1. Suppose the yield on short-term government securities (perceived to be risk-free) is about 3%. Suppose also that the expected return required by the market for a portfolio with a beta of 1 is 13.5%. According to the capital asset pricing model:
a. What is the expected return on the market portfolio?
b. What would be the expected return on a zero-beta stock?
c. Suppose you consider buying a share of stock at a price of $41. The stock is expected to pay a dividend of $2 next year and to sell then for $43. The stock risk has been evaluated at beta = -.5. Is the stock overpriced or underpriced?
2. Suppose there are two independent economic factors, M1 and M2. The risk-free rate is 5%, and all stocks have independent firm-specific components with a standard deviation of 50%. Portfolios A and B are both well diversified.
Portfolio Beta on M 1 Beta on M 2 Expected Return (%)
A 1.9 2.6 44
B 2.2 21.5 14
What is the expected return-beta relationship in this economy?
3. Consider a bond paying a coupon rate of 9% per year semiannually when the market interest rate is only 6%. The bond has five years until maturity.
a. Find the bond's price today and six months from now after the next coupon is paid.
b. What is the total rate of return on the bond?
4. Consider a firm that pays no dividends. Next year's earnings are projected to be $1,500,000. The present value of growth opportunities is estimated to be $13,500,000. Suppose that there are 250,000 shares outstanding. If investors require a return of 12 percent, what is the fair value of the company's stock (Find the price per share)?
5. Suppose the risk-free rate is 4%. Suppose that the expected market risk premium is 5%, the excess return of a stock for a small firm over that of a stock for a large firm is 3%, the excess return of a stock for a firm with a high book-market value over that of a stock for a firm with a high book-market value is 4%. Suppose that company XYZ has the following exposures:
Market factor: 1.2
Size factor: .7
Book-market factor: .9
Find the expected return for Stock XYZ.
6. A 30-year bond of a firm in severe financial distress has a coupon rate of 12% and sells for $940. The firm is currently renegotiating the debt, and it appears that the lenders will allow the firm to reduce coupon payments on the bond to one-half the originally contracted amount. The firm can handle these lower payments. What are the stated and expected yields to maturity of the bonds? The bond makes its coupon payments annually?
7. A common stock pays an annual dividend per share of $2.20. The risk-free rate is 4% and the risk premium for this stock is 5%. If the annual dividend is expected to remain at $2.20, what is the value of the stock?
8. Suppose that today's date is May 14, 2014. A Treasury bond with a 4¼ % coupon paid semiannually every January 15 and July 15 is listed in The Wall Street Journal as selling at an ask price of 102-4+. If you buy the bond from a dealer today,
a. What is clean (list or quoted) price?
b. What is the accrued interest?
c. What is dirty (full or invoice) price?
d. What is the ask yield?
e. What is your expected overall return on this investment?
9. A 30-year maturity bond with par value $1,000 makes semiannual coupon payments at a coupon rate of 12%. Find the bond equivalent and effective annual yield to maturity of the bond if the bond price is:
10. A 30-year maturity, 10% coupon bond paying coupons semiannually is callable in ten years at a call price of $1,100. The bond currently sells at a yield to maturity of 8%.
a. What is the yield to call?
b. What is the yield to call if the call price is only $1,050?
c. What is the yield to call if the call price is $1,100 but the bond can be called in five years instead of ten years?
11. 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 .25. Its earnings this year will be $2.10 per share. Investors expect a 10% 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?
12. Consider an 9% coupon bond selling for $950 with 4 years until maturity making annual coupon payments. The interest rates in the next four years will be, with certainty, r1=8%, r2=9%, r3=12%, and r4=14%.
a. Calculate the yield to maturity of the bond.
b. Calculate the realized compound yield of the bond.
c. Explain why the realized compound yield is different form the yield to maturity computed in part (a).
13. Consider a 10% 10-year bond with a yield to maturity of 8 percent.
a. Find its Macaulay duration.
b. Find its modified duration.
c. If the yield increases by 25 basis points, find:
i. The exact percentage change in the price of the bond.
ii. The approximate percentage change in the price of the bond.
14. You will be paying $34,000 a year in tuition expenses at the end of the next two years. Bonds currently yield 10%.
a. What is the present value and duration of your obligation?
b. What maturity zero-coupon bond would immunize your obligation?
c. Suppose you buy a zero-coupon bond with value and duration equal to your obligation. Now suppose that rates immediately increase to 11%. What happens to your net position, that is, to the difference between the value of the bond and that of your tuition obligation? What if rates fall to 9%?
15. FinCorp's free cash flow to the firm is reported as $206 million. The firm's interest expense is $21 million. Assume the tax rate is 34% and the net debt of the firm increases by $3 million. What is the market value of equity if the FCFE is projected to grow at 3.5% indefinitely and the cost of equity is 8%?
16. You are managing a portfolio of $2 million. Your target duration is 15 years, and you can choose from two bonds: a zero-coupon bond with maturity 10 years, and a perpetuity, each currently yielding 10%.
a. How much of each bond will you hold in your portfolio?
b. How will these fractions change next year if target duration is now 14 years.
17. A 30-year maturity bond making annual coupon payments with a coupon rate of 12% has duration of 11.54 years and convexity of 192.4. The bond currently sells at a yield to maturity of 8%.
a. Find the price of the bond if its yield to maturity falls to 7.5% or rises to 8.5%.
b. What prices for the bond at these new yields would be predicted by the duration rule?
c. What prices for the bond at these new yields would be predicted by the duration-with-convexity rule?
d. What is the percent error for each rule?
e. What do you conclude about the accuracy of the two rules?
18. What must be the beta of a portfolio with expected return of 25%, if the risk-free rate is 4% and the expected market return is 16%?
19. Consider the following table, which gives a security analyst's expected return on two Market Return Aggressive Stock Defensive Stock
6% 3% 5.5%
22 34 16
a. What are the betas of the two stocks?
b. What is the expected rate of return on each stock if the market return is equally likely to be 6% or 22%?
c. If the T-bill rate is 5%, and the market return is equally likely to be 6% or 22%, draw the SML for this economy.
d. Plot the two securities on the SML graph. What are the alphas of each?
e. What hurdle rate should be used by the management of the aggressive firm for a project with the risk characteristics of the defensive firm's stock?