Question

What is the value of a 7-year, 7.7% coupon rate, $1,000 face value bond with annual coupon payments, if similar bonds (same maturity, same risk profile) are trading at a yield to maturity of 3.4%? Round to the nearest cent.

Answer 1

Annual coupon=1000*7.7%=77

Hence value of bond=Annual coupon*Present value of annuity factor(3.4%,7)+$1000*Present value of discounting factor(3.4%,7)

=77*6.137428067+$1000*0.791327445

=$1263.91(Approx).

NOTE:

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

=77[1-(1.034)^-7]/0.034

=77*6.137428067

2.Present value of discounting factor=1000/1.034^7

=1000*0.791327445