Question

A 20-year XXX bond has a coupon rate of 8 percent and sells at a yield...

A 20-year XXX bond has a coupon rate of 8 percent and sells at a yield to maturity of 10 percent.

a. Assuming annual coupon payments, at what price does the bond sell?
b. If XXX wants to issue a new 20-year bond at face value, what coupon rate must the bond offer?

Homework Answers

Answer #1

Answer a.

Face Value = $1,000

Annual Coupon Rate = 8%
Annual Coupon = 8% * $1,000
Annual Coupon = $80

Annual YTM = 10%
Time to Maturity = 20 years

Current Price = $80 * PVIFA(10%, 20) + $1,000 * PVIF(10%, 20)
Current Price = $80 * (1 - (1/1.10)^20) / 0.10 + $1,000 / 1.10^20
Current Price = $829.73

Answer b.

If the company wants to issue new bonds at face value, then its coupon rate must be equal to its YTM.

So, the bond must offer a coupon rate of 10% to trade at par.

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