Question

1. (2pts) Bond X is a premium $1000 par value bond making annual payments. The bond has a coupon rate of 9%, a YTM of 7%, and has 13 years to maturity. Bond Y is a discount $1000 par value bond making annual payments. This bond has a coupon rate of 7%, a YTM of 9%, and also has 13 years to maturity. What are the prices of these bonds today? If interest rates remain unchanged, what do you expect the prices of these bonds to be in 8 years? In 13 years? What’s going on here? Illustrate your answers by graphing bond prices versus time to maturity.

Answer 1

(a) Current Time:

Bond X: Face Value = $ 1000, Coupon Rate = 9 %, YTM = 7 % and Tenure = 13 years

Annual Coupon = 0.09 x 1000 = $ 90

Bond Price = 90 x (1/0.07) x [1-{1/(1.07)^(13)}] + 1000 / (1.07)^(13) = $ 1167.15

Bond Y: Face Value = $ 1000, Coupon Rate = 7% and YTM = 9 %, Tenure = 13 years

Annual Coupon = 0.07 x 1000 = $ 70

Bond Price = 70 x (1/0.09) x [1-{1/(1.09)^(13)}] + 1000 / (1.09)^(13) = $ 850.26

(b) 8 Years Later:

Bond X: Face Value = $ 1000, Coupon Rate = 9 %, YTM = 7 % and Remaining Tenure = (13-8) = 5 years

Annual Coupon = 0.09 x 1000 = $ 90

Bond Price = 90 x (1/0.07) x [1-{1/(1.07)^(5)}] + 1000 / (1.07)^(5) = $ 1082.004

Bond Y: Face Value = $ 1000, Coupon Rate = 7% and YTM = 9 %,  Remaining Tenure = (13-8) = 5 years

Annual Coupon = 0.07 x 1000 = $ 70

Bond Price = 70 x (1/0.09) x [1-{1/(1.09)^(5)}] + 1000 / (1.09)^(5) = $ 922.21

(c) 13 Years Later:

Bond X: Bond Price = Face Value = $ 1000 and Bond Y: Bond Price = $ 1000

As is observable, the premium bond's price goes down over the bond's tenure, thereby implying that the bond is amortizing its premium. The discount bond's price goes up over its tenure, thereby amortizing the discount. Both prices converge on their face value at maturity.