Question

How do I solve this? Need to show work.

Question: XYZ currently has 21 long-term bond issues outstanding with various times-to-maturity and coupon rates. One of these bonds matures on Dec 1, 2031, approximately 15 years from today. It has a yield to maturity of 4.8%. For simplicity, assume that coupons are paid annually. The bond is currently selling for $1,105, based on a face (par) value of $1,000.  What is the coupon rate? (Closest number)

Answer: 5.78%

Answer 1

Current price=Annual coupon*Present value of annuity factor(4.8%,15)+$1000*Present value of discounting factor(4.8%,15)

1105=Annual coupon*10.52141362+$1000*0.494972146

Annual coupon=(1105-494.972146)/10.52141362

=$57.98(Approx).

Coupon rate=Annual coupon/Par value

=(57.98/1000)

=5.78%(Approx).

NOTE:

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

=Annual coupon[1-(1.048)^-15]/0.048

=Annual coupon*10.52141362

2.Present value of discounting factor=1000/1.048^15

=$1000*0.494972146