Question

Gabriele Enterprises has bonds on the market making annual payments, with eight years to maturity, a par value of $1,000, and selling for $948. At this price, the bonds yield 5.1 percent. What must the coupon rate be on the bonds? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

Answer:

Coupon rate = 0.04292 or 4.292%

Explanation:

To calculate the coupon rate of the bond, we will, use the formula for the price of the bond. As the bond is an annual bond, the coupon payment, number of periods and semi annual YTM will be,

Coupon Payment (C) = x

Total periods (n)= 8

r or YTM = 0.051 or 5.1%

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

948 = x * [( 1 - (1+0.051)^-8) / 0.051]  +  1000 / (1+0.051)^8

948 = x * 6.437166243  +  671.7045216

948 - 671.7045216  =  x * 6.437166243

276.2954784 / 6.437166243  =  x

x = $42.92191128 rounded off to $42.92

Thus, the coupon payment on bond is $42.92

As the coupon payment is calculated by multiplying the coupon rate with the face value of the bond, then the coupon rate will be:

Coupon payment = face value * coupon rate

42.92 = 1000 * Coupon rate

Coupon rate = 42.92 / 1000

Coupon rate = 0.04292 or 4.292%