A company has liabilities that require it to make payments of 1000 at the end of each of the next five years. The only investments available to the company are as follows:

Investment	Price	Subsequent Cash Flows
J	1500	500 at the end of each year for 5 years
K	500	1000 at the end of year 5
L	1000	500 at the end of each year for 4 years
M	4000	1000 at the end of each year for 5 years

The company is able to purchase as many of each investment as it wants, but only in whole units. The company’s investment objective is to be fully immunized over the next five years.

Calculate the lowest possible cost to achieve this objective.

• 1500
• 2000
• 2500
• 3000
• 4000

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: C

Options for full immunization are: 2J (cost is 3000), K+2L (cost is 2500), and M (cost is 4000). The lowest possible cost is 2500. Another way to view this is that the prices divided by total cash flows are 0.6, 0.5, 0.5, and 0.8. The cheapest option will be to use K and L, if possible.

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.