4. A bond currently sells for $1,050, which gives it a yield to maturity of 6%. Suppose that if the yield inereases by 25 basis points, the price of the bond falls to $1,025. What is the modified duration of this bond? ( LO 11-2) 9. A ninesear bond has a yield of 10% and a duration of 7.194 years. If the bond's yield ehanges by 50 basis points, what is the percentage change in the bond's price? ( LO 112 ) 11. If the plan in the previous problem wants to fully fund and immunize its position, how much of its portfolio should it allocate to one-year zero-coupon bonds and perpetuities, respectively, if these are the only two assets funding the plan? ( LO (11-4) 12. You own a fixed-income asset with a duration of five years. If the level of interest rates, which is currently 8%, goes down by 10 basis points, how much do you expect the price of the asset to go up (in percentage terms)? ( LO II-2) 15. You will be paying $10,000 a year in tuition expenses at the end of the next two years. Bonds currently yield 8%. ( O (12) 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 9%. What happens to your net position, that is, to the difference between the value of the bond and that of your tuition obligation? d. What if rates fall to 7% ? 22. You manage a pension fund that will provide retired workers with lifetime annuities. You determine that the payouts of the fund are going to closely resemble level perpetuities of $1 million per year. The interest rate is 10%. You plan to fully fund the obligation using 5-year and 20-year maturity zero-coupon bonds. ( 11 -2) a. How much market value of each of the zeros will be necessary to fund the plan if you desire an immunized position? b. What must be the face value of each of the two zeros to fund the plan? 28. A 30-year maturity bond has a 7% coupon fate, paid annually. It sells today for $867.42. A 20 -year maturity bond has a 6.5% coupon rate, also paid annually. It sells today for $879.50. A bond market analyst forecasts that in five years, 25 year maturity bonds will sell at yields to maturity of 8s and that 15 -year maturity bonds will sell at yields of 7.5%. Because the yield curve is upward-sloping, the analyst believes that coupons can be invested in short-term securities at a rate of 6%. a. Calculate the expected rate of return of the 30 year bond over the fiveyear period. b. What is the expected return of the 20-year bond? (\$ LO 115 ) 2. Altria has issued bonds that pay annually with the following characteristics: ( OH2 ) a. Calculate modified duration using the information above. b. Explain why modified duration is a better measure than maturity when calculating the bond's sensitivity to changes in interest rates. c. Identify the direction of change in modified duration if: i. The coupon of the bond were 4%, not 8%. ii. The maturity of the bond were 7 years, not 15 years. 8. The ability to immunize a bond portfolio is very desirable for bond portfolio managers in some instances. LO(I4) a. Discuss the components of interest rate risk-that is, assuming a change in interest rates over time, explain the two risks faced by the holder of a bond. b. Define immunization and discuss why a bond manager would immunize his or her portfolio. c. Explain why a duration-matching strategy is a superior technique to a maturity-matching strategy for the minimization of interest rate risk