## 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%.

**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)

## Reviews

There are no reviews yet.