Many cities such as Detroit, MI have been in the news recently regarding underfunded pension funds. This exercise addresses a simplified version of some of the issues involved (doing this as a starting point is common: the key generally is to address the core work, adding more complexity later to make the analysis more accurate).

One way to handle pension obligations is to set aside money during the employee’s working life to fund an annuity that will pay out during the employee’s retirement years. The calculations will require assumptions about the number of years of working life (use 30 in this exercise), the number of years of pay-out, and the return on investment (interest rate) during the two periods.

One article states that for the last 26 years, Detroit has used an interest rate of 8.9% for calculations. Recent research suggests that a more accurate estimate would be 6.3%. Most companies use a rate between 7% and 8%.

Background data:

Life expectancy at age 55: male = 23.68 years, female = 27.31 years

Life expectancy at age 66: male = 15.86 years, female = 18.30 years

Average pension = $30,000 per year

Number years to earn full pension = 30

Number of city employees = 12,900

Number of current retirees = 21,000

Analysis: We will base the analysis on calculations for an average city employee. Calculations will be per year.

Requirements:

1. Calculate the value of the pay-out annuity at retirement. Do this twice: once for 6.3% and once for 8.9%. Use the same number of years for each (you will need to decide how many years to use in this calculation). Estimate the city obligation for each of these (first result times number of city employees).

2. Calculate how much must be set aside each year of working life to accumulate the value of the pay-out annuity at retirement. Do this for both 8.9% and 6.3%. Estimate the city obligation for each.