Question

What is the duration of a 4 year coupon bond with a face value of $1000, a coupon rate of 8% and interest rate is 10%?

A) 3.12

B) 3.56

C) 3.48

D) 3. 89

Answer 1

For calculating Duration, let us first find out the following:

1) Coupon= Cash inflows every year= $80 for 4 years

2) Redemption amount on maturity= one time cash inflow at the end of 4th year=$1000

We will first calculate the discounted values of above mentioned cash inflows, we will discount the cash inflows at the rate of 10%:

1) Discounted value of first year cash inflow= 72.72

2) Discounted value of second year cash inflow= 66.1157

3) Discounted value of Third year cash inflow= 60.1052

4) Discounted value of Fourth year cash inflow= 54.6410

5) Dicounted value of Fourth year cash inflow of redemption amount of $1000= 683.0135

Total of all above discounted cash inflows= $936.6026

We will now calculate the time weighted discounted values:

1) $72.72 multiply by ONE= $72.72

2) $66.1157 Multiply by TWO= $132.2314

3) $60.1052 Multiply by THREE= $180.3156

4) $54.6410 Multiply by Four= $218.564

5) $683.0135 Multiply by Four= $2732.054

Total of all above these values is $3335.8922

Duration= $3335.8922 Divided by $936.0135= 3.56 years

The duration of the above Bond is 3.56 years.