Question

Your broker is suggesting that you purchase a 10-year Ford Motor Company bond that is selling for $973.88. The par value of the bond is $1,000 and your broker tells you that the bond has a yield to maturity of 7.40%. If the bond pays annual coupon payments, what is the coupon rate on the bond?

a. 6.541% b. 7.021% c. 7.212% d. 7.572% e. 6.889%

Answer 1

Current price=Annual coupon*Present value of annuity factor(7.4%,10)+1000*Present value of discounting factor(7.4%,10)

973.88=Annual coupon*6.89553327+1000*0.489730538

Annual coupon=(973.88-489.730538)/6.89553327

=70.2120406(Approx)

Coupon rate=Annual coupon/Face value

=70.2120406/1000

=7.021%(Approx).

NOTE:

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

=Annual coupon[1-(1.074)^-10]/0.074

=Annual coupon*6.89553327

2.Present value of discounting factor=1000/1.074^10

=1000*0.489730538