Question

A bond has a coupon rate of 7.5% and matures in 10 years. The current required return for the bond is 6.8%. Calculate the current price of the bond and the current yield.

Answer 1

Annual coupon=1000*7.5%=$75

Hence current price-Annual coupon*Present value of annuity factor(6.8%,10)+1000*Present value of discounting factor(6.8%,10)

=75*7.08897698+1000*0.517949565

=$1049.62(Approx)

Current yield=Annual coupon/Current price

=75/1049.62

=7.15%(Approx)

NOTE:

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

=75[1-(1.068)^-10]/0.068

=75*7.08897698

2.Present value of discounting factor=1000/1.068^10

= 1000*0.517949565