A friend of yours works in the HR department of a small company. The company has decided to offer defined-benefit pension plans in which they will pay 75% of an employee’s last annual salary given the employee has worked there for 25 years. The pension amount will be reduced by 3% for each year less than 25 years (so an employee that retires after 15 years will receive 45% (75%-10*3%) of his final years salary). Payments begin at age 65 if the worker retires, though they may continue working and increase their pension if they have not worked for 25 years up to that age.

Your friend is trying to come up with some estimates of the cost of the plan and is looking to you for help. She has provided you with information on two employees, Jack and Jill. Jack has worked at the company for 27 years, is 58 years old, and makes $34,000 per year. It is believed he will remain at the firm until he retires and that his salary will increase by 4% annually until that time. Jill has worked at the company for 3 years, is 47 years old, and makes $42,000 annually. She will likely receive a 7% annual raise until she is retirement age.

You must help your friend determine how much money the company must invest annually. The company can borrow money at 8% and feels that this is the minimal rate their invested funds should be able to earn. The life expectancy of each employee is 15 years at age 65.

1. If Jack and Jill both retire at the age of 65, how much will each person’s pension be?

2. If the firm purchases an annuity from an insurance company to fund each pension, and the insurance company claims to be able to earn 9% on the funds, what is the cost or the amount required to purchase the annuity contracts (at the time of retirement)?

3. If the firm can earn 8% on the money it must invest annually to fund the pensions, how much will the firm have to invest annually to have the funds necessary to purchase both annuities?

4. What would be the impact of each of the following situations on the amount that the firm must invest annually to fund the pension?

a) Life expectancy is increased to 20 years.

b) The rate of interest on the annuity contract with the insurance company is reduced to 7%.