Solved Question: Assume that an asset has the following end-of-year cash payments

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Question:

Assume that an asset has the following end-of-year cash payments

Year Payment

1 $2000

2 $3500

3 $4200

4 $1500

What is this asset’s duration if the interest rate is 8%? Using duration, estimate the percentage change in the price of the asset if the interest rate decreased to 7%.

Answer:

First, compute the present value of the cash payments using the given rate of 8%. Then we assign weight to these present values out of the total present value. Lastly, multiply these weights with life/ years and we would get the duration.

Year Payment PVF@8% Present Value Weight Weight x Year
1 $2000 0.92592592592 1851.852 0.1994 0.1994
2 $3500 0.85733882029 3000.686 0.3230 0.6460
3 $4200 0.793832241 3334.095 0.3589 1.0767
4 $1500 0.73502985277 1102.545 0.1187 0.4748
9289.178 1 2.3969

Duration = 2.3969 yrs

To compute the estimate change in price, we need modified duration. It is computed as follows –

Modified Duration = Duration / (1+r) = 2.3969 / (1.08) = 2.2194

Modified duration denotes that for every 1% change in rates, the asset price will change by 2.2194%. So, if the rate decrease to 7%, the bond price will increase by 2.2194% (inverse relation between bond price and interest rates)

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