Question

Polar Bear, Inc. issued one year ago annual coupon paying bonds that orignially had 13 years to maturity. These bonds have a face value of $1,000 and a current market value of $1,030. At this market value, the bonds have a yield-to-maturity of 4.14% What is the coupon rate for these bonds?

Answer 1

Face Value = $1,000
Current Price = $1,030

Annual YTM = 4.14%
Time to Maturity = 12 years

Let Annual Coupon be $C

$1,030 = $C * PVIFA(4.14%, 12) + $1,000 * PVIF(4.14%, 12)
$1,030 = $C * (1 - (1/1.0414)^12) / 0.0414 + $1,000 / 1.0414^12
$1,030 = $C * 9.309296 + $614.595138
$415.404862 = $C * 9.309296
$C = $44.62

Annual Coupon = $44.62

Coupon Rate = Annual Coupon / Face Value
Coupon Rate = $44.62 / $1,000
Coupon Rate = 0.04462 or 4.46%

Therefore, coupon rate for these bonds is 4.46%