Prof. Thomas J. Chemmanur s1

Prof. Thomas J. Chemmanur MF807 Corporate Finance

Problem Set - II

Valuing Bonds

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

2. Look again at Problem 1. Suppose that the German bund paid interest semiannually like a U.S. bond. (The bond would pay .025 x 100 = €2.5 every six months.) What is the PV in this case?

3. 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 semiannually 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%.

4. Suppose that five-year government bonds are selling on a yield of 4%. Value a five-year bond with a 6% coupon. Start by assuming that the bond is issued by a continental European government and makes annual coupon payments. Then rework your answer assuming that the bond is issued by the U.S. Treasury, that the bond pays semiannual coupons, and the yield refers to a semiannually compounded rate.

5. Refer again to Problem 4. How would the bond value in each case change if interest rates fall to 3%? 6. 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?

7. A 6% six-year bond yields 12% and a 10% six-year bond yields 8%. Calculate the six-year spot rate. Assume annual coupon payments. Hint: What would be your cash flows if you bought 1.2 10% bonds?

8. Is the yield on high-coupon bonds more likely to be higher than that on low- coupon bonds when the term structure is upward-sloping or when it is downward-sloping? Explain.