Mark Goldsmiths broker has shown him two bonds. Each has a maturity of 5 years,

Question

Mark Goldsmiths broker has shown him two bonds. Each has a maturity of 5 years, a par value of $1,000, and a yield to maturity of 12%. Bond A has a coupon interest rate of 6% paid annually. Bond B has a coupon interest rate of 14% paid annually.
a. Calculate the selling price for each of the bonds.
b. Mark has $20,000 to invest. Judging on the basis of the price of the bonds, how many of either one could Mark purchase if he were to choose it over the other? (Mark cannot really purchase a fraction of a bond, but for purposes of this question, pretend that he can.)
c. Calculate the yearly interest income of each bond on the basis of its coupon rate and the number of bonds that Mark could buy with his $20,000.
d. Assume that Mark will reinvest the interest payments as they are paid (at the end of each year) and that his rate of return on the reinvestment is only 10%. For each bond, calculate the value of the principal payment plus the value of Marks reinvestment account at the end of the 5 years.
e. Why are the two values calculated in part d different? If Mark were worried that he would earn less than the 12% yield to maturity on the reinvested interest payments, which of these two bonds would be a better choice?

Explanation / Answer

Bond A Bond B N 5 5 FV 1000 1000 Coupon 6% 14% YTM 12% 12% a ) Price of Bond A Price of Bond B $783.71 $1,072.10 b)               25.52                                     18.66 c) $    1,531.17 $                           2,611.71 d) T Reinvestment Account T Reinvestment Account Bond-A Reinvestment Account Bond-A Reinvestment Account 1 60 87.846 1 140 204.974 2 60 79.86 2 140 186.34 3 60 72.6 3 140 169.4 4 60 66 4 140 154 5 60 60 5 140 140 FV 1000 1000 FV 1000 1000 Total      1,366.31 Total    1,854.71 Annual Geometric Return 11.76% 11.59% ($783.71) ($1,072.10) 60 140 60 140 60 140 60 140 1060 1140 MIRR 11.76% 11.59% Alternatively we could calculate the FV of the coupon payments with 10% interest assumption. In this case: BOND A FV of Coupons BOND B FV of Coupons Coupon 60 Coupon 140 I 10% I 10% N 5 N 5 FV of Coupons $366.31 FV of Coupons $854.71 Face Value         1,000.00 Face Value 1000 Value at T=5 $1,366.31 Value at T=5 $1,854.71 e) The difference in the realized rate can be attributed to a key assumption in the bond yield. In the bond pricing formula, we assume that we will be able to reinvest the coupon receipts at 12% or at the rate of YTM. If this turns out to be the case, our internal rate of return in our bond investment is 12%. But if the coupon receipts are reinvested at lower rates than 10%, the actual yield as we calculated above will be lower. Between two bonds, the one that pays higher coupon rate is more sensitive to reinvestment rate. Therefore the geometric average return (or IRR with the realized cash flows) turned out to be lower than the bond that pays on 6% coupon.

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