Answered

Connect with a community of experts and enthusiasts on IDNLearn.com. Discover in-depth and trustworthy answers from our extensive network of knowledgeable professionals.

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.

Sagot :

Abiolataiwo2015idn

Answer:

3.04

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

We appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Your search for solutions ends here at IDNLearn.com. Thank you for visiting, and come back soon for more helpful information.