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What can we learn from all of this about the future rate of return on stocks? First, a note of optimism. Although timing the stock market is a very difficult and risky game, it may not be impossible. For example, we saw in Chapter 12 that some variables such as the market dividend yield seem to predict market returns.

However, if market history teaches us anything at all, it is that the market has great variability. Thus, although we can use a variety of methods to derive a best forecast of the expected holding-period return on the market, the uncertainty surrounding that forecast will always be high.

The most popular approach to forecasting the overall stock market is the earnings multiplier approach applied at the aggregate level. The first step is to forecast corporate profits for the coming period. Then we derive an estimate of the earnings multiplier, the aggregate P/E ratio, 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 18.8, 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 Treasury 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 distortions 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 mid-2000 forecast for 2001 earnings per share for the S&P 500 portfolio was about $65.66.14 The 10-year Treasury bond yield was about 5.8%. Because the earnings yield on the 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 4.8%. This would imply a P/E ratio of 1/.048 = 20.83. Our forecast for the S&P 500 index would then be 20.83 X 65.66 = 1,368.

Of course, there is uncertainty regarding all three inputs into this analysis: the actual earnings on the S&P 500 stocks, the level of Treasury yields at year end, and the spread between 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 Table 18.4, which shows a simple scenario analysis treating possible effects of variation in the Treasury bond yield. The scenario analysis shows that forecasted level of the stock market varies inversely and with dramatic sensitivity to interest rate changes.

Some analysts use an aggregate version of the dividend discount model rather than an earnings 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 economic fortunes of firms, it is not surprising that the performance of a broad-based stock

14 According to Institutional Brokers Estimate System (I/B/E/S) as of September 2000. I/B/E/S surveys a large sample of stock analysts and reports several analyses of their forecasts for both the economy and individual stocks.

PART V Security Analysis

Table 18.4 S&P 500 Price Forecasts under Various Scenarious

PART V Security Analysis

Table 18.4 S&P 500 Price Forecasts under Various Scenarious

Most Likely Scenario |
Pessimistic Scenario |
Optimistic Scenario | |

Treasury bond yield |
5.8% |
6.3% |
5.3% |

Earnings yield |
4.8% |
5.3% |
4.3% |

Resulting P/E ratio |
20.83 |
18.87 |
23.26 |

EPS forecast |
$ 65.66 |
$ 65.66 |
$ 65.66 |

Forecast for S&P 500 |
1,368 |
1,239 |
1,527 |

Forecast for the earnings yield on the S&P 500 equals Treasury bond yield minus 1%. The P/E ratio is the reciprocal of the forecasted earnings yield.

Forecast for the earnings yield on the S&P 500 equals Treasury bond yield minus 1%. The P/E ratio is the reciprocal of the forecasted earnings yield.

index like the S&P 500 is taken as a leading economic indicator, that is, a predictor of the performance 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 attributed to Paul Samuelson, is that the market has forecast eight of the last five recessions.

1. One approach to firm valuation is to focus on the firm's book value, either as it appears on the balance sheet or as adjusted to reflect current replacement cost of assets or liquidation value. Another approach is to focus on the present value of expected future dividends.

2. 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.

3. The constant-growth version of the DDM asserts that if dividends are expected to grow at a constant rate forever, the intrinsic value of the stock is determined by the formula

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. When the constant-growth assumption is reasonably satisfied and the stock is selling for its intrinsic value, the formula can be inverted to infer the market capitalization rate for the stock:

Pn g

Stock market analysts devote considerable attention to a company's price-to-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.

5. The expected growth rate of earnings is related both to the firm's expected profitability and to its dividend policy. The relationship can be expressed as g = (ROE on new investment) X (1 - Dividend payout ratio)

6. You can relate any DDM to a simple capitalized earnings model by comparing the expected ROE on future investments to the market capitalization rate, k. If the two rates are equal, then the stock's intrinsic value reduces to expected earnings per share (EPS) divided by k.

7. Many analysts form their estimate of a stock's value by multiplying their forecast of next year's EPS by a P/E multiple derived from some empirical rule. This rule can be consistent with some version of the DDM, although often it is not.

8. The free cash flow approach is the one used most often in corporate finance. The analyst first estimates the value of the entire firm as the present value of expected future free cash flows, assuming all-equity financing, then adds the value of tax shields arising from debt financing, and finally subtracts the value of all claims other than equity. This approach will be consistent with the DDM and capitalized earnings approaches as long as the capitalization rate is adjusted to reflect financial leverage.

9. We explored the effects of inflation on stock prices in the context of the constant-growth DDM. Although traditional theory has been that inflation should have a neutral effect on real stock returns, historical evidence shows a striking negative correlation between inflation and real stock market returns. There are four different explanations that may account for this negative correlation:

a. Economic "shocks" that simultaneously produce high inflation and lower real earnings.

b. Increased riskiness of stocks in a more inflationary environment.

c. Lower real after-tax earnings and dividends attributable to inflation-induced distortions in the tax system.

d. Money "illusion."

10. The models presented in this chapter can be used to explain and 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 TERMS

book value liquidation value replacement cost Tobin's q intrinsic value market capitalization rate dividend discount model

(DDM) constant-growth DDM dividend payout ratio plowback ratio earnings retention ratio present value of growth opportunities price-earnings multiple

Information on earnings announcements and other material announcements can be found at the sites listed below.

http://streetevents.ccbn.com http://earningswhispers.com

Several websites make it possible to listen in on conference calls surrounding earnings announcements. Several of these sites are listed below.

WEBSITES

http://www.investorbroadcast.com

WEBSITES |
A quick source for finding specific company information can be found on the Motley |

Fool Web Resource List. | |

http://www.fool.com/community/resource/company research.htm | |

Some of these websites provide stock screeners. | |

PROBLEMS

A common stock pays an annual dividend per share of $2.10. The risk-free rate is 7%, and the risk premium for this stock is 4%. If the annual dividend is expected to remain at $2.10, the value of the stock is closest to:

Which of the following assumptions does the constant-growth dividend discount model require?

I. Dividends grow at a constant rate.

II. The dividend growth rate continues indefinitely.

III. The required rate of return is less than the dividend growth rate. I only. III only. I and II only. I, II and III.

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?

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?

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?

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.

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6. The market consensus is that Analog Electronic Corporation has an ROE = 9%, has a beta of 1.25, and 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.

7. If the expected rate of return of the market portfolio is 15% and a stock with a beta of 1.0 pays a dividend yield of 4%, what must the market believe is the expected rate of price appreciation on that stock?

8. 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 (i.e., for an ROE on future investments that exceeds the market capitalization rate)?

9. Imelda Emma, a financial analyst at Del Advisors, Inc. (DAI), has been asked to assess the impact that construction of Disney's new theme parks might have on its stock. DAI uses a dividend discount valuation model that incorporates beta in the derivation of risk-adjusted required rates of return on stocks.

Until now, Emma has been using a five-year earnings and dividends per share growth rate of 15% and a beta estimate of 1.00 for Disney. Taking construction of the new theme parks into account, however, she has raised her growth rate and beta estimates to 25% and 1.15, respectively. The complete set of Emma's current assumptions is:

Current stock price $37.75

Beta 1.15

Risk-free rate of return (T-bill) 4.0%

Required rate of return on the market 10.0%

Short-term growth rate (five years) for earnings and dividends 25.0%

Long-term growth rate (beyond five years) for earnings and dividends 9.3%

Dividend forecast for 1994 (per share) $.287

a. Calculate the risk-adjusted required rate of return on Disney stock using Emma's current beta assumption.

b. Using the results of part (a), Emma's current assumptions, and DAI's dividend discount model, calculate the intrinsic, or fair, value of Disney stock at September 30, 1993.

c. After calculating the intrinsic value of Disney stock using her new assumptions and DAI's dividend discount model, Emma finds that her recommendation for Disney should be changed from a "buy" to a "sell." Explain how the construction of the new theme parks could have a negative impact on the valuation of Disney stock, despite Emma's assumption of sharply higher growth rates (25%).

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10. The risk-free rate of return is 10%, the required rate of return on the market is 15%, and High-Flyer stock has a beta coefficient of 1.5. If the dividend per share expected during the coming year, D1, is $2.50 and g = 5%, at what price should a share sell?

11. Your preliminary analysis of two stocks has yielded the information set forth below. The market capitalization rate for both Stock A and Stock B is 10% per year.

Stock A |
Stock B | |

Expected return on equity, ROE |
14% |
12% |

Estimated earnings per share, E, |
$ 2.00 |
$ 1.65 |

Estimated dividends per share, D, |
$ 1.00 |
$ 1.00 |

Current market price per share, P0 |
$27.00 |
$25.00 |

a. What are the expected dividend payout ratios for the two stocks?

b. What are the expected dividend growth rates of each?

c. What is the intrinsic value of each stock?

d. In which, if either, of the two stocks would you choose to invest?

12. Phoebe Black's investment club wants to buy the stock of either NewSoft Inc. or Capital Corp. In this connection, Black prepared the following table. You have been asked to help her interpret the data, based on your forecast for a healthy economy and a strong stock market over the next 12 months.

NewSoft Inc. |
Capital Corp. |
S&P 500 Index | |

Current price |
$30 |
$32 | |

Industry |
Computer software |
Capital goods | |

P/E ratio (current) |
25 |
14 |
16 |

P/E ratio | |||

(5-year average) |
27 |
16 |
16 |

P/B ratio (current) |
10 |
3 |
3 |

P/B ratio | |||

(5-year average) |
12 |
4 |
2 |

Beta |
1.5 |
1.1 |
1.0 |

Dividend yield |
.3% |
2.7% |
2.8% |

a. Newsoft's shares have higher price-earnings (P/E) and price-book value (P/B) ratios than those of Capital Corp. (The price-book ratio is the ratio of market value to book value.) Briefly discuss why the disparity in ratios may not indicate that NewSoft's shares are overvalued relative to the shares of Capital Corp. Answer the question in terms of the two ratios, and assume that there have been no extraordinary events affecting either company.

b. Using a constant-growth dividend discount model, Black estimated the value of NewSoft to be $28 per share and the value of Capital Corp. to be $34 per share. Briefly discuss weaknesses of this dividend discount model and explain why this model may be less suitable for valuing NewSoft than for valuing Capital Corp.

c. Recommend and justify a more appropriate dividend discount model for valuing NewSoft's common stock.

"Growth" and "value" can be defined in several ways, but "growth" usually conveys the idea of a portfolio emphasizing or including only issues believed to possess above-

CHAPTER 18 Equity Valuation Models average future rates of per-share earnings growth. Low current yield, high price-to-book ratios, and high price-to-earnings ratios are typical characteristics of such portfolios.

"Value" usually conveys the idea of portfolios emphasizing or including only issues currently showing low price-to-book ratios, low price-to-earnings ratios, above-average levels of dividend yield, and market prices believed to be below the issues' intrinsic values.

a. Identify and explain three reasons why, over an extended period of time, value stock investing might outperform growth stock investing.

b. Explain why the outcome suggested in part (a) above should not be possible in a market widely regarded as being highly efficient.

14. The stock of Nogro Corporation is currently selling for $10 per share. Earnings per share in the coming year are expected to be $2. The company has a policy of paying out 50% of its earnings each year in dividends. The rest is retained and invested in projects that earn a 20% rate of return per year. This situation is expected to continue indefinitely.

a. Assuming the current market price of the stock reflects its intrinsic value as computed using the constant-growth DDM, what rate of return do Nogro's investors require?

b. By how much does its value exceed what it would be if all earnings were paid as dividends and nothing were reinvested?

c. If Nogro were to cut its dividend payout ratio to 25%, what would happen to its stock price? What if Nogro eliminated the dividend?

15. Chiptech, Inc., is an established computer chip firm with several profitable existing products as well as some promising new products in development. The company earned $1 a share last year, and just paid out a dividend of $.50 per share. Investors believe the company plans to maintain its dividend payout ratio at 50%. ROE equals 20%. Everyone in the market expects this situation to persist indefinitely.

a. What is the market price of Chiptech stock? The required return for the computer chip industry is 15%, and the company has just gone ex-dividend (i.e., the next dividend will be paid a year from now, at t = 1).

b. Suppose you discover that Chiptech's competitor has developed a new chip that will eliminate Chiptech's current technological advantage in this market. This new product, which will be ready to come to the market in two years, will force Chiptech to reduce the prices of its chips to remain competitive. This will decrease ROE to 15%, and, because of falling demand for its product, Chiptech will decrease the plowback ratio to .40. The plowback ratio will be decreased at the end of the second year, at t = 2: The annual year-end dividend for the second year (paid at t = 2) will be 60% of that year's earnings. What is your estimate of Chiptech's intrinsic value per share? (Hint: Carefully prepare a table of Chiptech's earnings and dividends for each of the next three years. Pay close attention to the change in the payout ratio in t = 2.)

c. No one else in the market perceives the threat to Chiptech's market. In fact, you are confident that no one else will become aware of the change in Chiptech's competitive status until the competitor firm publicly announces its discovery near the end of year 2. What will be the rate of return on Chiptech stock in the coming year (i.e., between t = 0 and t = 1)? In the second year (between t = 1 and t = 2)? The third year (between t = 2 and t = 3)? (Hint: Pay attention to when the market catches on to the new situation. A table of dividends and market prices over time might help.)

16. The risk-free rate of return is 8%, the expected rate of return on the market portfolio is 15%, and the stock of Xyrong Corporation has a beta coefficient of 1.2. Xyrong pays out 40% of its earnings in dividends, and the latest earnings announced were $10 per

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V. Security Analysis

18. Equity and Valuation Models

© The McGraw-Hill Companies, 2001

PART V Security Analysis share. Dividends were just paid and are expected to be paid annually. You expect that Xyrong will earn an ROE of 20% per year on all reinvested earnings forever.

a. What is the intrinsic value of a share of Xyrong stock?

b. If the market price of a share is currently $100, and you expect the market price to be equal to the intrinsic value one year from now, what is your expected one-year holding-period return on Xyrong stock?

17. Janet Ludlow's firm requires all its analysts to use a two-stage dividend discount model (DDM) and the Capital Asset Pricing Model (CAPM) to value stocks. Using the CAPM and DDM, Ludlow has valued QuickBrush Company at $63 per share. She now must value SmileWhite Corporation.

a. Calculate the required rate of return for SmileWhite using the information in the following table:

QuickBrush |
SmileWhite | |

Beta |
1.35 |
1.15 |

Market price |
$45.00 |
$30.00 |

Intrinsic value |
$63.00 |
? |

Notes: | ||

Risk-free rate |
4.50% | |

Expected market return |
14.50% |

b. Ludlow estimates the following EPS and dividend growth rates for SmileWhite:

First three years: |
12% per year |

Years thereafter: |
9% per year |

Estimate the 1999 intrinsic value of SmileWhite using the table above, and the two-stage DDM. Dividends per share in 1999 were $1.72.

c. Recommend QuickBrush or SmileWhite stock for purchase by comparing each company's intrinsic value with its current market price.

d. Describe one strength of the two-stage DDM in comparison with the constant-growth DDM. Describe one weakness inherent in all DDMs.

18. The Digital Electronic Quotation System (DEQS) Corporation pays no cash dividends currently and is not expected to for the next five years. Its latest EPS was $10, all of which was reinvested in the company. The firm's expected ROE for the next five years is 20% per year, and during this time it is expected to continue to reinvest all of its earnings. Starting six years from now the firm's ROE on new investments is expected to fall to 15%, and the company is expected to start paying out 40% of its earnings in cash dividends, which it will continue to do forever after. DEQS's market capitalization rate is 15% per year.

a. What is your estimate of DEQS's intrinsic value per share?

b. Assuming its current market price is equal to its intrinsic value, what do you expect to happen to its price over the next year? The year after?

c. What effect would it have on your estimate of DEQS's intrinsic value if you expected DEQS to pay out only 20% of earnings starting in year 6?

19. At year-end 1991, the Wall Street consensus was that Philip Morris's earnings and dividends would grow at 20% for five years, after which growth would fall to a marketlike 7%. Analysts also projected a required rate of return of 10% for the U.S. equity market.

Bodie-Kane-Marcus: Investments, Fifth Edition

V. Security Analysis

18. Equity and Valuation Models

© The McGraw-Hill Companies, 2001

CHAPTER 18 Equity Valuation Models a. Using the data in the accompanying table and the multistage dividend discount model, calculate the intrinsic value of Philip Morris stock at year-end 1991. Assume a similar level of risk for Philip Morris stock as for the typical U.S. stock.

b. Using the data in the accompanying table, calculate Philip Morris's price-earnings ratio and the price-earnings ratio relative to the S&P 500 Stock Index as of December 31, 1991.

c. Using the data in the accompanying table, calculate Philip Morris's price-book ratio (i.e., ratio of market value to book value) and the price-book ratio relative to the S&P 500 Stock Index as of December 31, 1991.

Philip Morris Corporation Selected Financial Data Years Ending December 31 ($ millions except per share data) | ||

1991 |
1981 | |

Earnings per share |
$4.24 |
$0.66 |

Dividends per share |
$1.91 |
$0.25 |

Stockholders' equity |
12,512 |
3,234 |

Total liabilities and stockholders' equity |
$47,384 |
$9,180 |

Other data | ||

Philip Morris | ||

Common shares outstanding (millions) |
920 |
1,003 |

Closing price common stock |
$80.250 |
$6.125 |

S&P 500 Stock Index: | ||

Closing price |
417.09 |
122.55 |

Earnings per share |
16.29 |
15.36 |

Book value per share |
161.08 |
109.43 |

20. a. State one major advantage and one major disadvantage of each of the three valua tion methodologies you used to value Philip Morris in the previous problem. b. State whether Philip Morris stock is undervalued or overvalued as of December 31, 1991. Support your conclusion using your answers to previous questions and any data provided. (The past 10-year average S&P 500 Stock Index relative price-earnings and price-book ratios for Philip Morris were .80 and 1.61, respectively.)

21. The Duo Growth Company just paid a dividend of $1 per share. The dividend is expected to grow at a rate of 25% per year for the next three years and then to level off to 5% per year forever. You think the appropriate market capitalization rate is 20% per year.

a. What is your estimate of the intrinsic value of a share of the stock?

b. If the market price of a share is equal to this intrinsic value, what is the expected dividend yield?

c. What do you expect its price to be one year from now? Is the implied capital gain consistent with your estimate of the dividend yield and the market capitalization rate?

22. The Generic Genetic (GG) Corporation pays no cash dividends currently and is not expected to for the next four years. Its latest EPS was $5, all of which was reinvested in the company. The firm's expected ROE for the next four years is 20% per year, during which time it is expected to continue to reinvest all of its earnings. Starting five years from now, the firm's ROE on new investments is expected to fall to 15% per year. GG's market capitalization rate is 15% per year.

Bodie-Kane-Marcus: Investments, Fifth Edition

V. Security Analysis

18. Equity and Valuation Models

© The McGraw-Hill Companies, 2001

PART V Security Analysis a. What is your estimate of GG's intrinsic value per share?

b. Assuming its current market price is equal to its intrinsic value, what do you expect to happen to its price over the next year?

23. The MoMi Corporation's cash flow from operations before interest and taxes was $2 million in the year just ended, and it expects that this will grow by 5% per year forever. To make this happen, the firm will have to invest an amount equal to 20% of pretax cash flow each year. The tax rate is 34%. Depreciation was $200,000 in the year just ended and is expected to grow at the same rate as the operating cash flow. The appropriate market capitalization rate for the unleveraged cash flow is 12% per year, and the firm currently has debt of $4 million outstanding. Use the free cash flow approach to value the firm's equity.

24. The CPI Corporation is expected to pay a real dividend of $1 per share this year. Its expected growth rate of real dividends is 4% per year, and its current market price per share is $20.

a. Assuming the constant-growth DDM is applicable, what must be the real market capitalization rate for CPI?

b. If the expected rate of inflation is 6% per year, what must be the nominal capitalization rate, the nominal dividend yield, and the growth rate of nominal dividends?

c. If the expected real earnings per share are $1.80, what would be your estimate of intrinsic value if you used a simple capitalized earnings model?

25. The following questions are from past CFA examinations.

a. The constant-growth DDM will not produce a finite value if the dividend growth rate is:

i. Above its historical average.

ii. Above the market capitalization rate.

iii. Below its historical average.

iv. Below the market capitalization rate.

b. According to the constant-growth DDM, a fall in the market capitalization rate will cause a stock's intrinsic value to:

i. Decrease.

ii. Increase.

iii. Remain unchanged.

iv. Decrease or increase, depending on other factors.

c. You plan to buy a common stock and hold it for one year. You expect to receive both $1.50 in dividends and $26 from the sale of stock at the end of the year. If you wanted to earn a 15% return, what is the maximum price you would pay for the stock today?

d. In the dividend discount model, a factor not affecting the discount rate, k, is the:

i. Real risk-free rate.

ii. Risk premium for stocks.

iii. Return on assets.

iv. Expected inflation rate.

e. A share of stock is expected to pay a dividend of $1.00 one year from now and grow at 5% thereafter. In the context of a dividend discount model, the stock is correctly priced today at $10. According to the single-stage, constant-growth DDM, if the required return is 15%, what should be the value of the stock two years from now?

f. A stock is not expected to pay dividends until three years from now. The dividend is then expected to be $2.00 per share, the dividend payout ratio is expected to be 40%, and the return on equity is expected to be 15%. If the required rate of return is 12%, what should be the value of the stock today?

CHAPTER 18 Equity Valuation Models g. The constant-growth DDM would typically be most appropriate in valuing the stock of a:

i. New venture expected to retain all earnings for several years.

ii. Rapidly growing company.

iii. Moderate-growth, "mature" company.

iv. Company with valuable assets not yet generating profits.

h. A stock has a required return of 15%, a constant-growth rate of 10%, and a dividend payout ratio of 45%. The stock's price-earnings ratio should be:

Capital gains yield = (59.77 - 50)/50 = 19.54%. Total return = 4.3% + 19.54% = 23.84%.

c. V0 = ($2.15 + $59.77)/1.152 = $53.75, which exceeds the market price. This would indicate a "buy" opportunity.

c. The expected capital gain equals $59.77 - $53.75 = $6.02, for a percentage gain of 11.2%. The dividend yield is D1/P0 = 2.15/53.75 = 4%, for a holding-period return of 4% + 11.2% = 15.2%.

3. g = ROE X b = 20% X .60 = 12%. D1 = .4 X E1 = .4 X $5 = $2.

PVGO = P0 - E1/k = 400 - 5/.125 = 360. PVGO represents an extremely high fraction of the total value of the firm. This is because the assumed dividend growth rate, 12%, is nearly as high as the discount rate, 12.5%. The assumption that the growth rate can remain so close to the discount rate for an indefinitely long period represents an extremely optimistic (and probably unrealistic) view of the long-term growth prospects of the firm.

4. Given current management's investment policy, the dividend growth rate will be g = ROE X b = 10% X .6 = 6%

and the stock price should be

The present value of growth opportunities is

PVGO = Price per share - No-growth value per share = $22.22 - E1/k = $22.22 - $5/.15 = -$11.11

SOLUTIONS TO CONCEPT CHECKS

PART V Security Analysis

SOLUTIONS TO CONCEPT CHECKS

PVGO is negative. This is because the net present value of the firm's projects is negative: The rate of return on those assets is less than the opportunity cost of capital.

Such a firm would be subject to takeover, because another firm could buy the firm for the market price of $22.22 per share and increase the value of the firm by changing its investment policy. For example, if the new management simply paid out all earnings as dividends, the value of the firm would increase to its no-growth value, E1/k = $5/.15 = $33.33.

Now compute the sales price in 2004 using the constant-growth dividend discount model. The growth rate will be g = ROE X b = 15% X .91 = 13.65%.

$159.11

b = $.50/$2.00 = .25. g = ROE X b = 12% X .25 = 3%. P0 = D1/(k - g) = $1.50/(.10 - .03) = $21.43. P0/E1 = $21.43/$2.00 = 10.71. b. If b = .4, then .4 X $2 = $.80 would be reinvested and the remainder of earnings, or $1.20, would be paid as dividends. g = 12% X .4 = 4.8%.

P0 = D1/(k - g) = $1.20/(.10 - .048) = $23.08. P0/E1 = $23.08/$2.00 = 11.54. (1 - b)E1 .6 X $1

P0 P0

06, or 6% per year. The rate of price

iii.

.1024

ROE .166

Go to the MoneyCentral Investor page at the address listed below. Use the Research Wizard function to obtain fundamentals, price history, price target, catalysts, and comparison for EMC Corporation (EMC). For comparison, use Network Appliance Inc. (NTAP) and Silicon Storage (SSTI).

1. What has been the one-year sales and income growth for EMC?

CHAPTER 18 Equity Valuation Models

E-INVESTMENTS:

EQUITY

VALUATION

2. What has been the company's five-year profit margin percentage? How does that compare with the comparison firms?

3. What have been the percentage price changes for the last 3, 6 and 12 months? How do they compare with the comparison firms?

4. What is the estimated high and low price for EMC for the coming year using EMC's current P/E multiple?

5. Compare the price performance of EMC with NTAP and SSTI. Which of the companies appears to be the most expensive in terms of current earnings? Which of the companies is the least expensive in terms of current earnings?

http://moneycentral.msn.com/investor/home.asp

Bodie-Kane-Marcus: I V. Security Analysis I 19. Financial Statement I I © The McGraw-Hill

Investments, Fifth Edition Analysis Companies, 2001

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