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in whole or in part.

CHAPTER 14

VALUATION: MARKET-BASED APPROACHES

Solutions to Questions, Exercises, Problems, and Teaching Notes to Cases

14.1 Value Determinants. The same fundamental determinants of firm value (expected

future earnings, cash flows, growth, and risk) should also determine the firm’s

market value and share price. Therefore, these determinants should also impact

market-based multiples like MB and PE ratios.

14.2 Residual ROCE. Residual ROCE (return on common shareholders’ equity)

represents residual income scaled by beginning common shareholders’ equity. Al-

ternatively, residual ROCE represents ROCE minus the cost of equity capital

(RE). Thus, residual ROCE measures the rate of return on common shareholders’

equity above the required rate of return on equity capital.

14.3 Value-to-Book Valuation Approach. In conceptual terms, the value-to-book val-

uation approach measures the value of each dollar invested in book value of com-

mon shareholders’ equity. The value-to-book approach estimates value (per dollar

of book value) as one dollar plus (or minus) the present value of all future return

on common equity above (or below) the cost of equity capital. This model is a ver-

sion of the residual income valuation approach scaled by book value of sharehold-

ers’ equity. In that sense, the value-to-book approach presented in this chapter is

essentially the same as the residual income valuation approach presented in Chap-

ter 13. The only real difference is that the value-to-book approach scales all of the

variables in the valuation computation by beginning book value of equity.

14.4 Interpreting Value-to-Book Ratios. A firm with a value-to-book ratio that is ex-

actly equal to 1 when the book value of common equity plus the present value of

all future expected residual income exactly equals the book value of common eq-

uity. Alternately stated, such a firm is expected to produce no future residual in-

come, and is valued at an amount equal to existing book value of equity.

Likewise, a value-to-book ratio that is greater than (less than) 1 implies that the

firm is expected to create positive (negative) future residual income.

14.5 Interpreting Value-to-Book Ratios. A value-to-book ratio that is greater than

the market-to-book ratio indicates that the firm’s shares are under-priced in the

capital market. A value-to-book ratio that is less than the market-to-book ratio in-

dicates the firm’s shares are over-priced in the capital market.

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in whole or in part.

14.6 Value-to-Book Ratio Drivers. A firm’s value-to-book ratio will be higher than

that of other firms in the same industry under various economic conditions that

enable the firm to generate relatively more wealth for shareholders relative to

their investment. Such conditions could arise, for example, if (1) the firm’s

strategy enables it to earn a higher ROCE for a given cost of equity capital; (2) the

firm will earn the same ROCE but with lower risk and, therefore, a lower cost of

equity capital; or (3) the firm’s business model enables it to generate faster

growth provided the growth creates positive residual ROCE. Various accounting

factors can drive one firm’s value-to-book ratio to be higher than that of other

firms in the same industry, including (1) a greater proportion of assets in the form

of off-balance-sheet intangible assets such as brand equity, (2) a greater degree of

accounting conservatism involving expensing R&D activities that turn out to be

successful, or (3) a greater degree of accounting conservatism regarding faster

accelerated depreciation of PP&E.

14.7 Value-to-Book Ratio Drivers. Various economic factors will cause a firm’s

value-to-book ratio to decrease over time, including (1) increasing competition

driving the firm’s ROCE down, (2) increasing systematic risk that increases the

firm’s equity cost of capital over time, or (3) losing competitive advantage through

changes in technology or other factors, or (4) retaining earnings or issuing equity

capital and deploying the capital in activities that generate ROCE levels that are

lower than current levels. Various accounting factors will cause a firm’s value-to-

book ratio to decrease over time, including (1) earning a high ROCE (above the

equity cost of capital) on off-balance-sheet intangible assets (such as brand equity)

over time, (2) earning a high ROCE (above the equity cost of capital) on off-

balance-sheet R&D assets, or (3) recognizing unrealized gains on assets.

14.8 The Value-Earnings Ratio. In conceptual terms, the value-earnings ratio

expresses equity value as a multiple of one period of earnings. Similarly, the price-

earnings ratio expresses share price as a multiple of one period of earnings.

Because they are both scaled by earnings, the only difference between the value-

earnings ratio and the price-earnings ratio is the same as the difference between

value and price. Value is what the share is worth to the investor; price is value of

the share in the capital market. Both the value-earnings and price-earnings ratios

make the unrealistic assumption that one period of earnings is sufficient to

describe value (price). Both treat one period of earnings essentially as a perpetuity.

14.9 The Price-Earnings Ratio. In practice, it is common to observe price-earnings

ratios measured as current period price divided by trailing twelve months (or most

recent annual) earnings per share. This measurement of the price-earnings ratio as

a valuation multiple can be flawed if (1) historic earnings do not reflect expected

future earnings because of a change in the firm’s business model (perhaps due to

acquisitions or divestitures); (2) historic earnings contain transitory gains or losses

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in whole or in part.

that are not expected to persist; (3) the firm pays dividends, which reduce share

price but are not subtracted from earnings; and (4) share price is computed based

on year-ending shares outstanding, whereas earnings per share are based on

weighted-average shares outstanding during the year.

14.10 Price-Earnings Ratio Drivers. Various economic factors can cause one firm’s

price-earnings ratio to be higher than that of other firms in the same industry: (1)

investors expect that the firm’s strategy enables it to generate and sustain greater

profitability for a given cost of equity capital; (2) the firm will earn the same prof-

itability but with lower risk and, therefore, a lower cost of equity capital; or (3)

the firm’s business model enables it to generate faster growth in earnings pro-

vided the growth creates positive residual ROCE. Various accounting factors can

drive one firm’s price-earnings ratio in a given period to be higher than that of

other firms in the same industry, including (1) non-recurring expenses or losses in

that period, (2) a greater degree of accounting conservatism that requires expens-

ing R&D or other intangible asset-generating activities, or (3) a greater degree of

accounting conservatism regarding accelerated depreciation of PP&E.

14.11 Price-Earnings Ratio Drivers. Various economic factors can drive a firm’s

price-earnings ratio down over time, including (1) increasing competition driving

the firm’s share price down faster than earnings, (2) increasing systematic risk

that increases the firm’s equity cost of capital over time, (3) losing technological

competitive advantage, or (4) diminishing growth opportunities. Various

accounting factors can cause a firm’s price-earnings ratio to decrease from one

period to the next, including (1) implementing a change in accounting principle

that reduces earnings without altering the underlying economic value of the firm

(such as adopting SFAS No. 142 and ceasing the amortization of goodwill) (2)

earning a high degree of profitability on off-balance-sheet R&D assets (for

example, going from a period in which R&D is expensed to a period when the

R&D is successfully complete and the firm is harvesting profits from its R&D

investments), or (3) recognizing nonrecurring income or gains in a given period.

14.12 Market-to-Book versus Price-Earnings Ratios. Market-to-book multiples dem-

onstrate less volatility over time and less variance across firms than do price-

earnings multiples because earnings numbers are more variable across firms and

more volatile over time than are book values. One reason is because transitory

gains and losses have a proportionally larger impact on earnings than on the book

value of shareholders’ equity.

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in whole or in part.

14.13 Price Differentials. Explain Price Differentials in Conceptual Terms. Concep-

tually, price differentials reflect the difference between the price at which the

share would trade in a hypothetical risk-neutral market and the price at which the

share does trade in the real-world risk-averse market. Price differentials measure

the dollar amount by which the share has been discounted for risk from its risk-

neutral value. As such, price differentials reflect the discount for risk impounded

in share price. Price differentials reflect the amount by which the share price has

been discounted for risk. More risky shares should experience greater price diffe-

rentials, all else equal.

14.14 Reverse Engineering Share Prices. Reverse engineering share prices is a

process through which the analyst attempts to infer the assumptions that the capi-

tal market is making in valuing a particular share. By assuming that value equals

price and by making assumptions about two other valuation model parameters,

reverse engineering share prices enables an analyst to solve for the remaining as-

sumption that the capital markets appear to impound in share price. For example,

assuming that share value equals market price and that analysts’ earnings and

growth forecasts are reliable proxies for the market’s expectations for future earn-

ings and growth, the analyst can solve for the implicit discount rate impounded in

price (the implied rate of return on the share).

14.15 Market Efficiency. Market efficiency is a matter of degree that describes the

amount of information impounded in share prices and the speed with which prices

reflect new value-relevant information. Market efficiency does not mean that

share prices always reflect all available information for every firm (some shares

can be temporarily mispriced even in efficient markets), that share prices fully

anticipate future news (surprises happen even in very efficient markets), or that

share prices reflect private information. More efficient markets reflect greater

amounts of value-relevant information about share prices, and they reflect such

information more quickly and without bias (over- or under-pricing the

information).

14.16 Analysts’ Role in Market Efficiency. Analysts play a key role in making the

capital markets efficient by being active acquirers and processors of value-

relevant information and actively seeking and trading on shares they believe to be

temporarily mispriced. By acquiring and processing information and trading, ana-

lysts help make the capital markets more efficient.

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in whole or in part.

14.17 Market Efficiency with Respect to Quarterly Earnings Surprises. The evi-

dence presented in Exhibit 14.11 in the text, indicates that the market is highly ef-

ficient with respect to quarterly earnings surprises during the 60 trading days prior

to quarterly earnings announcements. Those results indicate that share prices move

in directions consistent with future earnings surprises well in advance of the earn-

ings news. However, that same evidence suggests that the market reacts to ex-

tremely good or bad earnings news with a delay. The results suggest that trading

portfolios can earn significant abnormal returns during the 60 trading days follow-

ing quarterly earnings announcements.

14.18 Using Market Multiples to Assess Values and Market Prices.

Steak ’n Shake:

a. Compre- Cum. Present Value/

hensive Implied Residual Share. Eq. Value Book

Year Income ROCE ROCE Growth Factor Ratio

+1 $24.5 0.148 0.054 1.000 0.915 0.049

+2 $25.8 0.145 0.052 1.071 0.836 0.047

+3 $27.6 0.144 0.050 1.158 0.765 0.044

+4 $29.6 0.144 0.050 1.242 0.700 0.043

+5 $31.8 0.147 0.053 1.306 0.640 0.044

+6 $34.2 0.150 0.057 1.373 0.585 0.046

+7 $36.8 0.157 0.064 1.413 0.535 0.048

+8 $39.5 0.166 0.072 1.436 0.490 0.051

+9 $53.9 0.225 0.132 1.444 0.448 0.085

+10 $57.0 0.223 0.129 1.543 0.409 0.081

Sum …………………………………………………………………………………………. 0.538

Continuing Value

+11 $58.7 0.218 0.124 1.626

Residual ROCE times growth in Year +11 = 0.124 × 1.626 = 0.202

Continuing Value in Present Value = 0.202/(0.0934 – 0.03) × 0.409 . 1.306

Factor for Common Shareholders’ Equity on January 1, Year +1 ……. 1.000

Sum …………………………………………………………………………………………. 2.844

Mid-Year Discounting Adjustment Factor: [1 + (0.0934/2)]……………. 1.0467

Value-to-Book Ratio ………………………………………………………………….. 2.977

Book Value of Common Shareholders’ Equity, January 1, Year +1 …. $165.8

Value of Common Shareholders’ Equity ………………………………………. $493.6

b. (1) Value-to-Book Ratio: $493.6/$165.8 = 2.98

(2) Market-to-Book Ratio: $309.98/$165.8 = 1.87

(3) Value-Earnings Year 0: $493.6/$21.8 = 22.6

(4) Price-Earnings Year 0: $309.98/$21.8 = 14.2

(5) Value-Earnings Year +1: $493.6/$24.5 = 20.1

(6) Price-Earnings Year +1: $309.98/$24.5 = 12.6

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in whole or in part.

c. To compute the risk-neutral value, we substitute the risk-free rate of 4.2% for

the cost of equity capital in the residual income valuation model. Because the

risk-free rate is close to the continuing value growth rate of 3%, the formula

for the valuing of a growing perpetuity (1 + g)/(r – g) increases exponentially.

We compute risk-neutral value as follows:

Compre- Cum. Present Value/

hensive Implied Residual Share. Eq. Value Book

Year Income ROCE ROCE Growth Factor Ratio

+1 $24.5 0.148 0.106 1.000 0.960 0.102

+2 $25.8 0.145 0.103 1.071 0.921 0.102

+3 $27.6 0.144 0.102 1.158 0.884 0.104

+4 $29.6 0.144 0.102 1.242 0.848 0.107

+5 $31.8 0.147 0.105 1.306 0.814 0.112

+6 $34.2 0.150 0.108 1.373 0.781 0.116

+7 $36.8 0.157 0.115 1.413 0.750 0.122

+8 $39.5 0.166 0.124 1.436 0.720 0.128

+9 $53.9 0.225 0.183 1.444 0.691 0.182

+10 $57.0 0.223 0.181 1.543 0.663 0.185

Sum …………………………………………………………………………………………. 1.260

Continuing Value

+11 $58.7 0.218 0.176 1.626

Residual ROCE times growth in Year +11 = 0.176 × 1.626 = 0.286

Continuing Value in Present Value = 0.286/(0.0420 – 0.03) × 0.663 .. 15.804

Factor for Common Shareholders’ Equity on January 1, Year +1 ……. 1.000

Sum …………………………………………………………………………………………. 18.064

Mid-Year Discounting Adjustment Factor: [1 + (0.0420/2)]……………. 1.0210

Value-to-Book Ratio …………………………………………………………………. 18.444

Book Value of Common Shareholders’ Equity, January 1, Year +1 …. $ 165.8

Risk-Neutral Value of Common Shareholders’ Equity …………………… $3,058.0

The risk-neutral value is $3,058 million. The current market value is 10.1% of

the risk-neutral value ($309.98/$3,058). The price differential is $2,748 mil-

lion. The market has discounted Steak ’n Shake shares roughly 90% below

risk-neutral value.

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in whole or in part.

d. Market Value ……………………………………………………………………. $ 309.98

Adjustment for Mid-Year Discounting …………………………………. 1.0467

Market Value Assuming Full-Year Discounting ……………………. $ 296.1

Less Book Value of Shareholders’ Equity, January 1, Year +1 .. (165.8)

Less Present Value of Residual Income, Year +1 to Year +10 … (89.8)

Present Value of Continuing Value on January 1, Year +1 ……… $ 40.5

Future Value Adjustment to Reflect Continuing Value on

January 1, Year +11 (1.0934)10. ……………………………………… 2.44225

Present Value of Continuing Value on January 1, Year +11 ……. $ 98.9

We then solve for the value of g in the formula for the present value of a

growing perpetuity, (1 + g)/(r – g). The equation is as follows:

$98.9 = {[$57.0 × (1 + g)] – (0.0934 × $269.5)}/(0.0934 – g)

g = –14.449%

e. The analyses in Solutions a–d as well as the values computed in Problem

13.18 indicate that the market is undervaluing Steak ’n Shake. The value-to-

book ratio of 2.98 is significantly greater than the market-to-book ratio of

1.87. The value-earnings ratios significantly exceed the corresponding price-

earnings ratios. The market value as a percentage of the risk-neutral value is

10.1%, compared to 19% for PepsiCo, which suggests that Steak ’n Shake is

significantly discounted for risk. Perhaps the most interesting insight is that

the market price implicitly assumes negative growth in residual income of

14.449% after Year +10. This result contrasts with projected positive growth

in residual income each year between Year +1 and Year +10 and higher rates

of growth during the last few years of that forecast horizon.

14.19 Interpreting Market-to-Book Ratios.

The variables that affect the market-to-book ratio are (1) the excess of ROCE over

the cost of equity capital; (2) the growth in common shareholders’ equity, which

is positively related to ROCE and negatively related to the dividend payout per-

centage; and (3) the number of years during which a firm is expected to earn an

excess return over its cost of equity capital. Summary data in the table below help

in interpreting the market-to-book ratios for these seven firms. The growth in

common shareholders’ equity equals one minus the dividend payout percentage

times ROCE.

Bristol-Myers Squibb—Bristol-Myers Squibb has the highest market-to-book

ratio because it has the largest excess of ROCE over the cost of equity of the sev-

en firms. Its price-earnings ratio for the year is close to average for the seven

companies, suggesting that its earnings are likely persistent and do not likely in-

clude significant transitory income items. The large number of years of excess

earnings at the ROCE of the current year required to generate a market-to-book

ratio of 13.9 is due to the large dividend payout percentage (77%). If the dividend

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in whole or in part.

payout ratio for Bristol-Myers Squibb were 44%, in line with those of the other

companies, the required years of excess earnings would be only 15.5 years.

Warner-Lambert—Compared to Bristol-Myers Squibb, Warner-Lambert has a

similarly high market-to-book ratio of 13.0 but a lower ROCE (35.0%) and a

slower historical rate of growth in earnings (5.1%). The relatively high price-

earnings ratio for the current year suggests that Warner-Lambert’s earnings for

the current year include some negative transitory items; so its recent ROCE is un-

derstated. Thus, its long-term ROCE can be expected to exceed the 35% for the

current year. The excess of ROCE over the cost of equity capital also would be

higher and would justify a higher market-to-book ratio.

Eli Lilly—The market-to-book ratio of Eli Lilly is quite high at 12.4 even though

the ROCE is the lowest of the seven firms. However, the price-earnings ratio of

Eli Lilly is extremely high, suggesting that earnings for the current year include

some negative transitory items. Thus, the ROCE for the current year likely

understates the long-term ROCE and the excess of ROCE over the cost of equity

capital. The relatively high cost of equity capital for Eli Lilly also reduces the

excess return. The market apparently filtered out the effect of these transitory

items and granted the firm a relatively high market-to-book ratio. The large

number of years of excess earnings needed to generate a market-to-book ratio of

12.4 also relates to the understated ROCE and high cost of equity capital.

Pfizer—Pfizer’s market-to-book ratio of 11.2 falls in the middle of the seven

companies. Its relatively high excess of ROCE over its cost of equity capital,

coupled with the highest growth rate in earnings in recent years, suggests that its

market-to-book ratio should perhaps be even higher. The fact that Pfizer’s price-

earnings ratio is not excessively high for this industry suggests that Pfizer is gene-

rating a normal level of earnings and that the market anticipates that it will sustain

this level of earnings and earnings growth in the future.

Abbott Laboratories—Abbott Laboratories has the second-largest excess of

ROCE over the cost of equity capital, the fastest growth rate in shareholders’

equity, and the smallest number of years of excess earnings required to generate a

market-to-book ratio of 10.4. Its price-earnings ratio, however, is on the low side

relative to the other companies, suggesting that the earnings for the current year

include some positive transitory items. Thus, future ROCE is likely to fall, and

lower future ROCE will reduce its excess return and the corresponding market-to-

book ratio. Abbott Laboratories has the highest growth rate in shareholders’

equity as a result of large ROCE and the lowest dividend payout percentage.

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in whole or in part.

Merck—Merck’s market-to-book ratio of 10.3 is a function of a somewhat lower

excess ROCE, which results in part from a high cost of equity capital. Its price-

earnings ratio falls near the middle of the seven firms, so earnings do not likely

include significant transitory items. The large number of years of excess earnings

required to generate a market-to-book ratio of 10.3 results from the relatively

small excess ROCE.

Wyeth—The market-to-book ratio of Wyeth is 6.9, the lowest of the seven firms.

Its price-earnings ratio is lowest of the seven firms, and its historical growth rate

in earnings is also on the low side. This suggests that Wyeth’s recent earnings re-

flect positive transitory items and that future earnings and ROCE will be lower,

which leads to a lower market-to-book ratio. The low market-to-book ratio results

in part from the somewhat higher dividend payout percentage and the slower

growth in shareholders’ equity.

You might ask the class why the market-to-book ratios in the pharmaceutical in-

dustry exceed 1.0 to such a significant extent. Pharmaceutical companies must

expense R&D costs in the year incurred, which reduces net income for the ex-

penditures made each year but reduces shareholders’ equity for cumulative R&D

expenditures. Because of the significant lag between making R&D expenditures

and generating revenues and positive earnings from those expenditures, the mar-

ket values the expected benefits several years before the accounting records rec-

ognize those benefits. Thus, market values of equity will exceed book values.

Summary of Data for Seven Pharmaceutical Companies

(Problem 14.19)

Market- Growth in Excess

to-Book Shareholders’ Earnings

Company Ratio ROCE – RE Equity Years

Bristol-Myers Squibb ….. 13.9 0.355 0.112 58.3

Warner-Lambert …………. 13.0 0.217 0.182 32.0

Eli Lilly ……………………… 12.4 0.126 0.163 89.8

Pfizer ………………………… 11.2 0.207 0.200 27.8

Abbott Laboratories …….. 10.4 0.315 0.261 13.5

Merck ………………………… 10.3 0.177 0.179 41.9

Wyeth ……………………….. 6.9 0.202 0.167 24.6

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in whole or in part.

14.20 Sensitivity of Value-Earnings and Value-to-Book to Changes in Assumptions.

a. Scenario Cost of Equity Capital Growth Rate in Earnings VE Ratio

A 0.15 0.06 11.8

B 0.15 0.08 15.4

C 0.15 0.10 22.0

D 0.13 0.06 15.1

E 0.13 0.08 21.6

F 0.13 0.10 36.7

G 0.11 0.06 21.2

H 0.11 0.08 36.0

I 0.11 0.10 110.0

b. The calculations project one-year-ahead earnings and then compute the value-

earnings ratio. Thus, the value-earnings ratios are computed as (1 + g)/(RE – g).

These ratios support the following observations:

1. Value-earnings ratios are inversely related to the cost of equity capital.

2. Value-earnings ratios are positively related to earnings growth rates.

3. A particular percentage reduction in the cost of equity capital results in a

greater-than-proportional increase in the value-earnings ratio. Value-

earnings ratios are nonlinear in the cost of equity capital.

4. The size of the proportional increase in the value-earnings ratio from a

reduction in the cost of equity capital increases as the growth rate

increases.

5. A particular percentage increase in the growth rate results in a greater-

than-proportional increase in the value-earnings ratio. Value-earnings

ratios also are nonlinear in growth rates.

6. The size of the proportional increase in the value-earnings ratio from an

increase in the growth rate increases as the growth rate increases.

7. The value-earnings ratio increases exponentially as the spread between the

cost of equity capital and the growth rate narrows.