by the firm each period. Accrual accounting also produces periodic statements of financial position—balance sheets that measure assets, liabilities, and shareholders’ equity—that report the economic resources (assets) that the firm can control and use to produce expected future economic benefits and the claims on those resources by creditors and investors (liabilities and equities). To produce informative measures of financial perfor mance and position that are relevant and reliable, the accounting profession devel- ops and implements accounting standards through which the accrual accounting process measures income, assets, liabilities, and shareholders’ equity using estimates of economic resources earned and consumed each period, rather than just relying on cash inflows and cash outflows, which often do not reflect economic value generated or consumed each period. To measure a firm’s economic performance and position in a given period, it makes sense to measure the following:

• Revenues earned from operating performance during that period, not just the amounts of cash collected from customers that period

• Expenses incurred for resources consumed in that period, not just the amounts of cash paid out of the firm that period

• A portion of the long-lived resources consumed during that period, such as periodic depreciation of a building each year of its useful life (rather than recognize the full cost of the building in the year the firm pays for it and ignore the consumption of the build- ing in all other years the firm uses it)

• The cost of commitments made during that period to pay retirement benefits to employees in future periods (rather than ignore those commitments and measure their effects only when the firm pays cash)

Accrual accounting earnings are far from perfect performance measures. However, recall the discussion in Chapter 2 (particularly Exhibit 2.4) that described how accounting standards are intended to optimize the relevance and reliability of accrual accounting information (asset and liability valuation and income recognition) for investors and other stakeholders. By virtue of accounting standards, accounting earnings will more closely match the firm’s underlying

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Earnings-Based Valuation: Practical Advantages and Concerns 1009

economic performance—the wealth created or destroyed for equity shareholders—in a given period than will the net cash inflows or outflows of that period.

Over the life of a firm, the capital invested in the firm by the shareholders plus the wealth created by the firm for the shareholders will determine the value of the firm to the share- holders. Cash is the ultimate medium of exchange; therefore, over the life of the firm, the cash flows that are distributable to shareholders will equal the shareholders’ capital invest- ments in the firm plus the lifetime earnings of the firm. Thus, valuation of shareholders’ equity in a firm using the capital invested in the firm plus earnings over the life of the firm is equivalent to valuation using distributable cash flows over the life of the firm, and both are equivalent to valuation using dividends over the life of the firm.5

EARNINGS-BASED VALUATION: PRACTICAL ADVANTAGES AND CONCERNS Although earnings, cash flows, and dividends are equally valid bases for valuation, several practical advantages and concerns arise with earnings-based valuation. One practical advan- tage arises because the emphasis placed on earnings by firms and the capital markets makes earnings a logical starting point for valuation. Analysts, investors, the capital markets, man- agers, boards, and the financial press focus on earnings forecasts and earnings reports rather than free cash flow forecasts and free cash flow amounts. Firms usually do not hold press conferences to announce free cash flows. Analysts publish earnings forecasts far more fre- quently than they publish free cash flow forecasts. The Wall Street Journal does not report a “free cash flow digest” every day (but it does track earnings for firms). Boards of directors and compensation committees typically do not establish managers’ bonus plans based on achieving free cash flow targets (more often relying on earnings-based measures of perform- ance). The reason for the tendency to rely on earnings is that they align more closely than dividends or free cash flows with the focus of the capital markets and corporate managers and boards of directors on periodic performance measurement.

Another practical advantage arises because it is more direct and efficient for the analyst to go straight from earnings to valuation rather than take a detour to free cash flows.6As Exhibit 13.2 depicts, estimating firm value using free cash flows adds an intermediary step to the valuation process. As demonstrated in Chapter 12, our approach to valuing a firm using free cash flows requires that we initially forecast future income statements and bal- ance sheets. Then we derive the implied forecasts of cash flows from those income state- ments and balance sheets by making adjustments for the accruals in earnings, for the cash flows invested in working capital, and for capital expenditures. We use these cash flows to determine free cash flows, which we then use to compute value. Under the residual income approach, we begin valuation immediately after we forecast future income statements and

5 Over sufficiently long time periods, net income equals free cash flows to common equity. The effect of year-end accruals to con-

vert cash flows to net income lessens as the measurement period lengthens. The correlation between firms’ earnings and stock

returns increases as the earnings measurement interval increases. The values of R2 for various intervals are one year, 5 percent; two

years, 15 percent; five years, 33 percent; and 10 years, 63 percent. See Peter D. Easton, Trevor S. Harris, and James A. Ohlson,

“Aggregate Accounting Earnings Can Explain Most of Security Returns,” Journal of Accounting and Economics (1992), pp. 119–142.

6 Researchers have directed considerable attention to the question of whether cash flows or earnings associate more closely with

stock returns. This research indicates that earnings and cash flows cumulated over long periods of time are highly positively cor-

related with stock returns over long periods (for example, five-year periods), but that for shorter periods, earnings show a stronger

association with stock returns than cash flows. See Patricia M. Dechow, “Accounting Earnings and Cash Flows as Measures of Firm

Performance: The Role of Accounting Accruals,” Journal of Accounting and Economics (1994), pp. 3–42; C. S. Cheng, Chao-Shin

Liu, and Thomas F. Schaefer, “Earnings Permanence and the Incremental Information Content of Cash Flow from Operations,”

Journal of Accounting Research (Spring 1996), pp. 173–181; Richard G. Sloan, “Do Stock Prices Fully Reflect Information in

Accruals and Cash Flows about Future Earnings,” The Accounting Review (July 1996), pp. 289–315.

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1010 Chapter 13 Valuation: Earnings-Based Approaches

balance sheets. The two valuations should ultimately be the same, but the free cash flows approach requires more computations, which requires more time and effort, and increases the potential for error.

Economists sometimes express concern that earnings are not a value-relevant attribute for valuation because earnings are not as reliable or as meaningful as cash or dividends for valuing investments. When considering earnings, economists sometimes point out that firms pay dividends in cash, not earnings; investors can spend cash but cannot spend earn- ings for future consumption. This concern is alleviated in valuation, however, by the fact that the differences between earnings, cash flows, and dividends are timing differences: earnings measure when the firm creates wealth, whereas free cash flows measure when the firm realizes wealth in cash, and dividends measure when the firm distributes wealth to shareholders. Over the life of the firm, the present values of future earnings, cash flows, and dividends will be equal.

Some economists worry that accrual accounting earnings reflect accounting methods that no longer capture changes in underlying economic values (for example, depreciation or amortization expenses based on outdated acquisition cost valuations of assets, expenses for research and development that have turned out to be successful, or advertising expenses that have created economically valuable brand equity). Value measurement based on expected earnings over the remaining life of the firm alleviates this concern. Over time, the accrual accounting process will ultimately self-correct measurement errors in accounting numbers. For example, if fixed asset book values are “too high” or “too low” for a company, over time (and it usually does not take long), accrual accounting will naturally correct these measurement errors because the subsequent depreciation expenses will be “too high” or “too low” accordingly. If the current balance sheet does not recognize intellectual capital value created by successful research and development or brand value created by successful

E X H I B I T 1 3 . 2

Residual Income Valuation Requires Fewer Steps Than Free Cash Flows Valuation

Residual Income Valuation

Free Cash Flows Forecasts

Income Statement and Balance Sheet

Forecasts

Free Cash Flows Valuation

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Theoretical and Conceptual Foundations for Residual Income Valuation 1011

marketing, accrual accounting will correct itself over time as the firm generates higher earnings from this intangible capital.7

Some economists voice concerns that earnings can be subject to purposeful manage- ment or manipulation by a firm. To be sure, analysts should always be alert to the possibil- ity that earnings management (or worse, earnings manipulation and fraudulent reporting) may occur in some periods by some firms. Earlier chapters devoted considerable attention to helping analysts understand how to assess firms’ accounting quality. But this is more of a concern about earnings as a measure of current period performance than about a firm’s future expected earnings for valuation purposes. In addition, this concern is not a major issue for valuation because residual income valuation relies on the analyst’s forecasts of expected future earnings, not on past earnings reports that the firm may have managed (unless, of course, the analyst’s forecasts naively project the past managed earnings will per- sist in future years). Ironically, firms can easily manage cash flows in a given period, but economists rarely voice this concern. Free cash flows each period depend on cash inflows and outflows, which the firm can easily manipulate by accelerating or delaying certain cash payments or cash collections in that particular period. Over the remaining life of the firm, which is the focus of the analyst’s forecasting and valuation, the firm’s earnings and cash flows will be determined ultimately by the success of the firm’s operating, investing, and financing activities, not by the manipulation of past earnings or cash flows.

THEORETICAL AND CONCEPTUAL FOUNDATIONS FOR RESIDUAL INCOME VALUATION8

Exhibit 13.1 indicates that the second step toward understanding residual income valuation is to establish the theoretical and conceptual foundation for the residual income valuation approach. The foundation for residual income valuation is the classical dividends-based valuation model from Chapter 11, in which the value of common shareholders’ equity is the present value of all future dividends to shareholders over the remaining life of the firm. As described in Chapter 11, we define dividends to be all-inclusive measures of the cash flows between the firm and the common equity shareholders, encompassing cash flows from the firm to shareholders through periodic dividend payments, stock buybacks, and the firm’s liquidating dividend, as well as cash flows from the shareholders to the firm when the firm issues shares (negative dividends).

Chapter 11 demonstrated how to estimate an appropriate discount rate (using the CAPM or some other risk-based asset-pricing model) based on the rate of return (denoted as R

E ) that the capital markets expect for the risk associated with common equity capital in

7 Indeed, when an analyst asserts that a firm’s current balance sheet accounting numbers do not reflect underlying economic val-

ues, how does the analyst know that? When an analyst asserts that a firm’s balance sheet omits a valuable intangible asset in the

form of intellectual property or brand equity, how has the analyst assessed the amount of the omission? Usually, analysts base

assertions like these on their assessments that the firm will generate future profits from operations that utilize these economic

assets. Earnings-based valuation captures exactly the same idea. Firm value depends on expected future earnings over the remain-

ing life of the firm.

8 Credit for the rigorous development of the residual income valuation model goes to James A. Ohlson, “A Synthesis of Security

Valuation Theory and the Role of Dividends, Cash Flows, and Earnings,” Contemporary Accounting Research (Spring 1990),

pp. 648–676; James A. Ohlson, “Earnings, Book Values, and Dividends in Equity Valuation,” Contemporary Accounting Research

(Spring 1995), pp. 661–687; Gerald A. Feltham and James A. Ohlson, “Valuation and Clean Surplus Accounting for Operating and

Financial Activities,” Contemporary Accounting Research (Spring 1995), pp. 216–230. The ideas underlying the earnings-based

valuation approach trace to early work by G.A.D. Preinreich, “Annual Survey of Economic Theory: The Theory of Depreciation,”

Econometrica (1938), pp. 219–241, and Edgar O. Edwards and Philip W. Bell, The Theory and Measurement of Business Income

(Berkeley, CA: University of California Press), 1961.

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1012 Chapter 13 Valuation: Earnings-Based Approaches

a firm. That chapter also demonstrated the dividends-based valuation approach, which measures the value of common shareholders’ equity (denoted as V

0 ) as the present value of

all expected future dividends (denoted as D) with the following general model:

Analysts and investors commonly find it desirable to identify and forecast economic vari- ables that determine the firm’s future dividends and can therefore substitute for dividends to yield an equivalent valuation. Accounting numbers provide a solution. Accounting for the book value of common shareholders’ equity (denoted as BV) in a firm can be expressed as follows:

BV t � BV

t�1 � NI

t � D

In this expression, book value of common shareholders’ equity at the end of Year t (BV t ) is

equal to book value at the end of Year t�1 (BV t�1

) plus net income for Year t (NI t ) minus

the all-inclusive dividends during Year t (D t ). As in the dividends valuation approach

described in Chapter 11, we assume that accounting for net income and book value of shareholders’ equity follows clean surplus accounting. Clean surplus accounting simply means that net income includes all of the recognized elements of income of the firm for common equity shareholders (that is, all of the amounts in the income statement plus all of the other comprehensive income items) and dividends include all direct capital transac- tions between the firm and the common equity shareholders (that is, periodic dividend payments, share repurchases, and share issues).

We can rearrange the accounting equation for the book value of common shareholders’ equity to isolate dividends as follows:

D t � NI

t � BV

t�1 � BV

In this expression, dividends equal net income plus the change in book value from direct capital transactions with common shareholders.

Example 1 Suppose the firm had shareholders’ equity on the balance sheet at a book value of $5,000 at the end of Year t�1. Suppose during Year t, the firm earns net income of $600, pays divi- dends to shareholders of $360, issues new stock to raise $250 of capital, and uses $50 to repurchase common shares. The book value of shareholders’ equity the end of Year t is

BV t � BV

t�1 � NI

t � D

t � $5,000 � $600 � $360 � $250 � $50 � $5,000 � $600 � $160 � $5,440.

In this example, all-inclusive dividends (D t ) in Year t amount to $160. Using the expression

for dividends shows that

D t � NI

t � BV

t�1 � BV

t � $600 � $5,000 � $5,440 � $160.

One can verify this amount of all-inclusive dividends in this example by recognizing that the dividends paid plus the cash paid for share repurchases minus the cash received from issuing shares equals the total amount of all-inclusive dividends of $160 (� $360 � $50 – $250).

∞ V

0 � ∑

D t

D 1

D 2

D 3

t = 1 (1 + RE) t �

(1 + R E )1

� (1 + R

E )2

� (1 + R

E )3

� . . .

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Because dividends equal net income plus the change in book value of common share- holders’ equity, we can substitute net income plus the change in the book value of common shareholders’ equity into the classical dividends valuation model, as follows:

∞ V

0 � ∑

D t

t = 1 (1 + RE) t

∞ � ∑

NI t + BV

t–1 – BV

t = 1 (1 – RE) t

� NI

1 + BV

0 – BV

(1 + R E )1

� NI

2 + BV

1 – BV

(1 + R E )2

� NI

3 + BV

2 – BV

(1 + R E )3

� . . .

BV t–1

� BV

t–1 �

R E

� BVt–1 (1 + R

E )t (1 + R

E )t–1 (1 + R

E )t

∞ V

0 � BV

0 � ∑

NI t � (R

E � BV

t–1 )

t = 1 (1 + RE) t

� BV 0 �

NI 1 � (R

E � BV

0 )

(1 + R E )1

� NI

2 � (R

E � BV

1 )

(1 + R E )2

� NI

3 � (R

E � BV

2 )

(1 + R E )3

� . . .

Algebraically, the present value of BV t –1

can be rewritten as follows:

We substitute the right-hand side expression for the present value of BV t–1

into the equa- tion for V

0 , rearrange terms, and simplify to obtain the following expression for the resid-

ual income valuation model:

The residual income valuation model above is a valuation model for common sharehold- ers’ equity that is equivalent to dividends-based valuation, yet relies on earnings and book values.9

Intuition for Residual Income Measurement and Valuation The intuition for the residual income valuation model is straightforward. The value of common shareholders’ equity is equal to the book value of common equity plus the pres- ent value of all expected future residual income, which is the amount by which expected future earnings exceed the required earnings, for the remaining life of the firm. The required earnings (also known as normal earnings) of the firm equals the product of the required rate of return on common equity capital times the book value of common equity capital at the beginning of each period. We compute required earnings for period t as R

E �

BV t�1

. Required earnings reflect the earnings the firm must earn in period t simply to pro- vide a return to common equity that is equal to the cost of common equity capital. Required earnings are analogous to a charge for the cost of equity capital, similar to inter- est expense as a charge for the cost of debt capital.

We measure residual income (sometimes called abnormal earnings) by the subtraction term NI

t � (R

E � BV

t–1 ). Residual income is the difference between the net income the

9 Chapter 14 demonstrates a version of this residual income approach that determines the intrinsic-value-to-book-value ratio for

the firm using the return on common equity (ROCE, described in Chapter 4) and expected growth in the book value of common

equity.

Theoretical and Conceptual Foundations for Residual Income Valuation 1013

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1014 Chapter 13 Valuation: Earnings-Based Approaches

analyst expects the firm to generate and the required earnings of the firm. Residual income in period t measures the amount of wealth creation (or destruction) the firm will generate in period t for common equity shareholders above (or below) the earnings required to cover the cost of equity capital. If the analyst expects the firm to generate net income each period in the future that is exactly equal to required earnings (that is, NI

t � (R

E � BV

t–1 ) � 0;

zero abnormal earnings for all future periods), the analyst also expects the firm to exactly cover the cost of equity capital, no more, no less. In that case, the value of the firm is exactly equal to the book value of common shareholders’ equity. On the other hand, if the analyst expects the firm to create wealth for the shareholders by earning positive amounts of resid- ual income, the value of the firm is equal to book value of common shareholders’ equity plus the present value of all expected future residual income.10

Illustrations of Residual Income Measurement and Valuation The following examples illustrate residual income measurement and the residual income valuation model under various assumptions.

Example 2 Suppose investors have invested $10,000 in common equity in a company. Given the risk of the company, the investors expect to earn a 12 percent return, and they expect the company to pay out 100 percent of income in dividends each year. The required earnings of the company each period are as follows:

R E

� BV t–1

� 0.12 � $10,000 � $1,200

Suppose the investors forecast that the company will generate exactly $1,200 in net income each year. The investors should compute the residual income of the firm as follows:

NI t � (R

E � BV

t–1 ) � $1,200 � (0.12 � $10,000) � $0

Using the residual income approach, investors would value this firm based on book value plus expected future residual income as follows:

10 The concept of residual income in the economics literature and the accounting literature predates the commercialization of

“Economic Value Added” by decades. Applications of the concept of residual income in valuation and corporate governance prac-

tices can be found in G. Bennett Stewart, The Quest for Value (New York: Harper Collins), 1991, and in the expanding literature

on EVA®.

∞ V

0 � BV

0 � ∑

NI t � (R

E � BV

t–1 )

t = 1 (1 + RE) t

∞ � $10,000 � ∑

$1,200 t � (0.12 � $10,000

t–1 )

t = 1 (1 + 0.12)t

∞ � $10,000 � ∑

$0 t

� $10,000 t = 1 (1 + 0.12)t

In this case, the firm’s expected future income exactly equals the required level of earnings necessary to cover the cost of equity capital. So residual income is zero and the value of the firm is equal to the book value of common equity invested in the firm. The value of the firm

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under the residual income model is identical to the value determined using the dividends valuation model, which would value the company as a stream of dividends in perpetuity with no growth as follows:

V 0

� $1,200

� $10,000 0.12

Example 3 Now assume the same facts as in Example 2, but suppose investors expect the company to pay out no dividends each year and all the earnings will be reinvested in projects that will generate the investors’ required 12 percent rate of return.11 The required earnings of the firm in Year �1 will be

R E

� BV 0

� 0.12 � $10,000 � $1,200.

After retained earnings of $1,200 are added to book value of equity at the end of Year �1, the required earnings of the company in Year �2 will be

R E

� BV 1

� 0.12 � [$10,000 � $1,200] � $1,344.

After retained earnings of $1,344 are added to book value of equity at the end of Year �2, the required earnings of the company in Year �3 will be

R E

� BV 2

� 0.12 � [$11,200 � $1,344] � $1,505.

These computations show that the required earnings of the firm will grow as the firm retains and reinvests earnings, on which the investors expect the firm to earn the required rate of return.

Suppose the investors expect the firm to generate future earnings each year that will exactly match required earnings each year; so earnings in Year �1 will be $1,200, earnings in Year �2 will be $1,344, and earnings in Year �3 will be $1,505. Also suppose the investors expect the firm to continue to reinvest all of its earnings and will continue to gen- erate the required level of earnings each year over the remaining life of the firm (that is, continuing in Year �4 and beyond). We can determine the value of equity capital in the firm using the residual income model as follows:

11 Although this is simply an illustration, note that this is an important assumption because it presumes that the firm can scale up

operations without diminishing future returns.

∞ V

0 � BV

0 � ∑

NI t � (R

E � BV

t–1 )

t = 1 (1 + RE) t

� $10,000 � $1,200 � (0.12 � $10,000)

(1.12)1 �

$1,344 � (0.12 � $11,200) (1.12)2

Theoretical and Conceptual Foundations for Residual Income Valuation 1015

� $1,505 � (0.12 � $13,544)

� (1.12)3

∞ ∑

NI t � (0.12 � BV

t–1 )

t = 4 (1 + 0.12)t

∞ � $10,000 �

$0 �

$0 � ∑

$0t (1.12)1 (1.12)2 (1.12)3 t = 4 (1 + 0.12)t

� $10,000

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1016 Chapter 13 Valuation: Earnings-Based Approaches

Example 4 Now assume the same facts as in Example 3, but suppose investors expect the firm simply to reinvest the earnings in cash or other types of assets that will earn no additional return for each of the next three periods. The investors expect the firm to continue to earn $1,200 each year on the original investment of $10,000, but they expect the reinvestment of earn- ings in the first three years to produce no incremental return. Also assume for simplicity that in Year �4 and beyond, the firm will invest in projects that will earn a total of 12 per- cent return for equity shareholders.

The required earnings of the firm in Year �1 will be

R E

� BV 0

� 0.12 � $10,000 � $1,200.

After retained earnings of $1,200 are added to book value of equity at the end of Year �1, the required earnings of the company in Year �2 will be

R E

� BV 1

� 0.12 � [$10,000 � $1,200] � $1,344.

After retained earnings of $1,200 are added to book value of equity at the end of Year �2, the required earnings of the company in Year �3 will be

R E

� BV 2

� 0.12 � [$11,200 � $1,200] � $1,488.

We can determine the value of equity capital in the firm using the residual income model as follows:

∞ V

0 � BV

0 � ∑

NI t � (R

E � BV

t–1 )

t = 1 (1 + RE) t

� $10,000 � $1,200 � (0.12 � $10,000)

(1.12)1 �

$1,200 � (0.12 � $11,200) (1.12)2

� $1,200 � (0.12 � $12,400)

� (1.12)3

∞ ∑

NI t � (0.12 � BV

t–1 )

t = 4 (1 + 0.12)t

∞ � $10,000 �

$0 �

$1,200 � $1,344 �

$1,200 � $1,488 � ∑

$0 t

(1.12)1 (1.12)2 (1.12)3 t = 4(1 + 0.12)t

� $10,000 � $0 � $115 � $205 � $0

� $9,680

This example shows that by reinvesting earnings to earn zero return rather than the required 12 percent return, the firm’s earnings will be $144 less than required earnings in Year �2 and $288 less than required earnings in Year �3. In present value terms, the firm will destroy $115 of shareholder value in Year �2 and $205 of shareholder value in Year �3. Therefore, investors would value the firm at only $9,680 in this example, as compared to $10,000 in the preceding two examples.

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Residual Income Valuation Model with Finite Horizon Earnings Forecasts 1017

Example 5 Now assume the same facts as in Example 2, where investors have invested $10,000 in com- mon equity in a firm, the investors expect to earn a 12 percent return, and they expect the company to pay out 100 percent of income in dividends each year. Now suppose investors expect the firm to earn net income of $1,000 in Year �1, $2,000 in Year �2, $1,500 in Year �3, and $1,200 each year thereafter. Investors should compute the residual income valuation as follows:

∞ V

0 � BV

0 � ∑

NI t � (R

E � BV

t–1 )

t = 1 (1 + RE) t

� $10,000 � $1,000 � (0.12 � $10,000)

(1.12)1 �

$2,000 � (0.12 � $10,000)

(1.12)2

� $1,500 � (0.12 � $10,000)

� (1.12)3

∞ ∑

$1,200 t � (0.12 � $10,000

t–1 )

t = 4 (1 + 0.12)t

� $10,000 � $178 � $638 � $214 � $0

� $10,674

∞ � $10,000 �

�$200 �

$800 �

$300 � ∑

$0 t

(1.12)1 (1.12)2 (1.12)3 t = 4 (1 + 0.12)t

In this example, the firm will generate residual income amounts of �$200 in Year �1, $800 in Year �2, $300 in Year �3, and $0 each year thereafter. The firm destroys shareholder wealth in Year �1 by failing to earn sufficient income to cover the cost of equity capital, but the firm generates increasing shareholder wealth in Years �2 and �3 and exactly covers the cost of equity capital each year thereafter. Given these assumptions, the present value of the firm under the residual income model is $10,674.

RESIDUAL INCOME VALUATION MODEL WITH FINITE HORIZON EARNINGS FORECASTS AND CONTINUING VALUE COMPUTATION Analysts cannot precisely forecast firms’ income statements and balance sheets for many years into the future. Therefore, analysts commonly forecast income statements and bal- ance sheets over a foreseeable finite horizon and then make simplifying growth rate assumptions for the years continuing after the forecast horizon. We can modify the resid- ual income valuation model to include explicit forecasts of net income and book value of common equity through Year T [where T is a finite horizon (for example, five or ten years in the future)] and then apply a constant growth rate assumption (denoted as g) to project residual income for Year T�1 and all years thereafter. We used similar approaches to fore- cast and value dividends in Chapter 11 and free cash flows in Chapter 12.

To deal with the uncertainty in long-run forecasts, the analyst must forecast net income, book value of shareholders’ equity, and residual income over an explicit forecast horizon until the point at which the analyst expects the firm’s growth pattern to settle into steady-state growth, during which time earnings, dividends, and cash flows are

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1018 Chapter 13 Valuation: Earnings-Based Approaches

expected to grow at a steady, predictable rate. We refer to residual income in this long- run steady-state growth period as continuing residual income because it reflects residual income earned by the firm continuing into the long-run future. The long-run steady- state growth rate in future continuing residual income may be positive, negative, or zero. Steady-state growth in residual income may be driven by long-run expectations for infla- tion, the industry’s sales, the economy in general, or the population. In some industries, competitive dynamics eventually drive long-run projections of the future returns earned by the firm (for example, the future ROCE) to an equilibrium level equal to the long-run expected cost of equity capital in the firm. Once a firm reaches that point, the firm can be expected to earn zero residual income in the future. The analyst should select a con- tinuing growth rate in residual income that captures realistic long-run expectations for the firm.

To compute residual income in Year T�1, the analyst should project Year T�1 net income by multiplying Year T net income by the growth factor (1 � g). Year T�1 residual income (denoted as RI

T�1 ) can then be computed as follows:

RI T�1

� [NI T

� (1 � g)] � [R E

� BV T ]

By estimating RI T�1

this way, the analyst also will be able to apply the same uniform long- run growth factor (1 � g) to estimate Year T�1 income statement and balance sheet amounts and to compute internally consistent projections for Year T�1 free cash flows and dividends, which the analyst can then use in free cash flow value models and dividends value models to determine internally consistent value estimates. Chapters 11 and 12 demonstrate these approaches.

After computing RI T�1

, the analyst can treat RI T�1

as a growing perpetuity of residual income beginning in Year T�1. The analyst can discount the perpetuity of residual income to present value using the perpetuity-with-growth value model described in Chapters 11 and 12. We include the continuing value computation into the finite horizon residual income model as follows:

∞ V

0 � BV

0 � ∑

NI t � (R

E � BV

t–1 )

t = 1 (1 + RE) t

T � BV

0 � ∑

NI t � (R

E � BV

t–1 )

t = 1 (1 + RE) t

1 1 � [((NIT � (1 � g)) � (RE � BVT)) � (R

E � g)

� (1 � R

E )T ]

(3)

(2)(1)

This model computes the value of common equity based on three parts: (1) book value of shareholders’ equity at time t�0 (the BV

0 term), (2) the present value of residual income

over the explicit forecast horizon through Year T (the summation term), and (3) the present value of continuing value based on residual income as a perpetuity with growth beginning in Year T�1 (the term in brackets). To compute continuing value, we compute residual income in Year T�1 [the term NI

T � (1 � g) � (R

E � BV

T )]. We assume that residual

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Valuation of PepsiCo Using the Residual Income Model 1019

income in Year T�1 will grow at constant rate g in perpetuity beginning in Year T�1, so we compute continuing value as of the start of Year T�1 using the perpetuity-with-growth valuation factor [the term 1/(R

E � g)]. Finally, we discount continuing value to present

value at time t � 0 using the present value factor [the term 1/(1 � R E )T].

Coaching Tip: Avoid This Crucial But Common Mistake The preceding subsection demonstrates how to compute residual income in Year T�1, as follows:

RI T�1

� [NI T

� (1 � g)] � [R E

� BV T ]

By estimating RI T�1

this way, you will effectively apply a uniform long-run growth factor (1 � g) to net income to compute residual income. Recall that Chapters 11 and 12 also demonstrated how to correctly compute free cash flows and dividends in Year T�1 by applying the same long-run growth factor (1 � g) to project all of the Year T�1 income statement and balance sheet amounts and then deriving internally consistent projections for Year T�1 free cash flows and dividends. With this simple but important step, you can use the residual income value model, the free cash flows value model, and the dividends value models to determine internally consistent value estimates. This approach will enable you to avoid the all-too-common mistake of deriving different values for the same firm using different valuation models.

The common mistake analysts make (and you can avoid with the approach shown above) is forecasting RI

T�1 by simply projecting RI

T�1 � RI

T � (1 � g). This (likely erro-

neous) shortcut projection implicitly assumes that

RI T

� (1 � g) � [NI T

� (R E

� BV T�1

)] � (1�g) � NI

T � (1 � g) � [R

E � BV

T�1 � (1 � g)].

This assumption requires BV T

� BV T�1

� (1 � g), which is not necessarily true. Residual income in Year T�1 depends on book value at the end of Year T. We assume constant growth at rate (1 � g) in residual income beginning in Year T�1. Thus, the only way resid- ual income in Year T�1 will equal residual income in Year T times (1 � g) is if book value in Year T happened to grow (by coincidence) at the same rate (1 � g). This will not likely be the case. The analyst can easily avoid this forecasting and valuation error for RI

T�1 by

correctly computing RI T�1

� [NI T

� (1 � g)] � [R E

� BV T ].

VALUATION OF PEPSICO USING THE RESIDUAL INCOME MODEL Step three toward understanding residual income valuation, as Exhibit 13.1 illustrates, is the practical application step. In this step, we apply the residual income valuation approach to value the common shareholders’ equity in PepsiCo. As Chapters 11 and 12 described, PepsiCo shares closed trading at $54.77 on the New York Stock Exchange at the end of 2008. In Chapter 11, we determined our central estimate of the value of PepsiCo shares at the end of 2008 to be roughly $83.03 using the projected financial statement forecasts developed in Chapter 10 and applying the dividends-based valuation approach. We obtained the same

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1020 Chapter 13 Valuation: Earnings-Based Approaches

value estimate for PepsiCo shares in Chapter 12 using the same projected financial state- ment forecasts developed in Chapter 10 and the free cash flow valuation approaches. Next, we illustrate the valuation of PepsiCo shares using the residual income valuation model techniques described in this chapter and the forecasts developed in Chapter 10. The Forecast and Valuation spreadsheets of FSAP (Appendix C) also demonstrate the forecasts and valuation estimates.

We value PepsiCo with the residual income approach following these five steps:

1. Estimate the appropriate discount rate using the risk-adjusted required rate of return on equity capital.

2. Determine the book value of common shareholders’ equity on PepsiCo’s 2008 bal- ance sheet, project expected future residual income from the financial statement forecasts for PepsiCo described in Chapter 10, and project long-run growth in resid- ual income in the continuing periods beyond the forecast horizon.

3. Discount the expected future residual income to present value, including continuing value.

4. Add the book value of equity and the present value of expected future residual income to determine the total value of common shareholders’ equity, correct for midyear discounting, and divide by the number of shares outstanding to convert this total to an estimate of share value for PepsiCo.

5. Analyze the sensitivity of the estimate of PepsiCo’s share value to determine the reasonable range of values for PepsiCo shares.

After illustrating this five-step valuation process, we will compare the range of reason- able values to PepsiCo’s share price in the market and suggest an appropriate investment decision indicated by the analysis.

Discount Rates for Residual Income To compute the appropriate discount rate for residual income, we again use the CAPM to estimate the market’s required rate of return on PepsiCo’s common stock, as demon- strated in Chapters 11 and 12. At the end of 2008, PepsiCo’s common stock had a market beta of roughly 0.75. At the same time, U.S. Treasury bills with one to five years to matu- rity traded with a yield of approximately 4.0 percent, which we use as the risk-free rate. Assuming a 6 percent market risk premium, the CAPM indicates that PepsiCo had a cost of common equity capital of 8.50 percent [R

E � 8.50 � 4.0 � (0.75 � 6.0)] at the end of

2008, the beginning of the valuation period. We used this same cost of common equity capital to value PepsiCo shares in Chapter 11 using the present value of future dividends and in Chapter 12 using the free cash flows to common equity shareholders’ valuation model.

Using the residual income valuation model, we do not need to compute the weighted average cost of capital. This does not mean that we ignore debt capital or the costs related to debt capital. Instead, we rely on accounting to capture the effects of debt. We project book value of shareholders’ equity after subtracting debt from total assets, and we project net income after subtracting interest expense net of tax effects.

Pepsico’s Book Value of Equity and Residual Income According to PepsiCo’s balance sheet (Appendix A), book value of common shareholders’ equity is $12,203.0 million at the end of 2008. This amount is the starting point for the residual income valuation model, the term denoted BV

0 in the valuation equations.

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We project residual income each period in the finite forecast horizon using the follow- ing four steps:

1. Forecast expected future net income for each period. 2. Forecast expected future book value of common shareholders’ equity at the begin-

ning of each period. 3. Compute expected future required income, which is the product of the cost of equity

capital times the book value of common shareholders’ equity at the beginning of each period (� R

E � BV

t–1 ).

4. Determine expected future residual income by subtracting expected future required income from expected future net income [� NI

t � (R

E � BV

t–1 )].

We completed the first and second steps in Chapter 10. Chapter 10 developed our pro- jections of PepsiCo’s future net income by making specific assumptions regarding each line item in the income statement. Chapter 10 also developed specific forecasts of common shareholders’ equity on the balance sheet by making specific assumptions about PepsiCo’s assets, liabilities, and common equity, including specific forecasts of dividends, stock issues, and stock buybacks. For projections of net income and book value of shareholders’ equity beyond Year �5, we assume that PepsiCo will grow in steady state at a rate of 3.0 percent per year in Year � 6 and beyond. Exhibit 13.3 presents projections of PepsiCo’s net income, book value of shareholders’ equity, required income, and residual income through Year �5 using the forecasts discussed in Chapter 10 and an 8.50 percent cost of equity capital.

In Year �1, for example, we projected PepsiCo’s net income to be $6,110.9 million. We forecasted other comprehensive income items to be zero, so projected comprehensive income and net income are equal. (Recall from the earlier discussion that the residual income model requires that we measure income for common equity shareholders compre- hensively by using clean surplus accounting.) We projected that preferred stock outstand- ing would be liquidated, requiring liquidating dividends of $169.0 million in Year �1; so net income available to common shareholders is $5,941.9 million. Given that PepsiCo’s

E X H I B I T 1 3 . 3

Valuation of PepsiCo: Present Value of Residual Income Year �1 through Year �5

(dollar amounts in millions)

Year �1 Year �2 Year �3 Year �4 Year �5

Common Shareholders’ Equity (at beginning of year; denoted BV

t–1 ) $12,203.0 $12,656.1 $13,467.4 $14,465.3 $15,323.5

Net (Comprehensive) Income Available for Common Shareholders (denoted NI

t ) $ 5,941.9 $ 6,602.1 $ 7,272.7 $ 7,726.4 $ 8,427.3

Required Income (R E

× BV t–1

) (1,037.3) (1,075.8) (1,144.7) (1,229.5) (1,302.5)

Residual Income [NI t – (R

E × BV

t–1 )] $ 4,904.6 $ 5,526.3 $ 6,128.0 $ 6,496.9 $ 7,124.8

Present Value Factors (R E

� 8.50 percent) 0.922 0.849 0.783 0.722 0.665

Present Value of Residual Income $ 4,520.4 $ 4,694.4 $ 4,797.6 $ 4,688.0 $ 4,738.3

Sum of Present Value Residual Income Year �1 through Year �5 $23,438.7

Valuation of PepsiCo Using the Residual Income Model 1021

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1022 Chapter 13 Valuation: Earnings-Based Approaches

book value of common shareholders’ equity at the beginning of Year �1 is $12,203.0 mil- lion and PepsiCo’s cost of equity capital is 8.50 percent, we project Year �1 required earn- ings to be $1,037.3 million (� 0.085 � $12,203.0 million). Therefore, we project Year �1 residual income will be $4,904.6 million (� $5,941.9 million � $1,037.3 million).

To project PepsiCo’s residual income continuing in Year �6 and beyond, we forecast that PepsiCo can sustain long-run growth of 3.0 percent per year, consistent with long-run aver- age growth in the economy of 3.0 percent. It is the same assumption we made in forecasting long-run growth in Year �6 and beyond for dividends in Chapter 11 and for free cash flows in Chapter 12. We project Year �6 residual income will be $7,281.5 million, computed by projecting Year �5 net income to grow by 3.0 percent and subtracting required earnings, measured as the equity cost of capital times book value at the end of Year �5, as follows:

RI 6

� [NI 5

� (1 � g)] � [R E

� BV 5 ]

� ($8,427.3 million � 1.03) � (0.085 � $16,453.6 million)

� $8,680.1 million � $1,398.6 million � $7,281.5 million

Discounting Pepsico’s Residual Income to Present Value We discount residual income to present value using PepsiCo’s 8.50 percent cost of equity capital. Exhibit 13.3 shows that the sum of the present value of PepsiCo’s residual income from Year �1 through Year �5 is $23,438.7 million.

We compute the present value of PepsiCo’s continuing value of residual income as a per- petuity beginning in Year �6 with growth at a 3.0 percent rate. To compute the continuing value estimate, we use the perpetuity-with-growth valuation model, which determines the present value of the growing perpetuity at the start of the perpetuity period. We then dis- count that value back to present value at time t�0. We compute the present value of the continuing value of PepsiCo’s residual income as follows (allowing for rounding):

Present Value of Continuing Value

0 � [NI

6 � (1 � g)] � (R

E � BV

5 )] � [1/(R

E � g)]� [1/(1 � R

E )5]

� [($8,427.3 million � 1.03) � (0.085 � $16,453.6 million)]

� [1/(0.085 � 0.03)] � [1/(1 � 0.085)5] � [$8,680.1 million � $1,398.6 million] � 18.18182 � 0.665 � $7,281.5 million � 18.18182 � 0.665 � $88,046.5 million

The total present value of PepsiCo’s residual income is the sum of these two parts:

Present Value of Residual Income Year �1 through Year �5 (Exhibit 13.3) $ 23,438.7 million

Present Value of Continuing Value in Year �6 and beyond 88,046.5 million Present Value of Residual Income $111,485.2 million

Computing Pepsico’s Common Equity Share Value To compute the total value of common equity, we add PepsiCo’s book value of common equity to the present value of residual income. The total value of common equity of PepsiCo as of the beginning of Year �1 is the sum of these two amounts:

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Present Value of Residual Income $111,485.2 million Book Value of Common Shareholders’ Equity 12,203.0 million Present Value of Common Shareholders’ Equity

Before Mid-Year Discounting $123,688.2 million

As Chapter 11 and 12 describe, our present value calculations overdiscount because they discount each year’s residual income for full periods when, in fact, residual income is gen- erated throughout each period and should be discounted from the midpoint of each year to the present. Therefore, to make the correction, we multiply the total by the midyear adjustment factor of 1.0425 [� 1 � (R

E /2) � 1 � (0.085/2)]. Therefore, the total present

value of common shareholders’ equity should be computed as follows:

Present Value of Common Shareholders’ Equity Before Mid-Year Discounting $123,688.2 million

Mid-Year Discounting Adjustment Factor � 1.0425 Total Present Value of Common Shareholders’ Equity $128,945.0 million

Dividing the total present value of common shareholders’ equity of $128,945.0 million by 1,553 million shares outstanding indicates that PepsiCo’s common equity shares have a value of $83.03 per share. This value estimate is identical to the value estimate based on div- idends in Chapter 11 and free cash flows to common equity shareholders in Chapter 12. Exhibit 13.4 summarizes the computations to arrive at PepsiCo’s common equity share value. Exhibit 13.5 presents the residual income model application for PepsiCo from FSAP.

E X H I B I T 1 3 . 4

Valuation of PepsiCo Using the Residual Income Valuation Model (dollar amounts in millions except per-share amounts)

Valuation Steps Computations Amounts

Sum of Present Value of Residual See Exhibit 13.3. Income, Year �1 through Year �5 $ 23,438.7

Add Present Value of Continuing Value Year �6 residual income assumed to grow at 3.0%; discounted at 8.50% � 88,046.5

Total Present Value of Residual Income � $111,485.2

Add: Beginning Book Value of Equity Beginning Book Value of Equity from 2008 Balance Sheet � 12,203.0

Total � $123,688.2

Adjust to Midyear Discounting Multiply by 1�(R E /2) × 1.0425

Total Present Value of Common Equity � $128,945.0

Divide by Shares Outstanding 1,553 million shares outstanding ÷ 1,553.0

Estimated Value per Share � $ 83.03

Current Price per Share $ 54.77 Percent Difference Positive number indicates underpricing 52%

Valuation of PepsiCo Using the Residual Income Model 1023

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1024 Chapter 13 Valuation: Earnings-Based Approaches

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Residual Income Model Implementation Issues 1025

Sensitivity Analysis and Investment Decision Making We cautioned in Chapters 11 and 12 and we reiterate here that one should not place too much confidence in the precision of a single point estimate of firm value using these (or any) forecasts for residual income over the remaining life of any firm, even a mature firm such as PepsiCo. Although we have constructed these forecasts and value estimates with care, the forecasting and valuation process has an inherently high degree of uncertainty and estimation error. Therefore, the analyst should not rely too heavily on any one point esti- mate of the value of a firm’s shares; instead, the analyst should describe a reasonable range of values for a firm’s shares.

Two critical forecasting and valuation parameters are the long-run growth assumption, which we forecast to be 3.0 percent, and the cost of equity capital, which we forecast to be 8.50 percent. With these assumptions, our base case estimate is that PepsiCo common shares should be valued at roughly $83 per share. As in Chapters 11 and 12, we assess the sensitivity of our estimate of PepsiCo’s share value by varying these two parameters across reasonable ranges. Exhibit 13.6 contains the results of sensitivity analysis in FSAP varying the long-run growth assumption from 0–10 percent and the cost of equity capital from 5–20 percent. The data in Exhibit 13.6 show that value estimates of PepsiCo are inversely related to discount rates, holding growth constant. In contrast, share value estimates are positively related to growth rates, holding discount rates constant. We omit value estimates from this analysis when the growth rate equals or exceeds the discount rate because the continuing value computation is meaningless.

As we observed in our sensitivity analyses in Chapters 11 and 12, these data suggest that our value estimate is sensitive to slight variations of our baseline assumptions of 3.0 per- cent long-run growth and an 8.50 percent discount rate. Slight adverse variations in valu- ation parameters (such as 0 percent long-run growth and a 10 percent discount rate) reduce PepsiCo’s share value to as low as $51, whereas slightly more favorable variations (such as 4 percent long-run growth and a 7 percent discount rate) increase PepsiCo’s share value to $145. If our forecast and valuation assumptions are realistic, our baseline value estimate for PepsiCo is $83 per share at the end of 2008. At that time, the market price of $54.77 per share indicates that PepsiCo shares were underpriced by about 52 percent. Under our forecast assumptions, PepsiCo’s share value could vary within a range of a low of $51 per share to a high of $145 per share with only minor perturbations in our growth rate and discount rate assumptions. Given PepsiCo’s $54.77 share price, these value esti- mates would have supported a buy recommendation at the end of 2008.

RESIDUAL INCOME MODEL IMPLEMENTATION ISSUES The residual income valuation model is a rigorous and straightforward valuation approach, but the analyst should be aware of four important implementation issues: (1) “dirty sur- plus” accounting items, (2) common stock transactions, (3) portions of net income attrib- utable to equity claimants other than common shareholders, and (4) negative book value of equity. The next four sections describe these issues.

Dirty Surplus Accounting The first implementation issue arises because the residual income model requires that the analyst follow clean surplus accounting in developing expectations for future earnings, dividends, and book values. This means that the expected future income amounts should

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1026 Chapter 13 Valuation: Earnings-Based Approaches

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include all of the income recognized by the firm for the common equity shareholders and that all-inclusive dividends should include all capital transactions with common equity shareholders. Currently, U.S. GAAP and IFRS do not follow clean surplus accounting. U.S. GAAP admits four dirty surplus items. These items are the other comprehensive income amounts that firms recognize directly in shareholders’ equity. The four dirty surplus items are unrealized fair value gains and losses on available-for-sale investment securities, foreign currency translation gains and losses, changes in assets and liabilities related to pensions and postemployment benefits that arise from plan amendments and actuarial experience, and the effects of cash flow hedges. U.S. GAAP requires that firms recognize these items in comprehensive income but does not allow firms to recognize them in net income until they are realized (for example, when the firm realizes gains or losses by selling an available-for- sale investment security). Under U.S. GAAP and IFRS, firms usually report comprehensive income in the Statement of Common Shareholders’ Equity or in a note to the financial statements.

For example, PepsiCo reported in the Consolidated Statement of Common Shareholders’ Equity and again in Note 13, “Accumulated Other Comprehensive Loss” (Appendix A), that in 2008, other comprehensive income items totaled �$3,793 million. As a result of these items, PepsiCo’s comprehensive income in 2008 was $1,349 million (� net income of $5,142 million minus other comprehensive income items totaling $3,793 mil- lion). By the end of 2008, total accumulated other comprehensive loss (which measures total accumulated other comprehensive income adjustments over the life of PepsiCo and is included as a component of shareholders’ equity) declined from �$952 million to �$4,694 million. As Chapters 7 and 10 described, the main two culprits driving other comprehen- sive income for PepsiCo have been foreign currency translation adjustments, amounting to �$2,484 million in 2008, and a cumulative total of �$2,271 million, as well as pension and retiree benefits adjustments amounting to �$1,303 million in 2008, and a cumulative total of �$2,435 million.

The four dirty surplus items in U.S. GAAP typically arise because of unrealized gains and losses attributable to changes in market prices, such as changes in investment security fair values, foreign currency exchange rates, or interest rates. Thus, in expectation, the ana- lyst may determine that such gains and losses are certain to occur but that it is impossible to predict with precision either the sign or amount of the future unrealized gains and losses. In that case, the analyst would likely forecast the expected future dirty surplus items to be zero, on average, and therefore forecast net income and comprehensive income to be equal. We used this assumption in building forecasts for PepsiCo in Chapter 10.

On the other hand, if the analyst can project the amounts and timing of future unreal- ized gains and losses from available-for-sale investment securities, gains and losses from foreign currency translations, gains and losses from cash flow hedges, and adjustments to assets and liabilities related to pension and postretirement benefits from plan amendments and actuarial experience, the analyst should incorporate these unrealized gains and losses in comprehensive income forecasts and base the residual income valuation on comprehen- sive income rather than net income. To allow for either possibility (expectations of zero or nonzero comprehensive income items in the future), the residual income model in the Valuation spreadsheet in FSAP begins with forecasts of future comprehensive income.

Common Stock Transactions Common stock transactions that change the intrinsic value of existing common sharehold- ers’ equity also can cause violations of the clean surplus accounting relation and hinder the ability of the residual income model to measure firm value correctly. To illustrate, consider the firm that sells common shares or repurchases common shares at transaction prices that

Residual Income Model Implementation Issues 1027

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1028 Chapter 13 Valuation: Earnings-Based Approaches

exactly reflect the intrinsic value of the shares (that is, share sales or repurchases that are zero net present value projects for existing shareholders). Such transactions leave the exist- ing shareholders’ value unchanged, and clean surplus accounting holds for these transac- tions. On the other hand, suppose the firm issues common shares at a price that is lower than their intrinsic value. This transaction has a dilutive effect on (that is, reduces the value of ) all of the existing common shares. Net income and the all-inclusive dividend do not reflect this loss in value to existing shareholders, so it violates clean surplus accounting.

It is reasonable to assume that clean surplus accounting for most common stock transac- tions holds, in expectation, because most issues and repurchases of common shares are accounted for at market value. Most of these capital transactions will likely have zero net present value effects on existing shareholders and will conform to clean surplus accounting.

The most prominent exception, however, is the issuance of common equity shares for employee stock options exercises. As Chapter 6 discusses, the exercise of stock options by employees at strike prices below the prevailing market price dilutes the existing sharehold- ers’ equity value. If the firm estimates the fair value of the employee stock options at the time it grants them and recognizes the estimated value of the grants as an expense in measuring net income, it mitigates the violation of clean surplus accounting. In this case, the analyst should forecast the fair value of expected future options grants and subtract these estimated expenses when forecasting expected future net income. We followed this approach in Chapter 10 in building our forecasts of net income for PepsiCo because PepsiCo expenses the fair value of stock options at the date of grant. Under Statement No. 123 (Revised 2004) and IAS 2, firms are required to expense the fair value of stock options by amortizing them over the vesting period, beginning at the date of grant.12

It is not uncommon for firms to repurchase common equity shares in the open market and then use these shares to fulfill stock option exercises. In that case, the accounting for the stock repurchase at market value and the issue of the treasury share at the option strike price captures the dilutive effect of the option exercise on shareholders’ equity. For exam- ple, if the firm repurchases a share in the market for $60 and issues it to an employee exer- cising an option with a strike price of $40, the net effect of the accounting will capture the $20 decrease in shareholders’ equity. On the other hand, if the firm fulfills stock option exercises by issuing new shares (or treasury shares repurchased in prior periods at prices that do not reflect the current period market value), the accounting will reflect the issue of the shares at the option’s strike price and the dilutive effect on existing shareholders will violate clean surplus accounting.

In 2008, for example, PepsiCo reports in the Consolidated Statement of Common Shareholders’ Equity (Appendix A) that it repurchased a total of 68 million shares for $4,720 million, implying an average cost of $69.41 per share. PepsiCo also discloses in that statement that it reissued 15 million treasury shares for options exercises, thereby increas- ing equity capital by $603 million ($883 million in the Repurchased Common Stock account less $280 million in the Capital in Excess of Par Value account), for an average book value of $40.20 per share issued. The difference between the average cost of $69.41 per share and the average book value of $40.20 per share indicates an average dilution of $29.21 per share issued. Given that PepsiCo issued 15 million shares, the total dilution is $438 mil- lion. With 1,553 million shares outstanding, that amounts to $0.282 dilution per outstand- ing share, which is roughly 0.5 percent of the year-end share price of $54.77.

The analyst should devote particular time and attention to stock-based compensation when valuing a firm with substantial amounts of options outstanding that will likely be

12 The FASB Statement No. 123 (Revised 2004) “Accounting for Share-Based Payment,” and the IASB International Financial

Reporting Standard 2 “Share-Based Payment” were issued in 2004.

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Consistency in Residual Income, Dividends, and Free Cash Flow Value Estimates 1029

exercised (options that the analyst expects will ultimately expire or be forfeited pose no problems for valuation) or a firm that is likely to grant large numbers of options in the future that will probably be exercised. In cases like these, the analyst should explicitly fore- cast future stock-based compensation expenses that include the fair values of future options grants. In addition, the analyst should forecast the future dilutive effects of options exercises on the book value of common equity. The analyst should capture both effects (stock-based compensation expense effects on income and stock option exercise effects on book value of equity) in valuation.13

Portions of Net Income Attributable to Equity Claimants Other Than Common Shareholders In some circumstances, a portion of net income is attributable to equity claimants other than common shareholders. For example, preferred stockholders may be entitled to prefer- ence in dividends over common shareholders. Also, minority shareholders have a claim on the portion of net income that is attributable to their share of the equity in the subsidiary they own. For purposes of residual income measurement and valuation, these portions of net income do not represent net income available to the common equity shareholders and should be excluded from residual income. Residual income valuation should be based on the net income available for common equity shareholders. In the case of PepsiCo in Year �1, for example, we forecast that PepsiCo will pay a $169 million liquidating dividend to retire outstanding preferred stock; so we measure residual income after subtracting this dividend to determine net income available to common equity shareholders. PepsiCo did not disclose any minority equity shareholders at the end of 2008.

Negative Book Value of Common Shareholders’ Equity Some firms report negative amounts for total common shareholders’ equity (liabilities exceed assets). This is not common, but it can arise among firms that are in the start-up phase of the life cycle, when the firm’s operations may be generating significant losses. Negative book value of common equity also can arise following a significant releveraging, during which time the firm may use debt capital to repurchase shares or pay dividends, driving total shareholders’ equity below zero.

In these uncommon cases, the analyst should not use the residual income valuation approach because the computation of required earnings (R

E � BV

t–1 ) will be negative. The

computation of residual income [NI t � (R

E � BV

t–1 )] will then effectively result in adding

(subtracting a negative amount) required earnings to net income, which is not correct. In this situation, the analyst should simply rely on the dividends valuation approach and the free cash flows valuation approach.14

CONSISTENCY IN RESIDUAL INCOME, DIVIDENDS, AND FREE CASH FLOW VALUE ESTIMATES As Exhibit 13.1 illustrates, the fourth and final step toward understanding residual income valuation—and valuation in general—is to understand the internal consistency between

13 For an illustration of stock options and valuation, see Leonard Soffer, “SFAS No. 123 Disclosures and Discounted Cash Flow

Valuation,” Accounting Horizons Vol. 14, No. 2 (June 2000), pp. 169–189.

14 Note that this implementation issue arises only when total book value of common shareholders’ equity is negative. This imple-

mentation issue does not arise when retained earnings is a negative amount (in such circumstances, it is termed retained deficit),

but when total book value of common shareholders’ equity is positive. This situation is not uncommon among firms that have

generated significant operating losses, particularly during the start-up phase.

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1030 Chapter 13 Valuation: Earnings-Based Approaches

the dividends valuation approach, the free cash flows valuation approach, and the earnings- based valuation approach. Throughout Chapters 11–13, we have anchored the discussions of each of the valuation approaches on the common, general valuation model and have conceptually and theoretically linked each valuation approach to that general model. Along the way, we have demonstrated the internal consistency of these approaches through our analysis and valuation of PepsiCo and have demonstrated the equivalence of value esti- mates based on residual income, free cash flows, and dividends.

The former baseball player and coach Yogi Berra is reported to have said, “In theory, practice and theory are the same. In practice, they’re not.” In theory, all three valuation models, when correctly implemented with internally consistent assumptions, will produce the same estimates of value. In practice, the analyst may discover that the three models yield different value estimates. If so, the analyst should check the analysis for one or more of the following three common errors (errors that we have experienced ourselves).15

1. Incomplete or inconsistent earnings and cash flow forecasts. The analyst should make sure that projected earnings, cash flows, and dividends are complete and based on assumptions that are consistent with one another. As Chapter 10 emphasized, the analyst can reduce the chance of incomplete or inconsistent forecasts by forecasting complete financial statements in which the balance sheets balance, the income state- ments add up, and the statements of cash flows articulate with the income statements and the changes in the balance sheets. The analyst also should ensure that projected shareholders’ equity reflects clean surplus accounting. As suggested in Chapter 10, relying on the additivity and articulation of financial statements will help the ana- lyst avoid inconsistent forecasts and valuations.

2. Inconsistent estimates of weighted average costs of capital. Suppose the analyst com- putes the present value of free cash flows to all debt and equity capital using the weighted average cost of capital as a discount rate and then subtracts the present value of debt and preferred stock to determine the present value of common equity value (as shown in Chapter 12). The only way the value estimates from this approach will be identical with value estimates from the residual income approach or the divi - dends approach is if the weighted average cost of capital uses weights that are per- fectly internally consistent with the present values of debt, preferred stock, and common equity. Thus, the analyst may have to iterate the computation of the weighted average cost of capital a number of times until all of the weights and pres- ent values are internally consistent.

3. Incorrect continuing value computations. Chapters 11–13 have emphasized that the analyst must carefully estimate continuing value, particularly the Year T�1 amount for residual income, free cash flow, and dividends. If the analyst uses inconsistent assumptions to project the beginning amounts used to compute continuing value, the value estimates will not agree. To avoid this problem, the analyst should first project the Year T�1 income statement and balance sheet amounts assuming a uni- form rate of growth (1 � g) and then use these projections to derive the Year T�1 amounts for residual income, free cash flow, and dividends. The derived amounts for Year T�1 can then be used as the starting values of the perpetuity to calculate con- tinuing value. A common error that analysts make is simply to assume that all resid- ual income, free cash flows, and dividends in Year T will grow at the same rate g. This

15 For a more complete description of diagnosing errors that can cause differences in the three value model estimates, see Russell

Lundholm and Terry O’Keefe, “Reconciling Value Estimates from the Discounted Cash Flow Model and the Residual Income

Model,” Contemporary Accounting Research (Summer 2001), pp. 1–26.

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Questions, Exercises, Problems, and Cases 1031

shortcut will not ensure consistent assumptions and valuation. As described in the past three chapters, that shortcut may impound inconsistent assumptions in the Year T�1 amounts and therefore inconsistent value estimates.

SUMMARY COMMENTS ON VALUATION Chapters 11–13 have described and applied three different but equivalent approaches to valuation using the present value of projected dividends, the present value of projected free cash flows, and the present value of projected residual income. Together these approaches are theoretically sound and practical techniques to convert forecasts of future cash flows, earnings, and dividends into estimates of firm value. Our experience with valuation sug- gests that using several valuation approaches yields more useful insights than using just one approach in all circumstances. Chapter 14 demonstrates a variety of additional valuation techniques, including the use of market-based valuation multiples, such as market-to-book ratios and price-earnings ratios.

QUESTIONS, EXERCISES, PROBLEMS, AND CASES

Questions and Exercises 13.1 REQUIRED INCOME. Explain required income. What does required income represent? How is required income conceptually analogous to interest expense?

13.2 RESIDUAL INCOME. Explain residual income. What does residual income represent? What does residual income measure?

13.3 INTERPRETING RESIDUAL INCOME. If a firm’s residual income for a particular year is positive, does that mean the firm was profitable? Explain. If a firm’s residual income for a particular year is negative, does that mean the firm necessarily reported a loss on the income statement? Explain. What does it mean when a firm’s resid- ual income is zero?

13.4 THE EFFECTS OF INVESTMENTS ON RESIDUAL INCOME. Assume that the firm’s cost of equity capital is 10 percent and that the firm’s existing assets and operations generate a 10 percent return on common equity. If the firm raises additional equity capital and invests in assets that will generate a return less than 10 percent, what effect will that investment have on the firm’s residual income? If the firm raises additional equity capital and invests in assets that will generate a rate of return that exceeds 10 per- cent, what effect will that investment have on the firm’s residual income?

13.5 THE EFFECTS OF BORROWING ON RESIDUAL INCOME. If the firm borrows capital from a bank and invests it in assets that earn a return greater than the interest rate charged by the bank, what effect will that have on residual income for the firm? How does that effect compare with the effects of capital structure leverage described in Chapters 4 and 5?

13.6 THE EFFECTS OF COMPETITION ON RESIDUAL INCOME. If the firm competes in a very competitive, mature industry, what effect will competitive conditions have on residual income for the firm and others in the industry? Now suppose the firm holds a competitive advantage in an industry, but the advantage is not likely to be sustainable for

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1032 Chapter 13 Valuation: Earnings-Based Approaches

more than a few years because of the potential for entry in the industry. As the firm’s competi - tive advantage diminishes, what effect will that have on that firm’s residual income?

13.7 THE RESIDUAL INCOME VALUATION APPROACH. Explain the the- ory behind the residual income valuation approach. Why is residual income value-relevant to common equity shareholders?

13.8 THE RESIDUAL INCOME VALUATION APPROACH. Explain the two roles of book value of common shareholders’ equity in the residual income valuation approach.

13.9 VALUATION APPROACH EQUIVALENCE. Conceptually, why should an analyst expect valuation based on dividends, valuation based on the free cash flows for common equity shareholders, and valuation based on the residual income approach to yield equivalent value estimates?

13.10 APPROPRIATE DISCOUNT RATES. Why is it appropriate to use the required rate of return on equity capital (rather than the weighted average cost of capital) as the discount rate in the residual income valuation approach?

13.11 THE EFFECTS OF CONSERVATIVE ACCOUNTING ON RESID- UAL INCOME VALUATION. Suppose you are applying the residual income valu - ation model to value a firm with extremely conservative accounting. Suppose, for example, the firm is following U.S. GAAP or IFRS but the firm does not recognize a substantial intangible asset on the balance sheet. (Perhaps the firm has expensed substantial amounts of research and development expenditures that have lead to valuable intellectual property or substantial amounts of advertising that have created a valuable brand name). As a con- sequence of this extremely conservative accounting, the firm reports assets and equity at book values that are much lower than their respective economic values. Explain why the residual income value estimates will not be distorted by conservative accounting. How does the residual income valuation model correct for the effects of conservative accounting and understated book values of equity?

13.12 THE EFFECTS OF AGGRESSIVE ACCOUNTING ON RESIDUAL INCOME VALUATION. Suppose you are applying the residual income valuation model to value a firm with extremely aggressive accounting. Suppose, for example, the firm has a substantially overvalued asset on the balance sheet. (Perhaps the firm has a large amount of goodwill on the balance sheet from a prior acquisition and has delayed record- ing a necessary impairment charge that would write off the value of the goodwill.) As a con- sequence of this extremely aggressive accounting, the firm reports assets and equity at book values that are much higher than their respective economic values. Explain why the resid- ual income value estimates will not be distorted by aggressive accounting. How does the residual income valuation model correct for the effects of aggressive accounting and over- stated book values of equity?

Problems and Cases 13.13 COMPUTING RESIDUAL INCOME. The following data represent total assets, book value, and market value of common shareholders’ equity (dollar amounts in millions) for Abbott Labs, IBM, and Target Stores. Abbott Labs manufactures and sells

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health care products. IBM develops and manufactures computer hardware and offers related technology services. Target Stores operates a chain of general merchandise discount retail stores. In addition, these data include existing market betas for the three firms and analysts’ consensus forecasts of net income for Year �1 (in millions). Assume that for each firm, analysts expect other comprehensive income items for Year �1 to be zero; so Year �1 net income and comprehensive income will be identical. Assume that the risk-free rate of return in the economy is 4.0 percent and the market risk premium is 5.0 percent.

Abbott Target Labs IBM Stores

Total Assets $42,419 $109,524 $44,106 Common Equity:

Book Value $17,480 $ 13,466 $13,712 Market Value $83,050 $166,420 $34,600

Market Equity Beta 0.27 0.73 1.09 Analysts’ Consensus Forecasts

of Net Income for Year �1 $ 5,750 $ 12,956 $ 2,384

Required a. Using the CAPM, compute the required rate of return on equity capital for each

firm. b. Project required income for Year �1 for each firm. c. Project residual income for Year �1 for each firm. d. What do the different amounts of residual income imply about each firm? Do the

projected residual income amounts help explain the differences in market value of equity across these three firms? Explain.

13.14 COMPUTING RESIDUAL INCOME. The following data represent total assets, book value, and market value of common shareholders’ equity (dollar amounts in millions) for Microsoft, Intel, and Dell, three firms involved in different aspects of the computer technology industry. Microsoft engages primarily in the development, manu- facture, license, and support of software products. Intel develops and manufactures semi- conductor chips and microprocessors for the computing and communications industries. Dell designs and manufactures a range of computer hardware systems, such as laptops, desktops, and servers. These data also include existing market betas for these three firms and analysts’ consensus forecasts of net income for Year �1 (in millions). Assume that for each firm, analysts expect other comprehensive income items for Year �1 to be zero; so Year �1 net income and comprehensive income will be identical. Assume that the risk-free rate of return in the economy is 4.0 percent and the market risk premium is 5.0 percent.

Microsoft Intel Dell

Total Assets $ 77,888 $ 50,715 $26,500 Common Equity:

Book Value $ 39,558 $ 39,088 $ 4,271 Market Value $264,510 $112,480 $26,000

Market Equity Beta 0.96 1.12 1.28 Analysts’ Consensus Forecasts

of Net Income for Year �1 $ 16,250 $ 8,060 $ 1,882

Questions, Exercises, Problems, and Cases 1033

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1034 Chapter 13 Valuation: Earnings-Based Approaches

Required a. Using the CAPM, compute the required rate of return on equity capital for each

firm. b. Project required income for Year �1 for each firm. c. Project residual income for Year �1 for each firm. d. Rank the three firms using expected residual income for Year �1 relative to book

value of common equity. e. What do the different amounts of residual income imply about each firm? Do the

projected residual income amounts help explain the differences in market value of equity across these three firms? Explain.

13.15 COMPUTING RESIDUAL INCOME. The following data represent total assets, book value, and market value of common shareholders’ equity (dollar amounts in millions) for three firms. Each of these firms, Southwest Airlines, Kroger, and Yum! Brands, operates in a different industry, but all of them operate in very competitive industries. Southwest Airlines is a U.S. domestic airline that provides low-cost point-to-point air transportation services. Kroger operates retail supermarkets across the United States. Yum! Brands operates and franchises quick-service restaurants, including KFC, Pizza Hut, Taco Bell, Long John Silver, and A&W All American Food restaurants. These data also include existing market betas for the three firms and analysts’ consensus forecasts of net income for Year �1 (in millions). Assume that for each firm, analysts expect other comprehensive income items for Year �1 to be zero; so Year �1 net income and comprehensive income will be identical. Assume that the risk-free rate of return in the economy is 4.0 percent and the market risk premium is 5.0 percent.

Southwest Yum! Airlines Kroger Brands

Total Assets $14,308 $23,211 $ 7,242 Common Equity:

Book Value $ 4,953 $ 5,176 $ 1,139 Market Value $ 7,490 $14,870 $15,950

Market Equity Beta 1.10 0.35 1.04 Analysts’ Consensus Forecasts

of Net Income for Year �1 $ 252 $ 1,263 $ 1,010

Required a. Using the CAPM, compute the required rate of return on equity capital for each

value of common equity. e. What do the different amounts of residual income imply about each firm? Do the

projected residual income amounts help explain the differences in market value of equity across these three firms? Explain.

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13.16 EQUITY VALUATION USING THE RESIDUAL INCOME MODEL. Morrissey Tool Company manufactures machine tools for other manufacturing firms. The firm is wholly owned by Kelsey Morrissey. The firm’s accountant developed the following long-term forecasts of net income:

Year �1: $213,948 Year �2: $192,008 Year �3: $187,444 Year �4: $196,442 Year �5: $206,667

The accountant expects net income to grow 5 percent annually after Year �5. Kelsey with- draws 30 percent of net income each year as a dividend. Total common shareholders’ equity on January 1, Year �1, is $1,111,141. Kelsey expects to earn a rate of return on her invested equity capital of 12 percent each year.

Required a. Using the residual income valuation model, compute the value of Morrissey Tool

Company as of January 1, Year �1. b. What advice would you give Kelsey regarding her ownership of the firm?

13.17 EQUITY VALUATION USING THE RESIDUAL INCOME AND DIVIDEND DISCOUNT MODELS. Priority Contractors provides maintenance and cleaning services to various corporate clients in New York City. The firm has provided the following forecasts of net income for Year �1 to Year �5:

Year �1: $478,246 Year �2: $491,882 Year �3: $485,568 Year �4: $515,533 Year �5: $554,198

Total common shareholders’ equity was $2,224,401 on January 1, Year �1. The firm does not expect to pay a dividend during the period of Year �1 to Year �5. The cost of equity capital is 12 percent.

Required a. Compute the value of Priority Contractors on January 1, Year �1, using the residual

income valuation model. The firm expects net income to grow 5 percent annually after Year �5.

b. Compute the value of Priority Contractors on January 1, Year �1, using the divi- dend discount model. The firm will pay its first dividend in Year �6. (Hint: Solve for the dividend amount using clean surplus accounting and 5 percent growth in earn- ings and shareholders’ equity in Year �6.)

13.18 EQUITY VALUATION USING THE RESIDUAL INCOME, FREE CASH FLOW, AND DIVIDEND DISCOUNT MODELS. Exhibit 13.7 pres- ents selected data from projected financial statements for Steak ’n Shake for Year �1 to Year �11. The amounts for Year �11 reflect a long-term growth assumption of 3 percent. The cost of equity capital is 9.34 percent.

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1036 Chapter 13 Valuation: Earnings-Based Approaches

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Required a. Compute the value of Steak ’n Shake as of January 1, Year �1, using the residual

income model. b. Repeat Part a using the present value of expected free cash flows to the common

equity shareholders. c. Repeat Part a using the dividend discount model. d. Identify the reasons for any differences in the valuations in Parts a–c. e. The market value of Steak ’n Shake on January 1, Year �1, is $309.98 million. Based on

your valuations in Parts a–c, what is your assessment of the market value of this firm?

13.19 RESIDUAL INCOME VALUATION. The Coca-Cola Company is a global soft-drink beverage company (ticker: KO) that is a primary and direct competitor with PepsiCo. The data in Chapter 12’s Exhibits 12.13, 12.14, and 12.15 include the actual amounts for 2006, 2007, and 2008 and projected amounts for Year �1 to Year �6 for the income statements, balance sheets, and statements of cash flows, respectively, for Coca-Cola (in millions).

The market equity beta for Coca-Cola at the end of 2008 is 0.61. Assume that the risk- free interest rate is 4.0 percent and the market risk premium is 6.0 percent. Coca-Cola has 2,312 million shares outstanding at the end of 2008, when Coca-Cola’s share price was $44.42.

Required

Part I—Computing Coca-Cola’s Share Value Using the Residual Income Valuation Approach

a. Use the CAPM to compute the required rate of return on common equity capital for Coca-Cola.

b. Derive the projected residual income for Coca-Cola for Years �1 through �6 based on the projected financial statements. The financial statement forecasts for Year �6 assume that Coca-Cola will experience a steady-state long-run growth rate of 3 per- cent in Year �6 and beyond.

c. Using the required rate of return on common equity from Part a as a discount rate, compute the sum of the present value of residual income for Coca-Cola for Years �1 through �5.

d. Using the required rate of return on common equity from Part a as a discount rate and the long-run growth rate from Part b, compute the continuing value of Coca- Cola as of the start of Year �6 based on Coca-Cola’s continuing residual income in Year �6 and beyond. After computing continuing value as of the start of Year �6, discount it to present value at the start of Year �1.

e. Compute the value of a share of Coca-Cola common stock. (1) Compute the total sum of the present value of all residual income (from Parts c and d). (2) Add the book value of equity as of the beginning of the valuation (that is, as of the end of 2008, or the start of Year�1). (3) Adjust the total sum of the present value of resid- ual income plus book value of common equity using the midyear discounting adjustment factor. (4) Compute the per-share value estimate.

Part II—Sensitivity Analysis and Recommendation

f. Using the residual income valuation approach, recompute the value of Coca-Cola shares under two alternative scenarios. Scenario 1: Assume that Coca-Cola’s long-run growth will be 2 percent, not 3 percent as above, and that Coca-Cola’s required rate

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1038 Chapter 13 Valuation: Earnings-Based Approaches

of return on equity is 1 percent higher than that calculated in Part a. Scenario 2: Assume that Coca-Cola’s long-run growth will be 4 percent, not 3 percent as above, and that Coca-Cola’s required rate of return on equity is 1 percent lower than that cal- culated in Part a. To quantify the sensitivity of your share value estimate for Coca- Cola to these variations in growth and discount rates, compare (in percentage terms) your value estimates under these two scenarios with your value estimate from Part e.

g. Using these data at the end of 2008, what reasonable range of share values would you have expected for Coca-Cola common stock? At that time, what was the market price for Coca-Cola shares relative to this range? What would you have recommended?

h. If you completed Problem 12.16 in Chapter 12, compare the value estimate you obtained in Part e of that problem (using the free cash flows to common equity shareholders valuation approach) with the value estimate you obtain here using the residual income valuation approach. The value estimates should be the same. If you have not completed Problem 12.16, you would benefit from doing so now.

13.20 RESIDUAL INCOME VALUATION. In Problem 10.16, we projected financial statements for Wal-Mart Stores, Inc. (Walmart) for Years �1 through �5. The data in Chapter 12’s Exhibits 12.16, 12.17, and 12.18 include the actual amounts for 2008 and the projected amounts for Year �1 to Year �5 for the income statements, balance sheets, and statements of cash flows, respectively, for Walmart (in millions).

Required

Part I—Computing Walmart’s Share Value Using the Residual Income Valuation Approach

a. Use the CAPM to compute the required rate of return on common equity capital for Walmart.

b. Derive the projected residual income for Walmart for Years �1 through �5 based on the projected financial statements.

c. Project the continuing residual income in Year �6. Assume that the steady-state long-run growth rate will be 3 percent in Year �6 and beyond. Project that the Year �5 income statement and balance sheet amounts will grow by 3 percent in Year �6; then derive the projected amount of residual income for Year �6.

d. Using the required rate of return on common equity from Part a as a discount rate, compute the sum of the present value of residual income for Walmart for Years �1 through �5.

e. Using the required rate of return on common equity from Part a as a discount rate and the long-run growth rate from Part c, compute the continuing value of Walmart as of the start of Year �6 based on Walmart’s continuing residual income in Year �6 and beyond. After computing continuing value as of the start of Year �6, discount it to present value at the start of Year �1.

f. Compute the value of a share of Walmart common stock. (1) Compute the total sum of the present value of all future residual income (from Parts d and e). (2) Add the book value of equity as of the beginning of the valuation (that is, as of the end of 2008, or the start of Year �1). (3) Adjust the total sum of the present value of resid- ual income plus book value of common equity using the midyear discounting adjustment factor. (4) Compute the per-share value estimate.

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Starbucks 1039

Part II—Sensitivity Analysis and Recommendation g. Using the residual income valuation method, recompute the value of Walmart shares

under two alternative scenarios. Scenario 1: Assume that Walmart’s long-run growth will be 2 percent, not 3 percent as above, and that Walmart’s required rate of return on equity is 1 percentage point higher than the rate you computed using the CAPM in Part a. Scenario 2: Assume that Walmart’s long-run growth will be 4 percent, not 3 percent as above, and that Walmart’s required rate of return on equity is 1 percent- age point lower than the rate you computed using the CAPM in Part a. To quantify the sensitivity of your share value estimate for Walmart to these variations in growth and discount rates, compare (in percentage terms) your value estimates under these two scenarios with your value estimate from Part f.

h. Using these data at the end of 2008, what reasonable range of share values would you have expected for Walmart common stock? At that time, what was the market price for Walmart shares relative to this range? What would you have recommended?

i. If you worked Problem 11.14 from Chapter 11 and computed Walmart’s share value using the dividends valuation approach, compare your value estimate from Part g of that problem with the value estimate you obtained here. Similarly, if you worked Problem 12.17 from Chapter 12 and computed Walmart’s share value using the free cash flows to common equity shareholders, compare your value estimate from Part f of that problem with the value estimate you obtained here. You should obtain the same value estimates for Walmart shares under all three approaches. If you have not worked both of those problems, you would benefit from doing so now.

INTEGRATIVE CASE 12.1

STARBUCKS

Residual Income Valuation of Starbucks’ Common Equity In Integrative Case 10.1, we projected financial statements for Starbucks for Years �1 through �5. In this portion of the Starbucks Integrative Case, we use the projected finan- cial statements from Integrative Case 10.1 and apply the techniques in Chapter 13 to com- pute Starbucks’ required rate of return on equity and share value based on the residual income valuation model. We also compare our value estimate to Starbucks’ share price at the time of the case to provide an investment recommendation.

The market equity beta for Starbucks at the end of 2008 is 0.58. Assume that the risk- free interest rate is 4.0 percent and the market risk premium is 6.0 percent. Starbucks has 735.5 million shares outstanding at the end of 2008. At the start of Year �1, Starbucks’ share price was $14.17.

Required

Part I—Computing Starbucks’ Share Value Using the Residual Income Valuation Approach

a. Use the CAPM to compute the required rate of return on common equity capital for Starbucks.

b. Using your projected financial statements from Integrative Case 10.1 for Starbucks, derive the projected residual income for Starbucks for Years �1 through �5.

c. Project the continuing residual income in Year �6. Assume that the steady-state long-run growth rate will be 3 percent in Year �6 and beyond. Project that the Year

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�5 income statement and balance sheet amounts will grow by 3 percent in Year �6; then derive the projected residual income for Year �6.

d. Using the required rate of return on common equity from Part a as a discount rate, compute the sum of the present value of residual income for Starbucks for Years �1 through �5.

e. Using the required rate of return on common equity from Part a as a discount rate and the long-run growth rate from Part c, compute the continuing value of Starbucks as of the start of Year �6 based on Starbucks’ continuing residual income in Year �6 and beyond. After computing continuing value as of the start of Year �6, discount it to present value at the start of Year �1.

f. Compute the value of a share of Starbucks common stock. (1) Compute the total sum of the present value of all future residual income (from Parts d and e). (2) Add the book value of equity as of the beginning of the valuation (that is, as of the end of 2008, or the start of Year �1). (3) Adjust the total sum of the present value of residual income plus book value of common equity using the midyear discounting adjustment factor. (4) Compute the per-share value estimate.

Part II—Sensitivity Analysis and Recommendation g. Using the residual income valuation approach, recompute the value of Starbucks

shares under two alternative scenarios. Scenario 1: Assume that Starbucks’ long-run growth will be 2 percent, not 3 percent as above, and that Starbucks’ required rate of return on equity is 1 percentage point higher than the rate you computed using the CAPM in Part a. Scenario 2: Assume that Starbucks’ long-run growth will be 4 per- cent, not 3 percent as above, and that Starbucks’ required rate of return on equity is 1 percentage point lower than the rate you computed using the CAPM in Part a. To quantify the sensitivity of your share value estimate for Starbucks to these variations in growth and discount rates, compare (in percentage terms) your value estimates under these two scenarios with your value estimate from Part f.

h. At the end of 2008, what reasonable range of share values would you have expected for Starbucks common stock? At that time, where was the market price for Starbucks shares relative to this range? What would you have recommended?

i. If you computed Starbucks’ common equity share value using the dividends valu - ation approach in Integrative Case 11.1 in Chapter 11, compare the value estimate you obtained in that case with the estimate you obtained in this case. Similarly, if you computed Starbucks’ common equity share value using the free cash flows to com- mon equity shareholders valuation approach in Integrative Case 12.1 in Chapter 12, compare the value estimate you obtained in that case with the estimate you obtained in this case. You should obtain the same value estimates under all three approaches. If you have not worked both of those cases, you would benefit from doing so now.

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Chapter 14

Valuation: Market-Based Approaches

Learning Objectives

1 Understand how to use market-based valuation multiples such as MB (market-to-book) and PE (price-earnings) ratios to evaluate how the capital markets value a particular stock, along with the practical advantages and disadvantages of using market-based valuation multiples.

2 Apply a version of the residual income valuation model to compute the VB (value-to- book) ratio and understand how to make investment decisions by comparing the VB ratio to the MB ratio.

3 Understand how to compute and use the firm’s VE (value-earnings ratio). Understand how to incorporate growth into the VE ratio to compute the VEG (value-earnings- growth) ratio. Make investment decisions by comparing the VE and VEG ratios to the PE ratio and the PEG (price-earnings-growth ratio), respectively. Use VE and VEG ratios and PE and PEG ratios to analyze firm value over time and across firms.

4 Analyze the impact of the following factors on market multiples: (a) risk and the cost of equity capital, (b) growth, (c) differences between current and expected future earnings, and (d) alternative accounting methods and principles. Use these factors to explain how VB, VE, and VEG ratios should differ across firms and why MB, PE, and PEG ratios do differ across firms.

5 Estimate the price differential, which is the difference between market price and “risk- neutral value”.

6 Reverse-engineer a firm’s stock price to determine the implicit expected return or the implicit expected long-run growth rate.

7 Understand the role of capital market efficiency in valuation and the academic evidence on the degree to which the capital markets efficiently impound earnings information into share prices. Exploit earnings information for investment decisions by forecasting future earnings, reacting when firms announce earnings each quarter and each year, and incorporating earnings into valuation.

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INTRODUCTION AND OVERVIEW Chapters 1–13 focus on using the information in accounting numbers, financial statements, and related notes to analyze firms’ fundamental characteristics of profitability, risk, growth, and value. These prior chapters establish a disciplined and effective six-step framework to attack a very difficult but interesting problem—how to analyze and value a business. To use this framework, we must first understand the firm’s industry and business strategy and then use that understanding to assess the quality of the firm’s accounting, making adjustments as necessary. We then evaluate the firm’s profitability, risk, growth, efficiency, liquidity, and leverage, using a set of financial ratios. On the foundation of these steps, we construct fore- casts of future financial statements, from which we derive the expected future earnings, cash flows, and dividends that form the bases for valuation. We then apply valuation models based on expected future dividends, free cash flows, and residual income to value the firm and assess the sensitivity of firm value estimates to key valuation parameters such as the cost of capital and the expected long-run growth rate. To culminate this process, we compute the realistic range of firm value estimates and compare this range to the firm’s share price in the market in order to make an intelligent investment decision.

Exhibit 14.1 provides a summary representation of this fundamentals-driven valuation process. The top of the exhibit depicts the firm’s value drivers, such as expected future earn- ings, cash flows, growth, and risk, which comprise the economic foundations of valuation. We capture these value drivers in forecasts of future financial statements, and then convert these forecasts into estimates of firm value using the residual income model, the free cash flows model, and the dividends model.

1042 Chapter 14 Valuation: Market-Based Approaches

E X H I B I T 1 4 . 1

Fundamentals of Valuation

Fundamental Value Drivers over the Remaining Life of the Firm: Expected Future Earnings, Cash Flows, Growth, Risk

Financial Statement Forecasts

Compute: Book Value of Common Equity + Present Value of Expected Future Residual Income

= Present Value of Expected Future Free Cash Flows to Common Equity Shareholders = Present Value of Expected Future Dividends

Firm Value

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Introduction and Overview 1043

In this chapter, we continue our focus on fundamental characteristics of profitability, risk, growth, and value, but we augment that analytical approach with techniques that allow us to exploit the information in market value and share price. We describe and apply a vari- ety of techniques that compare the firm’s market value or share price to the firm’s funda- mentals. The techniques described in this chapter include commonly used market multiples—MB (market-to-book) ratios, PE (price-earnings) ratios, and PEG (price-earnings- growth) ratios—which provide efficient shortcuts in the valuation process. As Exhibit 14.2 depicts, market multiples require an understanding of the same set of value drivers in the valuation process as the valuation models discussed in Chapters 11–13—expected earnings, cash flows, dividends, growth, and risk—but market multiples collapse the valuation process in two important ways:

1. Instead of developing financial statement forecasts, market multiples use just one or two summary accounting numbers (such as earnings or book value of equity) to represent the value drivers.

2. Instead of using extensive present value computations, market multiples summarize value using relatively simple ratios of market value of common equity to summary accounting numbers.

In this chapter, we also demonstrate two additional techniques to infer and exploit the information in share prices. First, we introduce a measure of the impact of risk on share price, which we call the price differential. Second, we demonstrate reverse-engineering share prices, which enables an analyst to infer the assumptions the capital market appears to be making in pricing a particular share. In the last section of the chapter, we summarize a few

E X H I B I T 1 4 . 2

Market Multiples

Fundamental Value Drivers over the Remaining Life of the Firm: Expected Future Earnings, Cash Flows, Growth, Risk

Summary Accounting Numbers: Book Value of Common Shareholders’ Equity, Earnings, Long-Run Growth

Market Multiples: Market-to-Book Ratios, Price-Earnings Ratios, Price-Earnings-Growth Ratios

Firm Value

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1044 Chapter 14 Valuation: Market-Based Approaches

key insights from the last 40 years of accounting and finance research suggesting that the capital markets are highly but not perfectly efficient in using accounting earnings informa- tion to price stocks. These research findings are encouraging for those interested in using earnings and accounting information for fundamental analysis and valuation of stocks and for developing trading strategies to exploit accounting information.

MARKET MULTIPLES OF ACCOUNTING NUMBERS Throughout this text, we have described how to analyze and exploit a wide array of finan- cial information: earnings, financial statements, footnotes, supplemental management dis- closures, financial ratios, growth rates, and others. However, we have not analyzed and exploited the information in one very important number: share price. The market price for a share of common equity is a special and informative number: it aggregates the expecta- tions of all of the market participants following that particular stock. The market price is the result of the market’s trading activity in that stock. It summarizes the aggregate infor- mation the market participants have about the firm and their aggregate expectations for the firm’s future profitability, growth, risk, and value.

The market price of a share does not mean that all market participants agree that the price is the correct value for the share. In fact, the prices at which potential buyers or sellers may be willing to trade differ across market participants and over time. Indeed, the market price sim- ply indicates that the equilibrium point at which the forces of supply (market participants potentially willing to sell the stock—the “ask” side of trading) and the forces of demand (mar- ket participants potentially willing to buy the stock—the “bid” side of trading) are momen- tarily in balance. Stock prices are dynamic, constantly changing with the arrival of new information that changes investors’ expectations about share value and triggers trading in the firm’s shares in the market. We can analyze share price to obtain a wealth of information.

Market participants commonly calibrate firm valuation using market value or share price expressed as a multiple of a fundamental summary accounting number, such as the MB ratio or the PE ratio. These market multiples play two important roles for analysts: as analytical tools and as valuation tools. As analytical tools, market multiples capture relative valuation per dollar of book value or per dollar of earnings. In this way, market multiples measure market value (or share price) relative to a key accounting number as a common denominator, thereby enabling analysts to draw inferences about a particular firm’s relative market capitalization, to assess changes in a firm’s relative valuation over time, to compare values across firms, and to project comparable firms’ values. For example, PE ratios allow an analyst to quickly gauge and compare the multiples at which the market is capitalizing different firms’ annual earnings. As analytical tools, market multiples enable analysts to conduct time-series and cross-sectional analyses to summarize and compare how the capi - tal markets are valuing stocks (in the same way analysts compare other ratios such as ROA and ROCE across firms and over time).

Market multiples also can serve as useful and efficient fundamental valuation tools, but they must be applied and interpreted carefully, after considering the firm’s expected future profitability, growth, and risk. Multiples such as MB ratios and PE ratios are relative value metrics; therefore, by themselves, they are not meaningful as valuation measures. For exam- ple, an analyst cannot determine whether a particular firm’s PE ratio should be 10, 20, 50, or some other number unless the analyst knows the firm’s fundamental characteristics— expected future profitability, growth, and risk. Similarly, an analyst cannot determine whether a particular firm’s PE ratio should be higher or lower than some other firm’s PE ratio or an industry average PE ratio unless the analyst knows how the firm’s expected future profitability, growth, and risk characteristics compare to those characteristics of the

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1 As noted in Chapter 13, credit for the rigorous development of the residual income model and its extension to the value-to-book

ratio model goes to James A. Ohlson, “A Synthesis of Security Valuation Theory and the Role of Dividends, Cash Flows, and

Earnings,” Contemporary Accounting Research (Spring 1990), pp. 648–676; James A. Ohlson, “Earnings, Book Values, and

Dividends in Equity Valuation,” Contemporary Accounting Research (Spring 1995), pp. 661–687; Gerald A. Feltham and James A.

Ohlson, “Valuation and Clean Surplus Accounting for Operating and Financial Activities,” Contemporary Accounting Research

(Spring 1995), pp. 216–230. The ideas underlying the value-to-book ratio also trace to early work by G.A.D. Preinreich, “Annual

Survey of Economic Theory: The Theory of Depreciation,” Econometrica (1938), pp. 219–241 and Edgar O. Edwards and Philip

W. Bell, The Theory and Measurement of Business Income (Berkeley, CA: University of California Press), 1961.

other firm or the industry as a whole. For example, a firm may have a very high PE ratio at a particular point in time for very different reasons: perhaps the share price is too high, per- haps the market expects and prices very high future earnings growth, or perhaps the firm experienced temporarily low earnings last period (because of a restructuring charge, for example). If an analyst uses market multiples to draw naive inferences about the firm’s mar- ket price without carefully researching the firm’s fundamentals, the analyst is at risk for badly misinterpreting market multiples.

Market multiples can be very useful shortcut valuation tools. Unfortunately, analysts sometimes apply market multiples as valuation tools to estimate value in ad hoc ways. Valuation using market multiples may be easy (the so-called “quick-and-dirty” approach), but also may be misleading. A naive analyst might be tempted to value a firm simply by using that firm’s historical average or the industry average market multiple. The firm’s his- torical average MB ratio, for example, may be an appropriate fit for the valuation of the firm today, but only if the firm’s current fundamental characteristics match those of the past. In the same vein, an industry average price-earnings multiple may be an appropriate yardstick for valuing a particular firm, but only if that firm’s fundamental characteristics match the industry averages. If the firm’s fundamentals are different today than they were in the past or if the firm’s fundamentals do not match the industry averages, market mul- tiples must be adjusted to reflect the firm’s fundamental characteristics.

This chapter continues to emphasize the distinction between value and price. The chap- ter focuses on how to compute value-based multiples that properly reflect the firm’s funda- mentals and that can be reliably compared to market price-based multiples. This focus also directs our attention to the factors that drive multiples so that the analyst can avoid being ad hoc and can adjust historical or industry average multiples correctly to reflect the firm’s expected profitability, growth, and risk appropriately.

MARKET-TO-BOOK AND VALUE-TO-BOOK RATIOS The MB ratio can be computed easily by dividing the firm’s market value of common equity at a point in time by the book value of common shareholders’ equity from the firm’s most recent balance sheet. For example, at the end of 2008, PepsiCo’s market value was $85,058 million (� $54.77 per share � 1,553 million shares) and PepsiCo’s 2008 book value of common shareholders’ equity was $12,203.0 million (Appendix A). Thus, PepsiCo was trading at an MB ratio equal to 6.97 (� $85,058 million/$12,203 million). The MB ratio measures market value as a multiple of accounting book value at a point in time. The MB ratio reflects what the market value is, but it does not tell us what the ratio should be given our estimate of intrinsic value.

A Theoretical Model of the Value-to-Book Ratio1

We can compute the ratio of the firm’s intrinsic value of common shareholders’ equity divided by the book value of common shareholders’ equity—the VB ratio—using a version

Market-to-Book and Value-to-Book Ratios 1045

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1046 Chapter 14 Valuation: Market-Based Approaches

of the residual income model developed in Chapter 13. In fact, the VB ratio model is sim- ply the residual income model scaled by book value of common shareholders’ equity. The numerator of the VB ratio is the estimated intrinsic value of common equity, which takes into account the book value of common shareholders’ equity, expected future profitability, growth, risk, and the time value of money. The analyst can compare the VB ratio to the MB ratio to evaluate share price and make an investment decision the same way previous chap- ters compared intrinsic value to share price. The analyst also can use the VB ratio of one firm to estimate the value of a comparable firm provided the analyst makes the appropri- ate and necessary adjustments to the VB ratio so that it reflects the comparable firm’s fun- damental characteristics. This section demonstrates the theoretical and empirical relation between intrinsic value, book value, and market value.

Using the same notation from prior chapters, we compute the VB ratio using the follow- ing model:

V 0

∞

BV t–1

� 1 � ∑

[ROCE t � R

E ] �

BV 0

BV 0 t = 1

(1 + R E )t

In short, the VB ratio should be equal to 1 plus the present value of expected future resid- ual return on common equity [the (ROCE

t � R

E ) term above] times cumulative growth

in book value (the BV t�1

/BV 0

term above). The growth in book value indicates the increase in net assets on which firms can earn residual income. The growth in book value depends on ROCE, dividend payout, and changes in common stock outstanding from share issues or repurchases. As the model shows, if a firm generates greater positive residual ROCE [ROCE

t � R

E ] and generates greater growth in book value (through reinvested earnings

and/or stock issues) on which the firm will earn positive residual ROCE, the firm will cre- ate greater value for shareholders (the numerator on the right-hand side will increase, so the value-to-book ratio will increase).

To derive this model, recall from Chapter 13 the residual income valuation model:

∞ V

0 � BV

0 � ∑

NI t � (R

E � BV

t–1 )

t = 1 (1 + RE) t

The residual income valuation model estimates the value of common shareholders’ equity as equal to the book value of common equity plus the present value of all expected future residual income, which is the amount by which expected future earnings exceed required earnings for the remaining life of the firm.2 We compute the required earnings (or “nor- mal” earnings) of the firm in Year t as the product of the required rate of return on com- mon equity capital times the book value of common equity at the beginning of Year t (R

E �

BV t�1

). Required earnings captures the amount of net income the firm must generate to provide a return to common equity capital that is equal to the cost of common equity capi - tal. We measure residual income (or “abnormal” earnings) by the subtraction term NI

t �

(R E

� BV t�1

). Residual income is the difference between expected net income in Year t and required earnings of the firm in Year t. Residual income measures the amount of wealth the

2 Chapter 13 described that the residual income valuation model depends on clean surplus accounting for book value of common

shareholders’ equity, which requires expected future earnings forecasts to be comprehensive measures of income for the firm’s

common equity shareholders and expected future dividends to reflect all capital transactions between the firm and common

equity shareholders. Throughout this chapter, when we refer to expected future “earnings” or “net income” in the context of resid-

ual income valuation, we mean expected future comprehensive income available for common shareholders under clean surplus

accounting.

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Market-to-Book and Value-to-Book Ratios 1047

analyst expects the firm to create (or destroy) in Year t for common equity shareholders above (or below) the required return to equity capital.

To convert the residual income model into a model for the VB ratio, we scale both sides of the equation by BV

0 , which produces the following equation:

V 0

BV 0

∞

NI t � (RE �

BV t–1)

� � ∑ BV

0 BV

BV 0

BV 0 t = 1

(1 � R E )t

The term BV 0

divided by BV 0

is, of course, equal to 1. We rewrite the NI t /BV

0 term as follows:

NI t

BV t –1

BV t–1

� � � ROCE t �

BV 0

BV t –1

BV 0

To rewrite NI t /BV

0 this way, we state ROCE

t � NI

t /BV

t�1 . Note that this computation of

ROCE t divides net income in period t by book value of common equity at the beginning of

period t. This ROCE computation differs slightly from the approach in Chapter 4 in which we compute ROCE as net income divided by the average book value of equity during period t.3

Also note that BV t�1

/BV 0

is the cumulative growth factor in book value of common equity between year 0 (the date of the valuation) and period t – 1. As indicated previously, growth in book value is a function of the earnings generated each period plus additional capital contributions by shareholders less equity capital paid out to shareholders through dividends and stock buybacks. The growth in book value indicates growth in net assets, on which a firm can earn residual income.4

By decomposing the term NI t /BV

0 into these two parts, we can restate NI

t /BV

0 as the

product of profitability times growth: ROCE in Year t times the cumulative growth in book value from year 0 to the start of Year t. Return on common equity is a function of profitabil- ity relative to beginning-of-year common equity; beginning-of-year common equity is a function of cumulative growth.

We then substitute these two components of NI t /BV

0 into the VB equation as follows:

3 Theoretical and empirical research on the VB ratio defines ROCE as net income to common shareholders for a year divided by

common shareholders’ equity at the beginning of the year. In contrast, in prior chapters (particularly Chapter 4) we used average

common shareholders’ equity in the denominator of ROCE. The theoretical development and application of the VB model in this

section uses shareholders’ equity at the beginning of the year, although the bias in using average shareholders’ equity should not

be particularly significant for most firms.

4 Indeed, as we will discuss in more detail later, if a firm increases common shareholders’ equity through retained earnings or com-

mon equity issues and it does not generate future earnings increases, the firm will experience a decline in the value-to-book ratio.

V 0

∞

BV t–1

� 1 � ∑ (ROCEt � BV

0 ) � (RE � BV

0 )

BV 0 t =1

(1 + R E )t

Now both terms in the numerator of the summation term are multiplied by the same cumulative book value growth factor. We rearrange that equation as follows:

We now have a useful model for the VB ratio. Let’s consider each term.

V 0

∞

BV t–1

� 1 � ∑

[ROCE t � R

E ] �

BV 0

BV 0 t =1 (1 + RE)

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1048 Chapter 14 Valuation: Market-Based Approaches

First, as a starting point, the VB ratio will equal 1, to reflect the book value of common equity invested in the firm. The summation term indicates how the VB ratio should differ from 1 as a function of the firm’s expected future abnormal profitability (the ROCE

t � R

E term) times the firm’s cumulative growth in book value (the BV

t�1 /BV

0 term), all of which

is discounted to present value, reflecting the firm’s cost of equity capital (R E ) and the time

value of money. Thus, the residual income model specifies the firm’s VB ratio as a function of the firm’s value drivers: capital in place, profitability, growth, cost of equity capital, risk, and the time value of money. The VB model provides a valuation approach in which all of the inputs to valuation can be expressed as forecasts of rates—expected future ROCE, R

E ,

and growth. The only dollar amount the analyst needs in order to use the VB ratio to compute the dollar value of common shareholders’ equity is the book value of common shareholders’ equity, which is observable from the shareholders’ equity section of the balance sheet.

The expression for the VB ratio provides some insights into valuation:

• Economics teaches that in equilibrium firms should expect to earn a return equal to the cost of capital (that is, ROCE � R

E ). The VB model indicates that a firm in steady-

state equilibrium earning ROCE � R E

will maintain (not create or destroy) share- holder wealth and will be valued at book value (that is, VB � 1).

• A firm’s value should be greater than its book value of common equity if the firm will generate wealth for common equity shareholders by earning a return (ROCE) that exceeds the cost of capital (R

E ). That is, VB > 1 if ROCE > R

E . Firms earning a return

that is less than the cost of equity capital (that is, ROCE < R E ) will destroy shareholder

wealth and will be valued below book value (that is, VB < 1). • By itself, growth does not add value. Growth adds value to shareholders only if the

growth creates additional residual income for common equity shareholders. If expected ROCE equals R

E on new projects (that is, zero NPV projects), these new proj-

ects will not create (or destroy) common shareholders’ equity value. New projects will be abnormally profitable and create new wealth for equity shareholders (that is, will be positive NPV projects) only when expected ROCE exceeds R

E .

• The risk of the firm increases the equity cost of capital. Increasing the equity cost of capital reduces firm value in two ways: (1) by increasing the required ROCE the firm must earn to cover the increased cost of capital R

E (that is, the “hurdle rate” goes up in

the numerator) and (2) by increasing the discount rate used to compute the present value of residual income (which increases the denominator).

• If a firm’s VB ratio differs from the industry average VB ratio, it should be because the firm’s expected future ROCE, R

E , and/or book value growth differ from the industry

averages. • If a firm’s VB ratio changes over time, current expectations for the firm’s future ROCE,

R E , and/or book value growth should differ from past expectations for the firm’s future

ROCE, R E , and/or book value growth, respectively.

Example 1 Suppose an analyst wants to value a firm with $1,000 of book value of common equity and a cost of equity capital equal to 10 percent. Assume that the analyst forecasts the firm will earn ROCE of 15 percent from Year �1 through Year �3 but that after Year �3, the firm will earn ROCE equal to 10 percent. The analyst also expects the firm will reinvest all net income (that is, pay zero dividends) and not issue or repurchase stock. Using the VB ratio approach, the analyst should assign the firm a VB ratio equal to 1 plus the present value of

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future residual ROCE times growth. The present value of future residual ROCE times growth is determined as follows:

PV of Residual Residual

Cumulative ROCE ROCE Residual Book Value � �

Expected ROCE Growth Factor Cumulative PV Cumulative Year ROCE (ROCE � R

E ) to Year t�1 Growth Factor Growth

+1 0.15 0.05 1.00 � (1.15)0 0.05000 0.9091 0.04545 +2 0.15 0.05 1.15 � (1.15)1 0.05750 0.8264 0.04752 +3 0.15 0.05 1.3225 � (1.15)2 0.06613 0.7513 0.04968 +4 0.10 0.00 1.52088 � (1.15)3 0.00000 0.6830 0.00000

Total 0.14265

The sum of the present values of residual ROCE times cumulative growth through Year �3 equals 0.14265, and the sum in all years after Year �3 is zero. Adding this present value amount to 1 (to reflect the book value of equity already in place), the VB ratio of this firm is 1.14265. Note that we have determined this VB ratio with all of the inputs expressed in rates. We can multiply the VB ratio by book value of equity to determine that firm value is $1,142.65 (� 1.14265 VB ratio � $1,000 book value of equity). We can confirm this value using dollar amounts and the residual income model approach from Chapter 13 as follows:

Cumulative Book Value at the end Required PV of

Expected Expected of Year t�1 Income Residual PV Residual Year ROCE Earnings (BV

t �1 ) (BV

t �1 � R

E ) Income Factor Income

+1 0.15 $150.00 $100 $50.00

� 0.15 � $1,000 $1,000 � $1,000 � 0.10 � $150 � $100 0.9091 $ 45.45

+2 0.15 $172.50 $1,150 $115 $57.50

� 0.15 � $1,150 � $1,000 � $150 � $1,150 � 0.10 � $172.50 � $115 0.8264 $ 47.52

+3 0.15 $198.38 $1,322.5 $132.25 $66.13

� 0.15 � $1,322.5 � $1,150 � $172.50 � $1,322.5 � 0.10 � $198.38 � $132.25 0.7513 $ 49.68

+4 0.10 $152.09 $1,520.88 $152.09 $0.00

� 0.10 � $1,520.88 � $1,322.50 � $198.38 � $1,520.88 � 0.10 � $152.09 � $152.09 0.6830 $ 0.00

Total $142.65

The sum of the present values of residual income through Year �3 equals $142.65, the sum in all years after Year �3 is zero, and book value of equity is $1,000; so the residual income model confirms that firm value is $1,142.65.

The Value-to-Book Model with Finite Horizon Earnings Forecasts and Continuing Value Computation As we discussed in Chapters 11–13, analysts commonly forecast income statements and balance sheets over a foreseeable, finite horizon and then make simplifying growth rate assumptions for

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1050 Chapter 14 Valuation: Market-Based Approaches

the years continuing after the forecast horizon. We can modify the value-to-book ratio model to include specific forecasts of net income, book value of common equity, and ROCE through Year T (where T is a finite horizon, for example, five or ten years in the future) and then apply a constant growth rate assumption (denoted as g) to project ROCE for Year T�1 and all years thereafter. We used similar approaches to forecast and value dividends in Chapter 11, free cash flows in Chapter 12, and residual income in Chapter 13.

To develop the value-to-book model with finite horizon earnings forecasts and continu - ing value computations, we will follow the same approach used in Chapter 13, with only slight modifications. Recall from Chapter 13 that we used specific forecasts of financial statements for a finite horizon through Year T and then projected Year T�1 net income by multiplying Year T net income by the long-run growth factor (1 � g). We then computed Year T�1 residual income (denoted as RI

T�1 ) as follows:

RI T�1

� [NI T

� (1 � g)] � [R E

� BV T ]

By estimating RI T�1

this way, we apply the same uniform long-run growth factor (1 � g) to estimate Year T�1 income statement and balance sheet amounts and compute internally consistent projections for Year T�1 free cash flows, dividends, and residual income.

As we discussed in Chapter 13, after computing RI T�1

, the analyst can treat RI T�1

as a growing perpetuity of residual income beginning in Year T�1. The analyst can compute the present value of the perpetuity of residual income using the perpetuity-with-growth value model as follows:

Present Value of Continuing Value

0 � [NI

T � (1 � g)] � [R

E � BV

T ] � [1/(R

E � g)] � [1/(1�R

E )T]

We can modify this computation to adapt it to the value-to-book model with two steps:

1. Divide the term [NI T

� (1 � g)] by BV T

to convert it to an ROCE measure for Year T�1.

2. Divide the BV T

term by BV 0

to measure the cumulative growth in book value.

The result of these two steps is a continuing value computation based on projected future residual ROCE and book value growth as follows:

Present Value of Continuing Value 0

� [{NI T

� (1 � g)/BV T } � R

E ] � [BV

T /BV

0 ] � [1/(R

E � g)] � [1/(1�R

E )T]

� [ROCE T+1

� R E ] � [BV

T /BV

0 ] � [1/(R

E � g)] � [1/(1�R

E )T]

(1) (2) (3) (4)

The first term in the computation is projected residual ROCE in Year T�1. The second term is the cumulative growth in book value from present (BV

0 ) to the beginning of the

continuing value period (BV T ). The third term is the familiar perpetuity-with-growth fac-

tor, computing the present value of the perpetuity as of the start of the continuing value period. And the fourth term is familiar as the present value factor that discounts continu- ing value to present value today.

We include the continuing value computation into the finite horizon value-to-book model as follows:

V 0

BV t–1

� 1 � ∑

[ROCE t � R

E ] �

BV 0

� [ROCE T+1

� R E ] � [BV

T /BV

0 ] � [1/(R

E � g)] � [1/(1�R

E )T]

BV 0 t = 1

(1 + R E )t

(1) (2) (3)

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Application of the Value-to-Book Model to PepsiCo 1051

This model computes the value-to-book ratio of common equity based on three parts: (1) book value scaled by book value (equal to 1, which represents BV

0 /BV

0 ), (2) the present

value of residual ROCE over the explicit forecast horizon through Year T (the summation term), and (3) the present value of continuing value based on the present value of residual ROCE as a perpetuity with growth beginning in Year T�1.

APPLICATION OF THE VALUE-TO-BOOK MODEL TO PEPSICO In Chapter 13, we determined that PepsiCo’s share value at the end of 2008 should be within a reasonable range centered on $83.03. We determined this amount using the finan- cial statement forecasts developed in Chapter 10 and the residual income valuation model. Next, we illustrate the valuation of PepsiCo shares using the value-to-book model. We rely on the same financial statement forecasts developed in Chapter 10, the same equity cost of capital (8.50 percent), and the same expected long-run growth rate (3.0 percent). We pre - sent all of the forecasts and valuation models in the FSAP Forecasts and Valuation spread- sheet in Appendix C.

To compute the VB model for PepsiCo and to use it to make an investment decision with regard to PepsiCo shares, we follow these nine steps:

1. For each forecast year, project the expected ROCE, computed as NI t /BV

t�1 .

2. For each forecast year, compute expected residual ROCE by subtracting the equity cost of capital from expected ROCE.

3. Determine the cumulative growth factor in book value of common shareholders’ equity to the beginning of each forecast year (computed as BV

t �1 /BV

0 ).

4. Multiply the expected residual ROCE by the cumulative growth factor each forecast year.

5. Discount to present value the expected residual ROCE times growth for each fore- cast year.

6. Compute continuing value based on expected residual ROCE as a perpetuity with growth beginning in Year T�1, and discount continuing value to present value.

7. Add 1 (the ratio of book value over book value) plus the sum of the present values of all expected future residual ROCE times growth plus the present value of continu - ing value.

8. Compute the implied VB ratio by multiplying the sum by the midyear discounting adjustment factor [1 � (R

E /2)], as described in prior chapters.

9. Compare the implied VB ratio to the MB ratio to determine whether market price is greater than, equal to, or less than the estimate of value. Equivalently, you can mul- tiply the implied VB ratio by book value of equity to determine the value of com- mon shareholders’ equity and then divide by the number of shares outstanding to convert this total to an estimate of share value, which you then compare directly to share price.

Next, we illustrate each of these nine steps with PepsiCo. The Year �1 projected ROCE is 48.7 percent, computed as projected comprehensive income available for common shareholders in Year �1 divided by book value of common equity at the start of Year �1 (� $5,941.9 million/$12,203.0 million). The residual ROCE is 40.2 percent after subtracting 8.50 percent for the cost of equity capital. The cumulative growth factor in book value (BV

t�1 /BV

0 ) in Year �1 is 1.0 because Year �1 is the first year of the valuation horizon.5

5 We project that PepsiCo’s book value of common equity will grow to $12,656.1 million during Year �1. Therefore, the cumulative

growth factor in book value of common equity as of the start of Year �2 will be 1.037 (� $12,656.1 million/$12,203.0 million).

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1052 Chapter 14 Valuation: Market-Based Approaches

Therefore, the product of Year �1 residual ROCE and the cumulative growth factor is 40.2 percent, which we discount to present value using the 8.50 percent cost of equity capital. Exhibit 14.3 presents these computations for PepsiCo for Year �1 through Year �5. The sum of the present value of residual ROCE times growth in Year �1 through Year �5 is 1.921.6

We use the same steps to compute the Year �6 residual ROCE for purposes of comput- ing continuing value. As described in the previous chapter, we project comprehensive income in Year �6 to grow by the 3.0 percent long-run growth rate. We compute book value as of the start of Year �6 (the end of Year �5), compute implied residual ROCE, and mul- tiply by the cumulative growth factor in book value up to the beginning of Year �6. The pro- jected ROCE in Year �6 is 52.8 percent [� (NI

5 � {1�g })/BV

5 � ($8,427.3 million �

1.03)/$16,453.6 million � $8,680.1 million/$16,453.6 million]. After subtracting the 8.50 percent cost of equity capital, the projected residual ROCE in Year �6 is 44.3 percent. Cumulative growth in book value from Year 0 to the beginning of Year �6 (the end of Year �5) is 1.348 (� BV

5 /BV

0 � $16,453.6 million/$12,203.0 million). Therefore, we project that

in Year �6, the product of residual ROCE times cumulative growth is 59.7 percent (� 44.3 percent � 1.348).

E X H I B I T 1 4 . 3

Valuation of PepsiCo Present Value of Residual ROCE in Year +1 through Year +5

(dollar amounts in millions)

Year +1 Year +2 Year +3 Year +4 Year +5

Comprehensive Income Available for Common Shareholders $ 5,941.9 $ 6,602.1 $ 7,272.7 $ 7,726.4 $ 8,427.3

Divide by Book Value of Common Shareholders’ Equity (at t–1) $12,203.0 $12,656.1 $13,467.4 $14,465.3 $15,323.5

Equals Implied ROCE 0.487 0.522 0.540 0.534 0.550 Residual ROCE (after subtracting

0.0850 percent required return on common equity) 0.402 0.437 0.455 0.449 0.465

Cumulative growth factor as of t–1 � 1.000 � 1.037 � 1.104 � 1.185 � 1.256 Residual ROCE times growth 0.402 0.453 0.502 0.532 0.584 Present Value Factors � 0.922 � 0.849 � 0.783 � 0.722 � 0.665 PV Residual ROCE times growth 0.370 0.385 0.393 0.384 0.388 Sum of PV Residual ROCE times

growth, Year +1 through Year +5 1.921

6 This amount should be interpreted as a component of the VB ratio because all of the computations in the model are scaled by

BV 0 . Thus, the amount 1.921 should be interpreted as an estimate of the amount of residual income PepsiCo will create in Years

�1 through �5 that, in present value, is equal to 1.921 times the book value of common equity. To reconcile this computation

with the residual income model computations in Chapter 13, recognize that 1.921 times book value of $12,203.0 million equals

$23,438.7 (allow for rounding), which is the sum of the present value of residual income in Year �1 through Year �5 computed

in Exhibit 13.2.

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We use the Year �6 residual ROCE times growth (59.7 percent) in the computation of the present value of continuing value as follows (allowing for rounding):

Present Value of Continuing Value 0

� [{NI 5

� (1 � g)/BV 5 } � R

E ] � [BV

5 � BV

0 ] � [1/(R

E � g)]� [1/(1 � R

E )5]

� [($8,427.3 � 1.03)/$16,453.6 � 0.085] � [$16,453.6/$12,203.0]

� [1/(0.085 � 0.03)] � [1/(1 � 0.085)5] � 0.443 � 1.348 � 18.182 � 0.665 � 7.215

The total present value of PepsiCo’s expected residual ROCE with growth, expressed as components of the VB ratio, is the sum of these two parts (allow for rounding):

Present Value of Residual ROCE in Year �1 through Year �5 1.921 Present Value of Continuing Value of ROCE in Year �6 and beyond 7.215 Present Value of All Future Residual ROCE 9.136

To compute the VB ratio for common equity, we need to add PepsiCo’s beginning book value of common equity expressed as a ratio of beginning book value of equity, which is, of course, equal to 1. Also, as described in prior chapters, our present value calculations overdiscount because they discount each year’s residual ROCE for full periods when, in fact, the firm generates residual ROCE throughout each period and we should discount from the midpoint of each year to the present. Therefore, to make the correction, we multiply the present value sum by the midyear discounting adjustment factor of 1.0425 [= 1 � (R

E /2) � 1 � (0.085/2)]. Making these two adjustments produces the implied VB

ratio as follows:

Present Value of All Future Residual ROCE 9.136 Add: Beginning Book Value � 1.000 Total 10.136 Multiply by the Midyear Correction Factor � 1.0425 Implied VB Ratio 10.567

These computations suggest that PepsiCo common equity should be valued at 10.567 times the book value of equity at the start of the valuation horizon, which is the end of 2008. At the end of 2008, PepsiCo’s market value was $85,058.0 million (� $54.77 per share � 1,553 million shares) and PepsiCo’s 2008 book value of common shareholders’ equity was $12,203.0 million (Appendix A). Thus, PepsiCo was trading at an MB ratio equal to 6.970 (� $85,058.0 million/$12,203.0 million). The VB ratio of 10.567 is 52 percent greater than the MB ratio of 6.970, implying that PepsiCo shares were underpriced by 52 percent at that time.

Equivalently, we can convert the VB ratio into a share value estimate for purposes of comparing to market price per share. If we multiply book value equity by the VB ratio, we obtain the value estimate of PepsiCo common equity of $128,945.0 million [� $12,203.0 million � 10.567 VB ratio (allow for rounding)]. Dividing by 1,553 million shares out- standing indicates that PepsiCo’s common equity shares have a value of $83.03 per share, which is identical to the value estimates we obtained from the residual income model in Chapter 13, the free cash flows to common equity shareholders model in Chapter 12, and the dividend models in Chapter 11. Comparing the share value estimate of $83.03 to market price per share of $54.77 also indicates that PepsiCo’s shares were underpriced by

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1054 Chapter 14 Valuation: Market-Based Approaches

52 percent at the end of 2008. We summarize the computations to arrive at PepsiCo’s com- mon equity share value using the value-to-book approach in Exhibit 14.4, where we pres- ent the value-to-book model for PepsiCo from FSAP.

We can conduct a sensitivity analysis for the estimate of PepsiCo’s VB ratio to assess a rea- sonable range of VB ratios for PepsiCo. We will find that the sensitivity of the VB ratio esti- mate is identical to the sensitivity of the residual income model value estimates demonstrated in Chapter 13. This is to be expected because both models use the same forecasts and valu - ation assumptions and the VB model is a scaled version of the residual income model.

Reasons Why VB Ratios and MB Ratios May Differ From 1 We described earlier that in long-run equilibrium, VB ratios and MB ratios should con- verge to 1. We also described a number of economic reasons why VB and MB ratios may dif- fer from 1. For example, the firm may have competitive advantages that enable it to earn a ROCE that is greater than R

E . To the extent that the firm can create and sustain these com-

petitive advantages, the firm will increase the magnitude and persistence over time of the degree to which ROCE exceeds R

E , thereby increasing the VB and MB ratios. In addition,

if the firm is expected to generate future growth by investing in abnormally profitable projects, the VB and MB ratios will differ from 1.

A firm’s VB and MB ratio may differ from 1 for accounting reasons in addition to eco- nomic reasons.7 The firm may have investments in projects for which accounting methods and principles cause ROCE to differ from R

E . For example, firms may make substantial

investments in successful R&D projects, brand equity, human capital, or other intangible resources. If these investments are internally generated through R&D activities, marketing and advertising activities, or human capital recruiting and training activities, firms are typi - cally required to expense investments in these activities according to conservative account- ing principles (as is common under GAAP and IFRS).8 If these investments subsequently develop into successful and profitable resources, the firm will have substantial off-balance- sheet assets and off-balance-sheet common shareholders’ equity. These off-balance-sheet assets generate net income, but by being off-balance-sheet, they cause common sharehold- ers’ equity to be understated; so ROCE is relatively high. These effects can be observed among certain firms in many industries, such as pharmaceuticals, biotechnology, software, and consumer goods.

Considering PepsiCo and Coca-Cola, these firms have created substantial off-balance- sheet brand equity over many years of successful product development, advertising, and brand-building activities. Following U.S. GAAP, these firms have expensed their invest- ments in these activities. Thus, for these firms, the book value of common shareholders’ equity does not recognize the off-balance-sheet value of brand equity. Relative to R

E , ROCE

for PepsiCo and Coca-Cola is very high and likely will continue to be very high for many years in the future.

7 Stephen Ryan (1995) found that book value changes lag market value changes in part because U.S. GAAP uses historical cost

valuations for assets. The lag varies in part based on the degree of capital intensity of firms. See Stephen Ryan, “A Model of

Accrual Measurement and Implications for the Evolution of the Book-to-Market Ratio,” Journal of Accounting Research (Spring

1995), pp. 95–112.

8 GAAP and IFRS typically require expensing (rather than capitalizing) expenditures on internally generated intangible resources

such as R&D (except IFRS does permit capitalization of development costs), advertising, and human capital because the highly

uncertain future cash flows associated with them are inherently difficult to measure reliably.

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Application of the Value-to-Book Model to PepsiCo 1055

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1056 Chapter 14 Valuation: Market-Based Approaches

Over a sufficiently long period of time, however, the impact of accounting principles on the VB and MB ratio will diminish because economics teaches us to expect that competi- tive equilibrium forces will drive ROCE to converge to R

E in the long run. Also, the self-cor-

recting nature of accounting will eventually eliminate biases in ROCE and book value of equity. For example, consider a biotechnology company that for several years invests in R&D to develop a particular drug. During the initial years of research, the firm incurs research costs that the firm is required to expense under U.S. GAAP. Its ROCE and book value of equity will be “low” during these years. After successfully developing and market- ing the drug, ROCE will be “high” because the firm generates revenues without matching expenses for research costs. The “high” ROCE will increase retained earnings, and over time, the initial conservative biases in ROCE and book value will be corrected.

Empirical Data on MB Ratios Exhibit 14.5 presents descriptive statistics for MB ratios across 37 industries during the decade from 1998–2007 (the same industries and years for which Exhibit 11.3 in Chapter 11 provided data on median market betas).9 The descriptive statistics include the 25th percentile, median, and 75th percentile MB ratios for the sample as a whole and for each industry, listed in ascending order of the median MB ratio. The median MB ratio for the 69,810 firm-years in this sample is 1.91. These data reveal substantial variation in MB ratios across industries and within industries during this period. The descriptive statistics on MB and other ratios across industries and years in Appendix D also reveal substantial variation in MB ratios.

The differences in industry median MB ratios in Exhibit 14.5 likely relate, in part, to dif- ferences in competitive conditions driving differences in growth and ROCE relative to R

E as well as differences in applicable accounting principles across firms and time. Economically, in an industry that can be characterized as mature and competitive, the median firm will likely generate ROCE that is close to R

E and will not likely generate unusu-

ally high rates of growth. Such firms tend to have median MB ratios closer to 1. For exam- ple, firms in mature competitive industries such as textiles, insurance, hotels, wholesalers of durables, primary metals, real estate, metal products, airlines, banks, and paper and wood products tend to have MB ratios that are lower than the sample average.

With respect to accounting, the assets of firms in some of these industries—particularly banks and insurers—are primarily investments in financial assets, some of which appear on the balance sheet at fair value; thus, MB ratios are closer to 1. In contrast, some of the industries with relatively high MB ratios are more likely to have off-balance-sheet assets and shareholders’ equity. For example, the tobacco industry contains firms with significant off-balance-sheet brand equity and the chemical industry includes pharmaceutical firms, which expense R&D expenditures in the year incurred. The balance sheet understates the economic value of key resources in these industries. These industries have MB ratios con- siderably in excess of 1.

Empirical Research Results on the Predictive Power of MB Ratios Several empirical studies have found that MB ratios are fairly stable, mean reverting slowly over time, and that MB ratios are reliable predictors of future growth in book value and

9 To compute these descriptive statistics on market-to-book value ratios, we deleted firm-years with negative book value of equity.

We also deleted firm-year observations in the top 1 percent of the distribution as potential outliers with undue influence on the

descriptive statistics.

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E X H I B I T 1 4 . 5

Descriptive Statistics on Market-to-Book Ratios, 1998–2007 Industries Sorted by Median Market-to-Book Ratio

Industry: 25th Percentile Median 75th Percentile

Full Sample on Compustat (N = 69,810 firm-years)* 1.17 1.91 3.52 Industry: Textiles 0.49 0.88 1.33 Insurers 0.90 1.24 1.72 Hotels 0.77 1.24 2.10 Wholesalers—Durables 0.80 1.31 2.35 Primary Metals 0.77 1.35 2.16 Real Estate 0.81 1.36 2.80 Metal Products 0.91 1.43 2.35 Transportation by Air 1.04 1.54 2.96 Paper 1.07 1.54 2.33 Depository Institutions 1.15 1.55 2.09 Lumber and Wood Products 0.91 1.57 2.42 Personal Services 0.86 1.70 3.12 Wholesalers—Nondurables 0.99 1.71 3.06 Restaurants 0.93 1.72 3.16 Utilities 1.34 1.75 2.34 Retailers—Home Furniture, Furnishings and Equipment 0.86 1.76 3.32 Retailers—General Merchandise 0.86 1.80 3.31 Grocery Stores 0.98 1.82 3.07 Transportation Equipment 1.12 1.83 3.19 Forestry 1.28 1.91 2.69 Motion Pictures 1.08 1.98 3.93 Amusements and Recreation 1.04 1.99 3.49 Retailers—Apparel 1.23 2.00 3.53 Printing and Publishing 1.18 2.00 3.56 Electronic and Electrical Equipment 1.24 2.08 3.79 Food Products 1.26 2.11 3.95 Health Services 1.23 2.12 3.70 Industrial and Commercial Machinery

and Computer Equipment 1.27 2.12 3.78 Oil and Gas Extraction 1.35 2.14 3.46 Petroleum Refining 1.52 2.16 3.01 Security and Commodity Brokers 1.28 2.20 4.75 Communications 1.37 2.40 4.77 Instruments and Related Products 1.46 2.54 4.49 Business Services 1.44 2.75 5.61 Metal Mining 1.47 2.84 4.95 Chemicals 1.88 3.43 6.53 Tobacco 2.69 5.52 14.43

* To compute these descriptive statistics on market-to-book value ratios, we deleted firm-years with negative book value of equity. We also deleted firm-

year observations in the top 1 percent of the distribution as potential outliers with undue influence on the descriptive statistics.

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1058 Chapter 14 Valuation: Market-Based Approaches

expected future ROCE (implying that ROCE also mean reverts slowly).10 For example, Victor Bernard grouped roughly 1,900 firms into ten portfolios each year between 1972 and 1981 based on their MB ratios. He then computed the mean ROCE for each portfolio in the formation year and for each of the ten subsequent years. Exhibit 14.6 summarizes a portion of Bernard’s results, grouping firms in the lowest three MB portfolios, middle four MB portfolios, and highest three MB portfolios.11

The data in Exhibit 14.6 indicate that firms with the highest MB ratios tend to have the highest ROCEs through Year �10 and firms with the lowest MB ratios tend to have the low- est ROCEs through Year �10. The results from the Bernard study also indicate that firms with the highest MB ratios have the highest growth rates in book value of equity through Year �10 and firms with the lowest MB ratios have the lowest growth rates through Year �10. In addition, the results in the Bernard study indicate (although it is not apparent from the summary of results in Exhibit 14.6) that the predictive power of MB ratios for future ROCEs tends to diminish as the horizon lengthens. In Year �10, for example, there is rela- tively little difference in ROCEs across firms in the third through ninth MB portfolios, as these firms experience ROCEs that tended to converge to 14 percent during Bernard’s sam- ple period. These results are consistent with the steady mean reversion in ROCEs over time, consistent with movement toward competitive equilibrium.

E X H I B I T 1 4 . 6

The Relation between MB Ratios, Future ROCE, and Future Book Value Growth

Median ROCE for Year:

MB Portfolio Mean MB Ratio 0 +1 +5 +10

Low 0.67 0.11 0.09 0.12 0.12 Medium 1.15 0.11 0.13 0.14 0.14 High 2.65 0.10 0.17 0.16 0.20

Cumulative Percent Increase in Book Value through Year:

MB Portfolio Mean MB Ratio 0 +1 +5 +10

Low 0.67 0% 15% 54% 190% Medium 1.15 0% 15% 69% 204% High 2.65 0% 21% 139% 394%

10 Victor L. Bernard, “Accounting-Based Valuation Methods, Determinants of Market-to-Book Ratios and Implications for

Financial Statement Analysis,” Working Paper, University of Michigan (1993); Jane A. Ou and Stephen H. Penman, “Financial

Statement Analysis and the Evaluation of Market-to-Book Ratios,” Working Paper, Columbia University (1995); Stephen H.

Penman, “The Articulation of Price-Earnings Ratios and Market-to-Book Ratios and the Evaluation of Growth,” Journal of

Accounting Research, Vol. 34, No. 2 (Autumn 1996), pp. 235–259; William H. Beaver and Stephen G. Ryan, “Biases and Lags in Book

Value and Their Effects on the Ability of the Book-to-Market Ratio to Predict Book Return on Equity,” Journal of Accounting

Research, Vol. 38, No. 1 (Spring 2000), pp. 127–149.

11 To reduce the effects of survivorship bias, Bernard included firms that did not survive the entire ten-year future horizon and

included any gain or loss on the cessation of the firm (from bankruptcy, takeover, or liquidation) in the final year ROCE.

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Price-Earnings and Value-Earnings Ratios 1059

PRICE-EARNINGS AND VALUE-EARNINGS RATIOS As noted in Chapter 13, the capital markets devote enormous amounts of time and energy to forecasting and analyzing firms’ earnings. Therefore, it is no surprise that the market multiple that receives most frequent use and attention is the PE ratio. Analysts’ reports and the financial press make frequent references to PE ratios. The Wall Street Journal reports PE ratios as part of the daily coverage of stock prices and trading activity. The capital markets increasingly evaluate ratios that integrate the PE ratio with expected future earnings growth to capture explicitly the links between price, profitability, and growth.

This section begins by describing the theoretical model for computing VE ratios and then describes computing and using PE ratios from a practical perspective. It then discusses the strict assumptions implied by PE ratios and describes the conditions in which PE ratios may not capture appropriately the theoretical relation between value and earnings for most firms and the difficulties encountered in reconciling actual PE ratios with those indicated by the theoretical value-earnings model. This section also incorporates the role of earnings growth and examines PEG ratios. The section concludes by describing empirical data on PE ratios, the predictive power of PE ratios, and the empirical evidence on the articulation between PE ratios and MB ratios.

A Model for the Value-Earnings Ratio The VE ratio is computed as the value of common shareholders’ equity divided by earnings for a single period. The previous chapter described how to determine common equity value as a function of present value of expected future earnings and the residual income model. In the residual income model, we use clean surplus accounting and measure future earn- ings as expected future comprehensive income (that is, income that includes all of the income to common shareholders). Thus, in theory, the analyst should measure the VE ratio as the value of common equity divided by the next period’s expected comprehensive income. This way, the VE ratio achieves consistent alignment of perspective (numerator and denominator both forward-looking) and measurement (numerator and denominator both based on comprehensive income).

If one has already computed firm value using the forecasting and valuation models developed in the last four chapters, computing the VE ratio is a simple matter of division. For example, in the preceding section and in prior chapters, we estimated PepsiCo’s com- mon shareholders’ equity value to be $128,945.0 million at the end of 2008. We also pro- jected that Year �1 comprehensive income will equal net income available for common shareholders, which will equal $5,941.9 million. Thus, we can compute the VE ratio for PepsiCo at the end of 2008 as follows:

V 0 /E

1 � $128,945.0 million/$5,941.9 million � 21.7

Or equivalently, on a per-share basis as:

Vps 0 /Eps

1 � ($128,945.0 million/1,553 million shares)/($5,941.9 million/1,553 million shares) � $83.03/$3.83 � 21.7.

We also can derive the VE ratio from the VB ratio determined using the residual income model in the previous section. For this derivation, we employ an algebraic step to derive the firm’s VE ratio from the firm’s VB ratio as follows:

V 0 /E

1 � V

0 /BV

0 � BV

0 /E

1 � V

0 /BV

0 � (1/ROCE

1 )

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1060 Chapter 14 Valuation: Market-Based Approaches

This formula shows that the same factors that drive the VB ratio (V 0 /BV

0 ) also drive the VE

ratio. In fact, the model shows that the VE ratio should be a multiple of the VB ratio, where the multiple is the inverse of ROCE. However, the VE ratio also makes an additional sim- plifying and restrictive assumption: that value can be summarized by one-period-ahead ROCE. A consequence of this assumption is that VE ratios vary inversely with expected future ROCE. Holding VB ratios constant, a firm with a temporarily high level of expected ROCE next period will have a temporarily low VE ratio, and vice versa.

Using this approach, we can derive PepsiCo’s VE ratio from the VB ratio we computed in the previous section, as follows:

V 0 /E

1 � V

0 /BV

0 � BV

0 /E

1 � V

0 /BV

0 � (1/ROCE

1 )

� ($128,945.0 million/$12,203.0 million) � ($12,203.0 million/$5,941.9 million)

� 10.567 � 2.054

� 10.567 � (1/0.487)

� 21.7

Thus, PepsiCo’s VE ratio should equal 21.7. We convert PepsiCo’s VB ratio of 10.567 into the VE ratio by multiplying by 1/ROCE

1 , which we project will be the inverse of 48.7 percent.

Notice that we derived the VE ratio simply from the computation that PepsiCo’s value is equal to $128,945.0 million, which is based on specific forecasts of PepsiCo’s future earn- ings. Obviously, using value to compute a VE ratio will not provide any new information about PepsiCo’s value. So what is the point of computing a VE ratio?

The VE ratio provides the analyst with a theoretically correct benchmark to evaluate the firm’s PE ratio. We can compare PepsiCo’s VE ratio of 21.7 to PepsiCo’s PE ratio to assess the market value of PepsiCo shares. This comparison is equivalent to comparing V to P (that is, value to price). We compute the PE ratio for PepsiCo as of the end of 2008 using our forecast that Year �1 earnings (comprehensive income available to common share- holders) will be $5,941.9 million as follows:

P 0 �E

+1 � Price per share

0 /Earnings per share

�1

� $54.77 per share/($5,941.9 million/1,553 million shares)

� $54.77/$3.83

� 14.3

Thus, at the end of 2008, PepsiCo shares traded at a multiple of 14.3 times the Year �1 earnings forecast. PepsiCo’s VE ratio of 21.7 is 52 percent greater than PepsiCo’s PE ratio of 14.3 at the end of 2008, consistent with our prior estimates of PepsiCo’s value.

With the theoretically correct VE ratio, we also can project VE ratios for other firms after we have made any necessary adjustments to capture the other firms’ fundamental charac- teristics of profitability, growth, and risk. In addition, with the theoretically correct VE ratio, we have a benchmark to gauge other firms’ PE ratios to assess whether the market is under- or overpricing their shares. In the next section, we discuss the practical advantages and disadvantages in using PE ratios as shortcut valuation metrics.

Price-Earnings Ratios As a practical matter, analysts, the financial press, and financial databases commonly mea - sure PE ratios as current period share price divided by reported (historical) earnings per share for the most recent prior fiscal year or the most recent four quarters (sometimes

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referred to as the lagged or trailing-twelve-months earnings per share).12 The Wall Street Journal and financial data websites such as Yahoo! Finance commonly compute PE ratios this way. With this approach, the PE ratio for PepsiCo as of the end of 2008 is equal to price per share

2008 /earnings per share

2008 � $54.77/$3.26 � 16.8. Thus, at the end of 2008,

PepsiCo shares traded at a PE multiple of 16.8 times 2008 earnings per share.13

The common approach to compute the PE ratio by dividing market price per share by earnings per share for the most recent year is practical because analysts can readily observe price and earnings per share for most firms. This approach is efficient because it does not require the analyst to produce a computation of value or a forecast of earnings. However, this common approach creates a logical misalignment for valuation purposes because it divides historical earnings into share price, which reflects the present value of future earn- ings. If historical earnings contain unusual or nonrecurring gains or losses that are not expected to persist in future earnings, the analyst should normalize the reported historical earnings by removing these effects to compute a PE ratio that reflects earnings that are likely to persist in the future. Chapter 9 describes techniques to identify elements of income that are unusual and nonrecurring, adjust reported earnings to eliminate their effects, and thereby measure recurring, persistent earnings.

As an alternative approach to create a more logical alignment of price and earnings, the analyst can compute the “forward PE ratio” by dividing share price by a forecast of future earnings per share (for example, analysts’ consensus forecast of expected earnings per share one year ahead). A PE ratio based on expected future earnings, however, requires the analyst to forecast future earnings (or have access to another analyst’s forecast). Thus, the reliability of a forward PE ratio depends on the reliability of the earnings forecast. Earnings forecast errors will distort forward PE ratios. In addition, as discussed previously for VE ratios, PE ratios will vary inversely with transitory earnings components. If the analysts uses trailing or forward earnings that are temporarily increased by transitory gains or temporarily decreased by transitory losses, the PE ratio will be temporarily biased down or up, respectively.

Recall that in the preceding subsection, we computed the forward PE ratio for PepsiCo as of the end of 2008 using our forecast that Year �1 earnings (comprehensive income available to common shareholders) will be $5,941.9 million as follows: price per share

0 /earnings per

share �1

� $54.77 per share/($5,941.9 million/1,553 million shares) � $54.77/$3.83 � 14.3. Thus, at the end of 2008, PepsiCo shares traded at a forward PE multiple of 14.3 times the Year �1 earnings forecast. PepsiCo’s VE ratio of 21.7 is 52 percent greater than PepsiCo’s for- ward PE ratio of 14.3 at the end of 2008, consistent with our prior estimates of PepsiCo’s value.14

Notice that we derived the PE ratio simply by dividing PepsiCo’s market share price by earnings per share of the past year or by our forecasts of PepsiCo’s future earnings per

12 In theory, to be consistent with clean surplus accounting and residual income valuation, the denominator should be based on com-

prehensive income per share. However, analysts, the financial press, and financial databases rarely compute PE ratios based on com-

prehensive income per share, in part because (1) U.S. GAAP does not yet require reporting comprehensive income on a per-share

basis and (2) the other comprehensive income items are usually unrealized gains and losses that are not likely to be a permanent com-

ponent of income each period. We follow traditional practice in this chapter and compute PE ratios using reported earnings figures.

13 The common approach to computing PE ratios also can be slightly distorted by differences in the number of shares outstand-

ing at year-end that the market uses to compute share price versus the weighted average number of shares outstanding used to

compute earnings per share under U.S. GAAP. If we compute PepsiCo’s PE ratio using amounts in millions rather than per-share

amounts, we obtain a PE ratio of 16.5 [� $85,058.0 million/(net income of $5,142 million � $1 million preferred dividends)].

This PE ratio is slightly lower than the PE ratio of 16.8 based on per share amounts because PepsiCo reports earnings per share

based on the weighted average number of common shares outstanding during the year (as required by U.S. GAAP) rather than the

number of shares outstanding at year-end.

14 In this case, our forecasts of net income and comprehensive income for PepsiCo in Year �1 are the same; so the PE ratio using

earnings per share is equal to that using comprehensive income per share.

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1062 Chapter 14 Valuation: Market-Based Approaches

share. Obviously, using price to compute a PE ratio will not provide any new information about PepsiCo’s share value. So what is the point of computing a PE ratio?

PE ratios are practical tools used by analysts interested in valuation shortcuts. In some circumstances, analysts need to react with timely ballpark estimates of valuation, and PE ratios provide a quick and efficient way to estimate firm value as a multiple of earnings. Analysts commonly assess benchmark PE ratios that they expect a firm to have based on past PE ratios for that firm, on industry-average PE ratios, or on comparable firms’ PE ratios. Analysts use benchmarks such as these to project a firm’s PE ratio quickly, using one- period earnings as a common denominator for relative valuations rather than engaging in the extensive computations necessary to determine the correct VE ratio to assess whether the market has priced the firm’s shares appropriately.

Analysts also use PE ratios as potentially informative benchmarks to compare valuations across companies or to project the valuations of other companies. For example, we could compare PepsiCo’s PE ratio to the PE ratios of Coca-Cola, Cadbury Schweppes, or other beverage companies. We also might use PepsiCo’s PE ratio to project valuations for these beverage companies or to project valuations for privately held firms or divisions of compa- nies. Investment bankers use comparable companies’ PE ratios, for example, to benchmark reasonable ranges of share prices for IPOs (initial public offerings).

PE ratios have the advantage of speed and efficiency, but they are not necessarily precise valuation estimates. Therefore, when using PE ratios, the analyst must be careful to adjust them to match the fundamental characteristics of different companies. For example, PepsiCo’s PE ratio should differ from Coca-Cola’s insofar as the fundamental characteris- tics of profitability, growth, and risk differ across the two firms. Such differences might arise, for example, because PepsiCo derives a major portion of earnings from the snack food business and Coca-Cola does not. Coca-Cola derives more of its earnings from inter- national beverage sales than does PepsiCo. These and other factors cause the profitability, growth, and risk of PepsiCo and Coca-Cola to differ and therefore cause their PE ratios to differ. We will describe PE ratio differences in more detail after we describe the conceptual basis for PE ratios.

PE Ratios Project Firm Value from Permanent Earnings What should a firm’s PE ratio be? What is an appropriate valuation multiple for a firm’s earnings? We have seen that in theory, the firm’s PE ratio should equal the firm’s VE ratio. However, if the analyst has not computed value to determine the VE ratio and wants to use a shortcut PE ratio instead, what is the correct PE ratio to use?

In projecting firm value using a simple PE ratio (that is, one that uses only one period of earnings and ignores earnings growth), the analyst imposes a very strong assumption on the earnings for a single period: the analyst treats these earnings (whether trailing earnings or a one-period-ahead forecast) as the beginning amount of a permanent stream of earn- ings, valued as a perpetuity. In essence, the PE assumes that one year of earnings is suffi- cient information to value a firm and to determine share price. Conceptually, suppose the firm’s common shareholders’ equity value equals its market value, the firm’s earnings will be constant in the future, and the firm’s investors expect a rate of return R

E . Under these

restrictive conditions, we can value the firm’s common equity using the perpetuity model based on one-year-ahead earnings (denoted as E

1 ) as follows:

V 0

� P 0

� E 1 /R

Rearranged slightly, under these assumptions, the firm’s VE and PE ratios are:

V 0 /E

1 � P

0 /E

1 � 1/R

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Thus, strictly speaking, the PE multiple assumes that firm value is the present value of a constant stream of expected future earnings, which is discounted at a constant expected future discount rate. Under these conditions, the analyst can value the firm using simply a multiple of one-period-ahead earnings and the PE ratio of the firm is simply the inverse of the discount rate.

To illustrate this model, assume that the market expects the firm to generate earnings of $700 next period and requires a 14 percent return on equity capital. The market value of the firm at the beginning of the next period should be $5,000 (� $700/0.14). Note that the inverse of the 14 percent discount rate translates into a PE ratio of 7.14 (� 1/0.14). Thus, $700 times 7.14 equals $5,000.

The simple PE ratio assumes that future earnings will be permanent, which is not real- istic for most firms. Most firms’ earnings are not expected to remain constant; most firms’ earnings grow. Not surprisingly, such strict assumptions match the fundamental character- istics of very few firms. We have already seen that such strict assumptions do not fit PepsiCo. Under the assumptions that PepsiCo’s earnings will be constant in the future and that PepsiCo’s constant future ROCE will equal the 8.50 percent cost of equity capital, PepsiCo’s PE ratio should be 11.8 (� 1/0.085). This PE ratio is far below the theoretically derived VE ratio of 21.7 for PepsiCo.

Descriptive Data on PE Ratios Exhibit 14.7 includes descriptive statistics on forward-looking PE ratios (share price to one- year-ahead earnings before extraordinary items: P

t /E

t�1 ) for the same 37 industries

described in Exhibit 14.5 (MB ratios) and Exhibit 11.3 (market betas) during 1998–2007. These data represent a broad cross-sectional sample of 33,671 firm-years drawn from the Compustat database, excluding all firm-years with negative earnings.15 Exhibit 14.7 lists the industries in ascending order of the median PE ratios. To describe the industry-wide vari- ation in PE ratios, Exhibit 14.7 also includes the 25th percentile PE ratio and the 75th per- centile PE ratio for each industry. Descriptive statistics on PE and other ratios across industries and years also appear in Appendix D.

These descriptive data indicate substantial differences in median PE ratios across indus- tries during 1998–2007. The firms in the petroleum refining, metals, insurance, and oil and gas extraction industries experienced the lowest median PE ratios during the period, whereas firms in the business services, motion pictures, and instruments and related prod- ucts industries experienced the highest median PE ratios. These data also depict wide vari- ation in PE ratios across firms in each industry. For example, most of these 37 industries experienced wide differences between the 25th percentile and the 75th percentile PE ratio during 1998–2007. With only a few exceptions, in most industries, the 75th percentile PE ratio was more than double the 25th percentile PE ratio.16

What Factors Cause PE Ratios to Differ across Firms? As noted earlier, the same set of economic factors that can cause firms’ MB ratios to differ also can cause PE ratios to differ across firms. The primary drivers of differences in PE ratios across firms are the fundamental drivers of value: risk, profitability, and growth. In addition to economic factors, differences across firms in accounting methods and account- ing principles and differences in earnings across time also can drive differences in PE ratios. We describe the effects of each of these determinants of PE ratios in the following sections,

15 It does not make sense to compute PE ratios on the basis of negative earnings. PE ratios assume that earnings are permanent;

negative earnings cannot be permanent.

16 The analyst must be careful with PE ratios because they are sensitive to earnings that are near zero. Firms with earnings that are

positive but temporarily very low will experience PE ratios that are temporarily very high.

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1064 Chapter 14 Valuation: Market-Based Approaches

E X H I B I T 1 4 . 7

Descriptive Statistics on Forward Price-Earnings Ratios (Pt /Et+1), 1998–2007 Industries Sorted by Median Forward PE Ratio

Industry: 25th Percentile Median 75th Percentile

Full Sample on Compustat (N = 33,671 firm-years)* 10.23 15.11 23.27 Industry: Petroleum Refining 6.36 8.87 14.23 Metals 5.89 10.66 17.35 Insurers 8.25 11.17 15.93 Oil and Gas Extraction 7.61 11.77 21.23 Tobacco 9.51 12.06 14.49 Transportation by Air 7.99 12.17 20.61 Textiles 6.58 12.42 18.56 Wholesalers—Durables 8.07 12.82 19.85 Forestry 6.85 12.95 43.53 Real Estate 7.16 13.05 24.71 Transportation Equipment 9.45 13.15 19.08 Metal Products 9.31 13.84 21.31 Depository Institutions 10.81 13.96 18.05 Wholesalers—Nondurables 8.24 14.06 21.14 Metal Mining 9.15 14.17 27.99 Utilities 11.41 14.58 19.10 Retailers—Apparel 11.32 14.59 20.43 Restaurants 11.08 15.82 24.57 Retailers—Home Furniture, Furnishings and Equipment 10.43 15.87 24.34 Health Services 10.67 16.03 24.10 Industrial and Commercial Machinery

and Computer Equipment 10.93 16.23 27.98 Hotels 9.21 16.25 23.34 Paper 10.98 16.39 22.85 Amusements and Recreation 10.09 16.40 26.41 Grocery Stores 12.05 16.45 24.57 Lumber and Wood Products 10.20 16.64 26.41 Security and Commodity Brokers 10.79 16.76 23.97 Personal Services 12.32 16.85 25.14 Printing and Publishing 11.28 17.01 24.28 Food Products 11.64 17.07 25.23 Communications 10.98 17.19 30.86 Retailers—General Merchandise 12.42 18.31 25.58 Chemicals 12.69 18.50 29.00 Electronic and Electrical Equipment 11.53 18.57 32.01 Instruments and Related Products 12.69 19.82 31.22 Motion Pictures 11.76 20.64 36.49 Business Services 13.81 22.28 36.49

* To compute these descriptive statistics on price-earnings ratios, we divided firm value (computed as year-end closing price times number of shares out-

standing) by one-year-ahead net income. We deleted firm-years with negative one-year-ahead net income.

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saving growth for last because we will expand on the role of growth in determining PE ratios.

Risk and the Cost of Capital. As the previous discussion points out, firms with equiva- lent amounts of earnings but different levels of risk and therefore different costs of equity capital will experience different PE ratios (and different VE ratios). All else equal, a riskier firm will experience a lower market value and PE ratio.

Profitability. A firm with competitive advantages will be able to earn ROCE that exceeds R

E . To the extent that the firm can sustain these competitive advantages, the persistence

over time of the degree to which ROCE exceeds R E

will increase, thereby increasing the PE ratio relative to similar firms that do not have sustainable competitive advantages. Thus, both the magnitude and persistence of the difference between ROCE and R

E will increase

PE ratios across firms. Accounting Differences. In addition to economic factors, firms’ PE ratios may differ for a

variety of accounting reasons, including the periodic nature of earnings measurement, and dif- ferences in accounting methods and principles. Some firms select accounting methods that are conservative with respect to income recognition and asset measurement (for example, LIFO for inventories during periods of rising input prices and accelerated depreciation of fixed assets). Some firms invest in projects for which accounting principles are conservative. For example, firms may make substantial expenditures on intangible activities that must be expensed under conservative accounting principles, leading to economic assets that are off-balance-sheet, such as successful R&D, brand equity, or human capital. The effects of accounting methods and prin- ciples on reported earnings and PE ratios will likely change over the life of the firm. All else equal, conservative accounting will reduce reported earnings early in the life of the firm (for example, when accelerated depreciation charges are high or R&D is being expensed), thereby increasing the PE ratio. Ironically, later in the life of the firm, after the investments have been completely expensed, reported earnings will be higher and PE ratios will be lower.

Accounting Measures Earnings in Annual Periods. Firms’ PE ratios will be significantly different when one-period earnings are unusually high or low and therefore not representa- tive of persistent earnings. For example, if earnings include an unusual loss that will not per- sist, the firm’s PE ratio will be unusually high. The transitory nature of a single period of accounting earnings can cause PE ratios to be more volatile than the long-run expectations of earnings warrant. In particular, if the analyst uses PE ratios based on trailing-twelve- months earnings that include nonrecurring gains or losses that are not expected to persist, the PE ratios will be artificially volatile. The variability in PE ratios will be inverse to the unusual and nonrecurring items in income. (That is, nonrecurring gains will drive PE ratios down temporarily, whereas nonrecurring losses will drive PE ratios up temporarily.)

Continuing the simple example introduced earlier, assume that the analyst expects the firm to generate earnings of $600 next period instead of $700 because the firm will recognize a nonrecurring $100 restructuring charge. Because this charge is nonrecurring (not a perma- nent change in earnings), the market price should fall to roughly $4,900 (� $5,000 � $100) in the no-growth scenario and the PE ratio for that period will be 8.17 (� $4,900/$600) instead of 7.14 (� $5,000/$700). Conversely, if the current period’s earnings exceed their expected permanent level, the PE ratio will be lower than normal.

The analyst must assess whether the lower or higher level of earnings for the period (and therefore higher or lower PE ratio) represents a transitory event or a change to a new level of permanent earnings. If the analyst expects that the decrease in earnings from $700 to $600 will be permanent, the market price (assuming no change in risk or growth) should decrease to $4,286 (� $600/0.14). Thus, the PE ratio remains the same at 7.14 (� 1/0.14).

To illustrate the effects of accounting differences on PE ratios across firms, consider the historical data in the following table, which includes PE ratios (computed as year-end share price over trailing earnings per share) for PepsiCo and Coca-Cola for 2000 and 2001.

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1066 Chapter 14 Valuation: Market-Based Approaches

PE Ratio Price per Share Earnings per Share

2000: PepsiCo 31.9 $46.25 $1.45 Coca-Cola 69.3 $60.94 $0.88

2001: PepsiCo 34.2 $46.18 $1.35 Coca-Cola 29.5 $47.15 $1.60

Considered at face value, the PE ratios for PepsiCo and Coca-Cola in 2000 indicate that the market valued Coca-Cola’s earnings at a multiple of 69.3, more than twice PepsiCo’s earnings multiple of 31.9, implying that Coca-Cola had lower cost of capital, higher growth, and/or greater profitability than PepsiCo. To the contrary, however, Coca-Cola rec- ognized a large restructuring charge in income in 2000, driving EPS down to only $0.88, thereby temporarily inflating Coca-Cola’s PE ratio. Thus, the big jump in Coca-Cola’s PE ratio occurred largely because earnings temporarily declined that year and did not reflect the market’s expectations for Coca-Cola’s long-term earnings. In 2001, both firms reported earnings closer to normal levels and their PE ratios were quite similar.

Growth. All else equal, market values and PE ratios will be greater for firms that the market expects will generate greater earnings growth with future investments in abnor- mally profitable projects. In the next section, we discuss techniques that analysts use to incorporate earnings growth into PE ratios.

Incorporating Earnings Growth into PE Ratios Analysts commonly modify the PE ratio to incorporate earnings growth. In this section, we describe and apply two related approaches to include expected future earnings growth in the computation of the PE ratio: (1) the perpetuity-with-growth approach and (2) the price-earnings-growth approach.17

The Perpetuity-with-Growth Approach. The perpetuity-with-growth approach assumes that the firm’s current period earnings will grow at a constant rate g. Therefore, the firm can be valued as the present value of a permanent stream of future earnings that will grow at constant rate g. In this case, we can express forward VE and forward PE ratios as perpetuity-with-growth models as follows:

E 0

� (1 � g) E 1

V 0

P 0

1 V

0 � P

0 � � , so � �

(R E

� g) (R E

� g) E 1

E 1

(R E

� g)

To continue the illustration, assume that the firm generated $666.67 in earnings in the cur- rent period. The market expects the firms’ earnings to grow 5 percent next year and each year thereafter, so that Year �1 earnings will be $700. The model suggests that the forward PE ratio incorporating growth should be 11.11 [� 1.0/(0.14 � 0.05)] and market value should be $7,778 (� $700 � 11.11). The present value of the expected future growth in earnings adds $2,778 (� $7,778 � $5,000) to the value of the firm.

Note that the above expression describes forward VE and forward PE ratios because they use E

1 (one-year-ahead earnings). As mentioned earlier, PE ratios are commonly measured

in practice using historical earnings. If current period (historical) earnings are expected to

17 In recent research, James Ohlson and Beate Juettner-Nauroth develop a theoretical model for the price-earnings ratio that

incorporates short-term and long-term earnings per share growth. The model is a promising addition to the earnings-based

valu ation literature, providing new insights into the relation between value, earnings, and growth. See James Ohlson and Beate

Juettner-Nauroth, “Expected EPS and EPS Growth as Determinants of Value,” Review of Accounting Studies (June–September

2005), pp. 349–365.

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grow at the constant rate g and if the VE and PE ratios are expressed as multiples of current period (historical) earnings (E

0 ):

Continuing with the illustration, the VE and PE ratios based on current period earnings would then be 11.667 [� (1�g)/(R

E � g) � 1.05/(0.14 � 0.05)]. Note that using this VE

and PE ratio will lead to market value for the firm of $7,778 (� $666.67 � 11.667). This is the same market value as we determined using the forward VE and PE ratios.

PE ratios are particularly sensitive to the growth rate. If the growth rate in our illustration becomes 6 percent instead of 5 percent, the forward PE ratio becomes 12.50 [� 1.0/(0.14 � 0.06)] and the market value becomes $8,750 (� $700 � 12.50). The sensitivity occurs because the model assumes that the firm will grow at the specified growth rate in perpetu- ity. Competition, new discoveries or technologies, or other factors eventually erode rapid growth rates in an industry. In using the constant growth version of the PE ratio, the ana- lyst should select a long-run equilibrium growth rate in earnings.

This expression for the VE and PE ratio underscores the joint importance of risk and growth in valuation. Given the relation between expected return (R

E ) and risk, the VE and

PE ratio should be inversely related to risk. Holding earnings and growth constant, higher risk levels should translate into lower PE and VE ratios, and vice versa. Risk-averse investors will not pay as much for a higher risk security as for a lower risk security with identical expected earnings and growth. In contrast, VE and PE should relate positively to growth. Holding earnings and R

E constant, firms with higher expected long-run growth rates in

earnings should experience higher VE and PE ratios. With respect to our valuation of PepsiCo at the end of 2008, we assumed that PepsiCo

would experience a long-run growth rate of 3.0 percent beginning in Year �6 and beyond. If we assume that PepsiCo will experience a 3.0 percent constant growth rate in earnings beginning in Year �1, using the perpetuity-with-growth approach, we calculate the for- ward PE ratio for PepsiCo as follows:

P 0 1 1

� � � 18.182 E

0 (R

E � g) (0.085 � 0.030)

Clearly, incorporating growth makes a big difference in PepsiCo’s forward PE ratio [as com- pared to the PE ratio of 11.8 (� 1/0.085) that ignores growth]. Assuming that PepsiCo’s earnings will grow at 3.0 percent per year beginning in Year �1, this PE with growth ratio would value PepsiCo shares at a multiple of 18.182 times the Year �1 earnings forecast. This PE ratio is still less than the theoretically correct VE ratio of 21.7, however, because it does not take into account our forecasts projecting that PepsiCo earnings will grow at an average rate of 10.4 percent during Year �1 to Year �5. Thus, this PE ratio understates the value of PepsiCo’s expected earnings growth during those years.

The Price-Earnings-Growth Approach. An alternative ad hoc approach to incorporate growth into PE ratios has emerged from practice in recent years. Using this approach, ana- lysts’ divide the PE ratio by the expected medium-term earnings growth rate (expressed as a percent). (Some analysts use the expected earnings growth rate over a three- to five-year horizon.) This approach produces the so-called PEG ratio seen with increasing frequency in practice. Analysts compute the PEG ratio as follows:

PEG 0

� (Price per share 0 /Earnings per share

0 )/(g � 100)

Price-Earnings and Value-Earnings Ratios 1067

E 0

� (1 � g) E 1

V 0

P 0

1 V

0 � P

0 � � , so � �

(R E

� g) (R E

� g) E 0

E 0

(R E

� g)

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1068 Chapter 14 Valuation: Market-Based Approaches

Analysts and the financial press use the PEG ratio as a rule of thumb to assess share price relative to earnings and expected future earnings growth. Although there is little theoreti- cal foundation for this rule of thumb (which tends to vary among analysts), proponents of PEG ratios generally assert that firms should have PEG ratios equal to 1.0, indicating that market price fairly reflects expected earnings and growth.

This rule of thumb implies the following value model for a VEG ratio under the follow- ing set of assumptions:

• The firm’s earnings behave as a perpetuity with growth. • The firm’s earnings generate an ROCE equivalent to R

E .

• All of the firm’s growth arises from reinvesting all of its earnings. • All of the reinvested earnings generate an ROCE equivalent to R

E , so the firm’s earn-

ings growth rate is equivalent to R E .

Under this set of restrictive assumptions, the VEG ratio follows. [For notation, assume that (g � 100) � G � R

E .]

VEG 0

� (Value per share 0 /Earnings per share

0 )/(g � 100)

� V 0 /E

1 /G � 1/R

E /R

E � 1

Alternatively, note that the VEG ratio is mathematically equivalent to a simple valuation model that values shares as next year’s earnings per share multiplied by the growth rate times 100 (that is, V

0 � E

1 � G).

Using the rule of thumb that VEG ratios should equal 1, proponents assert that market prices for firms with PEG ratios below 1 are underpriced given earnings and expected earn- ings growth and that market prices for firms with PEG ratios above 1 are overpriced rela- tive to earnings and expected earnings growth. Proponents of PEG ratios argue that this heuristic provides a convenient means to rank stocks, taking into account one-year-ahead earnings and expected earnings growth.18

In Chapter 10, we assumed that PepsiCo would experience earnings growth of roughly 10.4 percent per year through Year �5. Using this growth rate assumption and the 2008 reported earnings per share, we compute PepsiCo’s PEG ratio at the end of 2008 as follows:

PEG 2008

� (Price per share 2008

/ Earnings per share 2008

)/(g � 100)

� ($54.77/$3.26)/(0.104 � 100)

� 16.8/10.4 � 1.62

Thus, PepsiCo shares traded at the end of 2008 at a PEG ratio of 1.62. Based on the PEG heuristic, PepsiCo’s PEG ratio of 1.62 suggests that the market price for PepsiCo shares reflect substantial overpricing of PepsiCo’s earnings and expected earnings growth.

However, the PEG ratio heuristic does not take into account differences in risk and costs of equity capital across firms. For example, PepsiCo’s PEG ratio seems high because it does not account for the fact that PepsiCo’s expected future ROCE is significantly greater than PepsiCo’s R

E because of PepsiCo’s substantial off-balance-sheet brand equity. In addition,

this heuristic does not take into account the fact that PepsiCo is likely to achieve this future earnings growth with relatively low risk. (PepsiCo’s beta is 0.75.) The PEG ratio deserves considerable attention from researchers and practitioners so that its uses and limitations can be tested and understood.

18 Mark Bradshaw (2002) demonstrates that sell-side analysts’ target price estimates are highly correlated with valuation estimates

based on the PEG model in “The Use of Target Prices to Justify Sell-Side Analysts’ Stock Recommendations,” Accounting

Horizons, Vol. 16, No. 1 (March 2002), pp. 27–41.

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PE Ratio Measurement Issues Thus far, we have discussed a variety of different measurement issues for PE ratios. Forward-looking PE ratios divide share price by one-year-ahead earnings forecasts, which is theoretically more correct. However, at least two problems arise in using forward PE ratios. First, one-year-ahead earnings forecasts are not readily available for all firms. Second, the accuracy of the forecasts depends on the analysts’ forecast assumptions, which can differ widely. Therefore, as noted earlier, in practice PE ratios are most commonly measured as share price divided by earnings per share for the most recent prior fiscal year or for the most recent four quarters. This is a sensible approach because historical earnings are observable and unique; however, computation of PE ratios using historic earnings introduces the potential for bias. To recap, the analyst should be aware of (at least) the fol- lowing two types of measurement error:

1. Growth. Simple ratios of price over earnings do not explicitly consider firm-specific differences in long-term earnings growth. The price-earnings ratios described in prior sections provide mechanisms that incorporate growth into price-earnings multiples.

2. Transitory earnings. Past earnings are historical and may not be indicative of expected future “permanent” earnings levels. Insofar as historic earnings contain transitory gains or losses (or other elements that are not expected to recur), tem- porarily high or low earnings can cause the PE ratio to vary considerably. The ana- lyst should cleanse the earnings figure of nonrecurring or unusual gains or losses.

In addition, the analyst must be aware of the potential bias in PE ratios because of dif- ferences in firms’ dividend payouts. Dividends displace future earnings. A dividend paid in Year t reduces market price by the amount of the dividend, but the dividend is not sub- tracted from earnings. The dividend paid will cause future earnings to decline, all else equal, because the firm has paid out a portion of its resources to shareholders. Therefore, price should decline by the present value of the firm’s forgone amount of expected future return on assets distributed as dividends. Thus, for dividend-paying firms, dividends cause a mismatch between current period price and lagged earnings. To eliminate this mismatch, the analyst should compute a PE ratio with growth for a dividend-paying firm as follows: (P

t � D

t )/E

t � 1/(R

E � g).

Empirical Properties of PE Ratios The theoretical models indicate that the PE ratio is related to R

E , the cost of equity capital,

and g, the growth rate in future earnings. Several empirical studies have examined the rela- tion between PE ratios, risk (measured using market beta), and growth (measured using realized prior growth rates or analysts’ forecasts of future growth). These studies have found that approximately 50–70 percent of the variability in PE ratios across firms relates to risk and growth.19

PE Ratios as Predictors of Future Earnings Growth. Stephen Penman, a leading scholar in the relation between earnings, book values, and market values, studied the relation between PE ratios and changes in earnings per share for all firms on the Compustat data- base for 1968–1985.20 For each year, Penman grouped firms into 20 portfolios based on the

19 See William Beaver and Dale Morse, “What Determines Price-Earnings Ratios?,” Financial Analysts Journal (July–August 1978),

pp. 65–76; Paul Zarowin, “What Determines Earnings-Price Ratios: Revisited,” Journal of Accounting, Auditing and Finance

(Summer 1990), pp. 439–454.

20 Stephen H. Penman, “The Articulation of Price-Earnings Ratios and Market-to-Book Ratios and the Evaluation of Growth,”

Journal of Accounting Research (Autumn 1996), pp. 235–259.

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1070 Chapter 14 Valuation: Market-Based Approaches

level of their PE ratios, computed using lagged earnings per share. He then computed the percentage change in earnings per share for the formation year and for each of the nine subsequent years. Penman then aggregated the results across years. The table below pres- ents a subset of the aggregate results.

Median Percentage Change in Earnings per Share in:

PE Portfolio: Year 0 Year �1 Year �2 Year �3 Year �4

High 3.9% 52.2% 17.5% 17.8% 15.0% Medium 14.0% 11.8% 11.6% 13.7% 15.8% Low 18.4% 4.8% 10.2% 12.3% 13.1%

The results for the portfolio formation year are consistent with transitory components in earnings in Year 0. Firms with high PE ratios experienced, on average, low percentage changes in earnings (and many experienced earnings declines) during the formation year relative to the preceding year. Firms with low PE ratios experienced high percentage changes in earnings during the formation year. The results for Year 1 after the formation year suggest a counterbalancing effect of the earnings change in the formation year. A low percentage increase (or decrease) in earnings is followed by a high percentage earnings increase for the high PE portfolios, and vice versa for the low PE portfolios.

The results for subsequent years reflect the tendency toward mean reversion in percent- age earnings changes to a level in the midteens. This result is consistent with the data pre- sented in Exhibit 14.6 for ROCE, where Victor Bernard observed a mean reversion in ROCE toward the midteens during his sample period. The mean reversion suggests systematic directional changes in earnings growth over time (that is, serial autocorrelation), but the reversion takes several years to occur.

Articulation of MB and PE Ratios. In the same research study, Penman also utilized the residual income valuation model and empirical data to examine the articulation between firms’ PE and MB ratios.21 Penman collected data from the CRSP and Compustat databases on roughly 2,574 firms during 1968–1985. For each sample year, Penman ranked and grouped these firms into 20 portfolios based on PE ratios. He also ranked and grouped the same firms each year into three MB ratio portfolios, classifying MB ratios below 0.90 as low, MB ratios above 1.10 as high, and MB ratios between 0.90 and 1.10 as normal.

Exhibit 14.8 presents a matrix summarizing a portion of the results from Penman’s study. Exhibit 14.8 presents residual income figures after assuming a 10.0 percent cost of capital for all firm-years and after scaling by beginning-of-period book value of common equity (so that they are essentially residual ROCE figures). We denote current period residual income as CRI and future residual income one year ahead and six years ahead as FRI

1 and FRI

6 , respectively.

Penman’s research results generally support his predictions and shed light on the resid- ual income conditions that cause MB ratios and PE ratios to covary. His results show that future residual income is substantially higher for high MB firms than for low MB firms. Examining future residual income across columns of the matrix, Penman’s results show that MB ratios are positive predictors of future residual income, consistent with the results from Bernard in Exhibit 14.6. Examining the results across rows, high PE ratio firms tend to have current period residual income that is much lower than future residual income, sug- gesting that PE ratios for these firms are temporarily high because residual income is tem- porarily low. In contrast, firms with low PE ratios tend to have current residual income amounts that are greater than the future residual income amounts, suggesting that these

21 Stephen H. Penman, op. cit.

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firms are experiencing low PE ratios because residual income is temporarily high. Penman’s results provide intuition about when MB ratios should be high, low, or normal and, con- currently, when PE ratios should be high, low, or normal.

Summary of Value-Earnings and Price-Earnings Ratios Summarizing, the VE and PE ratios are determined by:

• Risk • Growth • Differences between current and expected future (permanent) earnings • Alternative accounting methods and principles The analyst must assess each of these elements when estimating VE ratios, particularly

when comparing VE ratios to PE ratios to assess whether shares appear to be under- or overpriced and when projecting VE ratios to value non-traded firms. The analyst should be aware of the following considerations when using VE and PE ratios:

1. The VE ratio is particularly sensitive to the cost of equity capital and to the earn- ings growth rate because it assumes that a firm can grow earnings at that rate for- ever. The analyst should select a sustainable long-term growth rate when computing the VE model.

2. The VE model does not work when the growth rate in earnings exceeds the cost of equity capital. Firms are not likely to grow earnings forever at rates exceeding the cost of equity capital. Competition will eventually force growth rates to diminish.

E X H I B I T 1 4 . 8

The Articulation of Market-to-Book (MB) and Price-Earnings (PE) Ratios

MB Ratio Portfolios:

PE Ratio Portfolios: High Normal Low

CRI < FRI > 0 CRI < FRI = 0 CRI < FRI < 0 High CRI: �0.50 to 0.07 CRI: �0.36 to �0.04 CRI: �0.24 to �0.06 (Portfolios 15–20) FRI

1 : �0.07 to 0.08 FRI

1 : �0.13 to �0.03 FRI

1 : �0.13 to �0.06

FRI 6 : 0.01 to 0.11 FRI

6 : �0.06 to 0.07 FRI

6 : �0.01 to 0.02

CRI = FRI > 0 CRI = FRI = 0 CRI = FRI < 0 Normal CRI: 0.07 to 0.10 CRI: �0.02 to 0.04 CRI: �0.05 to 0.00 (Portfolios 7–14) FRI

1 : 0.08 to 0.10 FRI

1 : �0.02 to 0.04 FRI

1 : �0.04 to 0.00

FRI 6 : 0.11 to 0.14 FRI

6 : 0.01 to 0.06 FRI

6 : �0.02 to 0.03

CRI > FRI > 0 CRI > FRI = 0 CRI > FRI < 0 Low CRI: 0.12 to 0.41 CRI: 0.05 to 0.22 CRI: 0.00 to 0.06 (Portfolios 1–6) FRI

1 : 0.12 to 0.25 FRI

1 : 0.05 to 0.15 FRI

1 : �0.01 to 0.04

FRI 6 : 0.11 to 0.24 FRI

6 : 0.07 to 0.12 FRI

6 : 0.03 to 0.05

Source: We obtained these data from Table 4 in Stephen H. Penman, “The Articulation of Price-Earnings Ratios and Market-to-Book Ratios and the

Evaluation of Growth,” Journal of Accounting Research vol. 34, no. 2 (Autumn 1996), pp. 235–259.

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1072 Chapter 14 Valuation: Market-Based Approaches

3. The VE model should not be used when the cost of equity capital and the growth rate in earnings are similar in amount. The denominator of the VE model (R

E � g)

approaches zero, and the VE ratio becomes exceeding large. 4. The VE and PE models should not be used when earnings are negative because the

VE and PE models assume that earnings are permanent, and negative earnings can- not persist in perpetuity.

5. Before concluding that the market is undervaluing or overvaluing a firm because the actual PE ratio differs from the theoretically correct VE ratio, the analyst should assess whether earnings of the period include transitory elements. The analyst should adjust the current period’s earnings to remove the effects of unusual, nonre- curring income items before measuring the PE ratio for the period.

6. When comparing PE ratios across firms, the analyst should consider the impact of the firms’ use of different accounting methods and principles.

Using Market Multiples of Comparable Firms The analyst can use the PE and MB ratios of comparable firms to assess the corresponding ratios of publicly traded firms. The analyst also can value firms whose common shares are not publicly traded by using PE ratios and MB ratios of comparable firms that are publicly traded. The theoretical models assist in this valuation task by identifying the variables the analyst should use in selecting comparable firms. Bhojraj and Lee (2002) demonstrate a technique for selecting comparable firms in multiples-based valuation by computing “war- ranted multiples” based on factors that drive cross-sectional differences in multiples, such as expected profitability, growth, and cost of capital.22 Alford (1992) examined the accuracy of the PE valuation models using industry, risk, ROCE, and earnings growth as the bases for selecting comparable firms.23 The results indicate that industry membership, particu- larly at a three-digit SIC code level, provides a useful basis for comparisons if firms in the same industry experience similar profitability, face similar risks, and grow at similar rates. Thus, in some circumstances, industry membership serves as an effective proxy for the vari- ables in the PE valuation model. However, as the data in Exhibit 14.7 reveal, substantial differ- ences commonly exist in PE ratios of firms in the same industry. The warranted-multiples approach of Bhojraj and Lee (2002) provides a mechanism to determine comparable com- panies within similar industries and across different industries.

PRICE DIFFERENTIALS24

In light of the critical role of risk and expected returns in valuation and in light of the uncertainty surrounding how to measure risk and expected returns, the analyst needs a variety of tools to assess the impact of risk on share prices and firm values. One such tool involves computing price differentials. Price differentials can be used to address questions such as these: To what extent has the market priced risk? What is the impact of risk on share price? Is the per-share price impact too large or too small relative to risk? We rely on an adaptation of the residual income model to address these questions by computing the price differential—the amount the market has discounted share price for risk.

22 Sanjeev Bhojraj and Charles M.C. Lee, “Who Is My Peer? A Valuation-Based Approach to the Selection of Comparable Firms,”

Journal of Accounting Research, Vol. 40, No. 2 (May 2002), pp. 407–439.

23 Andrew W. Alford, “The Effect of the Set of Comparable Firms on the Accuracy of the Price-Earnings Valuation Method,” Journal

of Accounting Research (Spring 1992), pp. 94–108.

24 This section relies heavily on Stephen Baginski and James Wahlen, “Residual Income Risk, Intrinsic Values, and Share Prices,”

The Accounting Review, Vol. 78, No. 1 (January 2003), pp. 327–351.

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Price Differentials 1073

As described in detail in the previous chapter, the residual income model determines the present value of common shareholders’ equity as follows:

To implement this model, the analyst must estimate the cost of equity capital (R E ) and then

use it to compute residual income [NI t � (R

E � BV

t�1 )] and discount residual income to

present value at 1/(1 � R E )t. But state-of-the-art in financial economics does not provide a

clear picture of how R E

should be determined. Substantial controversy surrounds expected returns models such as the CAPM. What is the appropriate measure for market beta? In addition to market betas, do other risk factors belong in the expected returns model, such as firm size, MB ratios, or some other set of risk factors? Assuming that one can identify the appropriate risk factors that are priced in the market, what are the appropriate risk premia to use to determine expected returns for each of these factors? At an even more fundamen- tal level, questions arise about whether risk and expected returns should be measured based on covariation between a firm’s returns and a market index of returns. These questions arise in part because market-based models such as the CAPM are essentially circular— should stock returns be used to estimate risk to determine expected returns to evaluate stock prices? Or should risk and expected returns be based on covariation between a firm’s returns and its fundamental risk characteristics (such as volatility in earnings)? Or should risk and expected returns derive from the covariation between a firm’s stock returns and an economy-wide measure of consumption, on the theory that investors’ risk aversion is driven by the need to diversify volatility in expected future consumption?

The procedure for computing price differential offers an alternative approach for evaluat- ing the market’s pricing of risk. To begin, substitute the prevailing risk-free rate of interest (denoted R

F ; for example, the yield on five-year U.S. Treasury securities) for the cost of equity

capital (R E ) and use the residual income model to estimate risk-neutral value (denoted as

RNV 0 ), which is an estimate of the hypothetical value of the firm in a risk-neutral market:

∞ V

0 � BV

0 � ∑

NI t � (R

E � BV

t–1 )

t = 1 (1 + RE) t

∞ RNV

0 � BV

0 � ∑

NI t � (R

F � BV

t–1 )

t = 1 (1 + RF) t

Risk-neutral value represents the value of the firm, based on book value of equity and fore- casts of expected future earnings, in the absence of discounting for risk. Dividing risk-neutral value by the number of shares outstanding gives risk-neutral value per share, which repre- sents the hypothetical value at which shares would trade in a risk-neutral market. Market price per share of common equity reflects the risk-discounted value in the real-world, which is risk-averse. Therefore, market price per share can be subtracted from risk-neutral value per share to determine the total amount by which share price has been discounted for risk. We refer to this difference as the price differential (denoted as PDIFF), computed as follows:

PDIFF 0

� RNV per share 0

� Price per share 0

The analyst can also divide PDIFF 0

by RNV 0

to determine the percentage PDIFF. The analyst can evaluate the PDIFF or the percentage PDIFF to assess whether the market discount for risk is sufficient to compensate the investor to hold the firm’s shares and bear risk. The analyst can also compare percentage PDIFF across time for a given firm or across firms to evaluate the extent to which the market is discounting share prices for risk. If the analyst assesses that PDIFF

0 is large relative to the risk of the firm, the firm’s

shares may be overdiscounted for risk (undervalued). On the other hand, if the analyst

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1074 Chapter 14 Valuation: Market-Based Approaches

assesses that PDIFF 0

is small relative to firm risk, perhaps the firm’s shares are underdiscounted for risk (overvalued). In the next section, we illustrate how to compute the PDIFF for PepsiCo. In the following section that discusses reverse engineering, we describe and apply more formal methods to gauge the relative magnitude of PDIFF.

Computing PDIFF for PepsiCo To compute the price differential of PepsiCo as of the end of 2008, we rely on the forecast assumptions developed in Chapter 10 and the residual income model developed in the pre- vious chapter. However, instead of using an 8.5 percent cost of equity capital for PepsiCo for purposes of computing residual income and discounting it to present value, we use the risk-free interest rate at the time of the valuation. At the end of 2008, U.S. Treasury bills with one to five years to maturity yielded roughly 4.0 percent. Exhibit 14.9 reports the pres- ent value of PepsiCo’s expected future residual income in Year �1 through Year �5 amounts to $29,399.3 million, computed using the 4.0 percent risk-free discount rate.

To compute continuing value, we use the now-familiar perpetuity-with-growth model [� 1/(R

F � g)] assuming that long-term growth for PepsiCo will be 3.0 percent and that

the risk-free discount rate is 4.0 percent. The present value of continuing value under this approach is $659,346.6 million. After adding book value of common equity at the end of 2008, adjusting for midyear discounting, and dividing by the number of shares outstand- ing, we estimate that PepsiCo shares have a risk-neutral value of $460.38. Subtracting the market price at 2008 of $54.77 per share, we estimate the PDIFF to be $405.61. These com- putations suggest that PepsiCo shares have been discounted by the risk-averse market by roughly $405.61 per share below the value at which they would trade in a hypothetical risk- neutral market, conditional on the forecast assumptions made in Chapter 10. These com- putations indicate that PepsiCo shares traded at the end of 2008 at a price equal to roughly 12 percent of risk-neutral value (� $54.77/$460.38). Alternately stated, at a price of $54.77,

E X H I B I T 1 4 . 9

Price Differential of PepsiCo: Present Value of Residual Income in Year +1 through Year +5 after

Discounting at the Risk-Free Rate of Interest (4.0 percent) (dollar amounts in millions)

Year +1 Year +2 Year +3 Year +4 Year +5

Lagged Book Value of Common Shareholders’ Equity (at t–1) $12,203.0 $12,656.1 $13,467.4 $14,465.3 $15,323.5

Comprehensive Income Available for Common Shareholders $ 5,941.9 $ 6,602.1 $ 7,272.7 $ 7,726.4 $ 8,427.3

Required Earnings $ 488.1 $ 506.2 $ 538.7 $ 578.6 $ 612.9 Residual Income $ 5,453.8 $ 6,095.8 $ 6,734.0 $ 7,147.8 $ 7,814.3 Present Value Factors � 0.962 � 0.925 � 0.889 � 0.855 � 0.822 Present Value of Residual Income $ 5,244.0 $ 5,635.9 $ 5,986.5 $ 6,110.0 $ 6,422.8 Sum of Present Value of Residual

Income, Year +1 through Year +5 $29,399.3

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Reverse Engineering 1075

PepsiCo’s shares have been discounted 88 percent relative to the risk-neutral value. Exhibit 14.10 presents these computations.

In Chapters 11�13, we estimated that PepsiCo shares may have been underpriced at the end of 2008 by roughly 52 percent, conditional on our forecast assumptions and valuation models. The price differential computation indicates that the market imposed a substantial discount to PepsiCo’s expected future residual income relative to the risk of PepsiCo. To more formally evaluate the relative magnitude of the price differential, we turn to the method of reverse-engineering market values.

REVERSE ENGINEERING Reverse engineering is an analytical approach through which the analyst can deduce and evaluate the assumptions implicit in a stock price. Throughout this text, we have empha- sized the process of using a firm’s fundamental characteristics to estimate firm value. The valuation process can be characterized essentially as a puzzle with four pieces, or as an equation with four variables, as follows:

1. Value 2. Expected future profitability 3. Expected long-run future growth 4. Expected risk-adjusted discount rates

Thus far, we have developed forecasts and expectations about three of the variables— expected future profitability, long-run growth, and risk-adjusted discount rates—and have

E X H I B I T 1 4 . 1 0

Price Differential of PepsiCo (dollar amounts in millions except per share amounts)

Valuation Steps: Computations: Amounts:

Sum of Present Value Residual Income Discounted at the risk-free rate of interest of in Year +1 through Year +5 4.0 percent. See Exhibit 14.9. $ 29,399.3

Add continuing value in present value Year +6 residual income assumed to grow at 3.0% in perpetuity; discounted at 4.0%. Computations not shown. � $659,346.6

Total Present Value Residual Income $688,745.9 Add: Beginning Book Value of Equity Book Value of Equity from

2008 Balance Sheet � $ 12,203.0 $700,948.9

Adjust to Midyear Discounting Multiply by 1 + (R F

/ 2) � 1.020 Present Value of Common Equity $714,967.8 Shares Outstanding � 1,553.0 Estimated Risk-Neutral Value per Share $ 460.38 Current Price per Share � $ 54.77 Price Differential $ 405.61 Price Differential as a Percent

of Risk-Neutral Value 88.1%

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1076 Chapter 14 Valuation: Market-Based Approaches

used them to solve for the fourth variable, firm value. In fact, we can make assumptions about any three of the four variables and then solve for the fourth variable.

For example, we can treat the market value of common equity as one of the “known” variables. We can assume that V

0 equals market value. (That is, we can assume that the mar-

ket is correct; hence, price equals value.) We can then develop forecast assumptions for any two other variables and solve for the missing fourth variable. We refer to this process as reverse-engineering stock prices because it takes the valuation process and reverses it. It is a process in which the analyst assumes that shareholders’ equity value equals market price and then solves for the assumptions the market appears to be making to value the firm’s shares. For example, if we assume that a firm’s share value equals the market’s share price and use the consensus analysts’ forecasts for future earnings and growth as reasonable prox- ies for the market’s expectations, we can solve for the implied expected risk-adjusted rate of return on common equity that is consistent with the observed market price, conditional on the analysts’ assumptions about earnings and growth. This is essentially equivalent to solv- ing for the internal rate of return on the stock.

As another example, suppose we assume that share value equals market price, that the market’s risk-adjusted expected return on a stock can be determined by an asset pricing model such as the CAPM, and that analysts’ consensus earnings forecasts through Year �5 are reasonable proxies for the market’s earnings expectations. We can then solve for the long- run growth rate implicit in the firm’s stock price, conditional on the other assumptions.

The process of reverse-engineering stock prices allows the analyst to infer a set of assumptions that the market appears to have impounded into a share price. The analyst can then assess whether the assumptions the market appears to be making are realistic, opti- mistic, or pessimistic. If the analyst determines that the market’s assumptions seem opti- mistic, it suggests that the market has overpriced the stock (or perhaps the analyst will question whether he or she is more pessimistic than the market). Alternatively, if the ana- lyst determines that the market’s assumptions seem pessimistic, it suggests that the market has underpriced the stock (or again, the analyst may be less pessimistic than the market).

Reverse-Engineering PepsiCo’s Stock Price To illustrate the process of reverse engineering, we apply the approach to PepsiCo using the end of 2008 market price of $54.77 per share. To reverse-engineer PepsiCo’s share price, we again rely on the residual income model in the previous chapter and the forecasts devel- oped in Chapter 10.

Assume that we want to solve for the expected rate of return (that is, the risk-adjusted discount rate) implied by PepsiCo’s 2008 share price of $54.77. Also assume that our fore- casts of earnings and book value of common equity for PepsiCo through Year �5 and our forecast of 3.0 percent long-run growth are realistic proxies for the market’s expectations. Armed with share price, earnings and growth forecasts through Year �5, and a constant long-run growth assumption beyond Year �5, we can use the residual income value model to solve for the discount rate that reduces future earnings and book value to a present value equal to the $54.77 market price per share.

Procedurally, one way to solve for the implied expected return on PepsiCo stock, condi- tional on the price, earnings, and growth assumptions, is to estimate the value of common equity using the risk-free discount rate, as in the price differential illustration above. The risk-neutral value will likely far exceed the market price because the future residual income has not been discounted for risk. In applying the price differential model to PepsiCo in the previous section, we determined that PepsiCo’s risk-neutral value was $460.38 per share. We then steadily increase the discount rate as necessary until the residual income model value exactly agrees with the market price of $54.77 per share. Following this approach, the

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The Relevance of Academic Research for the Work of the Security Analyst 1077

implied expected rate of return on PepsiCo stock is 11.32 percent. At this discount rate, conditional on our residual income and growth assumptions, the present value of PepsiCo shares is $54.77 per share, exactly equal to market price. Recall that we assumed that PepsiCo common equity had a required rate of return of 8.50 percent based on the CAPM. However, this reverse-engineering approach indicates that if we buy a share of PepsiCo stock at the market price of $54.77, it will yield an 11.32 percent rate of return, conditional on our other assumptions. The Valuation spreadsheet in FSAP allows the analyst to make these iterative computations easily by varying the discount rate for equity capital.

To demonstrate another example, we can reverse-engineer PepsiCo’s 2008 stock price to solve for the implicit long-run growth assumption. To illustrate, we again take the market price of $54.77 per share as given and our earnings and book value forecasts through Year �5 as reasonable proxies for the market’s expectations. We return to our original assump- tion that based on the CAPM the risk-adjusted discount rate for PepsiCo stock is 8.50 per- cent. With this, we have established three assumptions—value, earnings through Year �5, and the risk-adjusted discount rate—and can solve for the missing piece of the puzzle: long-run implied growth. We begin with the long-run growth assumption set at zero. We compute our first estimate of firm value using a zero growth assumption and compare that estimate to market price. The first estimate is normally substantially lower than market price because market price probably includes the present value of the market’s expectations for long-run growth. For PepsiCo, however, the initial value estimate assuming zero growth is $60.84 per share—above current share price. This suggests that conditional on our other valuation assumptions, the market is pricing negative long-run growth in PepsiCo shares. To determine the implied negative growth rate, we steadily decrease the long-run growth parameter assumption as necessary until the present value from the residual income model equals market price. In the case of PepsiCo at the end of 2008, market price of $54.77 reflects long-run negative growth of �1.5 percent (significantly lower than our expectation of 3.0 percent long-run growth). That is, conditional on our assumptions for residual income through Year �5 and on our assumption that PepsiCo’s cost of equity capital is 8.5 percent, if the market expects long-run growth to be �1.5 percent per year, the present value of PepsiCo shares exactly agrees with the market price of $54.77. Given that PepsiCo will not likely experience negative long-run growth, it further confirms our assessment that PepsiCo shares are underpriced at the end of 2008. Again, note that the valuation spread- sheet in FSAP is a useful tool that allows the analyst to establish assumptions for earnings and cost of capital and then vary the long-run growth assumption for reverse engineering.

THE RELEVANCE OF ACADEMIC RESEARCH FOR THE WORK OF THE SECURITY ANALYST Throughout this text, we have referred to relevant examples of empirical accounting research, including the classic study by Ball and Brown (1968) that helped set the stage for future research by being the first to show that changes in earnings correlate with unex- pected changes in stock prices.25 As demonstrated in Exhibit 1.21 in Chapter 1, the Nichols and Wahlen (2004) replication of the Ball and Brown results indicate that during their sam- ple period 1988�2002, merely the difference in the sign of the change in annual earnings (whether positive or negative) was associated with nearly a 35 percent difference in annual market-adjusted stock returns.26 The average sample firm that reported an earnings

25 Ray Ball and Philip Brown, “An Empirical Evaluation of Accounting Income Numbers,” Journal of Accounting Research (Autumn

1968), pp. 159–178.

26 D. Craig Nichols and James Wahlen, “How Do Earnings Numbers Relate to Stock Returns? A Review of Classic Accounting

Research with Updated Evidence,” Accounting Horizons (December 2004), pp. 263–286.

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1078 Chapter 14 Valuation: Market-Based Approaches

increase in a given year experienced stock returns that, on average, “beat” the market aver- age returns by 19 percent, while the average sample firm that reported an earnings decrease in a given year experienced stock returns that, on average, fell 16 percent short of the mar- ket average returns.

The results of academic research in accounting have provided many insights into mul- tifaceted dimensions of the relations between accounting numbers and a variety of capital market variables such as stock prices, stock price reactions around earnings announce- ments, stock returns cumulated over long periods of time, trading volume, analysts’ and managements’ earnings forecasts, equity costs of capital, implied market risk premia, mar- ket betas and other risk factors, bankruptcy, and earnings management. Despite the exis- tence of academic accounting research, the natural question for the security analyst is whether the academic research models and empirical findings are relevant to the task of making buy, sell, or hold recommendations on individual firms. This concluding section offers some thoughts on this important question. This section also summarizes the role of market efficiency and describes some striking empirical evidence on the relative degree of market efficiency with respect to earnings. In addition, this section describes an empirical study that used the residual income valuation models demonstrated in this chapter and in Chapter 13 to pick stocks and form portfolios. We consider the results to date to be very encouraging for analysts.

Creating Relevant Academic Research Results27

Accounting academics and the research process itself provide important elements that should lead to relevant and reliable insights into the relation between accounting numbers and stock market variables. Some of the elements of the research process that help aca- demic researchers are as follows:

• Rigor and Objectivity: Academic accounting researchers develop and test theories to explain the observed relation between accounting information and stock prices. Academics are trained to base their predictions and hypotheses as much as possible on formal theory integrating economics, finance, and accounting (rather than ad hoc or ex post reasoning). Academics commonly test these predictions with rigorous statisti- cal methods on large empirical samples of real data. Academics usually have no com- mercial interest in the results, so the findings should not be biased by the need to obtain a particular conclusion or the need to sell. Furthermore, academic research is not published in a leading scholarly research journal unless it survives the stringent peer review process. Few research studies pass the “publish” test; most “perish.”

• Level of Aggregation: Both academic and professional analyst communities must rec- ognize that their interests share common ground but involve different levels of aggre- gation. The academic seeks big picture explanations of general phenomena. Academic research in accounting seeks to develop conclusions and results that predict and explain the relation between accounting information and stock market variables in general. The analyst is concerned with specific assessments of the value of individual firms at particular points in time. Academic research results provide a basis for the analyst to assess the link between accounting numbers and a firm’s value and to iden- tify deviations from the average for individual firms. Professional analysts create value by acting on the deviations, that is, identifying and taking positions in under- or over- priced stocks.

27 This section draws heavily from Clyde P. Stickney, “The Academic’s Approach to Securities Research: Is It Relevant to the

Analyst?” Journal of Financial Statement Analysis (Summer 1997), pp. 52–60.

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• Theory and Practice Feed Each Other: The previous section identified the common ground that the academic and professional analyst communities share. Both commu- nities want to better understand how accounting information relates to stock prices. Academics predict and explain analysts’ earnings forecasts and price targets and, more generally, the actions of market participants on the whole. Analysts, directly or indi- rectly, rely on theories and results from academic research to inform their analysis. Much of what analysts learn in their academic training (such as in undergraduate and MBA programs) and in professional development training is developed and validated by academic work, including textbooks such as this one that seek to link practice, the- ory, and research.

What Does “Capital Market Efficiency” Really Mean? Academics generally perceive market efficiency from the perspective of the big picture, with a view of large samples and market movements in general. In contrast, many analysts view their task as the constant pursuit of market inefficiencies—temporarily mispriced securi- ties. Analysts see market efficiency from the front lines, experiencing daily swings in mar- ket prices that are sometimes hard to explain in the context of an efficient market. Thus, it is not surprising that the perspective on the degree of market efficiency (or the lack thereof ) differs substantially between academics and professional analysts. This section seeks to reach a common understanding, and the next section provides some striking evidence on the degree of market efficiency with respect to earnings and accounting information.

Capital markets may be described as “efficient” with regard to accounting information based on the degree to which market prices react completely and quickly to available accounting information. Notice that efficiency should be described as a matter of degree, not as an absolute. The issue is not whether the capital markets are or are not efficient. Rather, the issue is the degree to which the capital markets impound in prices all the avail- able value-relevant information.

The term completely in this description implies the degree to which share prices reflect the value-relevant implications of all available accounting information without systematic bias. A capital market that is relatively efficient will impound in stock prices the economic implications of all value-relevant financial statement information, even including account- ing items that may be disclosed in the notes.

The term quickly in this description suggests that market participants cannot consis- tently earn abnormal returns using accounting information for a long period of time after the information has been made public. If capital markets exhibit a high degree of efficiency, market prices should react quickly (within a matter of days) to capture any value-relevant signals in the accounting information.

The degree of efficiency, or the completeness and speed of price reactions, in an informa- tion-efficient capital market depends on analysts and financial statement analysis. Analysts study accounting information to assess appropriate values for stocks and to take positions in under- or overpriced securities, thereby driving stock market prices to efficient levels. Share prices move to new efficient levels based on the speed with which analysts can forecast and anticipate accounting information before it is released and on the speed with which they can analyze and react quickly to surprises in accounting information when it is released.

Also consider what a high degree of market efficiency does not imply. A capital market with a high degree of information efficiency does not necessarily price all stocks correctly every day. As a practical matter, relatively efficient markets experience valuation errors at the level of the individual firm, but these random inefficiencies cancel out at an aggregated

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1080 Chapter 14 Valuation: Market-Based Approaches

market level and do not persist for long periods of time.28 Analysts are driving forces involved in identifying and correcting security mispricings. A capital market with a high degree of information efficiency does not necessarily have perfect foresight—surprises hap- pen. Firms frequently surprise the market by announcing earnings that are higher or lower than the market’s expectations. Again, analysts drive market prices to react quickly and completely to new information.

Striking Evidence on the Degree of Market Efficiency and Inefficiency with Respect to Earnings Two studies by Victor Bernard and Jacob Thomas (1989 and 1990) provide the most strik- ing evidence to date on the degree of market efficiency and inefficiency with respect to accounting earnings.29 The Bernard and Thomas results during the post-earnings- announcement period suggest that the market’s reaction to quarterly earnings news is highly, but not completely, efficient. Nichols and Wahlen (2004) used data from 1988–2002 to replicate the seminal results in Bernard and Thomas (which were based on data from 1974–1986). Nichols and Wahlen collected a sample of 90,470 quarterly earnings announcements for firms on the CRSP and Compustat databases. They ranked all sample firms each quarter into ten portfolios on the basis of each firm’s unexpected earnings. (Unexpected earnings equals actual earnings per share minus analysts’ consensus forecast of earnings per share, scaled by price per share as of 60 trading days prior to the earnings announcement for cross-sectional comparability.) They studied the average abnormal (market-adjusted) stock returns to each portfolio over the 60 trading days leading up to the quarterly earnings announcement and over the 60 trading days following the announce- ment. Exhibit 14.11 depicts a portion of the Nichols and Wahlen results, which mirror the Bernard and Thomas results.

The results in Exhibit 14.11 during the pre-announcement period indicate that the market is highly efficient in anticipating and reacting to quarterly earnings surprises. Firms with quar- terly earnings surprises in the “good news” portfolios—portfolios 7 through 10—experience positive cumulative abnormal returns during the 60 days prior to and including the release of earnings. Firms with quarterly earnings surprises in the “bad news” portfolios—portfolios 1 through 4—experience negative cumulative abnormal returns during the 60 days prior to and including the release of earnings. The average difference in cumulative abnormal returns between portfolio 10 (roughly �6.7 percent) and portfolio 1 (roughly �6.8 percent) was roughly 13.5 percent per quarter. These results suggest that the market anticipates and reacts quickly to quarterly earnings information.

The results in Exhibit 14.11 during the post-announcement period suggest that the mar- ket’s reaction to quarterly earnings news is highly, but not completely, efficient. In the post- announcement period, Nichols and Wahlen measured the cumulative abnormal returns to the exact same portfolios over the 60 trading days after the earnings announcements. If the market’s reactions to quarterly earnings were, on average, quick and complete, these port- folios should exhibit no systematic abnormal returns in the post-announcement period. Upon the announcement of earnings, market prices should adjust efficiently within a few

28 For a discussion of these issues, see Ray Ball, “The Earnings-Price Anomaly,” Journal of Accounting and Economics (1992),

pp. 319–345.

29 Victor Bernard and Jacob Thomas, “Post-Earnings Announcement Drift: Delayed Price Response or Risk Premium?” Journal of

Accounting Research Vol. 27, (Supplement, 1989), pp. 1–36; and “Evidence that Stock Prices Do Not Fully Reflect the Implications

of Current Earnings for Future Earnings,” Journal of Accounting and Economics Vol. 13, No. 4 (1990), pp. 305–340.

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days of the announcement. Post-announcement abnormal returns should arise only from new information that arrives during those 60 days, and the post-announcement abnormal returns should not be associated with the prior quarter’s earnings news.

The results for the post-announcement period clearly indicate significant cumulative abnormal returns for the firms in portfolio 10 (best news) and portfolio 1 (worst news). Mean cumulative abnormal returns amount to roughly �3.0 percent and �2.2 percent for the best and worst news portfolios, respectively. In a follow-up study, Bernard and Thomas (1990) show that, in part, the market seems to underreact to the persistence in current period earnings for future period earnings, failing to fully anticipate the momentum in quarterly earnings changes.

E X H I B I T 1 4 . 1 1

Evidence from Nichols and Wahlen (2004) Replication of Bernard and Thomas (1989) on Market Efficiency with Respect to Quarterly Earnings

UE Decile

7/8/9

Days relative to earnings announcement

C u

m u

la ti

ve a

b n

o rm

al r

et u

–60 –50 –45 –40 –35 –30 –25 –20 –15 –10 –5 0–55 0 5 10 15 20 25 30 35 40 45 50 6055

10 8/9

6 7

3/4 2 1

0.08

–0.08

–0.06

–0.04

–0.02

0.00

0.02

0.04

0.06

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1082 Chapter 14 Valuation: Market-Based Approaches

Taken together, the Bernard and Thomas studies reveal that the market is highly, but not completely, efficient with respect to quarterly earnings. The results from the Nichols and Wahlen study using current data suggest that the Bernard and Thomas findings still hold. We consider these results to be very encouraging for analysts. We interpret the results to suggest that analysts who can sharpen their ability to forecast future earnings and take long positions in (buy) shares of firms experiencing earnings increases and short positions in (sell) shares of firms experiencing earnings decreases during the 60-day pre-announcement period have the potential to earn some portion of the pre-announcement abnormal returns. Similarly, analysts who can sharpen their ability to react appropriately once earn- ings are announced have some potential to earn a portion of the post-announcement abnormal returns. These findings suggest that there are returns to be earned by being good at forecasting and reacting to earnings.

We believe that the state-of-the-art of market efficiency is exactly where analysts would like it to be. The market is very efficient with respect to accounting information, but is not perfectly efficient. Some stocks are temporarily mispriced, but the market tends to correct mispricings in a relatively short time. Financial statements analysis, particularly focusing on earnings, can help the analyst identify stocks whose prices may be temporarily out of equilibrium. Insightful financial statement analysis can lead to intelligent investment deci- sions and better-than-average returns.

Striking Evidence on the Use of Valuation Models to Form Portfolios An empirical study by Richard Frankel and Charles Lee (1998) provides compelling evi- dence on the use of the residual income valuation models (which were demonstrated in this chapter and in Chapter 13) to pick stocks and form portfolios.30 Frankel and Lee imple- mented a three-year forecast horizon version of the residual income model to compute fun- damental share value for 18,162 firm-year observations from 1976 through 1993. During the early years of their study, the sample contained roughly 500 firms per year, while in the later years, it contained more than 1,300 firms per year.

To implement the residual income valuation model across a large sample of observations, Frankel and Lee needed data on earnings forecasts, book values and book value forecasts, and the cost of equity capital (R

E ) for each firm-year in the sample. For earnings forecasts,

Frankel and Lee collected from I/B/E/S the consensus analysts’ forecasts of one-year-ahead and two-years-ahead earnings per share as well as the analysts’ consensus earnings growth rate forecast for Year �3. They collected book-value-per-share data from Compustat and projected that future book value per share would grow with the consensus earnings-per- share forecast minus future dividends, assuming that each firm would maintain the current dividend payout policy. Finally, to determine the cost of equity capital, Frankel and Lee used an industry-average three-factor (beta, size, and market-to-book) expected returns model. They also assumed a constant cost of capital (11 percent, 12 percent, or 13 percent) across time and firms. Their results were not very sensitive to the R

E estimate.

Applying the three-year-horizon residual income model enabled Frankel and Lee to compute value per share (denoted as V) for each sample observation. They then scaled each firm’s V by market share price (P) to compute a V/P ratio. If a firm’s V/P ratio is exactly 1, it suggests that the market price per share is exactly equal to value per share. If a V/P ratio is greater than 1, it suggests that the share price is underpriced, whereas a V/P ratio of less

30 Richard Frankel and Charles M.C. Lee, “Accounting Valuation, Market Expectation, and Cross-Sectional Stock Returns,” Journal

of Accounting and Economics, Vol. 25 (1998), pp. 283–319.

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The Relevance of Academic Research for the Work of the Security Analyst 1083

than 1 suggests that the share is overpriced. During each year of the study, Frankel and Lee ranked all of the sample firms from highest to lowest V/P. They then formed five portfolios, from the quintile of firms with the highest V/P ratios that year (the top 20 percent) down to the quintile of firms with the lowest V/P ratios that year (the bottom 20 percent). They held these portfolios for 36 months and cumulated the average returns.

Exhibit 14.12 presents the Frankel and Lee results averaged across all of the years of their study. Judging by the bars in the graph and the axis on the left-hand side of the exhibit, the bottom quintile portfolio had an average V/P ratio of roughly 0.40, implying that these firms tended to be significantly overpriced. The top quintile portfolio had an average V/P ratio of roughly 1.5, indicating that these firms tended to be underpriced. The square dots and the right-hand axis of the graph indicate the average buy-and-hold returns cumulated by each portfolio over the 36 months after portfolio formation. Notice that the lowest quin- tile V/P firms generated, on average, cumulative three-year returns of only 35 percent, whereas the highest quintile V/P firms generated average cumulative three-year returns of nearly 65 percent. Frankel and Lee’s study also included various sensitivity analyses and control tests indicating that their results were robust. The V/P ratio seemingly distinguished under- and overpriced stocks.

E X H I B I T 1 4 . 1 2

Evidence from Frankel and Lee (1998) on Using Residual Income Valuation Models to Pick Stocks and Form Portfolios

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

1 2 3 4 5

V/P Quintile

V /P

10%

20%

30%

40%

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3 6

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1084 Chapter 14 Valuation: Market-Based Approaches

These results suggest that the valuation models we have discussed and demonstrated are useful in estimating share values and in evaluating which stocks are more likely to be under- or overpriced. Although these results are very encouraging for analysts, the results do not imply that the valuation process is simple or easy or error-proof. Indeed, we strongly encourage analysts to carefully follow the six steps of the analysis framework demonstrated throughout this book to conduct thorough financial statement analysis, develop accurate forecasts, and determine reliable estimates of value to increase the likeli- hood of making good investment decisions and decrease the likelihood of making poor decisions.

SUMMARY This chapter examines the use of market multiples in valuation by relying on the residual income model to develop the theoretical rationale relating market prices to economic driv- ers of value and to accounting fundamentals. This chapter describes the conceptual bases and practical applications of market multiples such as the market-to-book value ratio, the price-earnings ratio, and the price-earnings-growth ratio. The chapter focuses on four fac- tors that affect these market multiples: (1) risk and the cost of equity capital, (2) the expected future growth rate in earnings, (3) the presence of permanent and transitory com- ponents in the earnings of a particular year, and (4) the effects of accounting methods and principles on reported earnings and the book value of common shareholders’ equity. For decades, analysts have relied heavily on price-earnings ratios to relate market prices to earn- ings. However, in recent years, analysts and academics alike increasingly recognize that transitory elements in earnings and earnings growth can cloud the interpretation of the price-earnings ratio as an indicator of value. Analysts and academics are shifting emphasis to the price-earnings-growth ratio and to the market-to-book ratio. Transitory earnings elements of a particular period have less effect on the market-to-book ratio. This chapter also demonstrates techniques to exploit the information in market value by calculating price differentials and by reverse-engineering stock prices to infer the assumptions the mar- ket appears to be making. The chapter concludes by describing the relevance of academic research for the professional analyst, including highlighting key research results that appear to be very encouraging for the analyst interested in using earnings and financial statement data to analyze and value firms.

QUESTIONS, EXERCISES, PROBLEMS, AND CASES

Questions and Exercises 14.1 RESIDUAL ROCE. Explain residual ROCE (return on common shareholders’ equity). What does residual ROCE represent? What does residual ROCE measure?

14.2 THE VALUE-TO-BOOK VALUATION APPROACH. In conceptual terms, explain the value-to-book valuation approach. Explain how the value-to-book approach described and demonstrated in this chapter relates to the residual income valu - ation approach described and demonstrated in Chapter 13.

14.3 INTERPRETING VALUE-TO-BOOK RATIOS. Explain the implications of a value-to-book ratio that is exactly equal to 1. Compare the implications of a value- to-book ratio that is greater than 1 to those of a value-to-book ratio that is less than 1.

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14.4 INTERPRETING VALUE-TO-BOOK RATIOS. Explain the implications of a value-to-book ratio that is greater than the market-to-book ratio. Explain the implica- tions of a value-to-book ratio that is less than the market-to-book ratio.

14.5 VALUE-TO-BOOK RATIO DRIVERS. Identify three economic factors that will drive a firm’s value-to-book ratio to be higher than that of other firms in the same industry. Identify three accounting factors that will drive a firm’s value-to-book ratio to be higher than that of other firms in the same industry.

14.6 VALUE-TO-BOOK RATIO DRIVERS. Identify three economic factors that will drive a firm’s value-to-book ratio to decrease over time. Identify three accounting fac- tors that will drive a firm’s value-to-book ratio to decrease over time.

14.7 THE VALUE-EARNINGS RATIO. In conceptual terms, explain the value- earnings ratio. Explain the difference between the value-earnings ratio and the price- earnings ratio. What is the critical assumption about future earnings in both the value-earnings and price-earnings ratio?

14.8 THE PRICE-EARNINGS RATIO. In practice, it is common to observe price- earnings ratios measured as current period price divided by trailing twelve months (or most recent annual) earnings per share. Identify and explain three potential flaws inherent in this measurement of the price-earnings ratio as a valuation multiple.

14.9 PRICE-EARNINGS RATIO DRIVERS. Identify three economic factors that will drive a firm’s price-earnings ratio to be higher than that of other firms in the same industry. Identify three accounting factors that will drive a firm’s price-earnings ratio in a given period to be higher than that of other firms in the same industry.

14.10 PRICE-EARNINGS RATIO DRIVERS. Identify three economic factors that will drive a firm’s price-earnings ratio to decrease over time. Identify three accounting factors that will drive a firm’s price-earnings ratio down in a given period.

14.11 MARKET-TO-BOOK VERSUS PRICE-EARNINGS RATIOS. Explain why market-to-book multiples demonstrate less variance over time and across firms than do price-earnings multiples.

14.12 PRICE DIFFERENTIALS. EXPLAIN PRICE DIFFERENTIALS IN CONCEPTUAL TERMS. What does a price differential measure? How does a price differential relate to risk?

14.13 REVERSE-ENGINEERING SHARE PRICES. Explain reverse-engineer- ing of share prices in conceptual terms. How does reverse-engineering of share prices enable an analyst to infer (or deduce) the assumptions that the capital markets appear to impound in share price?

14.14 MARKET EFFICIENCY. What does market efficiency mean? What does mar- ket efficiency not mean? Explain how market efficiency relates to the amount of informa- tion that affects share prices and the speed with which information affects share prices.

14.15 ANALYSTS’ ROLE IN MARKET EFFICIENCY. Explain the analysts’ role in making the capital markets efficient.

Questions, Exercises, Problems, and Cases 1085

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1086 Chapter 14 Valuation: Market-Based Approaches

14.16 MARKET EFFICIENCY WITH RESPECT TO QUARTERLY EARN- INGS SURPRISES. Using the evidence presented in Exhibit 14.11, describe the extent to which the market is efficient with respect to quarterly earnings surprises during the 60 trading days prior to quarterly earnings announcements. Using the evidence presented in Exhibit 14.11, describe the extent to which the market is efficient with respect to quarterly earnings surprises during the 60 trading days following quarterly earnings announcements.

Problems and Cases 14.17 USING MARKET MULTIPLES TO ASSESS VALUES AND MARKET PRICES. Problem 13.18 and Exhibit 13.7 in Chapter 13 present selected data from projected financial statements for Steak ’n Shake for Year �1 to Year �11. The amounts for Year �11 reflect a long-term growth assumption of 3 percent. The cost of equity capital is 9.34 percent. The market value of common shareholders’ equity in Steak ’n Shake on January 1, Year �1, is $309.98 million.

Required a. Compute the value-to-book ratio as of January 1, Year �1, using the residual ROCE

valuation method. b. Using the analyses developed in Part a, prepare an exhibit summarizing the follow-

ing ratios for Steak ’n Shake as of January 1, Year �1:

1. Value-to-book ratio (using the amounts from Part a) 2. Market-to-book ratio 3. Value-earnings ratio, using reported earnings for Year 0 of $21.8 million 4. Price-earnings ratio, using reported earnings for Year 0 of $21.8 million 5. Value-earnings ratio, using projected earnings for Year �1 of $24.5 million 6. Price-earnings ratio, using projected earnings for Year �1 of $24.5 million

c. Compute the risk-neutral value of Steak ’n Shake as of January 1, Year �1, using a risk-free rate of 4.2 percent. Use the projected earnings for Year �1 to Year �10 and the projected earnings for Year �11 given in Exhibit 13.7. Maintain the continuing value growth assumption of 3 percent. Compute the price differential for Steak ’n Shake as of January 1, Year �1. Compute the ratio of market value to risk-neutral value for Steak ’n Shake as of January 1, Year �1.

d. Use reverse engineering to solve for the long-run growth rate in continuing residual income in Year �11 and beyond that is implicitly impounded in the market value of Steak ’n Shake on January 1, Year �1. Use the 9.34 percent cost of equity capital and the projected earnings amounts for Year �1 to Year �10 in Exhibit 13.7 before solv- ing for the long-run growth rate in continuing residual income.

e. Using the analyses in Parts a–d, evaluate the extent of the market’s mispricing (if any) of Steak ’n Shake.

14.18 INTERPRETING MARKET-TO-BOOK RATIOS. Exhibit 14.13 pres- ents data on market-to-book ratios, ROCE, the cost of equity capital, and price-earnings ratios for seven pharmaceutical companies. (Note that price-earnings ratios for these firms typically fall in the 30–35 range.) Exhibit 14.13 also provides historical data on the five-year average rate of growth in earnings and dividend payout ratios for each firm. The data on excess earnings years represent the number of years that each firm would need to earn a rate of return on common shareholders’ equity (ROCE) equal to that in Exhibit 14.13 in order to produce value-to-book ratios that equal the market-to-book ratios shown. For example, Bristol-Myers Squibb would need to earn a ROCE of 48.9 percent for 58.3 years in order

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Questions, Exercises, Problems, and Cases 1087

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1088 Chapter 14 Valuation: Market-Based Approaches

for the present value of the excess earnings over the cost of equity capital to produce a value-to-book ratio that matches the market-to-book ratio of 13.9.

Required Assume that market share prices for each firm are reasonably efficient. That is, do not simply assume that the market has over- or undervalued these firms. Considering the theoretical determinants of the market-to-book ratio, discuss the likely reasons for the relative ordering of these seven companies on their market-to-book ratios.

14.19 SENSITIVITY OF THE THEORETICAL MODELS OF VALUE- EARNINGS AND VALUE-TO-BOOK TO CHANGES IN ASSUMPTIONS. This problem explores the sensitivity of the value-earnings and value-to-book models to changes in underlying assumptions. We recommend that you design a computer spread- sheet to perform the calculations, particularly for the value-to-book ratio.

Required a. Assume that current period earnings per share were $1.00 for each of the following

scenarios. Compute the value-earnings ratio based on projected one-year-ahead earnings under each of the following sets of assumptions:

Scenario Cost of Equity Capital Growth Rate in Earnings

A 0.15 0.06 B 0.15 0.08 C 0.15 0.10 D 0.13 0.06 E 0.13 0.08 F 0.13 0.10 G 0.11 0.06 H 0.11 0.08 I 0.11 0.10

b. Assess the sensitivity of the value-earnings ratio to changes in the cost of equity capital and changes in the growth rate.

c. Compute the value-to-book ratio under each of the following sets of assumptions. Assume zero abnormal ROCE in the periods following the number of years of excess earnings.

Cost of Dividend Years of Equity Payout Excess

Scenario ROCE Capital Percentage Earnings

A 0.20 0.13 0.30 10 B 0.18 0.13 0.30 10 C 0.14 0.13 0.30 10 D 0.18 0.15 0.30 10 E 0.18 0.11 0.30 10 F 0.18 0.13 0.40 10 G 0.18 0.13 0.20 10 H 0.18 0.13 0.30 15 I 0.18 0.13 0.30 20

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d. Assess the sensitivity of the value-to-book ratio to changes in the assumptions made about the various underlying variables.

14.20 MARKET MULTIPLES AND REVERSE-ENGINEERING SHARE PRICES. In 2000, Enron enjoyed remarkable success in the capital markets. During that year, Enron’s shares increased in value by 89 percent, while the S&P 500 index fell by 9 percent. At the end of 2000, Enron’s shares were trading at roughly $83 per share and all of the sell-side analysts following Enron recommended the shares as a “buy” or a “strong buy.” With 752.2 million shares outstanding, Enron had a market capitalization of $62,530 million and was one of the largest firms (in terms of market capital) in the United States. At year-end 2000, Enron’s book value of common shareholders’ equity was $11,470 million.

At year-end 2000, Enron posted earnings per share of $1.19. Among sell-side analysts following Enron, the consensus forecast for earnings per share was $1.31 per share for 2001 and $1.44 per share for 2002, with 10 percent earnings growth expected from 2003–2005. At the time, Enron was paying dividends equivalent to roughly 40 percent of earnings and was expected to maintain that payout policy.

At year-end 2000, Enron had a market beta of 1.7. The risk-free rate of return was 4.3 percent, and the market risk premium was 5.0 percent.

[Note: The data provided in this problem, and the inferences you draw from them, do not depend on foresight of Enron’s declaring bankruptcy by the end of 2001.]

Required a. Use the CAPM to compute the required rate of return on common equity capital for

Enron. b. Use year-end 2000 data to compute the following ratios for Enron:

i. Market-to-book ii. Price-earnings (using 2000 earnings per share)

iii. Forward price-earnings (using consensus forecast earnings per share for 2001). c. Reverse-engineer Enron’s $83 share price to solve for the implied expected return on

Enron shares at year-end 2000. Do the reverse engineering under the following assumptions:

i. Enron’s market price equals value. ii. The consensus analysts’ earnings-per-share forecasts through 2005 are reliable

proxies for market expectations. iii. Enron will maintain a 40 percent dividend payout rate. iv. Beyond 2005, Enron’s long-run earnings growth rate will be 3.0 percent.

d. What do these analyses suggest about investing in Enron’s shares at a price of $83?

14.21 VALUATION OF COCA-COLA USING MARKET MULTIPLES. The Coca-Cola Company is a global soft-drink beverage company (ticker symbol � KO) that is a primary and direct competitor with PepsiCo. The data in Chapter 12’s Exhibits 12.13–12.15 include the actual amounts for 2008 and projected amounts for Year �1 to Year �6 for the income statements, balance sheets, and statements of cash flows for Coca- Cola (in millions).

In this problem, we use these actual and projected financial statement data to apply the techniques in Chapter 14 to compute Coca-Cola’s required rate of return on equity and share value based on the value-to-book valuation model. We also compare our value-to-book ratio

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estimate to Coca-Cola’s market-to-book ratio at the end of 2008 to determine an invest- ment recommendation. In addition, we compute the value-earnings and price-earnings ratios and the price differential and we reverse-engineer Coca-Cola’s share price as of the end of 2008.

Required Part I—Computing Coca-Cola’s Value-to-Book Ratio Using the Value-to-Book Valuation Approach.

a. Use the CAPM to compute the required rate of return on common equity capital for Coca-Cola.

b. Using the projected financial statements in Chapter 12’s Exhibits 12.13–12.15, derive the projected residual ROCE (return on common shareholders’ equity) for Coca- Cola for Years �1 through �5.

c. Assume that the steady-state long-run growth rate will be 3 percent in Year �6 and beyond. Project that the Year �5 income statement and balance sheet amounts will grow by 3 percent in Year �6; then derive the projected residual ROCE for Year �6 for Coca-Cola.

d. Using the required rate of return on common equity from Part a as a discount rate, compute the sum of the present value of residual ROCE for Coca-Cola for Years �1 through �5.

e. Using the required rate of return on common equity from Part a as a discount rate and the long-run growth rate from Part c, compute the continuing value of Coca- Cola as of the start of Year �6 based on Coca-Cola’s continuing residual ROCE in Year �6 and beyond. After computing continuing value as of the start of Year �6, discount it to present value at the start of Year �1.

f. Compute Coca-Cola’s value-to-book ratio as of the end of 2008 with the following three steps: (1) Compute the total sum of the present value of all future residual ROCE (from Parts d and e). (2) To the total from (1), add 1 (representing the book value of equity as of the beginning of the valuation as of the end of 2008). (3) Adjust the total sum from (2) using the midyear discounting adjustment factor.

g. Compute Coca-Cola’s market-to-book ratio as of the end of 2008. Compare the value-to-book ratio to the market-to-book ratio. What investment decision does the comparison suggest? What does the comparison suggest regarding the pricing of Coca-Cola shares in the market: underpriced, overpriced, or fairly priced?

h. Use the value-to-book ratio to project the value of a share of common equity in Coca-Cola.

i. If you computed Coca-Cola’s common equity share value using the free cash flows to common equity valuation approach in Problem 12.16 in Chapter 12 and/or the residual income valuation approach in Problem 13.19 in Chapter 13, compare the value estimate you obtained in those problems with the estimate you obtained in this case. You should obtain the same value estimates under all three approaches. If you have not yet worked those problems, you would benefit from doing so now.

Part II—Analyzing Coca-Cola’s Share Price Using the Value-Earnings Ratio, the Price- Earnings Ratio, Price Differentials, and Reverse Engineering

j. Use the forecast data for Year �1 to project Year �1 earnings per share. To do so, divide the projection of Coca-Cola’s comprehensive income available for common shareholders in Year �1 by the number of common shares outstanding at the end of 2008. Using this Year �1 earnings-per-share forecast and using the share value com- puted in Part h, compute Coca-Cola’s value-earnings ratio.

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k. Using the Year �1 earnings-per-share forecast from Part j and using the share price at the end of 2008, compute Coca-Cola’s price-earnings ratio. Compare Coca-Cola’s value-earnings ratio with its price-earnings ratio. What investment decision does the comparison suggest? What does the comparison suggest regarding the pricing of Coca-Cola shares in the market: underpriced, overpriced, or fairly priced? Does this comparison lead to the same conclusions you reached when comparing value-to- book ratios with market-to-book ratios in Part g?

l. Compute Coca-Cola’s price differential at the end of 2008. Compute Coca-Cola’s price differential as a percentage of Coca-Cola’s risk-neutral value. What dollar amount and what percentage amount has the market discounted Coca-Cola shares for risk?

m. Reverse-engineer Coca-Cola’s share price at the end of 2008 to solve for the implied expected rate of return. First, assume that value equals price and that the earnings and growth forecasts through Year �6 and beyond are reliable proxies for the mar- ket’s expectations for Coca-Cola. Then solve for the implied expected rate of return (the discount rate) the market has impounded in Coca-Cola’s share price. (Hint: Begin with the forecast and valuation spreadsheet you developed to value Coca-Cola shares. Vary the discount rate until you solve for the discount rate that makes your value estimate exactly equal the end of 2008 market price of $44.42 per share.)

n. Reverse-engineer Coca-Cola’s share price at the end of 2008 to solve for the implied expected long-run growth. First, assume that value equals price and that the earn- ings forecasts through Year �5 are reliable proxies for the market’s expectations for Coca-Cola. Also assume that the discount rate implied by the CAPM (computed in Part a) is a reliable proxy for the market’s expected rate of return. Then solve for the implied expected long-run growth rate the market has impounded in Coca-Cola’s share price. (Hint: Begin with the forecast and valuation spreadsheet you developed to value Coca-Cola shares and use the CAPM discount rate. Set the long-run growth parameter initially to zero. Increase the long-run growth rate until you solve for the growth rate that makes your value estimate exactly equal the end of 2008 market price of $44.42 per share.)

14.22 ANALYSIS OF COMPARABLE COMPANIES USING MARKET MULTIPLES. In this chapter, we evaluated shares of common equity in PepsiCo using the value-to-book approach, market multiples, price differentials, and reverse engineering. The Coca-Cola Company is a direct competitor with PepsiCo. The data in Chapter 12’s Exhibits 12.13–12.15 include the actual amounts for 2008 and projected amounts for Year �1 to Year �6 for the income statements, balance sheets, and statements of cash flows for Coca-Cola (in millions). In Problem 14.21, we evaluated shares of common equity in Coca-Cola using the value-to-book approach, market multiples, price differentials, and reverse engineering.

Required a. Prepare an exhibit using the data and analyses for PepsiCo from this chapter and the

data and analyses for Coca-Cola from the previous problem that will allow you to compare these two competitors on the following dimensions:

1. Cost of equity capital (R E )

2. ROCE for 2008 3. Projected ROCE for Year �1 4. Book value of common shareholders’ equity 5. Market value of common shareholders’ equity 6. Intrinsic value of common shareholders’ equity

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7. Value-to-book ratio 8. Market-to-book ratio 9. Value-earnings ratio (using Year �1 projected comprehensive income)

10. Price-earnings ratio (using Year �1 projected comprehensive income) 11. Value-earnings ratio (using 2008 reported earnings per share) 12. Price-earnings ratio (using 2008 reported earnings per share) 13. Price differential (on a per-share basis) 14. Price as a percentage of risk-neutral value 15. Reverse engineer share price to solve for implied expected rate of return (assum-

ing 3 percent long-run growth) 16. Reverse engineer share price to solve for implied long-run growth (assuming the

cost of equity capital as the discount rate) b. What inferences can you draw from these comparisons about the valuation of

PepsiCo versus Coca-Cola? In the chapter, we concluded that PepsiCo shares were underpriced by roughly 52 percent in the market at the end of 2008. In the previous problem, we concluded that Coca-Cola shares also were underpriced in the market at the end of 2008, by roughly 47 percent. Are these comparisons consistent with the conclusion that both PepsiCo and Coca-Cola shares could be underpriced at the end of 2008? Explain.

14.23 VALUATION OF WALMART USING MARKET MULTIPLES. In Problem 10.16, we projected financial statements for Walmart Stores for Years �1 through �5. The data in Chapter 12’s Exhibits 12.16–12.18 include the actual amounts for 2008 and the projected amounts for Year �1 to Year �5 for the income statements, balance sheets, and statements of cash flows for Walmart (in millions).

In this problem, we use these actual and projected financial statement data to apply the techniques in Chapter 14 to compute Walmart’s required rate of return on equity and share value based on the value-to-book valuation model. We also compare our value-to-book ratio estimate to Walmart’s market-to-book ratio at the end of 2008 to determine an invest- ment recommendation. In addition, we compute the value-earnings and price-earnings ratios and the price differential and we reverse-engineer Walmart’s share price as of the end of 2008.

Required Part I—Computing Walmart’s Value-to-Book Ratio Using the Value-to-Book Valuation Approach.

a. Use the CAPM to compute the required rate of return on common equity capital for Walmart.

b. Using the projected financial statements in Chapter 12’s Exhibits 12.16–12.18, derive the projected residual ROCE (return on common shareholders’ equity) for Walmart for Years �1 through �5.

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d. Using the required rate of return on common equity from Part a as a discount rate, compute the sum of the present value of residual ROCE for Walmart for Years �1 through �5.

e. Using the required rate of return on common equity from Part a as a discount rate and the long-run growth rate from Part c, compute the continuing value of Walmart as of the start of Year �6 based on Walmart’s continuing residual ROCE in Year �6 and beyond. After computing continuing value as of the start of Year �6, discount it to present value at the start of Year �1.

f. Compute Walmart’s value-to-book ratio as of the end of 2008 with the following three steps: (1) Compute the total sum of the present value of all future residual ROCE (from Parts d and e). (2) To the total from (1), add 1 (representing the book value of equity as of the beginning of the valuation as of the end of 2008). (3) Adjust the total sum from (2) using the midyear discounting adjustment factor.

g. Compute Walmart’s market-to-book ratio as of the end of 2008. Compare the value- to-book ratio to the market-to-book ratio. What investment decision does the com- parison suggest? What does the comparison suggest regarding the pricing of Walmart shares in the market: underpriced, overpriced, or fairly priced?

h. Use the value-to-book ratio to project the value of a share of common equity in Walmart.

i. If you computed Walmart’s common equity share value using the dividends valu - ation approach in Problem 11.14 in Chapter 11, and/or the free cash flows to com- mon equity valuation approach in Problem 12.17 in Chapter 12, and/or the residual income valuation approach in Problem 13.20 in Chapter 13, compare the value esti- mate you obtained in those problems with the estimate you obtained in this case. You should obtain the same value estimates under all four approaches. If you have not yet worked those problems, you would benefit from doing so now.

Part II—Analyzing Walmart’s Share Price Using the Value-Earnings Ratio, the Price- Earnings Ratio, Price Differentials, and Reverse Engineering

j. Use the forecast data for Year �1 to project Year �1 earnings per share. To do so, divide the projection of Walmart’s comprehensive income available for common shareholders in Year �1 by the number of common shares outstanding at the end of 2008. Using this Year �1 earnings-per-share forecast and the share value computed in Part h, compute Walmart’s value-earnings ratio.

k. Using the Year �1 earnings-per-share forecast from Part j and using the share price at the end of 2008, compute Walmart’s price-earnings ratio. Compare Walmart’s value-earnings ratio with its price-earnings ratio. What investment decision does the comparison suggest? What does the comparison suggest regarding the pricing of Walmart shares in the market: underpriced, overpriced, or fairly priced? Does this comparison lead to the same conclusions you reached when comparing value-to- book ratios with market-to-book ratios in Part g?

l. Compute Walmart’s price differential at the end of 2008. Compute Walmart’s price differential as a percentage of Walmart’s risk-neutral value. What dollar amount and what percentage amount has the market discounted Walmart shares for risk?

m. Reverse-engineer Walmart’s share price at the end of 2008 to solve for the implied expected rate of return. First, assume that value equals price and that the earnings and growth forecasts through Year �6 and beyond are reliable proxies for the mar- ket’s expectations for Walmart. Then solve for the implied expected rate of return (the discount rate) the market has impounded in Walmart’s share price. (Hint: Begin

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with the forecast and valuation spreadsheet you developed to value Walmart shares. Vary the discount rate until you solve for the discount rate that makes your value estimate exactly equal the end-of-2008 market price of $46.06 per share.)

n. Reverse-engineer Walmart’s share price at the end of 2008 to solve for the implied expected long-run growth. First, assume that value equals price and that the earn- ings forecasts through Year �5 are reliable proxies for the market’s expectations for Walmart. Also assume that the discount rate implied by the CAPM (computed in Part a) is a reliable proxy for the market’s expected rate of return. Then solve for the implied expected long-run growth rate the market has impounded in Walmart’s share price. (Hint: Begin with the forecast and valuation spreadsheet you developed to value Walmart shares and use the CAPM discount rate. Set the long-run growth parameter initially to zero. Increase the long-run growth rate until you solve for the growth rate that makes your value estimate exactly equal the end-of-2008 market price of $46.06 per share.)

INTEGRATIVE CASE 14.1

STARBUCKS

Valuation of Starbucks’ Common Equity Using Market Multiples In Integrative Case 10.1, we projected financial statements for Starbucks for Years �1 through �5. In this portion of the Starbucks Integrative Case, we use the projected finan- cial statements from Integrative Case 10.1 and apply the techniques in Chapter 14 to com- pute Starbucks’ required rate of return on equity and share value based on the value-to-book valuation model. We also compare our value-to-book ratio estimate to Starbucks’ market-to-book ratio at the time of the case to determine an investment recom- mendation. In addition, we compute the value-earnings and price-earnings ratios and the price differential and we reverse-engineer Starbucks’ share price as of the end of 2008.

Required Part I—Computing Starbucks’ Value-to-Book Ratio Using the Value-to-Book Valuation Approach

a. Use the CAPM to compute the required rate of return on common equity capital for Starbucks.

b. Using your projected financial statements from Integrative Case 10.1 for Starbucks, derive the projected residual ROCE (return on common shareholders’ equity) for Starbucks for Years �1 through �5.

d. Using the required rate of return on common equity from Part a as a discount rate, compute the sum of the present value of residual ROCE for Starbucks for Years �1 through �5.

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e. Using the required rate of return on common equity from Part a as a discount rate and the long-run growth rate from Part c, compute the continuing value of Starbucks as of the start of Year �6 based on Starbucks’ continuing residual ROCE in Year �6 and beyond. After computing continuing value as of the start of Year �6, discount it to present value at the start of Year �1.

f. Compute Starbucks’ value-to-book ratio as of the end of 2008 with the following three steps: (1) Compute the total sum of the present value of all future residual ROCE (from Parts d and e). (2) To the total from (1), add 1 (representing the book value of equity as of the beginning of the valuation as of the end of 2008). (3) Adjust the total sum from (2) using the midyear discounting adjustment factor.

g. Compute Starbucks’ market-to-book ratio as of the end of 2008. Compare the value- to-book ratio to the market-to-book ratio. What investment decision does the com- parison suggest? What does the comparison suggest regarding the pricing of Starbucks’ shares in the market: underpriced, overpriced, or fairly priced?

h. Use the value-to-book ratio to project the value of a share of common equity in Starbucks.

i. If you computed Starbucks’ common equity share value using the dividends valu - ation approach in Integrative Case 11.1 in Chapter 11, and/or the free cash flows to common equity valuation approach in Integrative Case 12.1 in Chapter 12, and/or the residual income valuation approach in Integrative Case 13.1 in Chapter 13, com- pare the value estimate you obtained in those cases with the estimate you obtained in this case. You should obtain the same value estimates under all four approaches. If you have not yet worked those prior cases, you would benefit from doing so now.

Part II—Analyzing Starbucks’ Share Price Using the Value-Earnings Ratio, the Price- Earnings Ratio, Price Differentials, and Reverse Engineering

j. Use your forecast data for Year �1 to project Year �1 earnings per share. To do so, divide your projection of Starbucks’ comprehensive income available for common shareholders in Year �1 by the number of common shares outstanding at the end of 2008. Using this Year �1 earnings-per-share forecast and using the share value com- puted in Part h, compute Starbucks’ value-earnings ratio.

k. Using the Year �1 earnings–per-share forecast from Part j and using the share price at the end of 2008, compute Starbucks’ price-earnings ratio. Compare Starbucks’ value-earnings ratio with its price-earnings ratio. What investment decision does the comparison suggest? What does the comparison suggest regarding the pricing of Starbucks’ shares in the market: underpriced, overpriced, or fairly priced? Does this comparison lead to the same conclusions you reached when comparing value-to- book ratios with market-to-book ratios in Part g?

l. Compute Starbucks’ price differential at the end of 2008. Compute Starbucks’ price differential as a percentage of Starbucks’ risk-neutral value. What dollar amount and what percentage amount has the market discounted Starbucks’ shares for risk?

m. Reverse-engineer Starbucks’ share price at the end of 2008 to solve for the implied expected rate of return. First, assume that value equals price and that your earnings and growth forecasts through Year �6 and beyond are reliable proxies for the mar- ket’s expectations for Starbucks. Then solve for the implied expected rate of return (the discount rate) the market has impounded in Starbucks’ share price. (Hint: Begin with the forecast and valuation spreadsheet you developed to value Starbucks’ shares. Vary the discount rate until you solve for the discount rate that makes your value estimate exactly equal the end-of-2008 market price of $14.17 per share.)

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n. Reverse-engineer Starbucks’ share price at the end of 2008 to solve for the implied expected long-run growth. First, assume that value equals price and that your earn- ings forecasts through Year �5 are reliable proxies for the market’s expectations for Starbucks. Also assume that the discount rate implied by the CAPM (computed in Part a) is a reliable proxy for the market’s expected rate of return. Then solve for the implied expected long-run growth rate the market has impounded in Starbucks’ share price. (Hint: Begin with the forecast and valuation spreadsheet you developed to value Starbucks’ shares and use the CAPM discount rate. Set the long-run growth parameter initially to zero. Increase the long-run growth rate until you solve for the growth rate that makes your value estimate exactly equal the end-of-2008 market price of $14.17 per share.)

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