Question

Boeing has a bond outstanding with 15 years to maturity, a $1,000 par value, a coupon rate of 6.8%, with coupons paid semiannually, and a price of 98.16 (percent of par).

If the company wants to issue a new bond with the same maturity at par, what coupon rate should it choose?

Answer 1

Current issue of bonds:

Face Value = $1,000

Current Price = 98.16% * $1,000
Current Price = $981.60

Annual Coupon Rate = 6.80%
Semiannual Coupon Rate = 3.40%
Semiannual Coupon = 3.40% * $1,000
Semiannual Coupon = $34

Time to Maturity = 15 years
Semiannual Period = 30

Let Semiannual YTM be i%

$981.60 = $34 * PVIFA(i%, 30) + $1,000 * PVIF(i%, 30)

Using financial calculator:
N = 30
PV = -981.60
PMT = 34
FV = 1000

I = 3.50%

Semiannual YTM = 3.50%
Annual YTM = 2 * 3.50%
Annual YTM = 7.00%

So, the company should set a coupon rate of 7.00% for the new bond issue to sell at par.