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Bond X is noncallable and has 20 years to maturity, a 11% annual coupon, and a $1,000 par value
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%; 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.
Expert Solution
For 15 year bond:
Nper (maturity of bond) = 15
PV (bond price) = ?
PMT (annual interest payment) = $1,000*11% = $110
FV (face value) = $1,000
Rate (YTM) = 7.5%
Now we use excel formula;
Price of the bonds at the end of 5 years:
= PV(rate,nper,pmt,fv)
= PV(7.5%,15,110,1000)
Price of the bonds at the end of 5 years = $1,308.95
Now, Required return is 15%
Nper (indicates the period) = 5
PV (indicates the price) = ?
PMT (annual interest payment) = $1,000*11% = $110
FV (indicates the value at the end of 5 year) = $1308.95
Rate (required return) = 12%
Now we use excel formula;
Willing to pay today for Bond X:
= PV(rate,nper,pmt,fv)
= PV(12%,5,110,1308.95)
Willing to pay today for Bond X = $1,139.26
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