Question

Calculate the fair present value of the following bonds, all of which have a 2 percent coupon rate (paid semiannually), face value of $1000, and a required rate of return (yield to maturity) of 6 percent.

a. The bond has 10 years remaining to maturity.

b. The bond has 15 years remaining to maturity.

c. The bond has 20 years remaining to maturity.

d. Wha do your answers say about the relationship between time to maturity and present value?

Answer 1

The semi-annual yield will be = 3% and coupon will be 1%.

a. The PV equation will be written as:

PV = 10/1.03 + 10/1.03^2 + ... + 10/1.03^20 + 1000/1.03^20 = 702.4505

b. Similarly, the PV equation will be:

PV = 10/1.03 + 10/1.03^2 + .... + 10/1.03^30 + 1000/1.03^30 = 607.9912

c. PV = 10/1.03 + 10/1.03^2 + .... + 10/1.03^40 + 1000/1.03^40 = 537.7046.

d. We see that as the time to maturity increases, the present value and hence the bond price decreases. This is because the face value which is the biggest payment in the bond is being discounted more for higher maturities.