Question

Joe must pay liabilities of 1,000 due 6 months from now and another 1,000 due one year from now. There are two available investments: \,1. Bond I: a 6-month bond with face amount of 1,000, a 8% nominal annual coupon rate convertible semiannually, and a 6% nominal annual yield rate convertible semiannually; and \,2. Bond II: a one year bond with face amount of 1,000, a 5% nominal annual coupon rate convertible semiannually, and a 7% nominal annual yield rate convertible semiannually Calculate the amount of each bond Joe should purchase in order to exactly match the liabilities.

Answer 1

future liabilities:

$1,000 in 6 months

$1,000 in 1 year

Present value of bond I (due in 6 months):

PV = $1,000 / (1 + 3%) = $970.87

Present value of bond II (due in 1 year):

PV = $1,000 / (1 + 3.5%)² = $933.51

The price of the bonds is determined by the annual yield rate (YTM), not the coupon rate. Joe will pay $970.87 for bond I and $933.51 for bond II.