Question

Ashes Divide Corporation has bonds on the market with 19 years to maturity, a YTM of 10.0 percent, and a current price of $1,316.50. The bonds make semiannual payments. What must the coupon rate be on these bonds?

Answer 1

Coupon Rate of the Bond

Yield to maturity = 5% [(10%/2), Since, the Semi-annual compounding]

Number of years = 38 Years [(19 Years x 2), Since, the Semi-annual compounding]

The Current Price of the bond = Present Value of the Coupon payments + Present Value of Face Value

= Coupon Amount[PVIFA 5%, 38 Years] + Face Value[PVIF 5%, 38 Years]

$1,316.50 = [Coupon Amount x 16.86789] + [$1,000 x 0.15661]

$1,316.50 = [Coupon Amount x 16.86789] + $156.61

Coupon Amount = ($1,316.50 - $156.61) / 16.86789

Coupon Amount = $68.75

Semi-annual Coupon Amount = $68.75

Annual Coupon Amount = $137.50 [$68.75 x 2]

Therefore, Annual Coupon Rate = [Annual Coupon Amount / Face Value ] x 100

= [$137.50 / $1,000] x 100

= 13.75%

“Hence, The coupon rate on these Bond = 13.75%”