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 $952. At this price, the bonds yield 6.1 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

Current price=Annual coupon*Present value of annuity factor(6.1%,8)+$1000*Present value of discounting factor(6.1%,8)

952=Annual coupon*6.18529143+1000*0.622697222

Annual coupon=(952-622.697222)/6.18529143

=$53.24(Approx).

Coupon rate=Annual coupon/Face value

=$53.24/1000

=5.32%(Approx)

NOTE:

1.Present value of annuity=Annuity[1-(1+interest rate)^-time period]/rate

=Annual coupon[1-(1.061)^-8]/0.061

=Annual coupon*6.18529143

2.Present value of discounting factor=1000/1.061^8

=1000*0.622697222