F I G U R E 12.9 16%

Earnings yield of S&P

500 versus 10-year 14%

Treasury bond yield

12%

10%

Treasury yield

8%

6%

Earnings yield

4%

2%

0%

1955 1958 1961 1964 1967 1970 1973 1976 1979 1982 1985 1988 1991 2000

based on a forecast of long-term interest rates. The product of the two forecasts is the estimate

of the end-of-period level of the market.

The forecast of the P/E ratio of the market is sometimes derived from a graph similar to that

in Figure 12.9, which plots the earnings yield (earnings per share divided by price per share,

the reciprocal of the P/E ratio) of the S&P 500 and the yield to maturity on 10-year Treasury

bonds. The figure shows that both yields rose dramatically in the 1970s. In the case of Trea-

sury bonds, this was because of an increase in the inflationary expectations built into interest

rates. The earnings yield on the S&P 500, however, probably rose because of inflationary dis-

tortions that artificially increased reported earnings. We have already seen that P/E ratios tend

to fall when inflation rates increase. When inflation moderated in the 1980s, both Treasury and

earnings yields fell. For most of the last 15 years, the earnings yield ran about one percentage

point below the T-bond rate.

One might use this relationship and the current yield on 10-year Treasury bonds to forecast

the earnings yield on the S&P 500. Given that earnings yield, a forecast of earnings could be

used to predict the level of the S&P in some future period. Let™s consider a simple example of

this procedure.

The late 2001 forecast for 2002 earnings per share for the S&P 500 portfolio was about $53.7

The 10-year Treasury bond yield at this time was about 5.2%. Since the earnings yield on the

12.7 EXAMPLE S&P 500 has been about one percentage point below the 10-year Treasury yield, a first guess

for the earnings yield on the S&P 500 might be 4.2%. This would imply a P/E ratio of 1/.042

Forecasting the

23.8. Our forecast for the level of the S&P 500 index would then be 23.8 53 1261.

Aggregate Stock

Of course, there is uncertainty regarding all three inputs into this analysis: the actual earn-

Market

ings on the S&P 500 stocks, the level of Treasury yields at year-end, and the spread between

(continued)

7

According to Thomson Financial, as of November 2001. Thomson surveys a large sample of stock analysts and

reports several analyses of their forecasts for both the economy and individual stocks.

Bodie’Kane’Marcus: IV. Security Analysis 12. Equity Valuation © The McGraw’Hill

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441

12 Equity Valuation

the Treasury yield and the earnings yield. One would wish to perform sensitivity or scenario

analysis to examine the impact of changes in all of these variables. To illustrate, consider

EXAMPLE 12.7

Table 12.4, which shows a simple scenario analysis treating possible effects of variation in the

Treasury bond yield. The scenario analysis shows that the forecast level of the stock market (concluded)

varies inversely and with dramatic sensitivity to interest rate changes.

Most Likely Pessimistic Optimistic

TA B L E 12.4 Scenario Scenario Scenario

S&P 500 price

Treasury bond yield 5.2% 5.7% 4.7%

forecasts under

various scenarios Earnings yield 4.2% 4.7% 3.7%

Resulting P/E ratio 23.8 21.3 27.0

EPS forecast $53 $53 $53

Forecast for S&P 500 1,261 1,129 1,431

Note: The forecast for the earnings yield on the S&P 500 equals the Treasury bond yield minus 1%. The P/E ratio is the reciprocal

of the forecasted earnings yield.

Some analysts use an aggregate version of the dividend discount model rather than an earn-

ings multiplier approach. All of these models, however, rely heavily on forecasts of such

macroeconomic variables as GDP, interest rates, and the rate of inflation, which are difficult

to predict accurately.

Because stock prices reflect expectations of future dividends, which are tied to the eco-

nomic fortunes of firms, it is not surprising that the performance of a broad-based stock index

like the S&P 500 is taken as a leading economic indicator, that is, a predictor of the perform-

ance of the aggregate economy. Stock prices are viewed as embodying consensus forecasts of

economic activity and are assumed to move up or down in anticipation of movements in the

economy. The government™s index of leading economic indicators, which is taken to predict

the progress of the business cycle, is made up in part of recent stock market performance.

However, the predictive value of the market is far from perfect. A well-known joke, often at-

tributed to Paul Samuelson, is that the market has forecast eight of the last five recessions.

SUMMARY

• One approach to firm valuation is to focus on the firm™s book value, either as it appears on

the balance sheet or adjusted to reflect the current replacement cost of assets or the

liquidation value. Another approach is to focus on the present value of expected future

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dividends.

• The dividend discount model holds that the price of a share of stock should equal the

present value of all future dividends per share, discounted at an interest rate commensurate

with the risk of the stock.

• The constant growth version of the DDM asserts that, if dividends are expected to grow at

a constant rate forever, then the intrinsic value of the stock is determined by the formula

D1

V0

k g

This version of the DDM is simplistic in its assumption of a constant value of g. There are

more sophisticated multistage versions of the model for more complex environments.

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442 Part FOUR Security Analysis

When the constant growth assumption is reasonably satisfied, the formula can be inverted

to infer the market capitalization rate for the stock

D1

k g

P0

• Stock market analysts devote considerable attention to a company™s price“earnings ratio.

The P/E ratio is a useful measure of the market™s assessment of the firm™s growth

opportunities. Firms with no growth opportunities should have a P/E ratio that is just the

reciprocal of the capitalization rate, k. As growth opportunities become a progressively

more important component of the total value of the firm, the P/E ratio will increase.

• The models presented in this chapter can be used to explain or to forecast the behavior of

the aggregate stock market. The key macroeconomic variables that determine the level of

stock prices in the aggregate are interest rates and corporate profits.

KEY book value, 414 intrinsic value, 415 price“earnings

TERMS constant growth DDM, 418 liquidation value, 414 multiple, 428

dividend discount model market capitalization replacement cost, 414

(DDM), 417 rate, 416 Tobin™s q, 414

dividend payout ratio, 420 plowback ratio, 421 two-stage DDM, 424

earnings management, 434 present value of growth

earnings retention opportunities

ratio, 421 (PVGO), 422

PROBLEM 1. A common stock pays an annual dividend per share of $2.10. The risk-free rate is 7%

SETS and the risk premium for this stock is 4%. If the annual dividend is expected to remain

at $2.10, what is the value of the stock?

2. Which of the following assumptions does the constant growth dividend discount model

require?

a. Dividends grow at a constant rate.

b. The dividend growth rate continues indefinitely.

c. The required rate of return is less than the dividend growth rate.

3. a. Computer stocks currently provide an expected rate of return of 16%. MBI, a large

computer company, will pay a year-end dividend of $2 per share. If the stock is

selling at $50 per share, what must be the market™s expectation of the growth rate of

MBI dividends?

b. If dividend growth forecasts for MBI are revised downward to 5% per year, what

will happen to the price of MBI stock? What (qualitatively) will happen to the

company™s price“earnings ratio?

4. Explain why the following statements are true/false/uncertain.

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a. Holding all else constant, a firm will have a higher P/E if its beta is higher.

b. P/E will tend to be higher when ROE is higher (assuming plowback is positive).

c. P/E will tend to be higher when the plowback rate is higher.

5. Even Better Products has come out with a new and improved product. As a result, the

firm projects an ROE of 20%, and it will maintain a plowback ratio of 0.30. Its earnings

this year will be $2 per share. Investors expect a 12% rate of return on the stock.

a. At what price and P/E ratio would you expect the firm to sell?

b. What is the present value of growth opportunities?

c. What would be the P/E ratio and the present value of growth opportunities if the firm

planned to reinvest only 20% of its earnings?

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12 Equity Valuation

6. a. MF Corp. has an ROE of 16% and a plowback ratio of 50%. If the coming year™s

earnings are expected to be $2 per share, at what price will the stock sell? The

market capitalization rate is 12%.

b. What price do you expect MF shares to sell for in three years?

7. The constant growth dividend discount model can be used both for the valuation of

companies and for the estimation of the long-term total return of a stock.

Assume:

$20 Price of a stock today

8% Expected growth rate of dividends

$0.60 Annual dividend one year forward

a. Using only the above data, compute the expected long-term total return on the stock

using the constant growth dividend discount model. Show calculations.

b. Briefly discuss two disadvantages of the constant growth dividend discount model in

its application to investment analysis.

c. Identify two alternative methods to the dividend discount model for the valuation of

companies.

8. At Litchfield Chemical Corp. (LCC), a director of the company said that the use of

dividend discount models by investors is “proof” that the higher the dividend, the higher

the stock price.

a. Using a constant growth dividend discount model as a basis of reference, evaluate

the director™s statement.

b. Explain how an increase in dividend payout would affect each of the following

(holding all other factors constant):

i. Sustainable growth rate.

ii. Growth in book value.

9. The market consensus is that Analog Electronic Corporation has an ROE 9% and a

beta of 1.25. It plans to maintain indefinitely its traditional plowback ratio of 2/3. This

year™s earnings were $3 per share. The annual dividend was just paid. The consensus

estimate of the coming year™s market return is 14%, and T-bills currently offer a 6%

return.

a. Find the price at which Analog stock should sell.

b. Calculate the P/E ratio.

c. Calculate the present value of growth opportunities.

d. Suppose your research convinces you Analog will announce momentarily that it will

immediately reduce its plowback ratio to 1/3. Find the intrinsic value of the stock.

The market is still unaware of this decision. Explain why V0 no longer equals P0 and

why V0 is greater or less than P0.

10. If the expected rate of return of the market portfolio is 15% and a stock with a beta of

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1.0 pays a dividend yield of 4%, what must the market believe is the expected rate of

price appreciation on that stock?

11. The FI Corporation™s dividends per share are expected to grow indefinitely by 5% per

year.

a. If this year™s year-end dividend is $8 and the market capitalization rate is 10% per

year, what must the current stock price be according to the DDM?

b. If the expected earnings per share are $12, what is the implied value of the ROE on

future investment opportunities?

c. How much is the market paying per share for growth opportunities (that is, for an

ROE on future investments that exceeds the market capitalization rate)?

Bodie’Kane’Marcus: IV. Security Analysis 12. Equity Valuation © The McGraw’Hill

Essentials of Investments, Companies, 2003

Fifth Edition

444 Part FOUR Security Analysis

12. Using the data provided, discuss whether the common stock of American Tobacco