Question

Bond valuation and yield to maturity  Mark Goldsmith’s 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 Mark’s 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?

Answer 1

a) Selling Price of Bond A = 60/1.12+60/1.12^2+...+60/1.12^5+1000/1.12^5

= 60/0.12*(1-1/1.12^5) +1000/1.12^5

=$783.71  

Selling Price of Bond B = 140/1.12+140/1.12^2+...+140/1.12^5+1000/1.12^5

= 140/0.12*(1-1/1.12^5) +1000/1.12^5

=$1072.10

b)

From $20000, no of Bonds A that can be purchased = 20000/783.71 = 25.52

From $20000, no of Bonds B that can be purchased = 20000/1072.10 = 18.66

c) If Bonds A are purchased , yearly interest income = 25.52*$60 = $1531.17

If Bonds B are purchased , yearly interest income = 18.66*$140 = $2611.71

d) Value of Mark’s reinvestment account at the end of the 5 years for purchase of Bond A

=1531.17*(1.1^4+1.1^3+1.1^2+1.1+1) + 1000* 25.52

= 1531.17*(1.1^5-1)/0.1 + 1000*25.52

= $34867.49

Value of Mark’s reinvestment account at the end of the 5 years for purchase of Bond B

=2611.71*(1.1^4+1.1^3+1.1^2+1.1+1) + 1000* 18.66

= 2611.71*(1.1^5-1)/0.1 + 1000*18.66

= $34599.79

e) The two values are different because of the reinvestment risk. As the reinvestment rate is less than YTM, the higher coupon bond (Bond B) is more affected by this risk, resulting in a lesser realised value at the end of maturity period. Similarly, Bond B will benefit more in case reinvestment rate is more than YTM.

If Mark were worried that he would earn less than the 12% yield to maturity on the reinvested interest payments, Mark should go for investment in Bond A as it has lesser reinvestment risk.Bond A therefore is better choice