Question

Find the current yield of a bond that makes annual payments and has an annual coupon payment of 5% and 12 years to maturity. Assume that bonds of similar risk and quality are returning 7% in the market today.

5.32% 6.01% 16.82% 5.94%

Answer 1

Annual coupon=$1000*5%=$50(Taking $1000 as par value)

Current price=Annual coupon*Present value of annuity factor(7%,12 years)+$1000*Present value of discounting factor(7%,12)

=$50*7.942686297+$1000*0.444011959

=$841.1462741

Current yield=Annual coupon/Current price

=(50/$841.1462741)

=5.94%(Approx)

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

=$50[1-(1.07)^-12]/0.07

=$50*7.942686297

2.Present value of discounting factor=$1000/1.07^12

=$1000*0.444011959