8-15. Suppose you purchase a 30-year Treasury bond with a 5% annual coupon, initially trading at par. In 10 years’ time, the bond’s yield to maturity has risen to 7% (EAR).
a. If you sell the bond now, what internal rate of return will you have earned on your investment in the bond?
b. If instead you hold the bond to maturity, what internal rate of return will you earn on your investment in the bond?
c. Is comparing the IRRs in (a) versus (b) a useful way to evaluate the decision to sell the bond? Explain.
8-16. Suppose the current yield on a one-year, zero coupon bond is 3%, while the yield on a five-year, zero coupon bond is 5%. Neither bond has any risk of default. Suppose you plan to invest for one year. You will earn more over the year by investing in the five-year bond as long as its yield does not rise above what level?
8-17. What is the price today of a two-year, default-free security with a face value of $1000 and an annual coupon rate of 6%? Does this bond trade at a discount, at par, or at a premium?
8-18. What is the price of a five-year, zero-coupon, default-free security with a face value of $1000?
8-19. What is the price of a three-year, default-free security with a face value of $1000 and an annual coupon rate of 4%? What is the yield to maturity for this bond?
8-20. What is the maturity of a default-free security with annual coupon payments and a yield to maturity of 4%? Why?
8-21. Consider a four-year, default-free security with annual coupon payments and a face value of $1000 that is issued at par. What is the coupon rate of this bond?
8-22. Consider a five-year, default-free bond with annual coupons of 5% and a face value of $1000.
a. Without doing any calculations, determine whether this bond is trading at a premium or at a discount. Explain.
b. What is the yield to maturity on this bond?
c. If the yield to maturity on this bond increased to 5.2%, what would the new price be?
8-23. Prices of zero-coupon, default-free securities with face values of $1000 are summarized in the following table:
Suppose you observe that a three-year, default-free security with an annual coupon rate of 10% and a face value of $1000 has a price today of $1183.50. Is there an arbitrage opportunity? If so, show specifically how you would take advantage of this opportunity. If not, why not?
8-24. Assume there are four default-free bonds with the following prices and future cash flows:
Do these bonds present an arbitrage opportunity? If so, how would you take advantage of this opportunity? If not, why not?
8-25. Suppose you are given the following information about the default-free, coupon-paying yield curve:
a. Use arbitrage to determine the yield to maturity of a two-year, zero-coupon bond.
b. What is the zero-coupon yield curve for years 1 through 4?
8-26. Explain why the expected return of a corporate bond does not equal its yield to maturity.
8-27. Grummon Corporation has issued zero-coupon corporate bonds with a five-year maturity. Investors believe there is a 20% chance that Grummon will default on these bonds. If Grummon does default, investors expect to receive only 50 cents per dollar they are owed. If investors require a 6% expected return on their investment in these bonds, what will be the price and yield to maturity on these bonds?
8-28. The following table summarizes the yields to maturity on several one-year, zero-coupon securities:
a. What is the price (expressed as a percentage of the face value) of a one-year, zero-coupon corporate bond with a AAA rating?
b. What is the credit spread on AAA-rated corporate bonds?
c. What is the credit spread on B-rated corporate bonds?
d. How does the credit spread change with the bond rating? Why?
8-29. Andrew Industries is contemplating issuing a 30-year bond with a coupon rate of 7% (annual coupon payments) and a face value of $1000. Andrew believes it can get a rating of A from Standard and Poor’s. However, due to recent financial difficulties at the company, Standard and Poor’s is warning that it may downgrade Andrew Industries bonds to BBB. Yields on A-rated, long-term bonds are currently 6.5%, and yields on BBB-rated bonds are 6.9%.
a. What is the price of the bond if Andrew maintains the A rating for the bond issue?
b. What will the price of the bond be if it is downgraded?
8-30. HMK Enterprises would like to raise $10 million to invest in capital expenditures. The company plans to issue five-year bonds with a face value of $1000 and a coupon rate of 6.5% (annual payments). The following table summarizes the yield to maturity for five-year (annualpay) coupon corporate bonds of various ratings:
a. Assuming the bonds will be rated AA, what will the price of the bonds be?
b. How much total principal amount of these bonds must HMK issue to raise $10 million today, assuming the bonds are AA rated? (Because HMK cannot issue a fraction of a bond, assume that all fractions are rounded to the nearest whole number.)
c. What must the rating of the bonds be for them to sell at par?
d. Suppose that when the bonds are issued, the price of each bond is $959.54. What is the likely rating of the bonds? Are they junk bonds?
8-31. A BBB-rated corporate bond has a yield to maturity of 8.2%. A U.S. Treasury security has a yield to maturity of 6.5%. These yields are quoted as APRs with semiannual compounding. Both bonds pay semiannual coupons at a rate of 7% and have five years to maturity.
a. What is the price (expressed as a percentage of the face value) of the Treasury bond?
b. What is the price (expressed as a percentage of the face value) of the BBB-rated corporate bond?
c. What is the credit spread on the BBB bonds?
Problems A.1–A.4 refer to the following table:
A.1. What is the forward rate for year 2 (the forward rate quoted today for an investment that begins in one year and matures in two years)?
A.2. What is the forward rate for year 3 (the forward rate quoted today for an investment that begins in two years and matures in three years)? What can you conclude about forward rates when the yield curve is flat?
A.3. What is the forward rate for year 5 (the forward rate quoted today for an investment that begins in four years and matures in five years)?
A.4. Suppose you wanted to lock in an interest rate for an investment that begins in one year and matures in five years. What rate would you obtain if there are no arbitrage opportunities?
A.5. Suppose the yield on a one-year, zero-coupon bond is 5%. The forward rate for year 2 is 4%, and the forward rate for year 3 is 3%. What is the yield to maturity of a zero-coupon bond that matures in three years?
Lecture Seven - Valuing Stocks
9-1. Assume Evco, Inc., has a current price of $50 and will pay a $2 dividend in one year, and its equity cost of capital is 15%. What price must you expect it to sell for right after paying the dividend in one year in order to justify its current price?
9-2. Anle Corporation has a current price of $20, is expected to pay a dividend of $1 in one year, and its expected price right after paying that dividend is $22.
a. What is Anle’s expected dividend yield?
b. What is Anle’s expected capital gain rate?
c. What is Anle’s equity cost of capital?
9-3. Suppose Acap Corporation will pay a dividend of $2.80 per share at the end of this year and $3 per share next year. You expect Acap’s stock price to be $52 in two years. If Acap’s equity cost of capital is 10%:
a. What price would you be willing to pay for a share of Acap stock today, if you planned to hold the stock for two years?
b. Suppose instead you plan to hold the stock for one year. What price would you expect to be able to sell a share of Acap stock for in one year?
c. Given your answer in part (b), what price would you be willing to pay for a share of Acap stock today, if you planned to hold the stock for one year? How does this compare to you answer in part (a)?
9-4. Krell Industries has a share price of $22 today. If Krell is expected to pay a dividend of $0.88 this year, and its stock price is expected to grow to $23.54 at the end of the year, what is Krell’s dividend yield and equity cost of capital?
9-5. NoGrowth Corporation currently pays a dividend of $2 per year, and it will continue to pay this dividend forever. What is the price per share if its equity cost of capital is 15% per year?
9-6. Summit Systems will pay a dividend of $1.50 this year. If you expect Summit’s dividend to grow by 6% per year, what is its price per share if its equity cost of capital is 11%?
9-7. Dorpac Corporation has a dividend yield of 1.5%. Dorpac’s equity cost of capital is 8%, and its dividends are expected to grow at a constant rate.
a. What is the expected growth rate of Dorpac’s dividends?
b. What is the expected growth rate of Dorpac’s share price?
9-8. Kenneth Cole Productions (KCP), suspended its dividend at the start of 2009. Suppose you do not expect KCP to resume paying dividends until 2011.You expect KCP’s dividend in 2011 to be $0.40 per year (paid at the end of the year), and you expect it to grow by 5% per year thereafter. If KCP’s equity cost of capital is 11%, what is the value of a share of KCP at the start of 2009?
9-9. DFB, Inc., expects earnings this year of $5 per share, and it plans to pay a $3 dividend to shareholders. DFB will retain $2 per share of its earnings to reinvest in new projects with an expected return of 15% per year. Suppose DFB will maintain the same dividend payout rate, retention rate, and return on new investments in the future and will not change its number of outstanding shares.
a. What growth rate of earnings would you forecast for DFB?
b. If DFB’s equity cost of capital is 12%, what price would you estimate for DFB stock?
c. Suppose DFB instead paid a dividend of $4 per share this year and retained only $1 per share in earnings. If DFB maintains this higher payout rate in the future, what stock price would you estimate now? Should DFB raise its dividend?
9-10. Cooperton Mining just announced it will cut its dividend from $4 to $2.50 per share and use the extra funds to expand. Prior to the announcement, Cooperton’s dividends were expected to grow at a 3% rate, and its share price was $50. With the new expansion, Cooperton’s dividends are expected to grow at a 5% rate. What share price would you expect after the announcement? (Assume Cooperton’s risk is unchanged by the new expansion.) Is the expansion a positive NPV investment?
9-11. Gillette Corporation will pay an annual dividend of $0.65 one year from now. Analysts expect this dividend to grow at 12% per year thereafter until the fifth year. After then, growth will level off at 2% per year. According to the dividend-discount model, what is the value of a share of Gillette stock if the firm’s equity cost of capital is 8%?
9-12. Colgate-Palmolive Company has just paid an annual dividend of $0.96. Analysts are predicting an 11% per year growth rate in earnings over the next five years. After then, Colgate’s earnings are expected to grow at the current industry average of 5.2% per year. If Colgate’s equity cost of capital is 8.5% per year and its dividend payout ratio remains constant, what price does the dividend-discount model predict Colgate stock should sell for?
9-13. What is the value of a firm with initial dividend Div, growing for nyears (i.e., until year n+ 1) at rate g1 and after that at rate g2 forever, when the equity cost of capital is r?
9-14. Halliford Corporation expects to have earnings this coming year of $3 per share. Halliford plans to retain all of its earnings for the next two years. For the subsequent two years, the firm will retain 50% of its earnings. It will then retain 20% of its earnings from that point onward. Each year, retained earnings will be invested in new projects with an expected return of 25% per year. Any earnings that are not retained will be paid out as dividends. Assume Halliford’s share count remains constant and all earnings growth comes from the investment of retained earnings. If Halliford’s equity cost of capital is 10%, what price would you estimate for Halliford stock?
9-15. Suppose Cisco Systems pays no dividends but spent $5 billion on share repurchases last year. If Cisco’s equity cost of capital is 12%, and if the amount spent on repurchases is expected to grow by 8% per year, estimate Cisco’s market capitalization. If Cisco has 6 billion shares outstanding, what stock price does this correspond to?
9-16. Maynard Steel plans to pay a dividend of $3 this year. The company has an expected earnings growth rate of 4% per year and an equity cost of capital of 10%.
a. Assuming Maynard’s dividend payout rate and expected growth rate remains constant, and Maynard does not issue or repurchase shares, estimate Maynard’s share price.
b. Suppose Maynard decides to pay a dividend of $1 this year and use the remaining $2 per share to repurchase shares. If Maynard’s total payout rate remains constant, estimate Maynard’s share price.
c. If Maynard maintains the dividend and total payout rate given in part (b), at what rate are Maynard’s dividends and earnings per share expected to grow?
9-17. Benchmark Metrics, Inc. (BMI), an all-equity financed firm, just reported EPS of $5.00 per share for 2008. Despite the economic downturn, BMI is confident regarding its current investment opportunities. But due to the financial crisis, BMI does not wish to fund these investments externally. The Board has therefore decided to suspend its stock repurchase plan and cut its dividend to $1 per share (vs. almost $2 per share in 2007), and retain these funds instead. The firm has just paid the 2008 dividend, and BMI plans to keep its dividend at $1 per share in 2009 as well. In subsequent years, it expects its growth opportunities to slow, and it will still be able to fund its growth internally with a target 40% dividend payout ratio, and reinitiating its stock repurchase plan for a total payout rate of 60%. (All dividends and repurchases occur at the end of each year.)
Suppose BMI’s existing operations will continue to generate the current level of earnings per share in the future. Assume further that the return on new investment is 15%, and that reinvestments will account for all future earnings growth (if any). Finally, assume BMI’s equity cost of capital is 10%.
a. Estimate BMI’s EPS in 2009 and 2010 (before any share repurchases).
b. What is the value of a share of BMI at the start of 2009?
9-18. Heavy Metal Corporation is expected to generate the following free cash flows over the next five years:
After then, the free cash flows are expected to grow at the industry average of 4% per year. Using the discounted free cash flow model and a weighted average cost of capital of 14%:
a. Estimate the enterprise value of Heavy Metal.
b. If Heavy Metal has no excess cash, debt of $300 million, and 40 million shares outstanding, estimate its share price.
9-19. IDX Technologies is a privately held developer of advanced security systems based in Chicago. As part of your business development strategy, in late 2008 you initiate discussions with IDX’s founder about the possibility of acquiring the business at the end of 2008. Estimate the value of IDX per share using a discounted FCF approach and the following data:
? Debt: $30 million
? Excess cash: $110 million
? Shares outstanding: 50 million
? Expected FCF in 2009: $45 million
? Expected FCF in 2010: $50 million
? Future FCF growth rate beyond 2010: 5%
? Weighted-average cost of capital: 9.4%
9-21. Consider the valuation of Kenneth Cole Productions in Example 9.7.
a. Suppose you believe KCP’s initial revenue growth rate will be between 4% and 11% (with growth slowing in equal steps to 4% by year 2011). What range of share prices for KCP is consistent with these forecasts?
b. Suppose you believe KCP’s EBIT margin will be between 7% and 10% of sales. What range of share prices for KCP is consistent with these forecasts (keeping KCP’s initial revenue growth at 9%)?
c. Suppose you believe KCP’s weighted average cost of capital is between 10% and 12%. What range of share prices for KCP is consistent with these forecasts (keeping KCP’s initial revenue growth and EBIT margin at 9%)?
d. What range of share prices is consistent if you vary the estimates as in parts (a), (b), and (c) simultaneously?
9-22. You notice that PepsiCo has a stock price of $52.66 and EPS of $3.20. Its competitor, the Coca-Cola Company, has EPS of $2.49. Estimate the value of a share of Coca-Cola stock using only this data.
9-23. Suppose that in January 2006, Kenneth Cole Productions had EPS of $1.65 and a book value of equity of $12.05 per share.
a. Using the average P/E multiple in Table 9.1, estimate KCP’s share price.
b. What range of share prices do you estimate based on the highest and lowest P/E multiples in Table 9.1?
c. Using the average price to book value multiple in Table 9.1, estimate KCP’s share price.
d. What range of share prices do you estimate based on the highest and lowest price to book value multiples in Table 9.1?