Question

Kiss the Sky Enterprises has bonds on the market making annual payments, with 17 years to maturity, and selling for $820. At this price, the bonds yield 9.8 percent. What must the coupon rate be on the bonds?

Multiple Choice

• 7.68%

• 9.25%

• 9.80%

• 15.17%

• 7.58%

Answer 1

Current price=Annual coupon*Present value of annuity factor(9.8%,17)+1000*Present value of discounting factor(9.8%,17)

820=Annual coupon*8.12182554+1000*0.204061097

Annual coupon=(820-204.061097)/8.12182554

=$75.8374949(Approx)

Coupon rate=Annual coupon/Face value

=75.8374949/1000

=7.58%(Approx)

NOTE:

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

=Annual coupon[1-(1.098)^-17]/0.098

=Annual coupon*8.12182554

2.Present value of discounting factor=1000/1.098^17

=1000*0.204061097