Question

Beam Inc. bonds are trading today for a price of ​$636.38. The bond currently has 11 years until maturity and has a yield to maturity of 9.46​%. The bond pays annual coupons and the next coupon is due in one year. What is the coupon rate of the​ bond?

Answer 1

Current price=Annual coupon*Present value of annuity factor(9.46%,11)+$1000*Present value of discounting factor(9.46%,11)

636.38=Annual coupon*6.659723971+$1000*0.369990112

Annual coupon=(636.38-369.990112)/6.659723971

=$40(Approx).

Coupon rate=Annual coupon/Face value

=(40/1000)=4%(Approx).

NOTE:

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

=Annual coupon[1-(1.0946)^-11]/0.0946

=Annual coupon*6.659723971

2.Present value of discounting factor=1000/1.0946^11

=1000*0.369990112