Question

Beam Inc. bonds are trading today for a price of ​$1,161.72. The bond currently has 10 years until maturity and has a yield to maturity of 7.63​%. 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(7.63%,10)+1000*Present value of discounting factor(7.63%,10)

1,161.72=Annual coupon*6.82352157+1000*0.479365304

Annual coupon=(1,161.72-479.365304)/6.82352157

=$100(Approx)

Coupon rate=Annual coupon/Face value

=100/1000

=10%(Approx).

NOTE:

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

=Annual coupon[1-(1.0763)^-10]/0.0763

=Annual coupon*6.82352157

2.Present value of discounting factor=1000/1.0763^10

=1000*0.479365304