Question

Bond X is noncallable and has 20 years to maturity, a 11% annual coupon, and a $1,000 par value. Your required return on Bond X is 12%; if you buy it, you plan to hold it for 5 years. You (and the market) have expectations that in 5 years, the yield to maturity on a 15-year bond with similar risk will be 11%. How much should you be willing to pay for Bond X today? (Hint: You will need to know how much the bond will be worth at the end of 5 years.) Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

Solution:

First, we should find the money we can expect to sell the bond in 5 years. In five years, there will be 15 years remaining until the bond matures and the YTM of the bond will be 11%.

We have n = 15, i = 11%, PMT = 110 and FV = 1000

The value of the bond, is given by:-

= 110 (PVIFA @ 11%, 15) + 1000 (PVIF @ 11%, 15)

= 110 (7.19087) + 1000 (0.20900)

= $1,000

It is the value of the bond in 5 years. Hence, the maximum price we would be willing to pay for the bond today to the required rate of return of 12%.

We have n = 5, i = 12, PMT = 110, FV = 1000

The value of the bond, is given by:-

= 110 (PVIFA @ 12%, 5) + 1000 (PVIF @ 12%, 5)

= 110 (3.60477) + 1000 (0.5674)

= $963.95

You would be willing to pay up to $963.95 for this bond today.