Question

Bond X is noncallable and has 20 years to maturity, a 9% annual coupon, and a $1,000 par value. Your required return on Bond X is 10%; 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 9.5%. 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.) Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

First calculated the selling price of the bond end of 5th year from today:

Using financial calculator BA II Plus - Input details:	#
I/Y = R = Rate or yield / frequency of coupon in a year =	9.500000
PMT = Coupon rate x FV / frequency =	-$90.00
N = Number of years remaining x frequency =	15.00
FV = Future Value =	-$1,000.00
CPT > PV = Selling price of bond End of 5th year =	$960.86
Formula for bond value: PV = |PMT| x ((1-((1+R%)^-N)) / R%) + (|FV|/(1+R%)^N) =
PV = (90* ((1-(1+0.095)^-15)/0.095) + 1000/(1+0.095)^15)	$960.86

Now, keeping the target of $960.86 at end of 5 years what should be paid today?

Using financial calculator BA II Plus - Input details:	#
I/Y = R = Rate or yield / frequency of coupon in a year =	10.000000
PMT = Coupon rate x FV / frequency =	-$90.00
N = Number of years remaining x frequency =	5.00
FV = Future Value = Selling price at end of 5th year =	-$960.86
CPT > PV = Present value of bond = Price of Bond = Current value of bond =	$937.79
Formula for bond value: PV = |PMT| x ((1-((1+R%)^-N)) / R%) + (|FV|/(1+R%)^N) =
PV = (86.4773212488187* ((1-(1+0.1)^-5)/0.1) + 960.859124986874/(1+0.1)^5)	$937.79