Question

•Consider three 30-year bonds with annual coupon payments. One bond has a 10% coupon rate, one has a 5% coupon rate, and one has a 3% coupon rate. If the yield to maturity of each bond is 5%, what is the price of each bond per $100 face value? Which bond trades at a premium, which trades at a discount, and which trades at par?

Answer 1

a)

Coupon = 0.1 * 100 = 10

Price = Coupon * [1 - 1 / (1 + r)ⁿ] / r + FV / (1 + r)ⁿ

Price = 10 * [1 - 1 / (1 + 0.05)³⁰] / 0.05 + 100 / (1 + 0.05)³⁰

Price = 10 * [1 - 0.231377] / 0.05 + 23.137745

Price = 10 * 15.37246 + 23.137745

Price = $176.86

Bond is trading at a PREMIUM

b)

When coupon rate is equal to yield to maturity, price of the bond will always be equal to its par value

Price = $1000

Bond is selling at PAR

c)

Coupon = 0.03 * 100 = 3

Price = Coupon * [1 - 1 / (1 + r)ⁿ] / r + FV / (1 + r)ⁿ

Price = 3 * [1 - 1 / (1 + 0.05)³⁰] / 0.05 + 100 / (1 + 0.05)³⁰

Price = 3 * [1 - 0.231377] / 0.05 + 23.137745

Price = 3 * 15.37246 + 23.137745

Price = $69.26

Bond is trading at a DISCOUNT