Question

Seether Co. wants to issue new 15-year bonds for some much-needed expansion projects. The company currently has 11.0 percent coupon bonds on the market that sell for $971.56, make semiannual payments, and mature in 15 years. What coupon rate should the company set on its new bonds if it wants them to sell at par?

Answer 1

Current Issue:

Face Value = $1,000
Current Price = $971.56

Annual Coupon Rate = 11.0%
Semiannual Coupon Rate = 5.50%
Semiannual Coupon = 5.5%*$1,000
Semiannual Coupon = $55

Time to Maturity = 15 years
Semiannual Period to Maturity = 30

Let Semiannual YTM be i%

$971.56 = $55 * PVIFA(i%, 30) + $1,000 * PVIF(i%, 30)

Using financial calculator:
N = 30
PV = -971.56
PMT = 55
FV = 1000

I = 5.70%

Semiannual YTM = 5.70%
Annual YTM = 2 * 5.70%
Annual YTM = 11.40%

New Issue of Bonds:

If company wants to issue new bonds at par value, then coupon rate on new issue of bonds is 11.40%