Question

Kaiser Industries has bonds on the market making annual payments, with 12 years to maturity, and selling for $1,382.01. At this price, the bonds yield 5.5 percent. What is the coupon rate? (show work if you can :) )

Answer 1

Current price=Annual coupon*Present value of annuity factor(5.5%,12)+$1000*Present value of discounting factor(5.5%,12)

1382.01=Annual coupon*8.618517849+$1000*0.525981518

Annual coupon=(1382.01-525.981518)/8.618517849

Annual coupon=$99.32(Approx).

Coupon rate=Annual coupon/Face value

=$99.32/1000

=9.93%(Approx).

NOTE:

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

=Annual coupon[1-(1.055)^-12]/0.055

=Annual coupon*8.618517849

2.Present value of discounting factor=1000/1.055^12

=1000*0.525981518