Financial management(BSM-410) problem solving 5
6-1 YIELD CURVES Assume that yields on U.S. Treasury securities were as follows: A. B. C. D. Plot a yield curve based on these data. What type of yield curve is shown? What information does this graph tell you? Based on this yield curve, if you needed to borrow money for longer than 1 year, would it make sense for you to borrow short term and renew the loan or borrow long term? Explain. 6-3 EXPECTED INTEREST RATE The real risk-free rate is 2.25%. Inflation is expected to be 2.5% this year and 4.25% during the next 2 years. Assume that the maturity risk premium is zero. What is the yield on 2-year Treasury securities? What is the yield on 3-year Treasury securities? 6-8 EXPECTATIONS THEORY Interest rates on 4-year Treasury securities are currently 6.7%, while 6-year Treasury securities yield 7.25%. If the pure expectations theory is correct, what does the market believe that 2-year securities will be yielding 4 years from now? Calculate the yield using a geometric average. 6-19 INFLATION AND INTEREST RATES In late 1980, the U.S. Commerce Department released new data showing inflation was 15%. At the time, the prime rate of interest was 21%, a record high. However, many investors expected the new Reagan administration to be more effective in controlling inflation than the Carter administration had been. Moreover, many observers believed that the extremely high interest rates and generally tight credit, which resulted from the Federal Reserve System’s attempts to curb the inflation rate, would lead to a recession, which, in turn, would lead to a decline in inflation and interest rates. Assume that, at the beginning of 1981, the expected inflation rate for 1981 was 13%; for 1982, 9%; for 1983, 7%; and for 1984 and thereafter, 6%. A. What was the average expected inflation rate over the 5-year period 1981–1985? (Use the arithmetic average.) B. Over the 5-year period, what average nominal interest rate would be expected to produce a 2% real risk-free return on 5-year Treasury securities? Assume MRP = 0 . C. Assuming a real risk-free rate of 2% and a maturity risk premium that equals 0.1 × (t)%, where t is the number of years to maturity, estimate the interest rate in January 1981 on bonds that mature in 1, 2, 5, 10, and 20 years. Draw a yield curve based on these data. D. Describe the general economic conditions that could lead to an upward-sloping yield curve. E. If investors in early 1981 expected the inflation rate for every future year to be 10% (i.e., I t = I t + 1 = 10 % for t = 1 to ∞), what would the yield curve have looked like? Consider all the factors that are likely to affect the curve. Does your answer here make you question the yield curve you drew in part c? 7-2 YIELD TO MATURITY AND FUTURE PRICE A bond has a $1,000 par value, 12 years to maturity, and an 8% annual coupon and sells for $980. A. 7-2 YIELD TO MATURITY AND FUTURE PRICE A bond has a $1,000 par value, 12 years to maturity, and an 8% annual coupon and sells for $980. B. Assume that the yield to maturity remains constant for the next three years. What will the price be 3 years from today? 7-6 BOND VALUATION An investor has two bonds in her portfolio, Bond C and Bond Z. Each bond matures in 4 years, has a face value of $1,000, and has a yield to maturity of 8.2%. Bond C pays an 11.5% annual coupon, while Bond Z is a zero coupon bond. A. Assuming that the yield to maturity of each bond remains at 8.2% over the next 4 years, calculate the price of the bonds at each of the following years to maturity: B. Plot the time path of prices for each bond. 7-19 BOND VALUATION Clifford Clark is a recent retiree who is interested in investing some of his savings in corporate bonds. His financial planner has suggested the following bonds: • • • Bond A has a 7% annual coupon, matures in 12 years, and has a $1,000 face value. Bond B has a 9% annual coupon, matures in 12 years, and has a $1,000 face value. Bond C has an 11% annual coupon, matures in 12 years, and has a $1,000 face value. Each bond has a yield to maturity of 9%. A. Before calculating the prices of the bonds, indicate whether each bond is trading at a premium, at a discount, or at par. B. Calculate the price of each of the three bonds. C. Calculate the current yield for each of the three bonds. (Hint: Refer to footnote 6 for the definition of the current yield and to Table 7.1.) D. If the yield to maturity for each bond remains at 9%, what will be the price of each bond 1 year from now? What is the expected capital gains yield for each bond? What is the expected total return for each bond? E. Mr. Clark is considering another bond, Bond D. It has an 8% semiannual coupon and a $1,000 face value (i.e., it pays a $40 coupon every 6 months). Bond D is scheduled to mature in 9 years and has a price of $1,150. It is also callable in 5 years at a call price of $1,040. 1. What is the bond’s nominal yield to maturity? 2. What is the bond’s nominal yield to call? 3. If Mr. Clark were to purchase this bond, would he be more likely to receive the yield to maturity or yield to call? Explain your answer. F. Explain briefly the difference between price risk and reinvestment risk. Which of the following bonds has the most price risk? Which has the most reinvestment risk? 1. A 1-year bond with a 9% annual coupon 2. A 5-year bond with a 9% annual coupon 3. A 5-year bond with a zero coupon 4. A 10-year bond with a 9% annual coupon 5. A 10-year bond with a zero coupon
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