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Consider two bonds, a 3-year bond paying an annual coupon of 7%, and a 20-year bond, also with an annual coupon of 7%
Consider two bonds, a 3-year bond paying an annual coupon of 7%, and a 20-year bond, also with an annual coupon of 7%. Both bonds currently sell at par value. Now suppose that interest rates rise and the yield to maturity of the two bonds increases to 10%.
a. What is the new price of the 3-year bond? (Round your answer to 2 decimal places.)
b. What is the new price of the 20-year bond? (Round your answer to 2 decimal places.)
c. Do longer or shorter maturity bonds appear to be more sensitive to changes in interest rates?
- Longer
- Shorter
Expert Solution
a. Computation of New Price of 3 Years Bond using PV Function in Excel:
=-pv(rate,nper,pmt,fv)
Here,
PV = Price of Bond = ?
Rate = 10%
Nper = 3 Years
PMT = $1,000*7% = $70
FV = $1,000
Substituting the values in formula:
=-pv(10%,3,70,1000)
PV or Price of Bonds = $925.39
b. Computation of New Price of 20 Years Bond using PV Function in Excel:
=-pv(rate,nper,pmt,fv)
Here,
PV = Price of Bond = ?
Rate = 10%
Nper = 20 Years
PMT = $1,000*7% = $70
FV = $1,000
Substituting the values in formula:
=-pv(10%,20,70,1000)
PV or Price of Bonds = $744.59
c.
?Longer
The longer duration bonds are more sensitive to changes in interest rate as the annuity of coupon plus face value payment happens far in future therefore the discounting impacts more to cash flows far in future.
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