3 Assume you have a 1-year investment horizon and are trying to choose among three bonds. All have the same degree of default risk and mature in 10 years. The first is a zero-coupon bond that pays $1,000 at maturity. The second has an 7.0% coupon rate and pays the $70 coupon once per year. The third has a 8.0% coupon rate and pays the $80 coupon once per year. a. If all three bonds are now priced to yield 6% to maturity, what are their prices? (Round your answers to 2 decimal places. Omit the "$" sign in your response.) Zero Coupon 7.0% Coupon 8.0% Coupon Current prices $ $ $ ________________________________________ b. If you expect their yields to maturity to be 6% at the beginning of next year, what will their prices be then? What is your before-tax holding-period return on each bond? If your tax bracket is 30% on ordinary income and 20% on capital gains income, what will your aftertax rate of return be on each?(Round your answers to 2 decimal places. Omit the "$ & %" signs in your response.) Zero Coupon 7.0% Coupon 8.0% Coupon Current prices $ $ $ Pre-tax rate of return % % % After-tax rate of return % % % ________________________________________ c. If you expect their yields to maturity to be 5% at the beginning of next year, what will their prices be then? What is your before-tax holding-period return on each bond? If your tax bracket is 30% on ordinary income and 20% on capital gains income, what will your aftertax rate of return be on each?(Round your answers to 2 decimal places. Omit the "$ & %" signs in your response.) Zero Coupon 7.0% Coupon 8.0% Coupon Current prices $ $ $ Pre-tax rate of return % % % After-tax rate of return % % % 4 Consider a bond (with par value = $1,000) paying a coupon rate of 6% per year semiannually when the market interest rate is only 3% per half-year. The bond has 3 years until maturity. a. Find the bond's price today and 6 months from now after the next coupon is paid. (Round your answers to 2 decimal places. Omit the "$" sign in your response.) Current price $ Price after six months $ ________________________________________ b. What is the total (6-month) rate of return on the bond? (Omit the "%" sign in your response.) Rate of return % 5. Suppose that todays date is April 15. A bond with a 5.0% coupon paid semiannually every January 15 and July 15 is listed in The Wall Street Journal as selling at an ask price of 101:18. If you buy the bond from a dealer today, what price will you pay for it? (Round your answer to 2 decimal places. Omit the "$" sign in your response.) Invoice price $ 6. The term structure for zero-coupon bonds is currently: Maturity (Years) YTM (%) 1 4% 2 5 3 6 ________________________________________ Next year at this time, you expect it to be: Maturity (Years) YTM (%) 1 5% 2 6 3 7 ________________________________________ a. What do you expect the rate of return to be over the coming year on a 3-year zero-coupon bond? (Omit the "%" sign in your response.) Rate of return % b-1. Under the expectations theory, what yields to maturity does the market expect to observe on 1- and 2-year zeros at the end of the year? (Round your answers to 2 decimal places. Omit the "%" sign in your response.) Maturity YTM 1 % 2 % ________________________________________ b-2. Is the market's expectation of the return on the 3-year bond greater or less than yours? Greater Or Less 7. Prices of zero-coupon bonds reveal the following pattern of forward rates: Year Forward Rate 1 5% 2 7 3 8 ________________________________________ In addition to the zero-coupon bond, investors also may purchase a 3-year bond making annual payments of $60 with par value $1,000. a. What is the price of the coupon bond? (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the "$" sign in your response.) Price $ b. What is the yield to maturity of the coupon bond? (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the "%" sign in your response.) Yield to maturity % c. Under the expectations hypothesis, what is the expected realized compound yield of the coupon bond?(Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the "%" sign in your response.) Realized compound yield % d. If you forecast that the yield curve in 1 year will be flat at 7%, what is your forecast for the expected rate of return on the coupon bond for the 1-year holding period? (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the "%" sign in your response.) Holding period return % 8. Suppose that a 1-year zero-coupon bond with face value $100 currently sells at $94.34, while a 2-year zero sells at $84.99. You are considering the purchase of a 2-year-maturity bond making annual coupon payments. The face value of the bond is $100, and the coupon rate is 12% per year. a. What is the yield to maturity of the 2-year zero? The 2-year coupon bond? (Do not round intermediate calculations. Round your answers to 3 decimal places. Omit the "%" sign in your response.) Yield to Maturity 2-year zero % 2-year coupon bond % ________________________________________ b. What is the forward rate for the second year? (Do not round intermediate calculations and rounded to whole number. Omit the "%" sign in your response.) Forward rate % c. If the expectations hypothesis is accepted, what are (1) the expected price of the coupon bond at the end of the first year and (2) the expected holding-period return on the coupon bond over the first year?(Do not round intermediate calculations. Round your answers to 2 decimal places. Omit the "$" & "%" signs in your response.) Expected price $ Holding-period return % ________________________________________ d. Will the expected rate of return be higher or lower if you accept the liquidity preference hypothesis? Higher Or lower 9. An insurance company must make payments to a customer of $10 million in 1 year and $4 million in 5 years. The yield curve is flat at 10%. a. If it wants to fully fund and immunize its obligation to this customer with a single issue of a zero-coupon bond, what maturity bond must it purchase? (Do not round intermediate calculations. Round your answer to 4 decimal places.) Maturity of zero coupon bond years b. What must be the face value and market value of that zero-coupon bond? (Do not round intermediate calculations. Enter your answers in millions rounded to 2 decimal places. Omit the "$" sign in your response.) Face value $ Market value $ 10. ou will be paying $10,000 a year in tuition expenses at the end of the next 2 years. Bonds currently yield 8%. a. What is the present value and duration of your obligation? (Do not round intermediate calculations. Round "Present value" to 2 decimal places and "Duration" to 4 decimal places. Omit the "$" sign in your response.) Present value $ Duration years ________________________________________ b. What maturity zero-coupon bond would immunize your obligation? (Do not round intermediate calculations. Round "Duration" to 4 decimal places and "Face value" to 2 decimal places. Omit the "$" sign in your response.) Duration years Face value $ ________________________________________ Suppose you buy a zero-coupon bond with value and duration equal to your obligation. c-1. Now suppose that rates immediately increase to 9%. What happens to your net position, that is, to the difference between the value of the bond and that of your tuition obligation? (Do not round intermediate calculations. Input the amount as a positive value. Round your answer to 2 decimal places. Omit the "$" sign in your response.) Net position(increase or decrease?) in value by $ c-2. Now suppose that rates immediately falls to 7%. What happens to your net position, that is, to the difference between the value of the bond and that of your tuition obligation? (Do not round intermediate calculations. Input the amount as a positive value. Round your answer to 2 decimal places. Omit the "$" sign in your response.) Net position (increase or decrease?) in value by $ 11. A 30-year maturity bond has a 7% coupon rate, paid annually. It sells today for $867.42. A 20-year maturity bond has 6.5% coupon rate, also paid annually. It sells today for $879.50. A bond market analyst forecasts that in 5 years, 25-year maturity bonds will sell at yields to maturity of 8% and 15-year maturity bonds will sell at yields of 7.5%. Because the yield curve is upward sloping, the analyst believes that coupons will be invested in short-term securities at a rate of 6%. Which bond offers the higher expected rate of return over the 5-year period? (Round your answer to 2 decimal places. Omit the "%" sign in your response.) Rate of Return 30 yr bond % 20 yr bond % ________________________________________