Question

Your company offers a denied-benefit pension plan to each of its employees. The plan will make a monthly payment to each retiree of $4 thousand, next month. In each subsequent month, the payment will grow by an annualized rate of 2% to adjust for inflation. There are currently 100 retirees, and you estimate that this number will remain the same, indefinitely. The government mandates that (i) pension liabilities must be discounted at an annualized rate of 4%, and (ii) pension liabilities must be 75% funded (that is, the pension fund must be funded at 75% of the present value of the liabilities). (a) How much money must your rm contribute to its pension fund. (b) Consider the following variation on (a). Yours is a young company { a sexy startup. You don't have any retirees right now, but you do make pension promises to your young workers. You estimate that 20 years from now the first cohort of 50 workers will retire, receiving their first monthly payment one month after retiring (received in 241 months). Going forward, you expect the pool of retirees to remain stable, at 50. How much money must your firm contribute now in order to fulfil the government mandate?

Answer 1

Part A)

• Pension amount = $4000 per retiree per month
• Number of retirees = 100
• Inflation rate = 2% pa
• Discount rate = 4%
• Pension liabiltity on company = 75% of the total pension corpus

Pension corpus can be calculated by using the present value of growing perpetuity.
Present Value of pension claim of 100 retirees = [First payment amount $4000 / (Discount Rate 4%/12 months- Inflation Rate 2%/12 months)] * Number of retirees 100

Present Value of pension claim of 100 retirees = $240,000 * 100 = $24,000,000

Contribution by the company to pension fund = 75% of $20,000,000 = $18,000,000

Part B)

Monthly pension amount 1 month after 20 years = $4000 * (1+ Inflation Rate 2%/12)^{Number of months 241}

Monthly pension amount = $5975.25

Like in previous part, we need to calculate the present value of growing perpetuity.

Present Value of pension claim of 50 retirees at 20 years from now = [First payment amount $5975.25 / (Discount Rate 4%/12 months- Inflation Rate 2%/12 months)] * Number of retirees 50

Present Value of pension claim of 50 retirees at 20 years from now = $3,585,152.65 * 50

Present Value of pension claim of 50 retirees at 20 years from now= $179,257,632.48

Now we need to calculate the value of pension corpus as on today i.e. 20 years before

Present Value of corpus = $179,257,632.48 / (1+Discount Rate 4%)^{Number of years 20}

Present Value of corpus = $81,810,843.47

Contribution by the start-up = $61,358,132.6 (75% of $81,810,843.47)