McConnel corporation has bonds on the market with 16.5 years to maturity, a YTM of 7.7 percent, a par value of 1000 and current price of 1065. The bonds make semiannual payment and have a par value of $1,000.Required:What must the coupon rate be on these bonds?

Coupon rate = 0.08402 or 8.402%

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,

Coupon Payment (C) = x

Total periods (n)= 16.5 * 2 = 33

r or YTM = 7.7% * 1/2 = 3.85% or 0.0385

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

Using the bond price formula and the available values, we calculate the coupon rate to be,

1065 = x * [( 1 - (1+0.0385)^-33) / 0.0385]  +  1000 / (1+0.0385)^33

1065 = x * (18.50739407)  +  287.4653284

1065 - 287.4653284 = x * 18.50739407

777.5346716 / 18.50739407  = x

x  =  42.012 rounded off to $42.01

If the semi annual coupon payment is $42.01, the annual coupon payment will be 42.01 * 2 = $84.02

The coupon rate on bonds is = 84.02 / 1000

Coupon rate = 0.08402 or 8.402%

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