Question

Problem 5-14
Current Yield with Semiannual Payments

A bond that matures in 7 years sells for $1,020. The bond has a face value of $1,000 and a yield to maturity of 10.5883%. The bond pays coupons semiannually. What is the bond's current yield? Do not round intermediate calculations. Round your answer to two decimal places.

%

Answer 1

Face Value = $1,000
Current Price = $1,020

Time to Maturity = 7 years
Semiannual Period = 14

Annual YTM = 10.5883%
Semiannual YTM = 5.29415%

Let Semiannual Coupon be $C

$1,020 = $C * PVIFA(5.29415%, 14) + $1,000 * PVIF(5.29415%, 14)
$1,020 = $C * (1 - (1/1.0529415)^14) / 0.0529415 + $1,000 / 1.0529415^14
$1,020 = $C * 9.715077 + $485.66924
$534.33076 = $C * 9.715077
$C = $55.00

Semiannual Coupon = $55.00

Semiannual Current Yield = Semiannual Coupon / Current Price
Semiannual Current Yield = $55.00 / $1,020
Semiannual Current Yield = 0.0539 or 5.39%

Annual Current Yield = 2 * Semiannual Current Yield
Annual Current Yield = 2 * 5.39%
Annual Current Yield = 10.78%