Chapter 13VALUATION: MARKET-BASED

Thom

son

Learn

ing™

Chapter 13VALUATION: MARKET-BASEDAPPROACHES

Learning Objectives

1. Understand the practical advantages and disadvantages ofusing 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-bookratio to the market-to-book ratio (MB). Also understand how tocompare VB ratios and MB ratios to analyze values of firmsover time and to compare values across firms.

3. Understand and estimate the firm’s value-earnings ratio (VE) asa theoretically correct earnings-valuation multiple. Understandhow to incorporate growth into the VE ratio to determine thevalue-earnings-growth ratio (VEG). Compare the VE and VEGratios to the price-earnings ratio (PE) and the price-earnings-growth ratio (PEG). Use VE and VEG ratios and PE and PEGratios to evaluate firms over time and compare valuationsacross 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 thesefactors to explain how VB, VE, and VEG ratios should differacross firms, and why MB, PE, and PEG ratios actually do dif-fer across firms.

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

912

Thom

son

Learn

ing™

Chapters 1 to 12 have all focused on using the information in a firm’s accountingnumbers, financial statements, and related notes to analyze the firm’s fundamentalcharacteristics of profitability, risk, growth, and value. These prior chapters haveestablished a coherent framework to attack a very difficult problem—how to analyzeand value a business. Using this framework to analyze and value a business, we mustfirst 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, andleverage, using a set of financial ratios. On the foundation of these steps, we constructforecasts of future financial statements, from which we derive the expected futureearnings, cash flows, and dividends that form the bases for valuation. We apply thefree 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 keyvaluation parameters, such as costs of capital and expected growth rates. To culminatethis process, we describe the realistic range of firm value estimates and compare thisrange 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 asexpected future earnings, cash flows, growth, and risk, which comprise the economicfoundations of valuation. We capture these value drivers in forecasts of future proforma financial statements, and then convert these forecasts into value estimatesusing valuation models, such as the residual income model, the free cash flowsmodel, and the dividends model.

In this chapter, we continue our focus on the firm’s fundamental characteristics ofprofitability, risk, growth, and value, but now we augment that analytical approachwith 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 chapterinclude commonly used market multiples—market-to-book ratios, price-earningsratios, and price-earnings-growth ratios. Market multiples provide efficient short-cuts to the valuation process. As Exhibit 13.2 depicts, market multiples rest on thesame foundation of value drivers in the valuation process as the valuation modelsdiscussed in Chapters 11 and 12—expected future earnings, cash flows, growth, andrisk—but market multiples collapse the valuation process in two important ways.

913Introduction and Overview

6. Reverse engineer the firm’s stock price by using the residualincome model to determine either the implicit expected returnor the implicit expected long-run growth rate.

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

INTRODUCTION AND OVERVIEW

Thom

son

Learn

ing™

(1) Instead of developing complete pro forma financial statement forecasts, mul-tiples use just one or two summary accounting numbers to represent the valuedrivers.

(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.

Chapter 13 Valuation: Market-based Approaches914

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

➡➡

➡

Thom

son

Learn

ing™

In this chapter, we also introduce techniques to infer and exploit the informationin share prices, including computing price differentials and reverse engineering shareprices. In the last section of the chapter, we briefly summarize a few key insights fromthe last 40 years of accounting, finance, and economics research on how efficientlythe market uses accounting earnings to price stocks. The research findings are veryencouraging for those interested in using accounting numbers for fundamentalanalysis and valuation of stocks.

The market price for a share of common equity is a very special and importantnumber: 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 marketparticipants have about the firm, and the aggregate expectation for the firm’s futureprofitability, growth, and risk. The market price of a share does not mean that allmarket participants agree that the price is the correct value for the share; indeed, themarket 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 theforces of demand (participants potentially willing to buy the stock—the “bid” side oftrading) are momentarily in balance. Stock prices are dynamic, constantly changingwith the arrival of new information that changes investors’ expectations about sharevalue and triggers trading in the firm’s shares in the market. We can analyze shareprice for value-relevant information.

Market participants commonly calibrate firm valuation using market value or shareprice expressed as a multiple of a fundamental summary accounting number, such asthe market-to-book ratio or the price-earnings ratio. Thus, market multiples capturerelative 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 relativemarket 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 butthey must be applied and interpreted carefully, after considering the firm’s expectedfuture 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’sfundamental 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 firmusing that firm’s historical average or the industry average market multiple. The

915Market Multiples of Accounting Numbers

MARKET MULTIPLES OF ACCOUNTING NUMBERS

Thom

son

Learn

ing™

firm’s historical average market-to-book ratio, for example, may be an appropriate fitfor the firm today, but only if the firm’s fundamental characteristics today matchthose 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 firmmatches the industry average fundamental characteristics. If the firm is differenttoday than it was in the past, or if the firm does not match the industry average, thenmarket multiples must be adjusted to reflect the firm’s fundamental characteristics.

This chapter continues to emphasize the distinction between value and price. Thechapter focuses attention on how to compute value-based multiples that reflect thefirm’s fundamentals and that can be compared to market price-based multiples. Thisfocus also directs our attention to the factors that drive multiples, so that the analystcan 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 marketvalue 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 Year11, PepsiCo’s market value was $86,131.8 million (= $49.05 per share × 1,756 millionshares), 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 to9.96 (=$86,131.8 million/$8,648.0 million). The MB ratio measures market value asa multiple of accounting book value at a point in time. The MB ratio reflects marketvalue 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 bookvalue, we need to compute the value-to-book ratio (VB)—the value of common share-holders’ equity divided by the book value of common shareholders’ equity. The VBratio 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 isscaled by book value of common shareholders’ equity. The numerator of the VB ratiois the estimated value of common equity, which takes into account the book value ofcommon shareholders’ equity, expected future profitability, growth, risk, and the time


MARKET-TO-BOOK AND VALUE-TO-BOOK RATIOS1

1As we noted in Chapter 12, credit for the rigorous development of the residual income model, and itsextension to the value-to-book ratio model, goes to James Ohlson in: J. A. Ohlson,“A Synthesis of SecurityValuation Theory and the Role of Dividends, Cash Flows, and Earnings,” Contemporary AccountingResearch (Spring 1990), pp. 648–676; J. A. Ohlson, “Earnings, Book Values, and Dividends in EquityValuation,” 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,” ContemporaryAccounting Research (Spring 1995), pp. 216–230. The ideas underlying the value-to-book ratio also traceto 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 BusinessIncome (Berkeley, CA: University of California Press), 1961.

A THEORETICAL MODEL OF THE VALUE-TO-BOOK RATIO

Thom

son

Learn

ing™

value of money. The VB ratio can be compared to the market-to-book ratio to identifywhether the stock is correctly priced in the market. The VB ratio of one firm can alsobe used to estimate the value of a different but comparable firm, provided the analystmakes the appropriate and necessary adjustments to the VB ratio so that it matches thecomparable firm’s fundamental characteristics. This section explores the theoreticaland empirical relation between estimated value, book value, and market value.

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

In short, the VB ratio should be equal to one, plus the present value of expected futureabnormal return on common equity (the [ROCE

t– R

E] term above) times cumulative

growth in book value (the BVt–1

/BV0

term above). The growth in book value indicatesthe increase in net assets on which firms can earn abnormal earnings. The growth inbook 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 allexpected future residual income, which is the amount by which expected future earn-ings exceed required earnings, for the remaining life of the firm.2 We compute therequired earnings (or “normal” earnings) of the firm in year t as the product of therequired rate of return on common equity capital times the book value of commonequity 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 equitycapital that is equal to the cost of common equity capital. We measure residualincome (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 thefirm in year t. Residual income measures the amount of wealth that the analystexpects the firm to create (or destroy) in year t for common equity shareholdersabove (or below) the cost of equity capital.

V BVNI R BV

Rt E t

Et

t0 0

1

11

= +− ×

+−

=

∞

∑ ( )

( )

V

BV

ROCE RBV

BV

R

t Et

Et

t

0

0

1

0

1

11

= +− ×

+

−

=

∞

∑[ ]

( )

917Market-to-Book and Value-to-Book Ratios

2Chapter 12 describes that the residual income valuation model depends on clean surplus accounting forbook value of common shareholders’ equity, which requires that expected future earnings forecasts arecomprehensive measures of income for the firm’s common equity shareholders, and that expected futuredividends reflect all capital transactions between the firm and common equity shareholders. Throughoutthis chapter, when we refer to expected future “earnings” or “net income” in the context of residualincome valuation, we mean expected future comprehensive income available for common shareholders.

Thom

son

Learn

ing™

To convert the residual income model into a model for the VB ratio, we scale bothsides of the equation by BV

0, which produces the following equation:

We rewrite BV0

divided by BV0

as equal to one. We rewrite the NIt/BV

0term as

follows:

To rewrite NIt/BV

0this way, we state ROCE

t= NI

t/BV

t–1. Note that this computation

of ROCEt

divides net income in period t by book value of common equity at thebeginning of period t. This ROCE computation differs slightly from the approach inChapter 4 in which we compute ROCE as net income divided by the average bookvalue of equity during period t.3 Also, note that BV

t–1/BV

0is 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, lessequity capital paid out to shareholders through dividends and stock buybacks. Thegrowth in book value indicates growth in net assets invested, on which a firm canearn abnormal returns.

By decomposing the term NIt/BV

0into these two parts, we can restate NI

t/BV

0as

the product of ROCE in year t times the cumulative growth in book value from year0 to the start of year t. Return on common equity is a function of profitability onbeginning of year common equity; beginning of year common equity is a functionof cumulative growth. We can substitute these two components of NI

t/BV

0into the

VB equation, as follows:

Now both terms in the numerator of the summation term are multiplied by the samecumulative book value growth factor. We rearrange that equation as follows:

V

BV

ROCEBV

BVR

BV

BV

R

tt

Et

Et

t

0

0

1

0

1

0

1

11

= +×

− ×

+

− −

=

∞

∑ ( )

NI

BV

NI

BV

BV

BVROCE

BV

BVt t

t

tt

t

0 1

1

0

1

0

= × = ×−

− −

V

BV

BV

BV

NI

BVR

BV

BV

R

tE

t

Et

t

0

0

0

0

0

1

0

11

= +− ×

+

−

=

∞

∑ ( )


3Theoretical and empirical research on the VB ratio typically defines ROCE as net income to commonshareholders 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 atthe beginning of the year, although the bias in using average shareholders’ equity should not be particu-larly significant.

Thom

son

Learn

ing™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 ofcommon equity invested in the firm. The summation term indicates how the VBratio should differ from one as a function of the firm’s expected future abnormalprofitability (the ROCE

t– R

Eterm) times the firm’s cumulative growth in book value

(the BVt–1

/BV0

term), all of which is discounted to present value, reflecting the firm’scost 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 inplace, profitability, cost of equity capital, growth, and time value of money. The VBmodel provides a valuation approach in which all of the inputs to valuation can beexpressed 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 dollar valueof 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 = RE). The VB model indicates that a firm in steady-

state equilibrium earning ROCE = RE

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 insofaras 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 > RE. Firms that earn a return that is less than the cost of equity capital

(that is, ROCE < RE) 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 RE

on new proj-ects (that is, zero NPV projects), then these new projects will not create (ordestroy) common shareholders’ equity value. New projects will be “abnormallyprofitable” only when their expected ROCE exceeds R

E.

• The risk of the firm increases the equity cost of capital. Increasing the equity costof capital reduces firm value in two ways: (1) by increasing the required ROCEthe 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 bebecause 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 becausecurrent expectations for the firm’s future ROCE, R

E, or book value growth differ

from the past expectations for the firm’s future ROCE, RE, or book value growth.

V

BV

ROCE RBV

BV

R

t Et

Et

t

0

0

1

0

1

11

= +− ×

+

−

=

∞

∑[ ]

( )


Thom

son

Learn

ing™

Example 1. Suppose an analyst is evaluating a firm with $1,000 of book value ofcommon 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 afterYear +3 the firm will earn ROCE equal to 10 percent. The analyst also expects thefirm will reinvest all net income (that is, pay zero dividends), and it will not issue orbuy back stock. Using the VB ratio approach, the analyst should assign the firm a VBratio equal to one plus the present value of future residual ROCE times growth. Thepresent value of future residual ROCE times growth is determined as follows:

The sum of the present values of residual ROCE times cumulative growth throughYear +3 equals 0.14265, and the sum in all years after Year +3 is zero. The VB ratio ofthis firm is therefore 1.14265. We can multiply the VB ratio by book value of equityto determine that firm value is $1,142.65 (= 1.14265 VB ratio × $1,000 book valueequity). Note that we have determined this VB ratio with all of the inputs expressedin rates. We can confirm this value using dollar amounts and the residual incomemodel 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 theresidual income model confirms that firm value is $1,142.65.


PV ofResidual Residual

Cumulative ROCE ROCEResidual Book Value times times

Expected ROCE Growth Factor Cumulative CumulativeYear ROCE = ROCE – R

Eto 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 BookValue at the end Required PV of

Expected Expected of Year t – 1 Income Residual PV ResidualYear ROCE Earnings (BV

t – 1) = BV

t – 1× R

EIncome 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

Thom

son

Learn

ing™

We described above a number of economic reasons why VB and MB ratios maydiffer from one. For example, the firm may have competitive advantages that enableit 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 byinvesting in abnormally profitable projects, the VB and MB ratios will differ fromone.

A firm’s VB and MB ratio may differ from one for accounting reasons in addition toeconomic reasons.4 The firm may have investments in projects for which accountingmethods 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 anddevelopment activities, marketing and advertising activities, or human capital recruit-ing and training activities, and if the investments in these activities were expensedaccording to conservative accounting principles (as is common under GAAP in theUnited States and most countries), then the firm will have substantial off-balance sheetassets and off-balance sheet common shareholders’ equity. These off-balance sheetassets generate net income, but common shareholders’ equity is understated, so ROCEwill be relatively high. These effects can be observed among certain firms in many dif-ferent industries, such as pharmaceuticals, biotechnology, software, and consumergoods.

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 theseactivities have been expensed. Thus, for these firms, the book value of commonshareholders’ 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 expectthat 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 inROCE and book value of equity. For example, consider a biotechnology companythat invests for several years in research and development to develop a particulardrug. During the initial years of research, the firm incurs research costs that GAAP


REASONS WHY VB RATIOS AND MB RATIOS MAY DIFFERFROM ONE

4Stephen Ryan found that book value changes lag market value changes in part because of GAAP’s use ofhistorical 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.

Thom

son

Learn

ing™

requires the firm to expense. Its ROCE and book value of equity will be “low” dur-ing these years. After developing and then marketing 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 conservativebiases 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 eachindustry, listed in ascending order of the median MB ratio. The median MB ratio forthe 64,297 firm-years in this sample is 1.85. These data reveal substantial variation inMB 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. Forexample, 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 thesample average.

With respect to accounting, the assets of firms in some of these industries—particularly banks and insurers—are primarily investments in financial assets, someof which appear on the balance sheet at fair value, and thus MB ratios are closer toone. In contrast, some of the industries with relatively high MB ratios are more likelyto have off-balance sheet assets and shareholders’ equity. For example, the chemicalindustry includes pharmaceutical firms, which expense research and developmentexpenditures in the year incurred. The health services, personal services, and businessservices 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. Theseindustries 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 inbook value and expected future ROCE (implying that ROCE also mean reverts


EMPIRICAL DATA ON MB RATIOS

5To 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 distributionas potential outliers with undue influence on the descriptive statistics.

EMPIRICAL RESEARCH RESULTS ON THE PREDICTIVE POWEROF MB RATIOS

Thom

son

Learn

ing™


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

*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.

Thom

son

Learn

ing™

slowly).6 For example, Victor Bernard grouped roughly 1,900 firms into 10 portfolioseach year between 1972 and 1981 based on their MB ratios. He then computed themean 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 firmsin 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 tohave the highest ROCEs through Year +10, and firms with the lowest MB ratios tendto have the lowest ROCEs through Year +10. The results from the Bernard study alsoindicate that firms with the highest MB ratios have the highest growth rates in bookvalue 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 thepredictive 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 ROCEsacross firms in the 3rd through 9th MB portfolios, as these firms experience ROCEsthat 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 0.12Medium 1.15 0.11 0.13 0.14 0.14High 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%

6Victor L. Bernard, “Accounting-Based Valuation Methods, Determinants of Market-to-Book Ratios andImplications for Financial Statement Analysis,” Working Paper, University of Michigan, 1993; Jane A. Ouand 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-EarningsRatios 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 Valueand Their Effects on the Ability of the Book-to-Market Ratio to Predict Book Return on Equity,” Journalof Accounting Research, Vol. 38, No. 1 (Spring 2000), pp. 127–149.

7To reduce the effects of survivorship bias, Bernard included firms that did not survive the entire 10-yearfuture horizon, and included any gain or loss on the cessation of the firm (from bankruptcy, takeover, orliquidation) in the final year ROCE.

Thom

son

Learn

ing™

reversion in ROCEs over time, consistent with movement toward competitiveequilibrium.

In Chapter 12, we estimated PepsiCo’s share value at the end of Year 11 to beroughly $69, based on the pro forma financial statement forecasts developed inChapter 10 and the residual income model valuation. We next illustrate the valuationof PepsiCo shares using the value-to-book model, implementing the same forecastsdeveloped in Chapter 10, the same equity cost of capital (8.0 percent), and the samelong-run growth rate (5.0 percent). We also demonstrate the forecasts and valuationestimates 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 NIt/BV

t–1;

(2) compute expected residual ROCE each period by subtracting the equity costof 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/BV

0);

(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 ROCEwith growth;

(7) compare the implied VB ratio to the MB ratio to determine whether marketprice 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 thevalue of common shareholders’ equity, and then divide by the number ofshares outstanding to convert this total to a per-share estimate of value forPepsiCo, which we then compare to market price.

We next illustrate each of these seven steps with PepsiCo. The Year +1 projected ROCEis 38.9 percent, computed as net income available for common shareholders in Year +1divided 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 percentfor the cost of equity capital. The cumulative growth 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.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 percent cost of equity capital. Exhibit 13.5 presents these

925Application of the Value-to-Book Model to PepsiCo

APPLICATION OF THE VALUE-TO-BOOK MODEL TOPEPSICO

8We 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 be1.095 (= $9,466.2 million/$8,648.0 million).

Thom

son

Learn

ing™

computations for PepsiCo for Year +1 through Year +10. The sum of the present valueof 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 ofcomputing continuing value. As described in the previous chapter, we project netincome in Year +11 to grow by the 5.0 percent long-run growth rate. We computebook value as of the start of Year +11 (the end of Year +10), compute implied residualROCE, and multiply by the cumulative growth factor in book value up to the begin-ning of Year +11. The projected ROCE

11is 36.3 percent (= NI

11/BV

10= $6,920.0

million/$19,073.7 million). The projected residual ROCE11

is therefore 28.3 percent.Cumulative growth in book value from Year 0 to the beginning of Year +11 (the endof Year +10) is 2.206 (= BV

10/BV

0= $19,073.7 million/$8,648.0 million). We there-

fore project in Year +11 the product of residual ROCE times cumulative growth is62.4 percent (= 28.3 percent × 2.206).

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


9This value should be interpreted as a component of the VB ratio, because all of the computations in themodel are scaled by BV

0. 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 currentbook 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 forrounding), 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 $10,364.7Implied ROCE (Comp Inc./Begin. Common Equity). . . . . . . . . . 0.389 0.386 0.384Residual 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 0.364Present 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

ContinuingValue NI g BV R BV BV R g RE E E0 10 10 10 0

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

. . . .

.

Thom

son

Learn

ing™

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 . . . . . . . . . . 2.846Present 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 RatioTo 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 presentvalue calculations overdiscount because they discount each year’s residual ROCE forfull periods when, in fact, the firm generates residual ROCE throughout each periodand we should discount from the midpoint of each year to the present. Therefore, tomake the correction, we multiply the present value sum by the mid-year adjustmentfactor [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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.476Add: Beginning Book Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . + 1.000

Total. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.476Multiply by the Mid-Year Correction Factor . . . . . . . . . . . . . . . . . . . . . × 1.040

Implied VB Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.015

927Application 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 0.3710.293 0.303 0.293 0.292 0.292 0.291 0.291

1.338 1.405 1.547 1.661 1.783 1.915 2.0550.392 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

Thom

son

Learn

ing™

These computations suggest that PepsiCo common equity should be valued at 14.015times the book value of equity at the start of the valuation horizon, which is the endof Year 11. At that time, PepsiCo’s market value was $86,131.8 million (= $49.05 pershare × 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 theMB 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 purposesof comparing to price. If we multiply book value equity by the VB ratio, we obtainthe 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 pershare, a value estimate that is identical to the value estimates we obtained from theresidual 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 atPepsiCo’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 toassess a reasonable range of VB ratios for PepsiCo. We will find that the sensitivity ofthe VB ratio estimate is identical to the sensitivity of the residual income model valueestimates demonstrated in Chapter 12. This is to be expected because both modelsuse the same forecasts and valuation assumptions. The VB model is simply a scaledversion 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. + 2.846through Year +10

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

Total PV Residual ROCE = 12.476Add: Beginning Book Value of Equity Ratio Beginning Book Value of Equity from + 1.000

Year 11 Balance Sheet. = 13.476Adjust to Midyear Multiply by 1 + (R

E/2) × 1.040

Value-to-Book Ratio of Common Equity = 14.015Book Value of Common Equity ×$ 8,648.0Value of Common Equity =$121,205.9Shares Outstanding ÷ 1,756.0

Estimated Value per Share =$ 69.02

Current Price per Share $ 49.05Percent Difference (Positive number indicates 41%

underpricing.)

Thom

son

Learn

ing™

As we noted in Chapter 12, the capital markets devote enormous amounts of timeand energy to forecasting and analyzing firms’ earnings numbers. It is, therefore, nosurprise that the market multiple that receives most frequent use and attention is theprice-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 ratiosthat 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-earningsratios. 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 thestrict assumptions implied by PE ratios, and describe the conditions in which PE ratiosmay not capture appropriately the theoretical relation between value and earnings formost firms and the difficulties one encounters in reconciling actual PE ratios with thoseindicated by the theoretical value-earnings model. In this section, we also incorporatethe 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 ofPE ratios, and the empirical evidence on the articulation between PE ratios and MBratios.

The VE ratio is the ratio of the value of common shareholders’ equity divided byearnings 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 theresidual income model. In the residual income model, we use clean surplus account-ing and measure future earnings as expected future comprehensive income (that is,income that includes all of the income to common shareholders). Thus, in theory, theanalyst should measure the VE ratio as the value of common equity divided by nextperiod’s expected comprehensive income. This way, the VE ratio achieves consistentalignment of perspective (numerator and denominator both forward-looking) andmeasurement (numerator and denominator both based on income measurementthat 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 chapters we estimated PepsiCo’s commonshareholders’ 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 commonshareholders, which will equal $3,367.3 million. Thus, we can compute the VE ratiofor PepsiCo at the end of Year 11 as:

V0/E

1= $121,205.9 million/$3,367.3 million = 36.0

929Price-Earnings and Value-Earnings Ratios

PRICE-EARNINGS AND VALUE-EARNINGS RATIOS

A THEORETICAL MODEL FOR THE VALUE-EARNINGS RATIO

Thom

son

Learn

ing™

Or equivalently, on a per-share basis as:

Vps0/Eps

1= ($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 residualincome model in the previous section. We can employ an algebraic step to derive thefirm’s VE ratio from the firm’s VB ratio, as follows:

V0/E

1= V

0/BV

0× BV

0/E

1= V

0/BV

0× (1/ROCE

1)

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

V0/E

1= V

0/BV

0× BV

0/E

1= V

0/BV

0× (1/ROCE

1)

= ($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’sVB ratio of 14.015 into the VE ratio by multiplying by 1/ROCE

1, 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’sfuture earnings. Obviously, using value to compute a VE ratio will not provide anynew information about PepsiCo’s value. So what is the point of computing a VEratio?

The VE ratio provides the theoretically correct benchmark to evaluate the firm’sPE ratio. We can compare PepsiCo’s VE ratio of 36.0 to PepsiCo’s PE ratio to assessthe market value of PepsiCo shares. This comparison is equivalent to comparing V toP (that is, value to price). With the theoretically correct VE ratio, we can also projectVE ratios for other firms, including making adjustments as necessary to capture theother firms’ fundamental characteristics of profitability, growth, and risk. In addi-tion, with the theoretically correct VE ratio, we have a benchmark to gauge otherfirms’ PE ratios in order to assess whether the market is under- or overpricing theirshares. In the next section, we discuss the practical advantages and disadvantages inusing 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 earningsper share for either the most recent prior fiscal year or the most recent four quarters


PRICE-EARNINGS RATIOS

Thom

son

Learn

ing™

(sometimes referred to as the trailing-twelve-months earnings).10 The Wall StreetJournal 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 ofthe end of Year 11 as follows: Price per share

11/Earnings per share

11= $49.05/$1.51 =

32.5. Thus, at the end of Year 11, PepsiCo shares traded at a multiple of 32.5 timesYear 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 readilyobserve price per share and historical earnings per share for most firms. However,this common approach creates a logical misalignment for valuation purposesbecause it divides share price—which reflects the present value of future earnings—by historical earnings. If historical earnings contain unusual or nonrecurring gains orlosses that are not expected to persist in future earnings, then the analyst shouldcleanse the reported historical earnings of these effects in order to compute a PE ratiothat 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, adjustreported 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’sforecast of future earnings per share—for example, expected earnings per share oneyear ahead. A PE ratio based on expected future earnings, however, requires the ana-lyst to forecast future earnings (or have access to another analyst’s forecast). The reli-ability of a forward-looking PE ratio then depends on the reliability of the earningsforecast. Earnings forecast errors will distort forward-looking PE ratios.

We compute the forward-looking PE ratio for PepsiCo as of the end of Year 11using our forecast that Year +1 earnings will be $3,367.3 million as follows: Price pershare

0/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 25.6times the Year +1 earnings forecast. PepsiCo’s VE ratio of 36.0 is 41 percent greaterthan PepsiCo’s PE ratio of 25.6 at the end of Year 11, consistent with our prior esti-mates of PepsiCo’s value.12


10In 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, andfinancial databases rarely, if ever, compute PE ratios based on comprehensive income per share, in partbecause (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 tobe a permanent component of income each period. We follow traditional practice in this chapter andcompute PE ratios using reported earnings figures.

11If we compute PepsiCo’s PE ratio using amounts in millions rather than per-share amounts, we obtain aPE 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 PepsiCoreports earnings per share based on the weighted average number of common shares outstanding duringthe year (which is consistent with U.S. GAAP) rather than the number of shares outstanding at year-end.

12In 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.

Thom

son

Learn

ing™

Notice that we simply derived the PE ratio by dividing PepsiCo’s market shareprice by either earnings per share of the past year or by our forecasts of PepsiCo’sfuture 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. Insome 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 afirm to have based on past PE ratios for that firm, or industry-average PE ratios, orcomparable firms’ PE ratios. Analysts use benchmarks like these to project a firm’s PEratio quickly, using one-period earnings as a common denominator for relative val-uations, rather than engaging in the extensive computations necessary to determinethe correct value-earnings ratio to assess whether the market has priced the firm’sshares appropriately.

Analysts also use PE ratios as potentially informative benchmarks to project earnings-based valuation multiples that they use to compare valuations across com-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 otherbeverage companies. We might also use PepsiCo’s PE ratio to project valuations forthese beverage companies, or to project valuations for privately held firms or divi-sions of companies. Investment bankers use comparable companies’ PE ratios, forexample, to benchmark reasonable ranges of share prices for IPOs.

PE ratios have the advantage of speed and efficiency, but they are not necessarilyprecise 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 ofearnings from the snack food business, which Coca-Cola does not have. Similarly,Coca-Cola derives more of its earnings from international sales than PepsiCo. Theseand other factors cause the profitability, growth, and risk of PepsiCo and Coca-Colato 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 EarningsWhat 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 thefirm’s VE ratio. However, if the analyst has not computed value in order to determinethe VE ratio and wishes to use a shortcut PE ratio instead, what is the correct PE ratioto 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 earningsnumber or a one-period-ahead forecast) as the beginning amount of a permanent


Thom

son

Learn

ing™

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 willbe 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 perpetuitymodel based on one-year-ahead earnings (denoted E

1), as follows:

V0

= P0

= E1/R

E

Rearranging slightly, the firm’s VE and PE ratios are:

V0/E

1= P

0/E

1= 1/R

E

Thus, strictly speaking, the PE multiple assumes that firm value is the present valueof a constant stream of expected future earnings, discounted at a constant expectedfuture discount rate. Under these conditions, the analyst can value the firm simplyusing 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 firmto generate earnings of $700 next period and requires a 14 percent return on equitycapital. 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 translatesinto 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; mostfirms’ earnings grow. Not surprisingly, such strict assumptions match the funda-mental characteristics of very few firms. We have already seen that such strictassumptions do not fit PepsiCo. Under the assumptions that PepsiCo’s earnings willbe constant in the future, and that PepsiCo’s constant future ROCE will equal the 8.0percent 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 RatiosThe table below includes descriptive statistics of price-earnings ratios (share price

to one-year-ahead earnings: Pt/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 of38,219 firm-years drawn from the Compustat database, excluding all firm-years withnegative earnings.13

Price-Earnings Ratio 25th percentile Median 75th percentile

Pt/E

t+19.60 13.91 21.39

Pt/E

t11.09 15.72 24.12


13It does not make sense to compute PE ratios on the basis of negative earnings. PE ratios assume earningsare permanent; negative earnings are not likely to be permanent.

Thom

son

Learn

ing™

Exhibit 13.7 includes descriptive statistics on forward-looking PE ratios (share priceto 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. Todescribe the industry-wide variation in PE ratios, Exhibit 13.7 also includes the 25thpercentile PE ratio and the 75th percentile PE ratio for each industry.

These descriptive data indicate substantial differences in median PE ratios acrossindustries during 1991 to 2000. The firms in the forestry, security brokers, and insur-ance industries experienced the lowest median PE ratios during that period, whereasfirms in the metal mining, business services, communications, and personal servicesindustries experienced the highest median PE ratios. These data also depict widevariation in PE ratios across firms within each industry. For example, most of these36 industries experienced wide differences between the 25th percentile and the 75thpercentile PE ratio during 1991 to 2000. With only a few exceptions, the 75th per-centile PE ratio was more than double the 25th percentile 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 firmsare the fundamental drivers of value: risk, profitability, and growth. In addition toeconomic factors, differences across firms in accounting methods and accountingprinciples, 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 ratiosin the sections that follow, saving growth for last because we will expand on the roleof growth in determining PE ratios.

Risk and the Cost of Capital. As the previous discussion points out, firms withequivalent amounts of earnings but different levels of risk and therefore differentcosts of equity capital will experience different PE ratios (and different VE ratios). Allelse equal, more risky firms will experience a lower market value and PE ratio.However, only firms facing rare circumstances experience PE ratios that equal theinverse of the equity cost of capital, so a variety of other forces also cause PE ratiosto differ.

Profitability. A firm with competitive advantages will be able to earn ROCE thatexceeds R

E. To the extent that the firm can sustain these competitive advantages, the

persistence over time of the degree to which ROCE exceeds RE

will increase, therebyincreasing the PE ratio relative to similar firms that do not have sustainable compet-itive advantages. Thus, both the magnitude and the persistence of the differencebetween ROCE and R

Ewill increase PE ratios across firms.


14The analyst must be careful with PE ratios because they are sensitive to earnings numbers that are nearzero. Firms with earnings that are positive but temporarily very low will experience PE ratios that aretemporarily very high.

Thom

son

Learn

ing™


EXHIBIT 13.7Descriptive Statistics on Share Price to One-Year-Ahead Earnings Ratios (P

t/E

t+1),

1991–2000

Price-Earnings Ratios (Pt/E

t+1)

Industry 25th Percentile Median 75th Percentile

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

Thom

son

Learn

ing™

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 selectaccounting methods that are conservative with respect to income recognition andasset measurement (for example, LIFO for inventories during periods of rising inputprices and accelerated depreciation of fixed assets). Some firms invest in projects forwhich accounting principles are conservative. For example, firms may make sub-stantial investments in intangible activities that must be expensed under conservativeaccounting principles, leading to economic assets that are off-balance sheet, such assuccessful research and development, brand equity, or human capital. The effects ofaccounting methods and principles on reported earnings and PE ratios will likelychange over the firm’s lifetime. All else held equal, conservative accounting willreduce reported earnings early in the life of the firm (for example, when accelerateddepreciation 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 PEratios 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 thereforenot 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 ratiowill be unusually high. The transitory nature of a single period of accounting earn-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 twelvemonths earnings that include non-recurring gains or losses that are not expected topersist, the PE ratios will be artificially volatile.

Continuing the example, assume that the analyst expects the firm to generateearnings next period of $650 instead of $700 because the firm will recognize a $50restructuring charge. If the market views this charge as nonrecurring (that is, not apermanent 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 be7.62 (= $4,950/$650), instead of 7.14 (= $5,000/$700). Conversely, if the currentperiod’s earnings exceed their expected permanent level, then the PE ratio will be lessthan normal.

The analyst must assess whether the lower or higher level of earnings for theperiod (and therefore higher or lower PE ratio) represents a transitory phenomenonor a change to a new lower or higher level of permanent earnings. If the analystexpects the decrease in earnings from $700 to $650 will be permanent, then themarket 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 10and 11.


Thom

son

Learn

ing™

Price per Earnings perPE Ratio Share Share

Year 10:PepsiCo 34.2 $49.56 $1.45Coca-Cola 69.3 $60.94 $0.88

Year 11:PepsiCo 32.5 $49.05 $1.51Coca-Cola 29.5 $47.15 $1.60

Considered at face value, the PE ratios for PepsiCo and Coca-Cola in Year 10 indicatethat the market valued Coca-Cola’s earnings at a multiple of 69.3, more than twicePepsiCo’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 downto only $0.88, thereby inflating Coca-Cola’s PE ratio. Thus, the big jump in Coca-Cola’s PE ratio occurred largely because earnings temporarily declined that year, anddid not reflect the market’s expectations for Coca-Cola’s long-term earnings. In Year11, both firms reported earnings closer to normal levels and their PE ratios werequite similar.

Growth. Holding all else equal, PE ratios will be greater for firms that the marketexpects will generate greater earnings growth with future investments in abnormallyprofitable projects. In the next section, we discuss techniques analysts use to incor-porate earnings growth into PE ratios.

Incorporating Earnings Growth into Price-Earnings RatiosAnalysts commonly modify the PE ratio to incorporate earnings growth. In this

section, we describe and apply two related approaches to include expected futureearnings growth in the computation of the PE ratio: (1) the perpetuity-with-growthapproach; and (2) the price-earnings-growth approach.15

The Perpetuity-with-Growth Approach. The perpetuity-with-growth approachassumes that the firm can be valued as the present value of a permanent stream offuture earnings that will grow at constant rate g. In this case, we can express VE andPE ratios as perpetuity-with-growth models, as follows:

V0

= P0

= E1× 1/(R

E– g), so V

0/E

1= P

0/E

1= 1/(R

E– g)

To continue the illustration, assume that the market expects the firms’ earnings willbe $700 next year and will grow 5 percent each year thereafter. The model suggests


15In recent research, James Ohlson and Beate Juettner-Narouth develop a theoretical model for the price-earnings ratio that incorporates short-term and long-term earnings per share growth. The modelappears to be a promising addition to the earnings-based valuation literature, providing new insightsinto the relation between value, earnings, and growth. However, the model has not yet been subject toextensive empirical testing or practical application. See James Ohlson and Beate Juettner-Nauroth,“Expected EPS and EPS Growth as Determinants of Value,” Working Paper, New York University, 2000.

Thom

son

Learn

ing™

the PE ratio 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 growth in earnings adds $2,778 (= $7,778– $5,000) to the value of the firm.

PE ratios are particularly sensitive to the growth rate. If the growth rate is 6 per-cent instead of 5 percent, the ratio becomes 12.50 [= 1.0/(0.14 – 0.06)] and the mar-ket value becomes $8,750 (= $700 × 12.50). The sensitivity occurs because the modelassumes that the firm will grow at the specified growth rate forever. Competition,new discoveries or technologies, or other factors eventually erode rapid growth ratesin an industry. In using the constant growth version of the PE ratio, the analystshould select a long-run equilibrium growth rate in earnings.

This expression for the VE and PE ratio underscores the joint importance of riskand 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 con-stant, higher risk levels should translate into lower PE and VE ratios, and vice versa.Investors will not pay as much for a higher risk security as for a lower risk securitywith identical expected earnings and growth. In contrast, VE and PE should relatepositively to growth. Holding earnings and R

Econstant, firms with high expected

long-run growth rates in earnings should experience higher VE and PE ratios.With respect to PepsiCo at the end of Year 11, we assumed that PepsiCo would

experience a long-run growth rate of 5.0 percent. Thus, using the perpetuity-with-growth approach, we calculate the PE ratio as:

P0/E

1= 1/(R

E– g) = 1/(0.080 – 0.050) = 33.33

Clearly, incorporating growth makes a big difference in PepsiCo’s PE ratio (as com-pared to the PE ratio of 12.5 that ignores growth). Assuming PepsiCo’s earnings growat 5.0 percent per year beginning in Year +1, this PE with growth ratio would valuePepsiCo shares at a multiple of 33.33 times the Year +1 earnings forecast. This PEratio is still less than the theoretically correct VE ratio of 36.0, however, because itdoes not take into account our forecast that PepsiCo earnings would grow at roughly7.2 percent from Year +1 to Year +10. Thus, this PE ratio understates the value ofPepsiCo’s expected earnings growth during those years.

The Price-Earnings-Growth Approach. An alternative ad hoc approach to incor-porate growth into PE ratios has emerged from practice in recent years, in which ana-lysts’ divide the price-earnings ratio by the expected short-term earnings growth rate(expressed as a percent; some analysts will use the expected earnings growth rate forthe medium-term horizon of 3 to 5 years). This approach produces the so-calledPEG ratio seen with increasing frequency in practice. Analysts compute the PEGratio as follows:

PEG0

= (Price per share0/Earnings per share

0)/(g × 100)

Analysts and the financial press use the PEG ratio as a rule-of-thumb to assess shareprice relative to earnings and expected future earnings growth. Although there is littletheoretical foundation for this rule-of-thumb (which tends to vary across analysts),proponents of PEG ratios generally assert that firms normally have PEG ratios near1.0, indicating market price fairly reflects expected earnings growth. Using this rule-of-


Thom

son

Learn

ing™

thumb, proponents assert that market prices for firms with low PEG ratios (0.5 andbelow) are low relative to growth, and market prices for firms with high PEG ratios(1.5 and above) are high relative to growth. Proponents of PEG ratios argue that thisheuristic provides a convenient means to rank stocks, taking into account one-year-ahead earnings and expected earnings growth.16

In Chapter 10, we assumed that PepsiCo would experience earnings growth ofroughly 7.2 percent per year through Year +5. Using this growth rate assumption andour Year 11 reported earnings per share, we compute PepsiCo’s PEG ratio at the endof Year 11 as follows:

PEG11

= (Price per share11

/Earnings per share11

)/(g × 100)= ($49.05/$1.51)/(0.072 × 100)= 32.5/7.2 = 4.51

Thus, PepsiCo shares traded at the end of Year 11 at a PEG ratio of 4.51. Based on thePEG heuristic, PepsiCo’s PEG ratio of 4.51 suggests the market price for PepsiCoshares reflect substantial overpricing of PepsiCo’s growth. This heuristic does nottake into account, however, the fact that PepsiCo’s expected future ROCE is signifi-cantly greater than PepsiCo’s R

Ebecause of PepsiCo’s substantial off-balance sheet

brand equity. The PEG ratio deserves considerable attention from researchers andpractitioners so that its uses and limitations can be tested and understood.

PE Ratio Measurement IssuesThus 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, such forecasts are not readily availablefor all firms, and they depend on analysts’ forecast assumptions, which can differwidely. Therefore, as noted earlier, in practice the analyst is most likely to encounterPE ratios in the Wall Street Journal or on financial data web sites that are most com-monly measured as share price divided by earnings per share for either the mostrecent prior fiscal year or the most recent four quarters. This is a sensible approachbecause historical earnings are observable and unique; however, computation of PEratios using historic earnings introduces the potential for bias. To recap, the analystshould be aware of (at least) the following 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 ratiosdescribed in the prior sections provide mechanisms that incorporate growthinto price-earnings multiples.

(2) Transitory earnings. Past earnings are historical and may not be indicative ofexpected future “permanent” earnings levels. Insofar as historic earnings


16Mark Bradshaw demonstrates an empirical link between PEG ratios and sell-side analysts’ target pricerecommendations in “The Use of Target Prices to Justify Sell-Side Analysts’ Stock Recommendations,”Accounting Horizons, Vol. 16, No. 1 (March 2002), pp. 27–41.

Thom

son

Learn

ing™

contain transitory gains or losses, or other elements that are not expected torecur, it can cause the PE ratio to vary wildly.

In addition, the analyst must also be aware of the potential bias in PE ratios becauseof differences in firms’ dividend payouts. Dividends displace future earnings. A divi-dend paid in year t reduces market price by the amount of the dividend, but the div-idend is not subtracted from earnings. The dividend paid will cause future earningsto decline because the firm has paid out a portion of its resources to shareholders.Price should therefore decline by the present value of the firm’s foregone amount ofexpected future return on assets distributed as dividends. Thus, for dividend-payingfirms, 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 adividend-paying firm as follows: (P

t+ D

t)/E

t= 1/(R

E– g).

Empirical Properties of PE RatiosThe 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 haveexamined the relation between PE ratios, risk (measured using market beta), andgrowth (measured using realized prior growth rates or analysts forecasts of futuregrowth). These studies have found that approximately 50 percent to 70 percent of thevariability in PE ratios across firms relates to risk and growth.17

PE Ratios as Predictors of Future Earnings Growth. Stephen Penman, a leadingscholar in the relation between earnings, book values, and market values, studied therelation between PE ratios and changes in earnings per share for all firms on theCompustat database for the years 1968 to 1985.18 For each year, Penman groupedfirms into 20 portfolios based on the level of their PE ratios. He then computed the percentage change in earnings per share for the formation year, and for each ofthe nine subsequent years. Penman then aggregated the results across years. The tablebelow presents 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%


17See William Beaver and Dale Morse, “What Determines Price-Earnings Ratios?,” Financial AnalystsJournal (July–August 1978), pp. 65–76, and Paul Zarowin, “What Determines Earnings-Price Ratios:Revisited,” Journal of Accounting, Auditing and Finance (Summer 1990), pp. 439–454.

18Stephen H. Penman, “The Articulation of Price-Earnings Ratios and Market-to-Book Ratios and theEvaluation of Growth,” Journal of Accounting Research (Autumn 1996), pp. 235–259.

Thom

son

Learn

ing™

The results for the formation year are consistent with transitory components in earn-ings. Firms with high PE ratios experienced low percentage changes in earnings duringthe formation year relative to the preceding year. Firms with low PE ratios experiencedhigh percentage changes in earnings during the formation year. The results for Year 1after the formation year suggest a counter-balancing effect of the earnings change in theformation year. A low percentage increase in earnings is followed by a high percentageearnings 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 inpercentage earnings changes to a level in the mid-teens. This result is consistent withthe data presented in Exhibit 13.4 for ROCE, where Bernard observed a mean rever-sion in ROCE toward the mid-teens. The mean reversion suggests systematic direc-tional changes in earnings growth over time (that is, serial autocorrelation), but thereversion takes several years to occur.

Articulation of MB and PE Ratios. In the same research study, Stephen Penmanalso utilized the residual income valuation model and empirical data to examine thearticulation between firms’ PE and MB ratios.19 Penman predicts that MB should be“normal” (that is, equal to one) when the market expects the firm to earn zero resid-ual income in the future. The MB ratio will be high (above one) or low (below one)if the market expects the firm to earn positive or negative future residual income. Atthe same time, Penman predicts that PE ratios will be normal (that is, equal to theinverse of R

E) when the firm earns current period residual income that is equal to

expected future residual income (that is, a firm with current ROCE equal to long-runexpected ROCE, which should equal long-run expected R

E). In contrast, PE ratios

should be high when the firm earns current residual income below long-runexpected residual income (that is, current ROCE is unusually low, causing PE to behigh). PE ratios should be low when the firm earns current residual income that isgreater than long-run expected residual income (that is, current ROCE is temporar-ily high, causing PE to be low.) Thus, MB ratios will be determined primarily byexpected future residual income, whereas PE ratios will be a function of the differ-ence between current and expected future residual income.

To study the articulation of PE and MB ratios, Penman collected data from theCRSP and Compustat databases on roughly 2,574 firms during the years 1968–1985.Each sample year, Penman ranked and grouped these firms into 20 portfolios basedon PE ratios. He also ranked and grouped the same firms each year into 3 MB ratioportfolios, classifying MB ratios below 0.90 as low, MB ratios above 1.10 as high, andMB ratios in between as normal.

Exhibit 13.8 presents a matrix summarizing a portion of the results fromPenman’s study. Exhibit 13.8 presents residual income figures after assuming a 10.0percent cost of capital for all firm-years, and after scaling by beginning of periodbook value of common equity (so they are essentially residual ROCE figures). Wedenote current period residual income as CRI, and future residual income one-year-ahead and six-years-ahead as FRI

1and FRI

6, respectively.


19Stephen H. Penman, op cit.

Thom

son

Learn

ing™

Penman’s research results generally support his predictions and shed light on theresidual income conditions that cause MB ratios and PE ratios to covary. Examiningfuture residual income across columns of the matrix, Penman’s results suggest that MBratios correlate positively with future residual income, consistent with the results fromBernard in Exhibit 13.4. Future residual income is substantially higher for high MBfirms than for low MB firms. Examining the results across rows, high PE ratio firmstend to have current period residual income that is much lower than future residualincome, suggesting PE ratios for these firms are temporarily high because residualincome is temporarily low. In contrast, firms with low PE ratios tend to have currentresidual income amounts that are greater than the future residual income amounts,suggesting these firms are experiencing low PE ratios because residual income is tem-porarily high. Penman’s results provide intuition about when MB ratios should behigh, low, or normal, and concurrently, when PE ratios should be high, low, or normal.

Summarizing, the VE and PE ratios are determined by:

1. Risk2. Growth3. Differences between current and expected future (permanent) earnings4. Alternative accounting methods and principles.


EXHIBIT 13.8

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 < 0High CRI: –0.50 to 0.07 CRI: –0.36 to –0.04 CRI: –0.24 to –0.06

(Portfolios 15–20) FRI1: –0.07 to 0.08 FRI

1: –0.13 to –0.03 FRI

1: –0.13 to –0.06

FRI6: 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 < 0Normal CRI: 0.07 to 0.10 CRI: –0.02 to 0.04 CRI: –0.05 to 0.00

(Portfolios 7–14) FRI1: 0.08 to 0.10 FRI

1: –0.02 to 0.04 FRI

1: –0.04 to 0.00

FRI6: 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 < 0Low CRI: 0.12 to 0.41 CRI: 0.05 to 0.22 CRI: 0.00 to 0.06

(Portfolios 1–6) FRI1: 0.12 to 0.25 FRI

1: 0.05 to 0.15 FRI

1: –0.01 to 0.04

FRI6: 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 theEvaluation of Growth,” Journal of Accounting Research Vol. 34, No. 2, Autumn 1996, pp. 235–259.

SUMMARY OF VE AND PE RATIOS

Thom

son

Learn

ing™

The analyst must assess each of these elements when estimating VE and PE ratios,particularly when evaluating PE ratios based on reported earnings and when pro-jecting PE ratios to value non-traded firms. The theoretical model indicates the fac-tors affecting the PE ratio but does not provide an unambiguous signal of the“correct” PE ratio for a particular firm. The analyst should be aware of the followingconsiderations when using PE ratios:

1. The PE ratio is particularly sensitive to the cost of equity capital and to theearnings growth rate because it assumes a firm can grow earnings at that rateforever. The analyst should select a sustainable long-term growth rate whenapplying the PE model.

2. The theoretical PE model does not work when the growth rate in earningsexceeds the cost of equity capital. Firms are unlikely to grow earnings at ratesexceeding the cost of equity capital forever. Competition will eventually forcegrowth rates to decrease.

3. The theoretical PE model does not work when the cost of equity capital and the growth rate in earnings are similar in amount. The denominator ofthe theoretical model approaches zero and the theoretical PE ratio becomesexceeding large.

4. The PE model does not work when earnings are negative.5. Before concluding that the market is undervaluing or overvaluing a firm

because the actual PE ratio differs from the theoretically correct VE ratio, theanalyst should assess whether earnings of the period include transitory ele-ments. The analyst should adjust the current period’s earnings for unusual,nonrecurring income items before measuring the PE ratio for the period.

6. When comparing actual PE ratios of firms, the analyst should consider theimpact of their use of different accounting methods and principles.

The analyst can use the PE and MB ratios of comparable firms to assess the cor-responding ratios of publicly traded firms. The analyst can also value firms whosecommon shares are not publicly traded by using PE ratios and MB ratios of compa-rable firms that are publicly traded. The theoretical models assist in this valuationtask by identifying the variables that the analyst should use in selecting comparablefirms. Bhojraj and Lee demonstrate a technique for selecting comparable firms inmultiples-based valuation by computing “warranted multiples” based on factors thatdrive cross-sectional differences in multiples, such as expected profitability, growth,and cost of capital.20 Alford examined the accuracy of the PE valuation models usingindustry, risk, ROCE, and earnings growth as the bases for selecting comparable

943Using Market Multiples of Comparable Firms

USING MARKET MULTIPLES OF COMPARABLE FIRMS

20Sanjeev Bhojraj and Charles M.C. Lee, “Who is My Peer? A Valuation-Based Approach to the Selectionof Comparable Firms,” Journal of Accounting Research Vol. 40, No. 2 (May 2002), pp. 407–439.

Thom

son

Learn

ing™

firms.21 The results indicate that industry membership, particularly at a three-digitSIC code level, provides a useful basis for comparisons if firms in the same industryexperience similar profitability, face similar risks, and grow at similar rates. Thus, insome circumstances, industry membership serves as an effective proxy for the vari-ables in the PE valuation model. However, as the data in Exhibit 13.7 reveal, sub-stantial differences commonly exist in PE ratios of firms within the same industry.The warranted-multiples approach of Bhojraj and Lee provides a mechanism todetermine comparable companies within industries and across different industries.

To what extent has the market discounted the value of a firm’s common equity forrisk? On a per-share level, what is the per-share price impact of risk? Is the market’sdiscount for risk implicit in a firm’s share price sufficient to compensate for risk? Oris the discount too large or too small relative to risk? We rely on an adaptation of theresidual income model to address these questions. We use the residual income modeland risk-free rates of return to estimate risk-free value. We then subtract market pricefrom risk-free value to assess the price differential—the amount the market has dis-counted share price for risk.

As we described in detail in the previous chapter, the residual income modeldetermines the present value of common shareholders’ equity as follows:

To implement this model, the analyst must estimate the cost of equity capital (RE) for

purposes of computing residual income [NIt– (R

E× BV

t–1)] and for discounting resid-

ual income to present value at 1/(1 + RE)t. But the state-of-the-art in financial eco-

nomics does not provide a clear picture of how RE

should be determined. Substantialcontroversy surrounds expected returns models like the CAPM. What is the appro-priate measure for market beta? In addition to market betas, do other risk factorsbelong in the expected returns model, such as firm size or some other set of risk fac-tors? Assuming one can identify the appropriate risk factors that are priced in themarket, what are the appropriate risk premia to use to determine expected returns? Atan even more fundamental level, questions arise about whether risk and expectedreturns should be measured based on covariation between a firm’s returns and a mar-ket index of returns. These questions arise in part because market-based models likethe CAPM are essentially circular—should stock prices and realized returns be usedto estimate risk to determine expected returns to evaluate stock prices? Or should risk

V BVNI R BV

Rt E t

Et

t0 0

1

11

= +− ×

+−

=

∞

∑ ( )

( )


21Andrew W. Alford, “The Effect of the Set of Comparable Firms on the Accuracy of the Price-EarningsValuation Method,” Journal of Accounting Research (Spring 1992), pp. 94–108.

22This section relies heavily on Stephen Baginski and James Wahlen, “Residual Income Risk, IntrinsicValues, and Share Prices,” The Accounting Review Vol. 78, No. 1 (January 2003), pp. 327–351.

PRICE DIFFERENTIALS22

Thom

son

Learn

ing™

and expected returns be based on covariation between a firm’s returns and an economy-wide measure of consumption, on the theory that investors’ risk aversion isdriven by the need to diversify volatility in expected future consumption?

In light of the critical role of risk and expected returns in valuation, and in lightof the uncertainty surrounding how to measure risk and expected returns, the ana-lyst needs a variety of tools to assess the impact of risk on share prices and firm val-ues. One such tool involves computing price differentials. If the analyst substitutesthe prevailing risk-free rate of interest (denoted R

F; for example, the yield on one- to

five-year U.S. Treasury securities) for the cost of equity capital, the residual incomemodel can be used to determine risk-free value (denoted RFV

0), which is an estimate

of the value of the firm in a risk-neutral market:

Risk-free value represents the value of the firm, based on book value of equity andforecasts of expected future earnings, in the absence of discounting for risk. On a per-share basis, risk-free value per share represents the hypothetical value at which shareswould trade in a risk-neutral market. Market price of a share of common equityreflects the risk-discounted value. Therefore, market price can be subtracted fromrisk-free value per share to determine the total discount in share price for risk. Werefer to this difference as the price differential (denoted PDIFF), computed as follows:

PDIFF0

= RFV0

– MV0

The analyst can evaluate the price differential to assess whether the market discountfor risk is sufficient to compensate the investor to hold the firm’s shares and bear risk.If the analyst assesses that PDIFF

0is large relative to the risk of the firm, then per-

haps the firm’s shares may be over-discounted for risk (undervalued). On the otherhand, if the analyst assesses that PDIFF

0is small relative to firm risk, then perhaps

the firm’s shares are under-discounted for risk (overvalued). In the next section, weillustrate how to compute the PDIFF for PepsiCo. In the following section that dis-cusses reverse engineering, we describe and apply more formal methods to gauge themagnitude of PDIFF.

To compute the price differential of PepsiCo as of the end of Year 11, we rely onthe forecast assumptions developed in Chapter 10 and the residual income modeldeveloped in the previous chapter. However, instead of using an 8.0 percent cost ofequity capital for PepsiCo for purposes of computing residual income and discount-ing it to present value, we instead use the risk-free interest rate at the time of the val-uation. At the end of Year 11, U.S. Treasury bills with one to five years to maturityyielded roughly 4.2 percent. Exhibit 13.9 reports the present value of PepsiCo’sexpected future residual income in Year +1 through Year +10, computed using the 4.2percent risk-free discount rate.

RFV BVNI R BV

Rt F t

Ft

t0 0

1

11

= +− ×

+−

=

∞

∑ ( )

( )

945Price Differentials

COMPUTING PDIFF FOR PEPSICO

Thom

son

Learn

ing™

To compute continuing value, we cannot use the perpetuity-with-growth model[= 1/(r – g)], because our long-term growth assumption for PepsiCo is 5.0 percent,which is greater than the risk-free discount rate of only 4.2 percent. Therefore, wederive PepsiCo’s Year +11 residual income, project it to grow uniformly at the long-term growth rate for an arbitrarily long time (until Year +50), and then discount eachyear of residual income to present value.23 The present value of continuing valueunder this approach is $181,404.5 million. After adding book value of commonequity at the end of Year 11, adjusting for mid-year discounting, and dividing by the number of shares outstanding, we estimate the PepsiCo shares have a risk-freevalue of $130.24. Subtracting the market price at Year 11 of $49.05 per share, we esti-mate the PDIFF to be $81.19. These computations suggest that PepsiCo shares havebeen discounted by the risk-averse market by roughly $81.19 per share below thevalue at which they would trade in a hypothetical risk-neutral market, conditional onthe forecast assumptions in Chapter 10. These computations indicate PepsiCo sharestraded at the end of Year 11 at a price equal to roughly 38 percent of risk-free value(= $49.05/$130.24). Exhibit 13.10 presents these computations.

In Chapters 11 and 12, we estimated that PepsiCo shares may have been under-priced at the end of Year 11. The price differential computation indicates that the mar-ket 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 theprice differential, we next turn to the method of reverse engineering market values.


EXHIBIT 13.9

Price Differential of PepsiCo:Present Value of Residual Income in Year +1 through Year +10 after

Discounting at the Risk-Free Rate of Interest

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

Required Income (RF

× BVt–1

) . . . . . . . . . . . . . . . . . . . . . . . . . . $ 363.2 $ 397.6 $ 435.3

Residual Income [NIt– (R

F× BV

t–1)] . . . . . . . . . . . . . . . . . . . . . $ 3,004.1 $3,258.8 $ 3,540.4

Present Value Factors (at RF

= 4.2 percent) . . . . . . . . . . . . . . . . 0.960 0.921 0.884

PV Residual Income . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 2,883.0 $3,001.4 $ 3,129.4

Sum of PV Residual Income in Year +1 through Year +10 . . . . $33,946.3

23Although we compute present value of continuing value over an arbitrarily long horizon, it will nonethe-less understate continuing value (and therefore the risk-free value) because the present value computa-tion does not extend to infinity. By using a long horizon, we seek to reduce the understatement.

Thom

son

Learn

ing™

947Price Differentials

EXHIBIT 13.9

Exhibit 13.9—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

$ 486.1 $ 510.3 $ 562.0 $ 603.4 $ 647.8 $ 695.4 $ 746.4

$ 3,826.2 $ 4,139.3 $ 4,429.0 $ 4,746.6 $ 5,087.1 $ 5,452.1 $ 5,844.0

0.848 0.814 0.781 0.750 0.720 0.691 0.663

$ 3,245.6 $ 3,369.7 $ 3,460.2 $ 3,558.9 $ 3,660.4 $ 3,764.9 $ 3,872.9

EXHIBIT 13.10

Price Differential of PepsiCo

Valuation Steps Computations Amounts

Sum of PV Residual Income in Year +1 Discounted at the risk-free rate of +$ 33,946.3through Year +10 interest. See Exhibit 13.9.

Add Continuing Value in Present Value Year +11 residual income assumed +$181,404.5to grow at 5.0%; projected to Year+50, discounted at 4.2%.

Computations not shown.Total PV Residual Income =$215,350.8Add: Beginning Book Value of Equity Beginning Book Value of Equity from

Year 11 Balance Sheet. +$ 8,648.0

=$223,998.8Adjust to Midyear Multiply by 1+(R

E/2) × 1.021

PV of Common Equity =$228,702.8Shares Outstanding ÷$ 1,756.0

Estimated Value per Share $ 130.24

Current Price per Share $ 49.05Price Differential $ 81.19

Thom

son

Learn

ing™

Throughout this text we have emphasized the process of using a firm’s funda-mental characteristics to estimate firm value. This process can be characterizedessentially as a puzzle with four missing pieces, or as an equation with four unknownvariables: value, expected future profitability, expected long-run future growth, andexpected risk-adjusted discount rates. Thus far, we have developed forecasts andexpectations about three of the variables—expected future profitability, long-rungrowth, and risk-adjusted discount rates—and we have used them to solve for thefourth, firm value. In fact, we can make assumptions about any three of the four vari-ables and then solve for the fourth variable.

We can, for example, treat the market value of common equity as one of the“known” variables. We can assume that V

0equals market value. We can then build fore-

casts for any two other variables, and solve for the missing fourth variable. We refer tothis process as reverse engineering stock prices because it takes the valuation processand reverses it. It is a process in which the analyst takes market value as given, and thensolves for the assumptions the market appears to be making in order to value the firm’sstock at market price. For example, if we take a firm’s market price as given, and if weuse an analyst’s forecasts for future earnings and growth as reasonable proxies for themarket’s expectations, then we can solve for the implied expected risk-adjusted rate ofreturn on common equity that is consistent with the observed market value, expectedfuture earnings, and growth. This is essentially equivalent to solving for the internalrate of return on the stock.

As another example, suppose we take market value as given, we assume that therisk-adjusted expected return on a stock can be determined by an asset pricing modelsuch as the CAPM, and we assume analysts’ consensus earnings forecasts throughYear +5 are reasonable proxies for the market’s earnings expectations. We can thensolve for the long-run growth rate implicit in the firm’s stock price, conditional onthe other assumptions.

The process of reverse engineering stock prices allows the analyst to infer a set ofassumptions that appear to be impounded into the firm’s share price. The analyst canthen assess whether the assumptions the market appears to be making are realistic,optimistic, or pessimistic. If the analyst determines that the market’s assumptionsseem optimistic, then it suggests the market has overpriced the stock (or perhaps theanalyst is just too pessimistic). Alternatively, if the analyst determines that the mar-ket’s assumptions are pessimistic, then it suggests the market has underpriced thestock (or again, the analyst may be wrong). Reverse engineering is a mechanism bywhich the analyst can infer and judge the assumptions implicit in a stock price.

To illustrate the process of reverse engineering, we will apply the approach toPepsiCo, using the end of Year 11 market price of $49.05 per share. To reverse engi-neer PepsiCo’s $49.05 share price, we will again rely on the residual income model inthe previous chapter and the forecasts developed in Chapter 10.


REVERSE ENGINEERING

REVERSE ENGINEERING PEPSICO’S STOCK PRICE

Thom

son

Learn

ing™

Assume we want to solve for the expected return (that is, the risk-adjusted dis-count rate) on PepsiCo’s stock implied by the Year 11 share price of $49.05. Assumealso that we believe our forecasts of earnings and book value of common equity forPepsiCo through Year +10 and our forecast of 5.0 percent long-run growth are real-istic proxies for the market’s expectations. Armed with share price, specific prof-itability and growth forecasts through Year +10, and a constant long-run growthassumption beyond Year +10, we can use the residual income value model to solvefor the discount rate that reduces future earnings and book value to a present valueequal to $49.05 per share.

Procedurally, one way to solve for the implied expected return on PepsiCo stock,conditional on the price, earnings, and growth assumptions, is to begin by estimat-ing the value of common equity using the risk-free discount rate, as in the price dif-ferential illustration above. The initial value will likely far exceed the market pricebecause the future residual income has not been discounted for risk. In applying theprice differential model to PepsiCo in the previous section, we determined thatPepsiCo’s risk-free value was $130.24 per share. We then steadily increase the dis-count rate as necessary until the residual income model value exactly agrees with themarket price of $49.05 per share. Following this approach, the implied expected rate of return on PepsiCo stock is 9.178 percent. At this discount rate, conditional onthe residual income and growth assumptions, the present value of PepsiCo shares is$49.05 per share, exactly equal to market price. Recall we assumed PepsiCo commonequity had a required rate of return of 8.0 percent based on the CAPM. However, thisreverse engineering approach indicates that if we buy a share of PepsiCo stock at themarket price of $49.05, it will yield a 9.178 percent rate of return, conditional on ourother assumptions. The Valuation spreadsheet in FSAP allows the analyst to makethese iterative computations easily by simply varying the discount rate for equitycapital.

We can also reverse engineer PepsiCo’s Year 11 stock price to solve for the implicitlong-run growth assumption. To illustrate, we again take the market price of $49.05per share as given, and our earnings and book value forecasts through Year +10 asreasonable proxies for the market’s expectations. We now return to our originalassumption that the risk-adjusted discount rate for PepsiCo stock is 8.0 percent,based on the CAPM. With this, we have established three assumptions—value, earn-ings through Year +10, and the risk-adjusted discount rate—and we can solve for themissing piece of the puzzle: long-run implied growth. We begin with the long-rungrowth assumption set at zero growth. We compute our first estimate of firm valueusing the zero growth assumption, and we compare that estimate to market price.The first estimate will likely be substantially lower than market price because marketprice probably includes the present value of the market’s expectations for long-rungrowth. For PepsiCo, the initial value estimate assuming zero growth is $38.20 pershare. We steadily increase the long-run growth parameter assumption as necessaryuntil the present value from the residual income model equals market price. In thecase of PepsiCo at the end of Year 11, market price of $49.05 only reflects long-rungrowth of 2.96 percent (significantly lower than our expectation of 5.0 percent long-run growth). That is, conditional on our assumptions for residual income through

949Reverse Engineering

Thom

son

Learn

ing™

Year +10 and on our assumption that PepsiCo’s cost of equity capital is 8.0 percent,if the market expects long-run growth will be 2.96 percent, then the present value ofPepsiCo shares exactly agrees with the market price of $49.05. Again, note that theValuation spreadsheet in FSAP is a useful tool that allows the analyst to establishassumptions for earnings and cost of capital, and then vary the long-run growthassumption for reverse engineering.

Academic accounting researchers develop and test models to explain the observedrelation between accounting information and stock prices. The research usually pro-poses theories and models for this relation analytically and then tests the modelsempirically on large data sets involving many firms for many years. The results ofthis research have provided many insights into multi-faceted dimensions of the rela-tions between accounting numbers and a wide variety of capital market variablessuch as stock prices, stock returns reactions around announcements, stock returnscumulated over long periods of time, trading volume, analysts’ and managements’earnings forecasts, equity costs of capital, implied market risk premia, market betas,other risk factors, bankruptcy, earnings management, and many others. Throughoutthis text, we have referred to relevant examples of empirical accounting research,including the classic study by Ball and Brown that helped set the stage for futureresearch by being the first to show that changes in earnings correlate with unexpectedchanges in stock prices.25 As we described in Chapter 1, the Ball and Brown resultsindicate that, in their sample, merely the difference in the sign of the change inannual earnings (whether positive or negative) was associated with nearly a 16 per-cent difference in annual market-adjusted stock returns. Firms that reportedincreases in earnings experienced returns that on average “beat” the market averageby 7 percent, while firms that reported decreases in earnings experienced returns thaton average fell 9 percent short of the market average.

Accounting academics and the research process itself provide important elementsthat should lead to reliable insights into the relation between accounting numbersand stock market variables. For example, as researchers, academics are trained to basetheir predictions and hypotheses as much as possible on formal theory integratingeconomics, finance, and accounting (rather than ad hoc or ex post reasoning).Academics commonly test these predictions with rigorous quasi-scientific methodson large empirical samples of real data. Academics usually have no commercial inter-est in the results, so the findings should not be biased by the need to obtain a partic-ular conclusion, or the need to sell. Furthermore, academic research is not published


THE RELEVANCE OF ACADEMIC RESEARCH FOR THEWORK OF THE SECURITY ANALYST24

24This section draws heavily from Clyde P. Stickney, “The Academic’s Approach to Securities Research: IsIt Relevant to the Analyst?” Journal of Financial Statement Analysis (Summer 1997), pp. 52–60.

25Ray Ball and Philip Brown, “An Empirical Evaluation of Accounting Income Numbers,” Journal ofAccounting Research (Autumn 1968), pp. 159–178.

Thom

son

Learn

ing™

in a leading scholarly research journal until after it passes the stringent peer reviewprocess. Few research studies pass the “publish” test; most “perish.”

Despite these strong advantages leading the academic accounting research processtoward reliable conclusions and insights about the relation between accountingnumbers and market variables, the natural question for the security analyst is: Ofwhat relevance are the academic research models and empirical findings to my taskof making buy, sell, or hold recommendations on individual firms? This concludingsection offers some thoughts on this important question. This section also summa-rizes the role of market efficiency, and describes some of the empirical evidence todate on the relative degree of market efficiency with respect to earnings numbers. Weconsider the results to date to be very encouraging for analysts.

Both the academic and professional analyst communities must recognize that theirinterests involve different levels of aggregation. The academic is interested primarilyin “big picture” explanations; conclusions and results that predict and explain therelation between accounting information and stock market variables in general. Theanalyst is concerned with specific assessments of the value of individual firms. Theacademic might seek to answer the question, what is the sign and significance of therelation between investments in research and development and stock market returns?Does this relation differ across industries? The analyst is more concerned withwhether the specific investments in research and development by a particular firm,such as Eli Lilly or Intel, are likely to enhance profitability and stock returns. Academicresearch describes general tendencies that provide a basis for the analyst to assess thelink between accounting numbers and a firm’s value, and to identify deviations fromthe average for individual firms. Professional analysts create value by acting on thedeviations (that is, taking positions in under- or overpriced stocks). Academics shouldnot expect immediate application of their research findings to the work of the pro-fessional analyst. Professional analysts should not expect to apply the results of aca-demic research immediately and specifically to their day-to-day responsibilities.

The previous section suggests the common meeting place between the academicand professional analyst communities. Both communities share the desire to under-stand better how accounting information relates to stock prices. The activities of eachcommunity do influence the other. Academics are keenly interested in predicting andexplaining analysts’ earnings forecasts and price targets, and, more generally, inexplaining 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 undergraduateand MBA programs) and in professional development training, is developed and val-idated by academic work (including textbooks like this one, that seek to link practice,theory, and research). Consider, for example, the impact that academic researchrelating to earnings forecasts, market reactions to earnings, risk and expectedreturns, and bankruptcy prediction have had on the work of the securities analyst

951The Relevance of Academic Research for the Work of the Security Analyst

LEVEL OF AGGREGATION ISSUE

THEORY DEVELOPMENT AND PRACTICE FEED EACH OTHER

Thom

son

Learn

ing™

during the last several decades. Consider the success of the academic community toidentify and explain market pricing “anomalies,” such as why the market does notfully incorporate information about past earnings changes when making earningspredictions, and the numerous portfolios and trading strategies that have emerged toexploit these anomalies.

For most of the last several decades, academic research has presumed that the cap-ital markets exhibit a relatively high degree of efficiency with respect to accountinginformation. In contrast, many analysts view their task as the constant pursuit ofmarket inefficiencies—mispriced securities. Academics generally perceive marketefficiency from the perspective of the big picture, with a view of large samples andmarket movements in general, whereas analysts see market efficiency from the frontlines, experiencing daily swings in market prices which are sometimes hard toexplain in the context of an efficient market. Thus, it is not surprising that at timesthe differences in perspective on the degree of market efficiency may create more ofa wall, rather than a bridge, between academics and professional analysts. This sec-tion seeks to reach a common understanding, and the next section provides somestriking evidence on the degree of market efficiency with respect to earnings.

Capital markets may be described as “efficient” with regard to accounting infor-mation if market prices react completely and quickly to available accounting infor-mation. Notice that efficiency should be described as a matter of degree, not as anabsolute. 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 market par-ticipants identify the value-relevant implications of all available accounting infor-mation so that market prices reflect economic values without systematic bias. Forexample, a market that reflects a relatively high degree of information efficiencywould impound in prices the value-relevant information in the persistence of earn-ings over time, and accounting information disclosed in footnotes as well as in thefinancial statements. A market that is relatively efficient will impound in stock pricesthe economic implications of all value-relevant accounting information, evenincluding items such as comprehensive income or pro forma stock options expense,which may be disclosed in the notes.

The term “quickly” in this description suggests that market participants cannotconsistently earn abnormal returns using accounting information for a long periodof time after the information has been made publicly available. If capital marketsexhibit a high degree of efficiency, market prices should react quickly (within a matter of hours or days) to capture any value-relevant signals in the accountinginformation.

The degree of efficiency with respect to complete and quick reactions in an information-efficient capital market depends on analysts and financial statementanalysis. Analysts study accounting information to assess appropriate values for


HAS THE THEORY OF CAPITAL MARKET EFFICIENCY GOTTENIN THE WAY?

Thom

son

Learn

ing™

stocks and to take positions in under- or overvalued securities, thereby driving stockmarket prices to efficient levels. The speed with which analysts can forecast, antici-pate, and react to accounting information causes prices to move before accountinginformation is released, and to react quickly to surprises in the information when itis released.

Also consider what a high degree of market efficiency does not imply. A capitalmarket with a high degree of information efficiency does not necessarily price allstocks correctly every day. As a practical matter, relatively efficient markets experi-ence valuation errors at the level of the individual firm; but these random inefficien-cies cancel out at an aggregated market level and do not tend to persist for longperiods of time.26 Analysts are driving forces involved in identifying and correctingsecurity mispricings. A capital market with a high degree of information efficiencydoes not necessarily have perfect foresight—surprises happen. Firms frequently sur-prise the market by announcing earnings numbers that are higher or lower than themarket’s expectations. Again, analysts drive market prices to react quickly and com-pletely to new information.

Two studies by Victor Bernard and Jacob Thomas provide the most striking evi-dence to date on the degree of market efficiency and inefficiency with respect toaccounting earnings.27 Bernard and Thomas collected a sample of 84,792 quarterlyearnings announcements for firms on the CRSP and Compustat databases over theyears 1974 to 1986. They ranked each firm each quarter into 10 portfolios on thebasis of each firm’s standardized unexpected earnings (denoted SUE—the seasonalquarterly change in earnings standardized by the firm’s standard deviation in earnings changes over the prior 16 quarters). They studied the average abnormal(market-adjusted) stock returns to each portfolio over the 60 trading days leading upto the quarterly earnings announcement, and over the 60 trading days following theannouncement. Exhibit 13.11 depicts a portion of their results.

The results in Exhibit 13.11 during the pre-announcement period indicate thatthe market is highly efficient in anticipating and reacting to quarterly earnings sur-prises. Firms with quarterly earnings surprises in the “good news” portfolios—port-folios 7 through 10—experience positive cumulative abnormal returns during the 60days prior to and including the release of earnings. Firms with quarterly earningssurprises in the “bad news” portfolios—portfolios 1 through 4—experience negativecumulative abnormal returns during the 60 days prior to and including the release ofearnings. The average difference in cumulative abnormal returns between portfolio

953The Relevance of Academic Research for the Work of the Security Analyst

26For a discussion of these issues, see Ray Ball, “The Earnings-Price Anomaly,” Journal of Accounting andEconomics (1992), pp. 319–345.

27Victor Bernard and Jacob Thomas, “Post-Earnings Announcement Drift: Delayed Price Response or RiskPremium?” Journal of Accounting Research Vol. 27, (Supplement, 1989), pp. 1–36; and “Evidence thatStock Prices Do Not Fully Reflect the Implications of Current Earnings for Future Earnings,” Journal ofAccounting and Economics Vol. 13, No. 4 (1990), pp. 305–340.

STRIKING EVIDENCE ON THE DEGREE OF MARKET EFFICIENCY AND INEFFICIENCY WITH RESPECT TO EARNINGS

Thom

son

Learn

ing™


Source: Victor Bernard and Jacob Thomas, “Post-Earnings Announcement Drift: Delayed Price Response or Risk Premium?” Journal ofAccounting Research Vol. 27, (Supplement, 1989), pp.1–36.

EXHIBIT 13.11

Evidence from Research by Bernard and Thomas on Market Efficiencywith Respect to Standardized Unexpected Earnings (SUE)

SUEdeciles

123

4

5

67

89

10

–60 –40 –20 0 0 20 60

–8

–6

–4

–2

0

2

4

CumulativeAbnormalReturns

(%)

Pre-announcement Period Post-announcement Period

SUEdeciles

Event Time in Trading Days Relative to Earnings Announcement Day

1

2

3

4

5

6

7

8

9

10

6

40

Thom

son

Learn

ing™

10 (roughly +4 percent) and portfolio 1 (roughly –6 percent) was more than 10percent per quarter! These results suggest the market anticipates and reacts quickly toquarterly earnings information.

The results in Exhibit 13.11 during the post-announcement period suggest thatthe market’s reaction to quarterly earnings news is highly, but not completely, effi-cient. In the post-announcement period, Bernard and Thomas measured the cumu-lative abnormal returns to the exact same portfolios over the 60 trading days after theearnings announcements. If the market’s reactions to quarterly earnings were onaverage quick and complete, these portfolios should exhibit no systematic abnormalreturns in the post-announcement period. Upon the announcement of earnings,market prices should adjust efficiently. Post-announcement abnormal returns shouldonly arise from new information that arrives during those 60 days, and the post-announcement abnormal returns should not be associated with the prior quarter’searnings news.

The results for the post-announcement period clearly indicate significant cumu-lative abnormal returns for the firms in portfolio 10 (best news) and portfolio 1(worst news). Mean cumulative abnormal returns amount to roughly +2 percent and–2 percent for the best and worst news portfolios, respectively. In their second study,Bernard and Thomas show that, in part, the market seems to underreact to the per-sistence in current period earnings for future period earnings, failing to fully antici-pate the momentum in quarterly earnings changes.

Taken together, the Bernard and Thomas studies reveal that the market is highlybut not completely efficient with respect to quarterly earnings. We consider theseresults to be very encouraging for analysts. We interpret the results to suggest thatanalysts who can sharpen their ability to forecast future changes in earnings, and takelong positions in (buy) shares of firms experiencing earnings increases and shortpositions in (sell) shares of firms experiencing earnings decreases during the 60-daypre-announcement period have the potential to earn some portion of the pre-announcement abnormal returns. Similarly, analysts who can sharpen their ability toreact appropriately once earnings are announced have some potential to earn a por-tion of the post-announcement abnormal returns. These findings suggest that thereare returns to be earned by being good at forecasting and reacting to earnings.

We believe the state-of-the-art of market efficiency is exactly where analysts wouldlike it to be. The market is very efficient with respect to accounting information, butnot perfectly efficient. Some stocks are temporarily mispriced, but the market tendsto correct mispricings in a relatively short period of time. Financial statements analy-sis, particularly focusing on earnings, can help the analyst identify stocks whoseprices may be temporarily out of equilibrium. Insightful financial statement analysiscan lead to intelligent investment decisions and better-than-average returns.

This chapter relies on the residual income model to develop the theoretical ration-ale relating market prices to economic drivers of value and to accounting funda-mentals. This chapter describes the conceptual basis and practical application of

955Summary

SUMMARY

Thom

son

Learn

ing™

market multiples—the market-to-book value (MB) ratio and the price-earnings(PE) ratio. The chapter focuses on four variables, or factors, that affect the market-to-book ratio and the price-earnings ratio: (1) risk and the cost of equity capital, (2)the expected future growth rate in earnings, (3) the presence of permanent and tran-sitory components in the earnings of a particular year, and (4) the effects of account-ing methods and principles on reported earnings and the book value of commonshareholders’ equity. For decades, analysts have relied heavily on PE ratios to relatemarket prices to earnings. However, in recent years, analysts and academics alikeincreasingly recognize that transitory elements in earnings and earnings growth cancloud the interpretation of the PE ratio as an indicator of value. Analysts and aca-demics are shifting emphasis to the price-earnings-growth ratio and to the MB ratio.Transitory earnings elements of a particular period have less effect on the MB ratio.This chapter also demonstrates techniques to exploit the information in marketvalue by calculating price differentials and by reverse engineering stock prices to inferthe assumptions the market must be making. The chapter concludes by describingthe relevance of academic research for the professional analyst, including highlight-ing key research results that appear to be very encouraging for the analyst interestedin using earnings and financial statement data to analyze and value firms.

13.1 USING MARKET MULTIPLES TO ASSESS VALUES AND MARKET PRICES.This problem continues Case 5.2 and Problems 10.7, 11.4, and 12.1 for The Gap andLimited Brands.

Requireda. Compute the value-to-book ratio of each firm as of January 1, Year 13, using

the residual ROCE valuation method.b. Using analyses developed in the case and problems listed above and in part a,

prepare an exhibit summarizing the following ratios for each firm as ofJanuary 1, Year 13:1. Value-to-book ratio (use the values derived from the value-to-book ratio in

part a).2. Market-to-book ratio (Problem 11.4 gives market value information).3. Value-to-earnings ratio, where earnings are reported earnings for Year 12

(Case 5.2 provides reported earnings information).4. Price-to-earnings ratio, where earnings are reported earnings for Year 12.5. Value-to-earnings ratio, where earnings are projected earnings for Year 13

(use the amounts of projected earnings in Problem 12.1).6. Price-to-earnings ratio, where earnings are projected earnings for Year 13.

c. Compute the risk-free value of each firm as of January 1, Year 13, using a risk-free rate of 4.2 percent. Use the projected earnings for Year 13 to Year 17 devel-oped in Problem 10.7, and the projected comprehensive income for Year 18developed in Problem 12.1. Maintain the continuing value growth assump-tions of 6 percent for The Gap and 3 percent for Limited Brands. Forecast


PROBLEMS

Thom

son

Learn

ing™

amounts out 50 years in total (that is, the initial five years plus 45 additionalyears). Compute the ratio of market value to risk-free value for each firm as ofJanuary 1, Year 13.

d. Solve for the growth rate in continuing residual income implicitly impoundedin the market value of each firm on January 1, Year 13. Use the residual incomeamounts in Problem 12.1 for Year 13 to Year 17 before solving for the growthrate in continuing residual income.

e. Using the analyses in parts a to d, evaluate the extent of mispricing of eachfirm by the market.

13.2 USING MARKET MULTIPLES TO ASSESS VALUES AND MARKET PRICES.Problem 12.4 presents selected pro forma financial information for Steak N Shake forYear 12 to Year 22.

Requireda. Compute the value-to-book ratio as of January 1, Year 12, using the residual

ROCE valuation method.b. Using analyses developed in part a and in Problem 12.4, prepare an exhibit

summarizing the following ratios for Steak N Shake as of January 1, Year 12:1. Value-to-book ratio (use the amounts from part a).2. Market-to-book ratio.3. Value-to-earnings ratio, where earnings are reported earnings for Year 11

of $21.8 million.4. Price-to-earnings ratio, where earnings are reported earnings for Year 11.5. Value-to-earnings ratio, where earnings are projected earnings for Year 12.6. Price-to-earnings ratio, where earnings are projected earnings for Year 12.

c. Compute the risk-free value of Steak N Shake as of January 1, Year 12, using arisk-free rate of 4.2 percent. Use the projected earnings for Year 12 to Year 21,and the projected net income for Year 22 given in Problem 12.4. Maintain thecontinuing value growth assumption of 3 percent. Forecast amounts out 50years in total (that is, the initial ten years plus 40 additional years). Compute the ratio of market value to risk-free value for Steak N Shake as of January 1,Year 12.

d. Solve for the growth rate in continuing residual income implicitly impoundedin the market value of Steak N Shake on January 1, Year 12. Use the residualincome amounts in Problem 12.4 for Year 12 to Year 21 before solving for thegrowth rate in continuing residual income.

e. Using the analyses in parts a to c, evaluate the extent of mispricing of Steak NShake by the market.

13.3 APPLYING VARIOUS VALUATION METHODS FOR COMMON EQUITY.The Coca-Cola Company (Coke) is a principal competitor of PepsiCo. This problemasks you to compute the value of Coke using various valuation methods discussed inChapters 11 to 13 and to compare the results to those illustrated in the chapters forPepsiCo. Exhibit 13.12 presents selected information from the actual financial state-

957Problems

Thom

son

Learn

ing™

ments of Coke for Year 11 and the forecasted amounts for Year 12 to Year 16. Exhibit13.12 also shows the forecasted amounts for Year 17 assuming that all amounts on theincome statement and balance sheet for Year 16 grow 6 percent. The market equitybeta for Coke is 0.419. Assume a risk-free interest rate of 4.2 percent and a market riskpremium of 5 percent. The market value of Coke on January 1, Year 12, is $117,214.9million (2,486 million shares outstanding at a market price per share of $47.15).

Requireda. Compute the value of Coke on January 1, Year 12, using the present value of

projected free cash flows to common equity capital.b. Repeat part a using the dividends discount model.c. Repeat part a using the residual income model.d. Repeat part a using the residual ROCE model.


EXHIBIT 13.12

The Coca-Cola CompanySelected Financial Information

(amounts in millions)(Problem 13.3)

ActualForecast

Year 11 Year 12 Year 13 Year 14 Year 15 Year 16 Year 17a

Common Equity,Beginning of Year . . . . . . . $ 9,694 $11,366 $13,563 $15,947 $18,536 $21,345 $24,395

Net Income . . . . . . . . . . . . . . 3,733 3,930 4,171 4,426 4,691 4,973 5,122Other Comprehensive

Income . . . . . . . . . . . . . . . (157) (167) (178) (189) (199) (212) (112)Change in Common Stock . . (113) 341 422 515 621 743 (199)Dividends. . . . . . . . . . . . . . . . (1,791) (1,907) (2,031) (2,163) (2,304) (2,454) (4,079)Common Equity, End

of Year . . . . . . . . . . . . . . . . $11,366 $13,563 $15,947 $18,536 $21,345 $24,395 $25,127

Cash Flow fromOperations . . . . . . . . . . . . $ 4,065 $ 3,828 $ 3,958 $ 4,209 $ 4,469 $ 4,746 $ 4,863

Cash Flow for Investing. . . . . (1,188) (513) (616) (653) (692) (734) (389)Cash Flow for Long-term

Debt . . . . . . . . . . . . . . . . . (926) 297 163 333 354 376 199Cash Flow from

Common Stock . . . . . . . . (113) 341 422 515 621 743 (199)Cash Flow for Dividends. . . . (1,791) (1,907) (2,031) (2,163) (2,304) (2,454) (4,079)

Net Change in Cash. . . . . . . . $ 47 $ 2,046 $ 1,896 $ 2,241 $ 2,448 $ 2,677 $ 395

aThe amounts for Year 17 result from increasing each income statement and balance sheet amount by the expected long-term growth rate of 6 percentand then deriving the amounts for the statement of cash flows.

Thom

son

Learn

ing™

e. Exhibit 13.13 shows the amounts for various multiples for PepsiCo as ofJanuary 1, Year 12. This exhibit also shows financial ratios from the forecastfinancial statements for each firm for Year 16. Enter the missing amounts inExhibit 13.13 for Coke.

f. Using the analyses in parts a to e, evaluate the extent of mispricing of PepsiCoand Coke by the market.

13.4 INTERPRETING MARKET-TO-BOOK RATIOS. Exhibit 13.14 presentsselected data for seven pharmaceutical companies for a recent year. The growth ratein earnings and the dividend payout ratios are five-year averages. The excess earningsyears represent the number of years that each firm would need to earn a rate ofreturn on common shareholders’ equity (ROCE) equal to that in Exhibit 13.14 inorder to produce the market-to-book ratios shown. For example, Bristol-MyersSquibb would need to earn an ROCE of 48.9 percent for 58.3 years in order for thepresent value of the excess earnings over the cost of equity capital to produce a market-to-book ratio of 13.9 when applying the theoretical model. For several yearsjust prior to the most recent year, Bristol-Myers Squibb recognized significant esti-mated losses related to breast implant claims.

959Problems

EXHIBIT 13.13

PepsiCo and CokeValue and Market Multiples and Financial Ratios

(dollar amounts in millions)(Problem 13.3)

PepsiCo Coke

Value-to-Book Ratio:$121,205.9/$8,648 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.02

Market-to-Book Ratio:$86,131.8/$8,648 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.96

Value-Earnings Ratio (Year 11 Actual Net Income): $121,205.9/$2,658 . . . . . . . . . . . . . . . . . . . . . 45.60

Price-Earnings Ratio (Year 11 Actual Net Income): $86,131.8/$2,658 . . . . . . . . . . . . . . . . . . . . . . 32.40

Value-Earnings Ratio (Year 12 Projected Net Income): $121,205.9/$3,367.3 . . . . . . . . . . . . . . . . . . . . 35.99

Price-Earnings Ratio (Year 12 Projected Net Income): $86,131.8/$3,367.3 . . . . . . . . . . . . . . . . . . . . . 25.58

Year 16 Forecasted Financial Ratios:Profit Margin for ROA . . . . . . . . . . . . . . . . . . . . . . . . . 12.1% 19.3%Total Assets Turnover . . . . . . . . . . . . . . . . . . . . . . . . . . 1.26 .72Rate of Return on Assets . . . . . . . . . . . . . . . . . . . . . . . . 15.3% 14.0%Profit Margin for ROCE . . . . . . . . . . . . . . . . . . . . . . . . 12.2% 18.5%Capital Structure Leverage Ratio . . . . . . . . . . . . . . . . . 2.37 1.62Rate of Return on Common Shareholders’ Equity. . . . 36.4% 21.7%

Thom

son

Learn

ing™

RequiredConsidering the variables in the theoretical market-to-book ratio, discuss the

likely reasons for the ordering of these seven companies on their market-to-bookratios.

13.5 SENSITIVITY OF THE THEORETICAL MODELS OF PRICE-EARNINGSAND MARKET-TO-BOOK TO CHANGES IN ASSUMPTIONS. This problemexplores the sensitivity of the price-earnings and market-to-book models to changesin underlying assumptions. We recommend that you design a computer spreadsheetto perform the calculations, particularly for the market-to-book ratio.

Requireda. Compute the price-earnings ratio under each of the following sets of

assumptions:

Scenario Cost of Equity Capital Growth Rate in Earnings

A .15 .06B .15 .08C .15 .10D .13 .06E .13 .08F .13 .10G .11 .06H .11 .08I .11 .10


EXHIBIT 13.14Selected Data for Pharmaceutical Companies

(Problem 13.4)

Dividend Growth ExcessCost of Payout in Earnings

Company MB ROCE Equity Percentage PE Earnings Years

Bristol-Myers Squibb . . . . . . . . . . 13.9 .489 .134 .77 32.4 .068 58.3Warner Lambert. . . . . . . . . . . . . . 13.0 .350 .133 .48 42.7 .051 32.2Eli Lilly . . . . . . . . . . . . . . . . . . . . . 12.4 .281 .155 .42 49.3 .110 89.8Pfizer . . . . . . . . . . . . . . . . . . . . . . 11.2 .350 .143 .43 40.4 .152 27.8Abbott Laboratories. . . . . . . . . . . 10.4 .428 .113 .39 26.9 .116 13.5Merck . . . . . . . . . . . . . . . . . . . . . . 10.3 .331 .154 .46 31.8 .130 41.9Wyeth . . . . . . . . . . . . . . . . . . . . . . 6.9 .340 .138 .51 25.0 .065 24.6

Thom

son

Learn

ing™

b. Assess the sensitivity of the price-earnings ratio to changes in the cost ofequity capital and changes in the growth rate.

c. Compute the market-to-book ratio under each of the following sets ofassumptions:

Dividend Years ofCost of Equity Payout Excess

Scenario ROCE Capital Percentage Earnings

A .20 .13 .30 10B .18 .13 .30 10C .14 .13 .30 10D .18 .15 .30 10E .18 .11 .30 10F .18 .13 .40 10G .18 .13 .20 10H .18 .13 .30 15I .18 .13 .30 20

d. Assess the sensitivity of the market-to-book ratio to changes in the assump-tions made about the various underlying variables.

Note: To provide up-to-date integrated valuation cases, we include cases forChapters 11 to 13 on the web site for this book (http://stickney.swlearning.com)instead of the text.

961Cases

CASES

Chapter 13VALUATION: MARKET-BASED

Documents

Transcript of Chapter 13VALUATION: MARKET-BASED