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

## Description

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%.

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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