Question

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%; 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

Solution

Step 1 :

Bond price at the end of 5 year = pv(rate, nper,pmt,fv)

Nper  (indicates the period) = 15

PV (indicates the price) = ?

PMT (indicate the annual payment) = 1000*11% = 110

FV (indicates the face value) = 1000

Rate (indicates YTM) = 9.5%

Bond price at the end of 5 year = pv(9.5%,15,110,1000)

Bond price at the end of 5 year = $1117.42

Step 2 :

Willing to pay for Bond X today = pv(rate, nper,pmt,fv)

Nper  (indicates the period) = 5

PV (indicates the price) = ?

PMT (indicate the annual payment) = 1000*11% = 110

FV (indicates the value at the end of 5 year) = 1117.42

Rate (indicates YTM) = 12%

Willing to pay for Bond X today = pv(12%,5,110,1117.42)

Willing to pay for Bond X today = $237.53