Homework

15. A 10-year German government bond (bund) has a face value of €100 and a coupon rate of 5% paid annually. Assume that the interest rate (in euros) is equal to 6% per year. What is the bond’s PV?

16. A 10-year U.S. Treasury bond with a face value of $10,000 pays a coupon of 5.5% (2.75% of face value every six months). The semi-annually compounded interest rate is 5.2% (a six-month discount rate of 5.2/2 2.6%).

a . What is the present value of the bond?

b . Generate a graph or table showing how the bond’s present value changes for semi-annually compounded interest rates between 1% and 15%.

17. A six-year government bond makes annual coupon payments of 5% and offers a yield of 3% annually compounded. Suppose that one year later the bond still yields 3%. What return has the bondholder earned over the 12-month period? Now suppose that the bond yields 2% at the end of the year. What return would the bondholder earn in this case?

21. Calculate durations and modified durations for the 4% coupon bond and the strip in Table 3.1. The answers for the strip will be easy. For the 4% bond, you can follow the procedure set out in T able 3.3 for the 11¼% coupon bonds. Confirm that modified duration predicts the impact of a 1% change in interest rates on the bond prices.

23. The formula for the duration of a perpetual bond that makes an equal payment each year in perpetuity is (1 yield)/yield. If each bond yields 5%, which has the longer duration—a perpetual bond or a 15-year zero-coupon bond? What if the yield is 10%?

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