Question

13. Tom Cruise Lines, Inc., issued bonds five years ago at $1,000 per bond. These bonds had a 25-year life when issued and the annual interest payment was then 12 percent. This return was in line with the required returns by bondholders at that point as described below: Real rate of return Inflation premium Risk premium Total return 3% 5 4 12% Assume that five years later the inflation premium is only 3 percent and is appro- priately reflected in the required return (or yield to maturity) of the bonds. The bonds have 20 years remaining until maturity. Compute the new price of the bond. 14. Further analysis of Problem 13. Find the present value of 2 percent X $1,000 (or $20) for 20 years at 10 percent. The $20 is assumed to be an annual payment. b. Add this value to $1,000. Explain why the answers to problem 14b and problem 13 are basically the same. (There is a slight difference due to rounding in the table C. 15

Answer 1

13). Bonds were originally issued at par value of $1,000 which means that the coupon rate was same as the bond yield. Now, 5 years later, bond yield becomes 12% - 2% = 10% (as inflation premium decreases from 5% to 3%).

FV (par value) = 1,000; PMT (annual coupon) = coupon rate*par value = 12%*1,000 = 120; N (number of payments pending) = 20; rate (YTM) = 10%, solve for PV.

Bond price = 1,170.27

14a). PV of 2% of 1,000 for 20 years at 10% discount rate (using PV of annuity formula) becomes

20*(1-(1+10%)^-20)/10% = 170.27

b). 170.27 + 1,000 = 1,170.27

c). Answers are same because in both cases, the same bond price is being calculated. In Ans.13, we use the fact that bond price is the sum of all discounted future cash flows. Whereas in Ans.14b, we use the fact that the bond price has to equal the par value plus the present value of reduction in inflation premium p.a. for 20 years which adds to the value of the bond.