Problem 7-15 Bond valuation Bond X is noncallable and has 20 years to maturity,
ID: 2650812 • Letter: P
Question
Problem 7-15
Bond valuation
Bond X is noncallable and has 20 years to maturity, a 10% annual coupon, and a $1,000 par value. Your required return on Bond X is 11%; and 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.) Round your answer to the nearest cent.
Explanation / Answer
First, we must find the amount of money we can expect to sell this bond for in 5 years. This is found using the fact that in five years, there will be 15 years remaining until the bond matures and that the expected YTM for this bond at that time will be 11%.
N = 15, I/YR = 11.0, PMT = 100, FV = 1000
PV = -$928.09. VB = $928.09
This is the value of the bond in 5 years. Therefore, we can solve for the maximum price we would be willing to pay for this bond today, subject to our required rate of return of 11%.
N = 5, I/YR = 11, PMT = 100, FV = 928.09
PV = -$920.37. VB = $920.37.
You would be willing to pay up to $920.37 for this bond today.