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 1

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)