Question

Bond X is a premium bond making semiannual payments. The bond pays a coupon rate of 9 percent, has a YTM of 7 percent, and has 15 years to maturity. Bond Y is a discount bond making semiannual payments. This bond pays a coupon rate of 7 percent, has a YTM of 9 percent, and also has 15 years to maturity. The bonds have a $1,000 par value. What is the price of each bond today

Answer 1

Bond Price today

Bond X = $1183.920454 rounded off to $1183.92

Bond Y = $837.1111146 rounded off to $837.11

Step-by-step explanation:

To calculate the price of the bond, we need to first calculate the coupon payment per period. We assume that the interest rate provided is stated in annual terms. As the bond is a semi annual bond, the coupon payment, number of periods and semi annual YTM will be,

For Bond X

Coupon Payment (C) = 0.09 * 1/2 * 1000 = $45

Total periods (n)= 15 * 2 = 30

r or YTM = 7% * 1/2 = 3.5% or 0.035

The formula to calculate the price of the bonds today is attached.

Bond Price = 45 * [( 1 - (1+0.035)^-30) / 0.035] + 1000 / (1+0.035)^30

Bond Price = $1183.920454 rounded off to $1183.92

For Bond Y

Coupon Payment (C) = 0.07 * 1/2 * 1000 = $35

Total periods (n)= 15 * 2 = 30

r or YTM = 9% * 1/2 = 4.5% or 0.045

Bond Price = 35 * [( 1 - (1+0.045)^-30) / 0.045] + 1000 / (1+0.045)^30

Bond Price = $837.1111146 rounded off to $837.11