Question

Your company currently has 1,000 ​par, 5.25% coupon bonds with 10 years to maturity and a price of $1,076. If you want to issue new​ 10-year coupon bonds at​ par, what coupon rate do you need to​ set? Assume that for both​ bonds, the next coupon payment is due in exactly six months.

Answer 1

Current issue of bonds:

Face Value = $1,000
Current Price = $1,076

Annual Coupon Rate = 5.25%
Semiannual Coupon Rate = 2.625%
Semiannual Coupon = 2.625% * $1,000
Semiannual Coupon = $26.25

Time to Maturity = 10 years
Semiannual Period = 20

Let Semiannual YTM be i%

$1,076 = $26.25 * PVIFA(i%, 20) + $1,000 * PVIF(i%, 20)

Using financial calculator:
N = 20
PV = -1076
PMT = 26.25
FV = 1000

I = 2.153%

Semiannual YTM = 2.153%
Annual YTM = 2 * 2.153%
Annual YTM = 4.31%

So, the company needs to set a coupon rate of 4.31% on the new issue of bonds.