Question

Suppose a five-year, $100 bond with annual coupons has a price of $70 and a yield to maturity of 18%. What is the bond’s coupon rate?

Answer 1

Current price=Annual coupon*Present value of annuity factor(18%,5)+100*Present value of discounting factor(18%,5)

70=Annual coupon*3.12717102+100*0.437109216

Annual coupon=(70-43.7109216)/3.12717102

=$8.40666476

Coupon rate=Annual coupon/Face value

=8.40666476/100

=8.41%(Approx)

NOTE:

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

=Annual coupon[1-(1.18)^-5]/0.18

Annual coupon*3.12717102

2.Present value of discounting factor=100/1.18^5

=100*0.437109216