Question

An Fl is planning the purchase of a $6 million loan to raise the existing average duration of its assets from 3.7 years to 5.2 years. It currently has total assets worth $23 million, $6 million in cash (O duration), and $17 million in loans. All the loans are fairly priced. a-1. Assuming it uses the cash to purchase the loan, calculate the duration of the existing loan. (Round your answer to 3 decimal places. (e.g., 32.161)) a-2. Assuming the Fl uses the cash to purchase the loan and that the loan has a 7.2 year duration, calculate the resulting duration of the asset portfolio. (Do not round intermediate calculations. Round your answer to 3 decimal places. (e.g., 32.161)) a-3. Should it purchase the loan if its duration is 7.2 years? b. What asset duration loans should it purchase in order to raise its average duration to 5.2 years? (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16))

Answer 1

a-1. If the FL is planning to purchase a $6 million loan to raise the average duration of its assets, we can use the following formula to calculate the duration of the existing loan:

Weighted average duration before purchase = (Duration of existing loans * Value of existing loans) / Total assets

5.2 = (Duration of existing loans * $17 million) / $23 million

Duration of existing loans = 3.852 years

Therefore, the duration of the existing loans is 3.852 years.

a-2. If the FL uses the $6 million in cash to purchase a loan with a 7.2-year duration, we can calculate the resulting duration of the asset portfolio using the following formula:

Weighted average duration after purchase = [(Duration of existing loans * Value of existing loans) + (Duration of purchased loan * Value of purchased loan)] / (Total assets + Value of purchased loan)

Weighted average duration after purchase = [(3.852 * $17 million) + (7.2 * $6 million)] / ($23 million + $6 million)

Weighted average duration after purchase = 4.847 years

Therefore, the resulting duration of the asset portfolio is 4.847 years.

a-3. Whether the FL should purchase the loan with a 7.2-year duration depends on its investment objectives and risk tolerance. If it believes that the loan will provide a sufficient return to compensate for the increased duration risk, then it may be a good investment. However, if the FL is not comfortable with the increased duration risk, it may choose to look for a loan with a lower duration instead.

b. To raise the average duration of its assets to 5.2 years, the FL needs to purchase a loan with a duration of:

Weighted average duration after purchase = (Duration of existing loans * Value of existing loans + Duration of purchased loan * Value of purchased loan) / Total assets

5.2 = (3.852 * $17 million + Duration of purchased loan * $6 million) / $23 million

Duration of purchased loan = 8.42 years

Therefore, the FL should purchase a loan with a duration of 8.42 years to raise the average duration of its assets to 5.2 years.