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P/E Ratios

Castles in the Sand generates a rate of return of 20 percent on its investments and maintains a plowback ratio of .30. Its earnings this year will be $2 per share. Investors expect a 12 percent rate of return on the stock.

a. Find the price and P/E ratio of the firm.

b. What happens to the P/E ratio if the plowback ratio is reduced to .20? Why?

c. Show that if plowback equals zero, the earnings-price ratio E/P falls to the expected rate of return on the stock.

24. Dividend Growth. Grandiose Growth has a dividend growth rate of 20 percent. The discount rate is 10 percent. The end-of-year dividend will be $2 per share.

a. What is the present value of the dividend to be paid in Year 1? Year 2? Year 3?

b. Could anyone rationally expect this growth rate to continue indefinitely?

25. Stock Valuation. Start-up Industries is a new firm which has raised $100 million by selling shares of stock. Management plans to earn a 24 percent rate of return on equity, which is more than the 15 percent rate of return available on comparable-risk investments. Half of all earnings will be reinvested in the firm.

a. What will be Start-up s ratio of market value to book value?

b. How would that ratio change if the firm can earn only a 10 percent rate of return on its investments?

26. Nonconstant Growth. Planned Obsolescence has a product that will be in vogue for 3 years, at which point the firm will close up shop and liquidate the assets. As a result, forecasted dividends are DIV1 = $2, DIV2 = $2.50, and DIV3 = $18. What is the stock price if the discount

rate is 12 percent?

27. Nonconstant Growth. Tattletale News Corp. has been growing at a rate of 20 percent per year, and you expect this growth rate in earnings and dividends to continue for another 3 years.

a. If the last dividend paid was $2, what will the next dividend be?

b. If the discount rate is 15 percent and the steady growth rate after 3 years is 4 percent, what should the stock price be today?

28. Nonconstant Growth. Reconsider Tattletale News from the previous problem.

a. What is your prediction for the stock price in 1 year?

b. Show that the expected rate of return equals the discount rate.

29. Sustainable Growth. Computer Corp. reinvests 60 percent of its earnings in the firm. The stock sells for $50, and the next dividend will be $2.50 per share. The discount rate is 15 percent. What is the rate of return on the company s reinvested funds?

30. Nonconstant Growth. A company will pay a $1 per share dividend in 1 year. The dividend in 2 years will be $2 per share, and it is expected that dividends will grow at 5 percent per year thereafter. The expected rate of return on the stock is 12 percent.

a. What is the current price of the stock?

b. What is the expected price of the stock in a year?

c. Show that the expected return, 12 percent, equals dividend yield plus capital appreciation.

31. Nonconstant Growth. Phoenix Industries has pulled off a miraculous recovery. Four years ago it was near bankruptcy. Today, it announced a $1 per share dividend to be paid a year from now, the first dividend since the crisis. Analysts expect dividends to increase by $1 a year for another 2 years. After the third year (in which dividends are $3 per share) dividend growth is expected to settle down to a more moderate long- term growth rate of 6 percent. If the firm s investors expect to earn a return of 14 percent on this stock, what must be its price?

32. Nonconstant Growth. Compost Science, Inc. (CSI), is in the business of converting Boston s sewage sludge into fertilizer. The business is not in itself very profitable. However, to induce CSI to remain in business, the Metropolitan District Commission (MDC) has agreed to pay whatever amount is necessary to yield CSI a 10 percent return on investment. At the end of the year, CSI is expected to pay a $4 dividend. It has been reinvesting 40 percent of earnings and growing at 4 percent a year.

a. Suppose CSI continues on this growth trend. What is the expected rate of return from purchasing the stock at $100?

b. What part of the $100 price is attributable to the present value of growth opportunities?

c. Now the MDC announces a plan for CSI to treat Cambridge sewage. CSI s plant will therefore be expanded gradually over 5 years. This means that CSI will have to reinvest 80 percent of its earnings for 5 years. Starting in Year 6, however, it will again be able to pay out 60 percent of earnings. What will be CSI s stock price once this announcement is made and its consequences for CSI are known?

33. Nonconstant Growth. Better Mousetraps has come out with an improved product, and the world is beating a path to its door. As a result, the firm projects growth of 20 percent per year for 4 years. By then, other firms will have copycat technology, competition will drive down profit margins, and the sustainable growth rate will fall to 5 percent. The most recent annual dividend was DIV0 = $1.00 per share.

a. What are the expected values of DIV1, DIV2, DIV3, and DIV4?

b. What is the expected stock price 4 years from now? The discount rate is 10 percent.

c. What is the stock price today?

d. Find the dividend yield, DIV1/P0.

e. What will next year s stock price, P1, be?

f. What is the expected rate of return to an investor who buys the stock now and sells it in 1 year?