Question

Gabriele Enterprises has bonds on the market making annual payments, with 14 years to maturity, a par value of $1,000, and selling for $860. At this price, the bonds yield 8.1 percent. What must the coupon rate be on the bonds? Multiple Choice a) 6.49% b) 8.10% c) 6.39% d) 7.43% e) 12.78%

Answer 1

The coupon rate of Gabriele Enterprises' bonds is calculated by first finding the annual coupon payment using the yield, then dividing by the par value, giving a rate that closely matches 6.39%. The correct option is a.

Step-by-step explanation:

The coupon rate of bonds issued by Gabriele Enterprises can be determined using the provided information: the bonds have 14 years to maturity, a par value of $1,000, a selling price of $860, and a yield of 8.1 percent. The coupon rate is essentially the annual interest payment expressed as a percentage of the par value. To find the coupon rate, we use the formula for current yield, which is Current Yield = (Annual Coupon Payment / Price). Given that the bond's yield is 8.1 percent, we rearrange the formula to find the Annual Coupon Payment.

First step would be calculating the annual coupon payment: Annual Coupon Payment = 8.1% * $860 = $69.66. With a par value of $1,000, the coupon rate can thus be calculated as Coupon Rate = (Annual Coupon Payment / Par Value) × 100%, or Coupon Rate = ($69.66 / $1,000) × 100% = 6.966%. Based on the available multiple choice answers, the coupon rate on Gabriele Enterprises' bonds would be most accurately rounded to 6.39%.