Question 1. Top hedge fund manager Diana Sauros believes that a stock with the same market risk as the S&P 500 will sell at yearend at a price of $58. The stock will pay a dividend at yearend of $3.00. Assume that risk free Treasury securities currently offer an interest rate of 1.7%.
Average rates of return on Treasury bills, government bonds, and common stocks, 1900-2013 (figures in percent per year) are as follows.
Portfolio Average Annual Rate of Return Average Premium (Extra return versus Treasury bills)
Treasury bills 3.9
Treasury bonds 5.2 1.3
Common stocks 11.5 7.6
What is the discount rate on the stock?
What price should she be willing to pay for the stock today?
Question 2: A stock is selling today for $80 per share. At the end of the year, it pays a dividend of $4 per share and sells for $88.
a. What is the total rate of return on the stock?
b. What are the dividend yield and percentage capital gain?
c. Now suppose the yearend stock price after the dividend is paid is $72. What are the dividend yield and percentage capital gain in this case?
d. Is there any change in the dividend yield calculated in parts (b) and (c)?
Question 3: You purchase 100 shares of stock for $50 a share. The stock pays a $2 per share dividend at yearend.
a. What is the rate of return on your investment if the endofyear stock price is (i) $48; (ii) $50; (iii) $55?
b. What is your real (inflationadjusted) rate of return if the inflation rate is 3%?
Question 4: Consider the following scenario analysis:
Rate of Return
Scenario Probability Stocks Bonds
Recession .20 -8% 16%
Normal economy .50 19 9
Boom .30 25 6
a. Is it reasonable to assume that Treasury bonds will provide higher returns in recessions than in booms?
Yes No
b. Calculate the expected rate of return and standard deviation for each investment.
Part -2:
1. Investors expect the market rate of return this year to be 15%. A stock with a beta of 1.1 has an expected rate of return of 16%. If the market return this year turns out to be 10%, what is the rate of return on the stock?
2. You are considering acquiring a firm that you believe can generate expected cash flows of $22,000 a year forever. However, you recognize that those cash flows are uncertain.
a. Suppose you believe that the beta of the firm is 1.6. How much is the firm worth if the riskfree rate is 4% and the expected rate of return on the market portfolio is 8%?
b. By how much will you overvalue the firm if its beta is actually 1.8?
3. The riskfree rate is 6% and the expected rate of return on the market portfolio is 10%.
a. Calculate the required rate of return on a security with a beta of 1.24.
b. If the security is expected to return 16%, is it overpriced or underpriced?
4. A share of stock with a beta of .77 now sells for $52. Investors expect the stock to pay a yearend dividend of $4. The Tbill rate is 4%, and the market risk premium is 7%. If the stock is perceived to be fairly priced today, what must be investors' expectation of the price of the stock at the end of the year?
5. A share of stock with a beta of .79 now sells for $61. Investors expect the stock to pay a yearend dividend of $3. The Tbill rate is 6%, and the market risk premium is 9%.
a. Suppose investors believe the stock will sell for $63 at yearend. Is the stock a good or bad buy? What will investors do?
The stock is a buy and the investors .
b. At what price will the stock reach an "equilibrium" at which it is perceived as fairly priced today?
6. We Do Bankruptcies is a law firm that specializes in providing advice to firms in financial distress. It
prospers in recessions when other firms are struggling. Consequently, its beta is negative, -.2.
a. If the interest rate on Treasury bills is 4% and the expected return on the market portfolio is 19%, what is the expected return on the shares of the law firm according to the CAPM? (Enter your answer as a whole percent.)
Expected return %
b. Suppose you invested 90% of your wealth in the market portfolio and the remainder of your wealth in the shares in the law firm. What would be the beta of your portfolio?
Part -3:
1. In 2013 Caterpillar Inc. had about 645 million shares outstanding. Their book value was $40 per share, and the market price was $82.00 per share. The company's balance sheet shows that the company had $27.5 billion of longterm debt, which was currently selling near par value.
a. What was Caterpillar's book debttovalue ratio?
b. What was its market debttovalue ratio?
c. Which measure should you use to calculate the company's cost of capital?
2. Olympic Sports has two issues of debt outstanding. One is a 9% coupon bond with a face value of $40 million, a maturity of 15 years, and a yield to maturity of 10%. The coupons are paid annually. The other bond issue has a maturity of 20 years, with coupons also paid annually, and a coupon rate of 10%. The face value of the issue is $45 million, and the issue sells for 95% of par value. The firm's tax rate is 30%.
a. What is the beforetax cost of debt for Olympic?
b. What is Olympic's aftertax cost of debt?
3. Pangbourne Whitchurch has preferred stock outstanding. The stock pays a dividend of $7 per share, and sells for $70. What is the percentage cost of the preferred stock?
4. Reliable Electric is a regulated public utility, and it is expected to provide steady dividend growth of 6% per year for the indefinite future. Its last dividend was $5 per share; the stock sold for $40 per share just after the dividend was paid. What is the company's cost of equity?
5. Reactive Industries has the following capital structure.
Security Market Value
Required Rate of Return
Debt $30 million 2%
Preferred stock 30 million 4
Common stock 40 million 8
Its corporate tax rate is 35%.
What is its WACC?
6. Icarus Airlines is proposing to go public, and you have been given the task of estimating the value of its equity. Management plans to maintain debt at 31% of the company's present value, and you believe that at this capital structure the company's debtholders will demand a return of 5% and stockholders will require 12%. The company is forecasting that next year's operating cash flow (depreciation plus profit after tax at 40%) will be $69 million and that investment expenditures will be $31 million. Thereafter, operating cash flows and investment expenditures are forecast to grow in perpetuity by 4% a year.
a. What is the total value of Icarus?
b. What is the value of the company's equity?