Bond X is noncallable and has 20 years to maturity, a 8% annual coupon, and a $1
ID: 2673826 • Letter: B
Question
Bond X is noncallable and has 20 years to maturity, a 8% annual coupon, and a $1,000 par value. Your required return on Bond X is 12%; 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 7.5%. 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
Known: I/Y=10%, N=5, PMT=9%*1000= $90. Unknown: FV = ??, PV = ?? To find out the price I should pay for today(PV05), we need to know how much we expect to sell it for in 5 yrs (FV05). FV05 should be the same as the value of a 15-yr-maturity new bond of the same par value & coupon rate & 8.5% YTM at that time( if you sell it higher, no one wants to buy it. If you sell it lower, you don’t want to sell it.) For the 15-yr-maturity new bond, we know: I/Y= 8.5%, N=15, FV=1000, PMT= 90 => PV= FV05 = -1041.52 Back to the original bond, I/Y=10%, N=5, FV=1041.52, PMT=90 => PV = -$987.87