Question

Assume that you are interested in a 4.50 percent coupon corporate bond that has ten years left to maturity. The market interest rate is 5.25 percent. If coupon payments are semiannual, what should the price of this bond be? Is this a discount bond or premium bond, and why?

Answer 1

Face Value = $1,000

Annual Coupon Rate = 4.50%
Semiannual Coupon Rate = 2.25%
Semiannual Coupon = 2.25% * $1,000
Semiannual Coupon = $22.50

Time to Maturity = 10 years
Semiannual Period to Maturity = 20

Annual Interest Rate = 5.25%
Semiannual Interest Rate = 2.625%

Price of Bond = $22.50 * PVIFA(2.625%, 20) + $1,000 * PVIF(2.625%, 20)
Price of Bond = $22.50 * (1 - (1/1.02625)^20) / 0.02625 + $1,000 / 1.02625^20
Price of Bond = $942.23

This is a Bond issued at discount, as the Coupon rate is less than the Market Interest Rate.