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%**

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