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.

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