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?
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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