VALUATION: MARKET-BASED APPROACHES. Learning Objectives

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VALUATION: MARKET-BASED

APPROACHES

Learning Objectives

1. Understand the practical advantages and disadvantages of using market multiples in valuation.

2. Apply a version of the residual income valuation model to esti-mate the value-to-book ratio (VB) as a theoretically correct val-uation multiple. Understand how to compare the value-to-book ratio to the market-to-book ratio (MB). Also understand how to compare VB ratios and MB ratios to analyze values of firms over time and to compare values across firms.

3. Understand and estimate the firm’s value-earnings ratio (VE) as a theoretically correct earnings-valuation multiple. Understand how to incorporate growth into the VE ratio to determine the value-earnings-growth ratio (VEG). Compare the VE and VEG ratios to the price-earnings ratio (PE) and the price-earnings-growth ratio (PEG). Use VE and VEG ratios and PE and PEG ratios to evaluate firms over time and compare valuations across firms.

4. Understand the role of the following factors on market multi-ples: (a) risk and the cost of equity capital, (b) growth rates, (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 actually do dif-fer across firms.

5. Estimate the price differential—the difference between market price and “risk-free value,” which is computed using the resid-ual income model and the risk-free discount rate.

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Chapters 1 to 12 have all focused on using the information in a firm’s accounting

numbers, financial statements, and related notes to analyze the firm’s fundamental characteristics of profitability, risk, growth, and value. These prior chapters have established a coherent framework to attack a very difficult problem—how to analyze and value a business. Using this framework to analyze and value a business, we must first understand the firm’s industry and business strategy, and then we use that under-standing to assess the quality of the firm’s accounting, making adjustments as neces-sary. 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 forecasts of future financial statements, from which we derive the expected future earnings, cash flows, and dividends that form the bases for valuation. We apply the free cash flows model, the residual income model, and the dividends model to value the firm, and we use these models to assess the sensitivity of firm value to key valuation parameters, such as costs of capital and expected growth rates. To culminate this process, we describe the realistic range of firm value estimates and compare this range of values to the firm’s market share price for an intelligent investment decision. Exhibit 13.1 provides a summary representation of the fundamentals-driven val-uation process. The bottom of the exhibit depicts the firm’s value drivers, such as expected future earnings, cash flows, growth, and risk, which comprise the economic foundations of valuation. We capture these value drivers in forecasts of future pro forma financial statements, and then convert these forecasts into value estimates using valuation models, such as the residual income model, the free cash flows model, and the dividends model.

In this chapter, we continue our focus on the firm’s fundamental characteristics of profitability, risk, growth, and value, but now we augment that analytical approach with techniques that allow us to exploit the information in the firm’s market value. We describe and apply a variety of techniques that compare the firm’s market value (or share price) to firm fundamentals. The techniques we describe in this chapter include commonly used market multiples—market-to-book ratios, price-earnings ratios, and price-earnings-growth ratios. Market multiples provide efficient short-cuts to the valuation process. As Exhibit 13.2 depicts, market multiples rest on the same foundation of value drivers in the valuation process as the valuation models discussed in Chapters 11 and 12—expected future earnings, cash flows, growth, and risk—but market multiples collapse the valuation process in two important ways.

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Introduction and Overview

6. Reverse engineer the firm’s stock price by using the residual income model to determine either the implicit expected return or the implicit expected long-run growth rate.

7. Understand the role of market efficiency in valuation, and the academic evidence on the degree to which the market effi-ciently impounds earnings information into share prices.

INTRODUCTION AND OVERVIEW

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(1) Instead of developing complete pro forma financial statement forecasts,

mul-tiples use just one or two summary accounting numbers to represent the value drivers.

(2) Instead of using extensive present value model computations, market

multi-ples summarize value using relatively simple ratios of market value of com-mon equity to summary accounting numbers.

EXHIBIT 13.1

Fundamentals of Valuation

Firm Value

Estimate:

Book Value of Common Equity plus 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

Pro Forma Financial Statement Forecasts

Fundamental Value Drivers over the Remaining Life of the Firm: Expected Future Earnings, Cash Flows, Growth, Risk

➡

➡

➡

EXHIBIT 13.2 Market Multiples Firm Value Market Multiples:

Market-to-Book Ratios, Price-Earnings Ratios, Price-Earnings-Growth Ratios

Summary Accounting Numbers:

Earnings; Book Value of Common Shareholders’ Equity; Long-run Growth

Fundamental Value Drivers over the Remaining Life of the Firm: Expected Future Earnings, Cash Flows, Growth, Risk

➡

➡

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In this chapter, we also introduce techniques to infer and exploit the information

in share prices, including computing price differentials and reverse engineering share prices. In the last section of the chapter, we briefly summarize a few key insights from the last 40 years of accounting, finance, and economics research on how efficiently the market uses accounting earnings to price stocks. The research findings are very encouraging for those interested in using accounting numbers for fundamental analysis and valuation of stocks.

The market price for a share of common equity is a very special and important number: it reflects the aggregated expectations of all of the market participants fol-lowing that particular stock. The market price reflects the result of the market’s trad-ing activity in that stock. It summarizes the aggregate information the market participants have about the firm, and the aggregate expectation for the firm’s future profitability, growth, and risk. The market price of a share does not mean that all market participants agree that the price is the correct value for the share; indeed, the market price simply indicates the equilibrium point at which the forces of supply (participants potentially willing to sell the stock—the “ask” side of trading) and the forces of demand (participants potentially willing to buy the stock—the “bid” side of trading) are momentarily 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 for value-relevant 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 market-to-book ratio or the price-earnings ratio. Thus, market multiples capture

relative valuation per dollar of book value or per dollar of earnings. In this way,

mar-ket multiples measure value relative to a key accounting number as a common denom-inator, thereby enabling analysts to draw inferences about a particular firm’s relative market capitalization, to assess changes in relative valuation over time, to make com-parisons of valuation across firms, and to make projections about comparable firms’ values. For example, price-earnings ratios allow an analyst to quickly gauge and com-pare the multiples at which the market is capitalizing different firms’ annual earnings. Market multiples can provide useful and efficient fundamental valuation ratios but they must be applied and interpreted carefully, after considering the firm’s expected future profitability, growth, and risk. Multiples like market-to-book ratios and price-earnings ratios are relative value metrics and therefore are not meaningful by them-selves. For example, whether a particular firm’s price-earnings ratio should be 10, 20, 30, or some other number cannot be determined unless the analyst knows the firm’s fundamental characteristics—expected future profitability, growth, and risk.

Analysts sometimes apply market multiples to estimate value in ad hoc ways. Valuation using market multiples may be efficient (the so-called “quick and dirty” approach) but may also be misleading. An analyst might be tempted to value a firm using that firm’s historical average or the industry average market multiple. The

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Market Multiples of Accounting Numbers

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firm’s historical average market-to-book ratio, for example, may be an appropriate fit

for the firm today, but only if the firm’s fundamental characteristics today match those of the firm’s past. In the same vein, an industry average price-earnings multi-ple may be an appropriate yardstick for valuing a particular firm, but only if that firm matches the industry average fundamental characteristics. If the firm is different today than it was in the past, or if the firm does not match the industry average, then market multiples must be adjusted to reflect the firm’s fundamental characteristics.

This chapter continues to emphasize the distinction between value and price. The chapter focuses attention on how to compute value-based multiples that reflect the firm’s fundamentals and that can be 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 correctly adjust historical or industry average multi-ples to reflect appropriately the firm’s expected profitability, growth, and risk.

The market-to-book ratio (MB) can be computed by dividing the firm’s market value of common equity at a point in time by the book value of common sharehold-ers’ equity from the firm’s most recent balance sheet. For example, at the end of Year 11, PepsiCo’s market value was $86,131.8 million (= $49.05 per share ×1,756 million shares), and PepsiCo’s Year 11 book value of common shareholders’ equity was $8,648.0 million (Appendix A). Thus, PepsiCo was trading at an MB ratio equal to 9.96 (=$86,131.8 million/$8,648.0 million). The MB ratio measures market value as a multiple of accounting book value at a point in time. The MB ratio reflects market value but it does not tell us what the ratio should be, given our estimate of value.

To compute a ratio that reflects our expectation of the firm’s intrinsic value to book value, we need to compute the value-to-book ratio (VB)—the value of common share-holders’ equity divided by the book value of common shareshare-holders’ equity. The VB ratio can be derived directly from the residual income model developed in Chapter 12. In fact, the VB ratio model is simply a version of the residual income model that is scaled by book value of common shareholders’ equity. The numerator of the VB ratio is the estimated value of common equity, which takes into account the book value of common shareholders’ equity, expected future profitability, growth, risk, and the time

MARKET-TO-BOOK AND VALUE-TO-BOOK RATIOS

1

1_{As we noted in Chapter 12, credit for the rigorous development of the residual income model, and its}

extension to the value-to-book ratio model, goes to James Ohlson in: J. 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; J. A. Ohlson, “Earnings, Book Values, and Dividends in Equity Valuation,” Contemporary Accounting Research (Spring 1995), pp. 661–687; G. A. Feltham and J. 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 E. Edwards and P. W. Bell, The Theory and Measurement of Business Income (Berkeley, CA: University of California Press), 1961.

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value of money. The VB ratio can be compared to the market-to-book ratio to identify

whether the stock is correctly priced in the market. The VB ratio of one firm can also be used to estimate the value of a different but comparable firm, provided the analyst makes the appropriate and necessary adjustments to the VB ratio so that it matches the comparable firm’s fundamental characteristics. This section explores the theoretical and empirical relation between estimated value, book value, and market value.

Using the same notation from prior chapters, we can compute the VB ratio with the following model:

In short, the VB ratio should be equal to one, plus the present value of expected future abnormal return on common equity (the [ROCE_t– R_E] term above) times cumulative growth in book value (the BV_t–1/BV₀term above). The growth in book value indicates the increase in net assets on which firms can earn abnormal earnings. The growth in book value depends on ROCE, dividend policy, and changes in common stock.

To show how we derive this model, recall from Chapter 12 the following expres-sion for the residual income valuation model:

Under the residual income valuation model, the value of common shareholders’ equity is 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 earn-ings exceed required earnearn-ings, for the remaining life of the firm.2_{We compute the} required earnings (or “normal” earnings) of the firm in year t as the product of the required rate of return on common 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 in order to provide a return to common equity capital that is equal to the cost of common equity capital. 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 and required earnings of the firm in year t. Residual income measures the amount of wealth that the analyst expects the firm to create (or destroy) in year t for common equity shareholders above (or below) the cost of equity capital.

V BV NI R BV R t E t E t t 0 0 1 1 1 = + − × + − = ∞

∑

( ) ( ) V BV ROCE R BV BV R t E t E t t 0 0 1 0 1 1 1 = + − × + − = ∞

∑

[ ( ]) 917

Market-to-Book and Value-to-Book Ratios

2_{Chapter 12 describes that the residual income valuation model depends on clean surplus accounting for}

book value of common shareholders’ equity, which requires that expected future earnings forecasts are comprehensive measures of income for the firm’s common equity shareholders, and that expected future dividends 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 residual income valuation, we mean expected future comprehensive income available for common shareholders.

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To convert the residual income model into a model for the VB ratio, we scale both

sides of the equation by BV₀, which produces the following equation:

We rewrite BV₀ divided by BV₀ as equal to one. We rewrite the NI_t/BV₀ term as follows:

To rewrite NI_t/BV₀this way, we state ROCE_t= NI_t/BV_t–1. Note that this computation of ROCE_tdivides 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/BV0is the cumulative growth factor in book value of common equity between year 0 (the date of the valuation) and period t – 1. As indicated above, growth in book value is a function of the earn-ings 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 invested, on which a firm can earn abnormal returns.

By decomposing the term NI_t/BV₀into these two parts, we can restate NI_t/BV₀as the product of 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 profitability on beginning of year common equity; beginning of year common equity is a function of cumulative growth. We can substitute these two components of NI_t/BV₀into the VB equation, as follows:

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:

V BV ROCE BV BV R BV BV R t t E t E t t 0 0 1 0 1 0 1 1 1 = + ×    − ×     + − − = ∞

∑

( ) NI BV NI BV BV BV ROCE BV BV t t t t t t 0 1 1 0 1 0 = × = × − − − V BV BV BV NI BV R BV BV R t E t E t t 0 0 0 0 0 1 0 1 1 = + − ×    + − = ∞

∑

_{( )}

3_{Theoretical and empirical research on the VB ratio typically defines ROCE as net income to common}

shareholders for a year divided by common shareholders’ equity at the beginning of the year. In contrast, we have used average common shareholders’ equity in the denominator of ROCE throughout this book. 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 particu-larly significant.

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We now have a useful model for the value-to-book ratio. Next we consider each term.

First, as a starting point, the VB ratio will equal one, to reflect the book value of common equity invested in the firm. The summation term indicates how the VB ratio should differ from one as a function of the firm’s expected future abnormal profitability (the ROCE_t– R_Eterm) times the firm’s cumulative growth in book value (the BV_t–1/BV₀term), 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, cost of equity capital, growth, and 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 dol-lar amount the analyst needs in order to use the VB ratio to compute the doldol-lar 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 will 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) shareholder 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 insofar as 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 that earn 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).

• Growth is not value-adding in itself. Growth adds value to shareholders only if the growth is abnormally profitable. If expected ROCE equals R_Eon new proj-ects (that is, zero NPV projproj-ects), then these new projproj-ects will not create (or destroy) common shareholders’ equity value. New projects will be “abnormally profitable” only when their 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); and (2) by increasing the discount rate used to compute the pres-ent value of residual income.

• 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, or book value growth differ from the industry averages. If a firm’s VB ratio changes over time, it should be because current expectations for the firm’s future ROCE, R_E, or book value growth differ from the past expectations for the firm’s future ROCE, R_E, or book value growth.

V BV ROCE R BV BV R t E t E t t 0 0 1 0 1 1 1 = + − × + − = ∞

∑

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Example 1. Suppose an analyst is evaluating a firm with $1,000 of book value of

common equity and a cost of equity capital equal to 10 percent. Assume that the ana-lyst forecasts that the firm will earn ROCE of 15 percent until Year +3, but then 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 it will not issue or buy back stock. Using the VB ratio approach, the analyst should assign the firm a VB ratio equal to one plus the present value of future residual ROCE times growth. The present value of future residual ROCE times growth is determined as follows:

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. The VB ratio of this firm is therefore 1.14265. 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 equity). Note that we have determined this VB ratio with all of the inputs expressed in rates. We can confirm this value using dollar amounts and the residual income model approach from Chapter 12, as follows:

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.

PV of

Residual Residual

Cumulative ROCE ROCE

Residual Book Value times times

Expected ROCE Growth Factor Cumulative Cumulative

Year ROCE = ROCE – RE to Year t–1 Growth PV 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}

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

$150.00 $100 $50.00 +1 0.15 = 0.15 ×1,000 $1,000 = 1,000 ×0.10 = 150 – 100 0.9091 $45.45 $172.50 $1,150 $115 $57.50 +2 0.15 = 0.15 ×1,150 = 1,000 + 150 = 1,150 ×0.10 = 172.50 – 115 0.8264 $47.52 $198.38 $1,322.5 $132.25 $66.13 +3 0.15 = 0.15 ×1,322.5 = 1,150 + 172.50 = 1,322.5 ×0.10 = 198.38 – 132.25 0.7513 $49.68 $152.09 $1,520.88 $152.09 $0.00 + 4 0.10 = 0.10 ×1,520.88 = 1,322.50 + 198.38 = 1,520.88 ×0.10 = 152.09 – 152.09 0.6830 $ 0.00

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We described above a number of economic reasons why VB and MB ratios may

differ from one. For example, the firm may have competitive advantages that enable it to earn an ROCE that is greater than R_E. To the extent that the firm can create and sustain these competitive advantages, the firm will increase the magnitude and per-sistence over time of the degree to which ROCE exceeds R_E, thereby increasing the VB and MB ratios. In addition, to the extent the firm will generate future growth by investing in abnormally profitable projects, the VB and MB ratios will differ from one.

A firm’s VB and MB ratio may differ from one for accounting reasons in addition to economic reasons.4_{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 research and development projects, brand equity, or human capital. If these investments were internally generated through research and development activities, marketing and advertising activities, or human capital recruit-ing and trainrecruit-ing activities, and if the investments in these activities were expensed according to conservative accounting principles (as is common under GAAP in the United States and most countries), then 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 common shareholders’ equity is understated, so ROCE will be relatively high. These effects can be observed among certain firms in many dif-ferent industries, such as pharmaceuticals, biotechnology, software, and consumer goods.

In the case of PepsiCo and Coca-Cola, for example, these firms have created sub-stantial off-balance sheet brand equity over many years of successful product devel-opment, advertising, and brand-building activities, and the investments in these activities have been expensed. 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.

Over a sufficiently long period of time, however, the impact of accounting princi-ples on the VB and MB ratio will diminish because economics teaches us to expect that competitive equilibrium forces will drive ROCE to converge to R_Ein the long run. Also, the self-correcting nature of accounting will eventually eliminate biases in ROCE and book value of equity. For example, consider a biotechnology company that invests for several years in research and development to develop a particular drug. During the initial years of research, the firm incurs research costs that GAAP

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Market-to-Book and Value-to-Book Ratios

REASONS WHY VB RATIOS AND MB RATIOS MAY DIFFER

FROM ONE

4_{Stephen Ryan found that book value changes lag market value changes in part because of GAAP’s use of}

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.

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requires the firm to expense. Its ROCE and book value of equity will be “low”

dur-ing these years. After developdur-ing and then marketdur-ing the final drug, ROCE will be “high” because the firm generates revenues without offsetting research costs. The “high” ROCE will increase retained earnings, and, over time, the initial conservative biases in ROCE and book value will be corrected.

Exhibit 13.3 presents descriptive statistics for MB ratios across 36 industries dur-ing the decade from 1991 to 2000.5 _{The descriptive statistics include the 25th} per-centile, 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 64,297 firm-years in this sample is 1.85. These data reveal substantial variation in MB ratios across industries and within industries during this period.

The differences in industry median MB ratios in Exhibit 13.3 likely relate in part to differences in competitive conditions driving differences in growth and ROCE relative to R_E, as well as differences in alternative accounting principles. Economically, in an industry that can be characterized as mature and competitive, the median firm will likely generate ROCE that is close to R_Eand will not likely generate unusually high rates of growth. Such firms tend to have median MB ratios closer to one. For example, firms in mature competitive industries such as textiles, real estate, insurance, banking, metals, and metal 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, and thus MB ratios are closer to one. 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 chemical industry includes pharmaceutical firms, which expense research and development expenditures in the year incurred. The health services, personal services, and business services industries expense compensation costs in the year incurred and do not cap-italize the value of their employees on the balance sheet. The balance sheet under-states the economic value of key resources in each of these industries. These industries have MB ratios considerably in excess of one.

Several empirical studies have found that MB ratios are fairly stable, mean revert-ing slowly over time, and that MB ratios are reliable predictors of future growth in book value and expected future ROCE (implying that ROCE also mean reverts

EMPIRICAL DATA ON MB RATIOS

5_{To compute these descriptive statistics on market-to-book value ratios, we deleted firm-years with}

nega-tive 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.

EMPIRICAL RESEARCH RESULTS ON THE PREDICTIVE POWER

OF MB RATIOS

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Market-to-Book and Value-to-Book Ratios

EXHIBIT 13.3

Descriptive Statistics on Market-to-Book Ratios, 1991–2000

25th Percentile Median 75th Percentile

Full Sample* on Compustat

(N = 64,297 firm-years) . . . 1.13 1.85 3.34 Industry: Textiles . . . 0.78 1.28 2.00 Real Estate . . . 0.73 1.31 2.50 Insurance . . . 0.94 1.33 1.93 Depository Institutions . . . 0.98 1.34 1.82 Metals . . . 0.89 1.45 2.31 Metal Products . . . 0.96 1.47 2.27 Hotels . . . 0.80 1.48 2.44 Retailers—General Merchandise . . . 0.83 1.49 3.01 Wholesale—Durables . . . 0.90 1.55 2.77 Lumber . . . 1.06 1.61 2.43 Utilities . . . 1.32 1.62 2.00 Paper . . . 1.17 1.64 2.58 Motion Pictures . . . 1.02 1.68 3.11 Security Brokers . . . 1.09 1.69 3.28 Metal Mining . . . 0.97 1.70 3.05 Oil and Gas Extraction . . . 1.09 1.74 2.84 Grocery Stores. . . 1.05 1.76 3.02 Restaurants . . . 1.04 1.81 3.02 Transportation by Air . . . 1.15 1.82 3.10 Petroleum and Coal . . . 1.28 1.83 2.55 Wholesale—Nondurables. . . 1.14 1.84 3.16 Transportation Equipment. . . 1.21 1.90 2.93 Amusements . . . 1.11 1.91 3.42 Retailing—Apparel . . . 1.14 1.95 3.50 Forestry . . . 0.90 2.02 2.85 Industrial Machinery and Equipment . . . 1.25 2.08 3.67 Food Processors . . . 1.23 2.15 3.75 Electronic and Electric Equipment . . . 1.25 2.21 3.85 Health Services . . . 1.30 2.21 3.83 Personal Services. . . 1.45 2.34 3.69 Instruments and Related Products . . . 1.37 2.39 4.46 Printing and Publishing . . . 1.40 2.41 3.74 Communication . . . 1.84 2.93 5.51 Business Services. . . 1.61 3.06 5.82 Chemicals . . . 1.96 3.34 5.96 Tobacco . . . 2.87 4.20 11.63

*To compute these descriptive statistics on market-to-book value ratios, we deleted 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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slowly).6_{For example, Victor Bernard grouped roughly 1,900 firms into 10 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 subse-quent years. Exhibit 13.4 summarizes a portion of Bernard’s results, grouping firms in the lowest 3 MB portfolios, middle 4 MB portfolios, and highest 3 MB portfolios.7 The data in Exhibit 13.4 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 lowest 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 low-est growth rates through Year +10. The results in the Bernard study also indicate (although it is not apparent from the summary of results in Exhibit 13.4) that the predictive power of MB ratios for future ROCEs does tend to diminish as the hori-zon lengthens. In Year +10, for example, there is relatively little difference in ROCEs across firms in the 3rd through 9th MB portfolios, as these firms experience ROCEs that tend to converge to 14 percent. These results are consistent with the steady mean

EXHIBIT 13.4

The Relation between MB Ratios and 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: 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%

6_{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.

7_{To reduce the effects of survivorship bias, Bernard included firms that did not survive the entire 10-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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reversion in ROCEs over time, consistent with movement toward competitive

equilibrium.

In Chapter 12, we estimated PepsiCo’s share value at the end of Year 11 to be roughly $69, based on the pro forma financial statement forecasts developed in Chapter 10 and the residual income model valuation. We next illustrate the valuation of PepsiCo shares using the value-to-book model, implementing the same forecasts developed in Chapter 10, the same equity cost of capital (8.0 percent), and the same long-run growth rate (5.0 percent). We also demonstrate the forecasts and valuation estimates in the FSAP Forecasts and Valuation spreadsheets in Appendix D.

To proceed with the VB model, we will follow seven steps:

(1) estimate the expected ROCE each period, computed as NI_t/BV_t–1;

(2) compute expected residual ROCE each period by subtracting the equity cost

of capital from expected ROCE;

(3) determine the cumulative growth factor in book value of common

sharehold-ers’ equity to the beginning of each period (computed as BV_t–1/BV₀);

(4) multiply the expected residual ROCE by the cumulative growth factor; (5) discount the expected residual ROCE with growth to present value, including

continuing value;

(6) compute the implied VB ratio by adding one (the ratio of book value over

book value) to the sum of the present value of the expected residual ROCE with growth;

(7) compare the implied VB ratio to the MB ratio to determine whether market

price is greater than, equal to, or less than our estimate of value. Equivalently, we can multiply the implied VB ratio by book value of equity to determine the value of common shareholders’ equity, and then divide by the number of shares outstanding to convert this total to a per-share estimate of value for PepsiCo, which we then compare to market price.

We next illustrate each of these seven steps with PepsiCo. The Year +1 projected ROCE is 38.9 percent, computed as net income available for common shareholders in Year +1 divided by book value of common equity at the start of Year +1 (= $3,367.3 mil-lion/$8,648.0 million). The residual ROCE is 30.9 percent after subtracting 8.0 percent for the cost of equity capital. The cumulative growth in book value (BV_t–1/BV₀) in Year +1 is 1.0, because Year +1 is the first year of the valuation horizon.8_{The product of Year} +1 residual ROCE and cumulative growth is 30.9 percent, which we discount to pres-ent value using an 8.0 percpres-ent cost of equity capital. Exhibit 13.5 prespres-ents these

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Application of the Value-to-Book Model to PepsiCo

APPLICATION OF THE VALUE-TO-BOOK MODEL TO

PEPSICO

8_{We project PepsiCo’s book value of common equity will grow to $9,466.2 million during Year +1.}

Therefore the cumulative growth factor in book value of common equity as of the start of Year +2 will be 1.095 (= $9,466.2 million/$8,648.0 million).

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computations for PepsiCo for Year +1 through Year +10. The sum of the present value

of residual ROCE times growth in Year +1 through Year +10 is 2.846.9

We use the same steps to compute the Year +11 residual ROCE for purposes of computing continuing value. As described in the previous chapter, we project net income in Year +11 to grow by the 5.0 percent long-run growth rate. We compute book value as of the start of Year +11 (the end of Year +10), compute implied residual ROCE, and multiply by the cumulative growth factor in book value up to the begin-ning of Year +11. The projected ROCE₁₁is 36.3 percent (= NI₁₁/BV₁₀= $6,920.0 million/$19,073.7 million). The projected residual ROCE₁₁is therefore 28.3 percent. Cumulative growth in book value from Year 0 to the beginning of Year +11 (the end of Year +10) is 2.206 (= BV₁₀/BV₀= $19,073.7 million/$8,648.0 million). We there-fore project in Year +11 the product of residual ROCE times cumulative growth is 62.4 percent (= 28.3 percent ×2.206).

We use the Year +11 residual ROCE with growth (62.4 percent) in the continuing value computation, as follows (allowing for rounding):

9_{This value should be interpreted as a component of the VB ratio, because all of the computations in the}

model are scaled by BV₀. Thus, the amount 2.846 can be interpreted as an estimate that PepsiCo will cre-ate residual income in Years +1 through +10 that, in present value, is equal to 2.846 times the current book value of common equity. To reconcile this computation with the residual income model computa-tions in Chapter 12, recognize that 2.846 times book value of $8,648.0 million equals $24,613.0 (allow for rounding), which is the present value of residual income through Year +10 computed in Exhibit 12.2.

EXHIBIT 13.5

Valuation of PepsiCo:

Present Value of Residual ROCE in Year +1 through Year +10

Year +1 Year +2 Year +3

COMPREHENSIVE INCOME AVAILABLE FOR

COMMON SHAREHOLDERS . . . $3,367.3 $3,656.4 $ 3,975.8 Common Shareholders’ Equity (at beginning of year) . . . $8,648.0 $9,466.2 $10,364.7 Implied ROCE (Comp Inc./Begin. Common Equity). . . 0.389 0.386 0.384 Residual ROCE (assuming R_E= 0.08) . . . 0.309 0.306 0.304 Cumulative Book Value Growth Factor as of the

Beginning of Year. . . 1 1.095 1.199 Residual ROCE times Cumulative Book Value Growth Factor . . . 0.309 0.335 0.364 Present Value Factors . . . 0.926 0.857 0.794 PV Residual ROCE times Growth . . . 0.286 0.287 0.289 Sum of PV Residual ROCE in Year +1 through Year +10 . . . 2.846

ContinuingValue₀ NI₁₀ g BV₁₀ R_E BV₁₀ BV₀ R_E g R_E 10 10 1 1 1 1 6 590 4 1 05 19 073 7 0 08 19 073 7 8 648 0 1 0 08 0 05 1 1 0 08 = × + − × × − × + = × − × × − × + [( ( )/ ) ] [ / ] [ / ( )] [ / ( ) ] [($ , . . / $ , . ) . ] [$ , . / $ , . ] [ / ( . . )] [ / ( . ) ] == × × × = 0 283 2 206 33 33 0 463 9 630 . . . . .

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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:

Present Value of Residual ROCE in Year +1 through Year +10 . . . 2.846 Present Value of Continuing Value of ROCE in Year +11 and beyond . . . . 9.630 Present Value of Residual ROCE . . . 12.476

Necessary Adjustments to Compute the Value-to-Book Ratio

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 one. As described in Chapters 11 and 12, 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 mid-year adjustment factor [1 + (R_E/2) = 1 + (0.080/2) = 1.040]. Making these two adjustments produces the implied VB ratio as follows:

Present Value of Residual ROCE . . . 12.476 Add: Beginning Book Value . . . + 1.000 Total. . . 13.476 Multiply by the Mid-Year Correction Factor . . . × 1.040 Implied VB Ratio . . . 14.015

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Application of the Value-to-Book Model to PepsiCo

EXHIBIT 13.5

Exhibit 13.5—continued

Year +4 Year +5 Year +6 Year +7 Year +8 Year +9 Year +10

$ 4,312.3 $ 4,649.6 $ 4,991.0 $ 5,350.0 $ 5,734.9 $ 6,147.5 $ 6,590.4 $11,572.9 $12,149.2 $13,380.8 $14,366.6 $15,423.7 $16,556.8 $17,771.4 0.373 0.383 0.373 0.372 0.372 0.371 0.371 0.293 0.303 0.293 0.292 0.292 0.291 0.291 1.338 1.405 1.547 1.661 1.783 1.915 2.055 0.392 0.425 0.453 0.486 0.520 0.558 0.598 0.735 0.681 0.630 0.583 0.540 0.500 0.463 0.288 0.289 0.286 0.283 0.281 0.279 0.277

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These computations suggest that PepsiCo common equity should be valued at 14.015

times the book value of equity at the start of the valuation horizon, which is the end of Year 11. At that time, PepsiCo’s market value was $86,131.8 million (= $49.05 per share ×1,756 million shares). Thus, PepsiCo was trading at an MB ratio equal to 9.96 (= $86,131.8 million/$8,648.0 million). The VB ratio is 41 percent greater than the MB ratio, implying PepsiCo shares were underpriced by 41 percent at that time.

Equivalently, we can convert the VB ratio into a share value estimate for purposes of comparing to price. If we multiply book value equity by the VB ratio, we obtain the value estimate of PepsiCo common equity of $121,205.9 million (= $8,648.0 mil-lion ×14.015 VB ratio; allow for rounding). Dividing by 1,756 million shares out-standing indicates that PepsiCo’s common equity shares have a value of $69.02 per share, a value estimate that is identical to the value estimates we obtained from the residual income and dividend models in Chapter 12 and the free cash flows to com-mon equity shareholders model in Chapter 11. The computations to arrive at PepsiCo’s common equity share value are summarized in Exhibit 13.6.

We can conduct a sensitivity analysis for the estimate of PepsiCo’s VB ratio to assess a reasonable range of VB ratios for PepsiCo. We will find that the sensitivity of the VB ratio estimate is identical to the sensitivity of the residual income model value estimates demonstrated in Chapter 12. This is to be expected because both models use the same forecasts and valuation assumptions. The VB model is simply a scaled version of the residual income model.

EXHIBIT 13.6

Valuation of PepsiCo using the Residual ROCE Valuation Model

Valuation Steps Computations Amounts

Sum of PV Residual ROCE in Year +1 See Exhibit 13.5. + 2.846

through Year +10

Add Continuing Value in Present Value Year +11 residual ROCE assumed to + 9.630 grow at 5.0%; discounted at 8.0%.

Computations in FSAP.

Total PV Residual ROCE = 12.476

Add: Beginning Book Value of Equity Ratio Beginning Book Value of Equity from + 1.000 Year 11 Balance Sheet. = 13.476

Adjust to Midyear Multiply by 1 + (R_E/2) × 1.040

Value-to-Book Ratio of Common Equity = 14.015

Book Value of Common Equity ×$ 8,648.0

Value of Common Equity =$121,205.9

Shares Outstanding ÷ 1,756.0

Estimated Value per Share =$ 69.02

Current Price per Share $ 49.05

Percent Difference (Positive number indicates 41%

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As we noted in Chapter 12, the capital markets devote enormous amounts of time

and energy to forecasting and analyzing firms’ earnings numbers. It is, therefore, no surprise that the market multiple that receives most frequent use and attention is the price-earnings (PE) ratio. Analysts’ reports and the financial press make frequent ref-erences to PE ratios. The Wall Street Journal reports PE ratios as part of the daily cov-erage of stock prices and trading. The capital markets increasingly evaluate ratios that integrate the PE ratio with expected future earnings growth, to capture explic-itly the links between price, earnings, and growth.

This section first describes the theoretical model for computing value-earnings ratios. The section then describes computing and using PE ratios from a practical per-spective because of the widespread use of PE ratios in practice. We then discuss the strict assumptions implied by PE ratios, and describe the conditions in which PE ratios may not capture appropriately the theoretical relation between value and earnings for most firms and the difficulties one encounters in reconciling actual PE ratios with those indicated by the theoretical value-earnings model. In this section, we also incorporate the role of earnings growth and examine price-earnings-growth (PEG) ratios. We conclude the section 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.

The VE ratio is the ratio of the value of common shareholders’ equity divided by earnings for a single period. The previous chapter described how to determine com-mon 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 account-ing and measure future earnaccount-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 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 income measurement

that is comprehensive).

If one has already computed firm value using the forecasting and valuation mod-els developed in the last three chapters, then computing the VE ratio is a simple mat-ter of division. For example, in prior chapmat-ters we estimated PepsiCo’s common shareholders’ equity value to be $121,205.9 million at the end of Year 11. We also pro-jected Year +1 comprehensive income will equal net income available for common shareholders, which will equal $3,367.3 million. Thus, we can compute the VE ratio for PepsiCo at the end of Year 11 as:

V₀/E₁= $121,205.9 million/$3,367.3 million = 36.0

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PRICE-EARNINGS AND VALUE-EARNINGS RATIOS

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Or equivalently, on a per-share basis as:

Vps₀/Eps₁= ($121,205.9 million/1,756 million shares)/($3,367.3 million/ 1,756 million shares) = $69.02/$1.92 = 36.0

We can also derive the VE ratio from the VB ratio determined using the residual income model in the previous section. We can employ an algebraic step to derive the firm’s VE ratio from the firm’s VB ratio, as follows:

V₀/E₁= V₀/BV₀×BV₀/E₁= V₀/BV₀×(1/ROCE₁)

Using this approach, we can derive PepsiCo’s VE ratio from the VB ratio we com-puted in the previous section, as follows:

V₀/E₁= V₀/BV₀×BV₀/E₁= V₀/BV₀×(1/ROCE₁)

= ($121,205.9 million/$8,648.0 million) ×($8,648.0 million/$3,367.3 million) = 14.015 ×2.5682

= 14.015 ×(1/0.389) = 36.0

Thus, we compute that PepsiCo’s VE ratio should equal 36.0. We convert PepsiCo’s VB ratio of 14.015 into the VE ratio by multiplying by 1/ROCE₁, which we project will be the inverse of 38.9 percent.

Notice that we simply derived the VE ratio from the computation that PepsiCo’s value is equal to $121,205.9 million, which is based on specific forecasts of PepsiCo’s future earnings. 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 theoretically correct benchmark to evaluate the firm’s PE ratio. We can compare PepsiCo’s VE ratio of 36.0 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). With the theoretically correct VE ratio, we can also project VE ratios for other firms, including making adjustments as necessary to capture the other firms’ fundamental characteristics of profitability, growth, and risk. In addi-tion, with the theoretically correct VE ratio, we have a benchmark to gauge other firms’ PE ratios in order 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.

As a practical matter, analysts, the financial press, and financial databases com-monly measure PE ratios as current period share price divided by reported earnings per share for either the most recent prior fiscal year or the most recent four quarters

PRICE-EARNINGS RATIOS

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(sometimes referred to as the trailing-twelve-months earnings).10_{The Wall Street}

Journal and financial data web sites such as Yahoo! Finance commonly compute

PE ratios this way. With this approach, we compute the PE ratio for PepsiCo as of the end of Year 11 as follows: Price per share₁₁/Earnings per share₁₁= $49.05/$1.51 = 32.5. Thus, at the end of Year 11, PepsiCo shares traded at a multiple of 32.5 times Year 11 earnings per share.11

The common approach to compute the PE ratio by dividing market price by earn-ings per share for the most recent year is practical because analysts can readily observe price per share and historical earnings per share for most firms. However, this common approach creates a logical misalignment for valuation purposes because it divides share price—which reflects the present value of future earnings— by historical earnings. If historical earnings contain unusual or nonrecurring gains or losses that are not expected to persist in future earnings, then the analyst should cleanse the reported historical earnings of these effects in order to compute a PE ratio that reflects earnings that are likely to persist in the future. Chapter 6 describes tech-niques to identify elements of income that are unusual and nonrecurring, adjust reported earnings to eliminate their effects, and thereby measure recurring, persist-ent earnings.

As an alternative approach to create a more logical alignment of price and earn-ings, the analyst can compute the PE ratio by dividing share price by the analyst’s forecast of future earnings per share—for example, expected earnings per share one year ahead. A PE ratio based on expected future earnings, however, requires the ana-lyst to forecast future earnings (or have access to another anaana-lyst’s forecast). The reli-ability of a forward-looking PE ratio then depends on the relireli-ability of the earnings forecast. Earnings forecast errors will distort forward-looking PE ratios.

We compute the forward-looking PE ratio for PepsiCo as of the end of Year 11 using our forecast that Year +1 earnings will be $3,367.3 million as follows: Price per share₀/Earnings per share₊₁ = $49.05 per share/($3,367.3 million/1,756 million shares) = 25.6. Thus, at the end of Year 11, PepsiCo shares traded at a multiple of 25.6 times the Year +1 earnings forecast. PepsiCo’s VE ratio of 36.0 is 41 percent greater than PepsiCo’s PE ratio of 25.6 at the end of Year 11, consistent with our prior esti-mates of PepsiCo’s value.12

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10_{In theory, to be consistent with clean surplus accounting and residual income valuation, the}

denomina-tor should be based on comprehensive income per share. However, analysts, the financial press, and financial databases rarely, if ever, compute PE ratios based on comprehensive income per share, in part because (a) U.S. GAAP does not yet require reporting comprehensive income on a per-share basis, and (b) the other comprehensive income items are usually unrealized gains and losses that are not likely to be a permanent component of income each period. We follow traditional practice in this chapter and compute PE ratios using reported earnings figures.

11_{If we compute PepsiCo’s PE ratio using amounts in millions rather than per-share amounts, we obtain a}

PE ratio of 32.4 (= $86,131.8 million/(Net Income of $2,662 million – $4 million preferred dividends)). This PE ratio is slightly lower than the PE ratio of 32.5 based on per-share amounts because PepsiCo reports earnings per share based on the weighted average number of common shares outstanding during the year (which is consistent with U.S. GAAP) rather than the number of shares outstanding at year-end.

12_{In this case, our forecasts of net income and comprehensive income for PepsiCo in Year +1 are the same,}

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Notice that we simply derived the PE ratio by dividing PepsiCo’s market share

price by either earnings per share of the past year or by our forecasts of PepsiCo’s future earnings per share. Obviously, using price to compute a PE ratio will not pro-vide any new information about PepsiCo’s share value. So what is the point of com-puting 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 valua-tion, and PE ratios provide a quick and efficient way to estimate firm value as a mul-tiple of earnings. Analysts commonly assess benchmark PE ratios that they expect a firm to have based on past PE ratios for that firm, or industry-average PE ratios, or comparable firms’ PE ratios. Analysts use benchmarks like these to project a firm’s PE ratio quickly, using one-period earnings as a common denominator for relative val-uations, rather than engaging in the extensive computations necessary to determine the correct value-earnings ratio to assess whether the market has priced the firm’s shares appropriately.

Analysts also use PE ratios as potentially informative benchmarks to project earnings-based valuation multiples that they use to compare valuations across panies or to project the valuations of other companies. For example, we could com-pare PepsiCo’s PE ratio to the PE ratios of Coca-Cola, Cadbury-Schweppes, or other beverage companies. We might also use PepsiCo’s PE ratio to project valuations for these beverage companies, or to project valuations for privately held firms or divi-sions of companies. Investment bankers use comparable companies’ PE ratios, for example, to benchmark reasonable ranges of share prices for IPOs.

PE ratios have the advantage of speed and efficiency, but they are not necessarily precise valuation estimates. When using PE ratios, therefore, the analyst must be care-ful 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 funda-mental characteristics of profitability, growth, and risk differ across these two firms. Such differences might arise, for example, because PepsiCo derives a major portion of earnings from the snack food business, which Coca-Cola does not have. Similarly, Coca-Cola derives more of its earnings from international sales than 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 differ-ences in more detail after we first 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 in order to determine the VE ratio and wishes 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 ignores earnings-growth), the analyst imposes a strong assumption on the earnings number for a sin-gle period: the analyst treats this earnings number (whether it is a trailing earnings number or a one-period-ahead forecast) as the beginning amount of a permanent

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stream of earnings, valued as a perpetuity. Conceptually, suppose that the firm’s

com-mon shareholders’ equity value equals its market value, that the firm’s earnings will be constant in the future, and that the firm’s investors expect a rate of return R_E. Under these conditions, we can value the firm’s common equity using the perpetuity model based on one-year-ahead earnings (denoted E₁), as follows:

V₀= P₀= E₁/R_E Rearranging slightly, the firm’s VE and PE ratios are:

V₀/E₁= P₀/E₁= 1/R_E

Thus, strictly speaking, the PE multiple assumes that firm value is the present value of a constant stream of expected future earnings, discounted at a constant expected future discount rate. Under these conditions, the analyst can value the firm simply using a multiple of one-period-ahead earnings, and the PE ratio of the firm is sim-ply the inverse of the discount rate.

To illustrate this model with an example, 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 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 funda-mental characteristics 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 8.0 percent cost of equity capital, then PepsiCo’s PE ratio should be 12.5 (= 1/0.080). This PE ratio is far below the theoretically derived VE ratio of 36.0 for PepsiCo.

Descriptive Data on PE Ratios

The table below includes descriptive statistics of price-earnings ratios (share price to one-year-ahead earnings: P_t/E_t+1, as well as share price to trailing earnings: P_t/E_t) during the years 1991–2000. These data represent a broad cross-sectional sample of 38,219 firm-years drawn from the Compustat database, excluding all firm-years with negative earnings.13

Price-Earnings Ratio 25th percentile Median 75th percentile

P_t/E_t+1 9.60 13.91 21.39

P_t/E_t 11.09 15.72 24.12

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13_{It does not make sense to compute PE ratios on the basis of negative earnings. PE ratios assume earnings}

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Exhibit 13.7 includes descriptive statistics on forward-looking PE ratios (share price

to one-year-ahead earnings: P_t/E_t+1) for the same 36 industries described in Exhibit 13.3 (MB ratios) and Exhibit 11.3 (market betas) during the years 1991 to 2000. Exhibit 13.7 lists the industries in ascending order of the median PE ratios. To describe the industry-wide variation in PE ratios, Exhibit 13.7 also includes the 25th percentile PE ratio and the 75th percentile PE ratio for each industry.

These descriptive data indicate substantial differences in median PE ratios across industries during 1991 to 2000. The firms in the forestry, security brokers, and insur-ance industries experienced the lowest median PE ratios during that period, whereas firms in the metal mining, business services, communications, and personal services industries experienced the highest median PE ratios. These data also depict wide variation in PE ratios across firms within each industry. For example, most of these 36 industries experienced wide differences between the 25th percentile and the 75th percentile PE ratio during 1991 to 2000. With only a few exceptions, the 75th per-centile PE ratio was more than double the 25th perper-centile PE ratio.14

What Factors Cause the PE Ratio to Differ Across Firms?

The same set of economic factors that may cause firms’ MB ratios to differ will also cause PE ratios to differ. 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 accounting principles, and differences across time in accounting earnings, can also drive differ-ences in PE ratios. We describe the effects of each of these determinants of PE ratios in the sections that follow, 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 equivalent 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, more risky firms will experience a lower market value and PE ratio. However, only firms facing rare circumstances experience PE ratios that equal the inverse of the equity cost of capital, so a variety of other forces also cause PE ratios to differ.

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_Ewill increase, thereby increasing the PE ratio relative to similar firms that do not have sustainable compet-itive advantages. Thus, both the magnitude and the persistence of the difference between ROCE and R_Ewill increase PE ratios across firms.

14_{The analyst must be careful with PE ratios because they are sensitive to earnings numbers 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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EXHIBIT 13.7

Descriptive Statistics on Share Price to One-Year-Ahead Earnings Ratios (Pt/Et+1), 1991–2000

Price-Earnings Ratios (P_t/E_t+1)

Industry 25th Percentile Median 75th Percentile

Forestry . . . 4.5 5.8 11.3 Security Brokers . . . 6.3 9.9 16.2 Insurance . . . 7.8 10.9 16.5 Depository Institutions . . . 8.8 11.5 15.6 Lumber . . . 8.1 11.6 17.4 Transportation by Air . . . 8.1 11.7 17.3 Metal Products . . . 8.4 11.8 17.2 Transportation Equipment . . . 8.8 12.1 18.6 Tobacco . . . 11.0 12.8 17.2 Wholesale—Durables . . . 8.4 12.8 20.5 Metals . . . 8.7 12.9 20.2 Wholesale—Nondurables . . . 9.2 13.0 21.0 Utilities . . . 10.8 13.0 16.1 Textiles . . . 10.0 13.3 19.6 Real Estate . . . 8.0 13.4 24.7 Industrial Machinery and Equipment . . . 9.7 14.4 23.9 Retailers—General Merchandise . . . 11.5 14.8 22.5 Retailing—Apparel . . . 10.2 14.8 21.9 Petroleum and Coal . . . 11.4 14.9 19.7 Hotels . . . 8.1 15.0 21.4 Motion Pictures . . . 9.7 15.3 25.5 Electronic and Electric Equipment . . . 9.7 15.6 25.4 Printing and Publishing . . . 11.2 15.6 22.0 Oil and Gas Extraction . . . 8.9 15.7 27.2 Restaurants . . . 10.7 15.7 24.8 Paper . . . 10.8 16.0 23.2 Grocery Stores . . . 12.2 16.1 23.3 Health Services . . . 11.3 16.6 26.6 Instruments and Related Products . . . 11.2 16.8 26.5 Amusements . . . 10.0 17.4 26.6 Chemicals . . . 12.5 17.6 26.5 Food Processors . . . 11.9 17.6 26.1 Personal Services . . . 14.3 18.8 24.2 Communication . . . 13.4 18.8 35.0 Business Services . . . 12.4 19.4 31.7 Metal Mining . . . 12.0 21.0 37.6

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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Accounting Differences. In addition to economic factors, firms’ PE ratios may differ for accounting reasons—especially differences in accounting methods, principles, and the periodic nature of earnings measurement. 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 sub-stantial investments in intangible activities that must be expensed under conservative accounting principles, leading to economic assets that are off-balance sheet, such as successful research and development, brand equity, or human capital. The effects of accounting methods and principles on reported earnings and PE ratios will likely change over the firm’s lifetime. All else held equal, conservative accounting will reduce reported earnings early in the life of the firm (for example, when accelerated depreciation charges are high or research and development is being expensed), thereby increasing the PE ratio. Ironically, later in the life of the firm, after the invest-ments 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 signifi-cantly different when one-period earnings are unusually high or low and therefore not representative of earnings in perpetuity. For example, if the analyst expects Year +1 earnings will include an unusual loss that will not persist, then the firm’s PE ratio will be unusually high. The transitory nature of a single period of accounting ings can cause PE ratios to be more volatile than the long-run expectations of earn-ings warrant. In particular, if the analyst uses PE ratios based on trailing twelve months earnings that include non-recurring gains or losses that are not expected to persist, the PE ratios will be artificially volatile.

Continuing the example, assume that the analyst expects the firm to generate earnings next period of $650 instead of $700 because the firm will recognize a $50 restructuring charge. If the market views this charge as nonrecurring (that is, not a permanent change in earnings), then the market price should fall to roughly $4,950 (= $5,000 – $50) in the no-growth scenario, and the PE ratio for the period will be 7.62 (= $4,950/$650), instead of 7.14 (= $5,000/$700). Conversely, if the current period’s earnings exceed their expected permanent level, then the PE ratio will be less 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 phenomenon or a change to a new lower or higher level of permanent earnings. If the analyst expects the decrease in earnings from $700 to $650 will be permanent, then the market price (assuming no change in risk or growth) should decrease to $4,643 (= $650/.14). Thus, the PE ratio remains the same at 7.14 (= 1/.14).

To illustrate the effects of accounting differences on PE ratios across firms, consider the table below, which includes PE ratios (computed as year-end share price over trailing earnings per share) for PepsiCo and Coca-Cola for the Years 10 and 11.

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Price per Earnings per PE Ratio Share Share

Year 10: PepsiCo 34.2 $49.56 $1.45

Coca-Cola 69.3 $60.94 $0.88

Year 11: PepsiCo 32.5 $49.05 $1.51

Coca-Cola 29.5 $47.15 $1.60

Considered at face value, the PE ratios for PepsiCo and Coca-Cola in Year 10 indicate that the market valued Coca-Cola’s earnings at a multiple of 69.3, more than twice PepsiCo’s earnings multiple of 34.2, implying Coca-Cola had lower cost of capital, higher growth, and/or greater profitability than PepsiCo. To the contrary, however, Coca-Cola recognized a restructuring charge in income in Year 10, driving EPS down to only $0.88, thereby inflating 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 Year 11, both firms reported earnings closer to normal levels and their PE ratios were quite similar.

Growth. Holding all else equal, PE ratios will be greater