Question

Problem 7-5 Coupon Rates [LO2] Essary Enterprises has bonds on the market making annual payments, with seven years to maturity, a par value of $1,000, and selling for $974. At this price, the bonds yield 7.2 percent. What must the coupon rate be on the bonds? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Coupon rate %

Answer 1

Current price=Annual coupon*Present value of annuity factor(7.2%,7)+$1000*Present value of discounting factor(7.2%,7)

974=Annual coupon*5.351913959+1000*0.614662195

Annual coupon=(974-614.662195)/5.351913959

Annual coupon=$67.14(Approx).

Coupon rate=Annual coupon/Face value

=$67.14/$1000

=6.71%(Approx).

NOTE:

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

=Annual coupon[1-(1.072)^-7]/0.072

=Annual coupon*5.351913959

2.Present value of discounting factor=1000/1.072^7

=1000*0.614662195