Gabriele Enterprises has bonds on the market making annual payments, with 18 years to maturity, a par value of $1,000, and selling for $780. At this price, the bonds yield 6.9 percent. What must the coupon rate be on the bonds?

The coupon rate on the bonds is 4.73%

Explanation:

To calculate the coupon rate of the bond, 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 an annual bond, the coupon payment, number of periods and annual YTM will be,

Let coupon rate be x.

Coupon Payment (C) = 1000 * x = 1000x

Total periods (n)= 18

r or YTM = 6.9%

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

We will input the values of the available variables.

780 = 1000x * [( 1 - (1+0.069)^-18) / 0.069]  +  1000 / (1+0.069)^18

780 = 1000x * (10.13209373)  +  300.8855326

780 - 300.8855326  =  1000x * 10.13209373

479.1144674 / 10.13209373  =  1000x

47.28681752 / 1000 = x

x = 0.04728681752 rounded off to 0.0473 or 4.73%

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