Question

McConnell Corporation has bonds on the market with 13.5 years to maturity, a YTM of 7.4 percent, a par value of $1,000, and a current price of $1,059. The bonds make semiannual payments. What must the coupon rate be on these bonds? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

Coupon rate = 8.10% stated in annual terms

Step-by-step explanation:

To calculate the price of the bond today, we will use the formula for the price of the bond. 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,

Let the semi annual coupon payment be x

Coupon Payment (C) = x

Total periods (n) = 13.5 * 2 = 27

r or YTM = 0.074 * 6/12 = 0.037 or 3.7%

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

Plugging in the available values, we can calculate the coupon payment to be,

1059 = x * [( 1 - (1+0.037)^-27) / 0.037] + 1000 / (1+0.037)^27

1059 = x * 16.89323812 + 374.9501896

1059 - 374.9501896 = x * 16.89323812

(1059 - 374.9501896) / 16.89323812 = x

x = $40.49252166 rounded off to $40.49

As the semi annual coupon payment is 40.49, the annual payment will be = 40.49252166 * 2 = $80.98504332

As coupon payment is a percentage of the face value of the bond, the annual coupon rate on bond will be = 80.98504332 / 1000 = 8.0985% rounded off to 8.10%