Question

Large Industries annual bonds are selling at 110.20 (i.e., the price is $1102 for the $1,000 bond). There are 13 years remaining until maturity on the bonds and the yield to maturity is 6.75%. Find the coupon rate. (Note: you may have to use a trial and error solution method)

Answer 1

Current price=Annual coupon*Present value of annuity factor(6.75%,13)+$1000*Present value of discounting factor(6.75%,13)

1102=Annual coupon*8.477376589+$1000*0.42777708

1102=Annual coupon*8.477376589+427.77708

Annual coupon=(1102-427.77708)/8.477376589

=$79.5320242

Coupon rate=Annual coupon/Face value

=$79.5320242/$1000

which is equal to

=7.95%(Approx).

NOTE:

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

=Annual coupon[1-(1.0675)^-13]/0.0675

=Annual coupon*8.477376589

2.Present value of discounting factor=$1000/1.0675^13

=$1000*0.42777708