Question

Beam Inc. bonds are trading today for a price of

$1,159.45.

The bond currently has

10

years until maturity and has a yield to maturity of

7.66​%.

The bond pays annual coupons and the next coupon is due in one year. What is the coupon rate of the​ bond?

The coupon rate of the bond is

___​%.

​ (Round to one decimal​ place.)

Answer 1

Current price=Annual coupon*Present value of annuity factor(7.66%,10)+1000*Present value of discounting factor(7.66%,10)

1159.45=Annual coupon*6.81421407+1000*0.478031202

Annual coupon=(1159.45-478.031202)/6.81421407

=99.9996171

Coupon rate=Annual coupon/Face value

=99.9996171/1000

=10%(Approx).

NOTE:

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

=Annual coupon[1-(1.0766)^-10]/0.0766

=Annual coupon*6.81421407

2.Present value of discounting factor=1000/1.0766^10

=1000*0.478031202