Question

Kiss the Sky Enterprises has bonds on the market making annual payments, with 6 years to maturity, and selling for $790. At this price, the bonds yield 10.0 percent. What must the coupon rate be on the bonds? (Note: first find the coupon payment, then the coupon rate. The face value of $1,000 x coupon rate = coupon payment).

rev: 09_18_2012

Multiple Choice

• 6.55%

• 5.28%

• 10.00%

• 5.18%

• 10.36%

Answer 1

Current price=Annual coupon*Present value of annuity factor(10%,6)+1000*Present value of discounting factor(10%,6)

790=Annual coupon*4.3552607+1000*0.56447393

Annual coupon=(790-564.47393)/4.3552607

=$51.7824501

Coupon rate=Annual coupon/Face value

=51.7824501/1000

=5.18%(Approx)

NOTE:

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

=Annual coupon*[1-(1.1)^-6]/0.1

=Annual coupon*4.3552607

2.Present value of discounting factor=1000/1.1^6

=1000*0.56447393