Question

A railroad company is required to pay 79,860, which is due three years from now. The company invests 15,000 in a bond with modified duration 1.80, and 45,000 in a bond with modified duration Dmod, to Redington immunize its position against small changes in the yield rate. The annual effective yield rate for each of the bonds is 10%. Calculate Dmod.

Answer 1

3.04

Step-by-step explanation:

Calculation to determine Dmod.

First step is to calculate the present value of the assets which also represent the present value of the liability

Present value of the assets =$15,000+$45,000

Present value of the assets = $60,000

Second step is to calculate the modified duration of the assets which is the weighted average

Modified duration of the assets=($15,000/$60,000)/1.80+$45,000/$60,000Dmod

Modified duration of the assets=0.25(1.80) + 0.75Dmod

Third step is to calculate the Modified duration of the liability

Modified duration of the liability =3/(1+0.1)

Modified duration of the liability =3/1.1

Now let calculate Dmod

Dmod = (3/1.1 – 0.45)/0.75

Dmod=(2.7272-0.45)/0.75

Dmod=2.2772/0.75

Dmod=3.036

Dmod=3.04 (Approximately)

Therefore Dmod is 3.04