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Present Value of a discount bond

Find the present value (price) of a discount bond with a one-year term to maturity and a 10% yield. Next, find the price of a ten-year discount bond that also yields 10%. Now, increase the yield on both instruments to 11%. On a percentage basis, which instrument demonstrates the greatest change in price? What does this indicate about the price risk of the one-year bond in relation to an otherwise comparable 10-year bond, and what are the attendant implications?

Solution Preview

The following calculations have been with a HP 10BII financial calculator.

Q1. PV of a 1-year bond at 10%
N = 1 (years to maturity)
FV = $1000 (face value of a bond is always $1000)
I/Y = 10 % (yield to maturity)
PMT = 0
Solve for the present value PV = $909.09

Q2. PV of a 10-year bond at 10%
N = 10 (years to maturity)
FV = $1000 (face value)
I/Y = 10 % (yield to maturity)
PMT = 0
Solve for the present value PV = $385.54

Q3. PV of a 1-year bond at 11%
N = 1 (years to maturity)
FV = $1000 (face value)
I/Y = 11 % (yield to maturity)
PMT = 0
Solve for the present value PV = $900.90

Q4. PV of a 10-year bond at 11%
N = 10 (years to maturity)
FV = $1000 (face value)
I/Y = ...

Solution Summary

This solution compares 1-year and 10-year discount bonds when the yield to maturity increases from 10% from 11%, including a concise discussion of risk.

$2.19