1.      A company’s (defined benefit) pension plan is considered to be overfunded if the present value of its assets is greater than the present value of its liabilities. It is considered to be underfunded if the present value of its liabilities is greater than the present value of its assets.

Your company’s pension plan has $3 billion in assets and 20,000 employees. The employees and the company are each required to contribute 8 percent of the employee’s pay into the plan each year. When an employee retires, his retirement benefit amount is calculated on that day as two percent of his average annual salary (calculated using the five highest earning years) multiplied by his number of years of service he worked for the company. Retirement payments are then indexed to inflation so that they increase at the same annual rate as the Consumer Price Index (CPI).  Retirement payments are sentto the employee for the rest of his life with the first payment coming exactly one year after the employee officially retires and has his retirement benefit amount determined.

Your job is to determine if your pension plan is overfunded or underfunded and by how much. To do this, you determine that your average employee has completed 20 years of service with your company and is expected to retire exactly 10 years from now. His life expectancy is 20 years after he retires. This average employee earned $50,000 last year (assume his salary is paid at the end of each year and he just received his $50,000 yesterday) and you expect that salary to increase each year at the rate of inflation. You expect inflation to be 2.5 percent per year and you expect your pension plan’s investments to earn a real rate of return of 4 percent per year. Based on this information, calculate the following:

a.       The expected nominal salaries for this average employee during his last five years of service

b.      The number of dollar bills he will receive when he gets his first retirement check.

c.       The present value (as of the retirement date) of this employee’s pension

d.      The present value (as of today) of this employee’s pension

e.       Use the above value to determine the present value of the pension’s liabilities for all 20,000 employees

f.       Determine the present value of the pension plan’s assets. These include current assets as well as future contributions by both the employees and the company

g.      Is the pension plan overfunded or underfunded, and by how much?

If you adjust your inflation estimate upwards (higher than 2.5%), how does this affect the pension’s funding (more overfunded, less overfunded, more underfunded, or less underfunded)?