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%; 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 8.5%. 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.

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Answer 1

Calculation of present value of the bond for the last 15 years:

FV = 1000
Nper = 15
PMT = 1000 * 8% = 80
Rate = 8.5%

Present value can be calculated by using the following excel formula:
=PV(rate,nper,pmt,fv)
=PV(8.5%,15,-80,-1000)
= $958.48

Calculation of current price of the bond:

Nper = 5
Rate = 12%
PMT = 80
FV = 958.48

Current price of the bond can be calculated by using the following excel formula:
=PV(rate,nper,pmt,fv)
=PV(12%,5,-80,-958.48)
= $832.25

Current price of the bond = $832.25