Question

Gustavo Fring, a seasoned businessman, has a lot of liquidity (cash) at his disposal. Accordingly, he decides to invest some of his earnings in a fixed income security. He has two Bonds to choose from. Each has a maturity of 5 years, a par value of $500, and a yield to maturity of 15%. Bond A has a coupon interest rate of 5% paid annually. Bond B has a coupon interest rate of 10% paid annually. a. Calculate the price of both the bonds. b. Gustavo will be investing 10,000 USD. Approximately how many of each of the two bonds could Gustavo purchase? c. Calculate the yearly interest income of each bond based on its coupon rate and the number of bonds that Gustavo could buy with his $10,000. d. Assume that Gustavo 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 8%. For each bond, calculate the value of the principal payment plus the value of Gustavo’s reinvestment account at the end of the 5 years. 3 e. Why are the two values calculated in part d different? If Gustavo were worried that he would earn less than the 15% yield to maturity on the reinvested interest payments, which of these two bonds would be a better choice?

Answer 1

(a) BOND A

Par Value	500
Coupon rate	5%
YTM	15%
Payment frequency	1 (annual)
Time to maturity	5
PV	332.39

BOND B

Par Value	500
Coupon rate	10%
YTM	15%
Payment frequency	1
Time to maturity	5
PV	416.20

(b) Bond A: No. of bonds purchased = $10,000/$332.39 = 30

Bond B: No. of bonds purchased = $10,000/$416.20 = 24

(e) Calculations of yield to maturity (YTM) assume that all coupon payments are reinvested at the same rate as the bond's current yield. If this is not true, one should use MIRR approach with a fixed reinvestment rate, which is different from bond's YTM.

YTM	15%
Reinvestment rate	8%

BOND A Cash Flows

	0	1	2	3	4	5
Cash flows	-332.39	25	25	25	25	525

IRR	15.00%
MIRR	14.24%

BOND B Cash flows

	0	1	2	3	4	5
Cash flows	-416.20	50	50	50	50	550

IRR	15.00%
MIRR	13.77%

Clearly, bond A with lower coupon payment has a higher MIRR because of its lower reinvestment risk.