Question

A bond has an 8.2 percent coupon (and makes semi-annual coupon payments), a $1,000 par value, matures in 12.5 years, and is priced to provide a yield to maturity of 7.00 percent.

What is the current yield?

Answer 1

First of all lets find prirce of the bond

Here face value = $1000 ,
Interest = face value x coupon rate
= 1000 x 8.2% x 1/2
= 41$
n = no of coupon payments= 12.5 x 2 = 25
YTM = 7%/2 = 3.5%
Value of bond = Interest x PVIFA(YTM%,n) + redemption value x PVIF(YTM%,n)
PVIFA(YTM%,n) = [1-(1/(1+r)^n / r ]
PVIFA(3.5%,25) = [1-(1/(1+3.5%)^25 / 3.5%]
=[1-(1/(1+0.035)^25 / 0.035]
=[1-(1/(1.035)^25 / 0.035]
=[1-0.4231/ 0.035]
=0.5769/0.035
=16.4815
PVIF(3.5%,25) = 1/(1+3.5%)^25
=1/(1.035)^25
= 0.42315
Value of bond = 41 x 16.4815 + 1000 x 0.42315
=675.74 + 423.15
= 1098.89 $

Current yield = Coupon payment/current market price

=41/1098.89

=3.73%

Annual current yield = 3.73% x 2 = 7.46%