Question

Company Xyz's outstanding bind shave a $1000 par value and they mature in 25 years. their nominal yeild to maturity is 9.88%, theybpay interest semiannually and they sell at a price of $850. What is bonds annual coupon interest rate.

8.15

7.96

8.06

7.86

8.25

Answer 1

Answer is 8.25%

Par Value = $1,000
Current Price = $850

Annual YTM = 9.88%
Semiannual YTM = 9.88% / 2
Semiannual YTM = 4.94%

Time to Maturity = 25 years
Semiannual Period = 50

Let semiannual coupon be $x

$850 = $x * PVIFA(4.94%, 50) + $1,000 * PVIF(4.94%, 50)
$850 = $x * (1 - (1/1.0494)^50) / 0.0494 + $1,000 * (1/1.0494)^50
$850 = $x * 18.426479 + $1,000 * 0.089732
$850 = $x * 18.426479 + $89.732
$760.268 = $x * 18.426479
$x = $41.25

Semiannual Coupon = $41.25

Annual Coupon = 2 * Semiannual Coupon
Annual Coupon = 2 * $41.25
Annual Coupon = $82.50

Coupon Rate = Annual Coupon / Par Value
Coupon Rate = $82.50 / $1,000
Coupon Rate = 0.0825 or 8.25%