Income Optimization: FSA Accounts

Employees of the University are permitted to contribute a portion of their paychecks to a flexible spending account to cover healthcare expenses that are not covered by their insurance plan. These contributions are tax-deductible (that is, paid with pre-tax dollars), but any amounts not spent in the plan year are forfeited; “use it or lose it.” Suppose an employee makes $60,000 (gross) and is subject to a total marginal tax rate of 33%. The employee estimates that for her family, medical expenses not covered by insurance will be somewhere between $500 and $5,000 (the maximum out-of-pocket amount), with a most likely value of $1,300. Assume these amounts will not be tax-deductible and that they follow a triangular distribution.

a. Build a spreadsheet model and simulate 1,000 years to determine the amount that she should contribute to the FSA to maximize the amount of money she will have left over after taxes and medical expenses are paid.

b. With that contribution amount, what is the probability that there will be leftover funds in the account that will be forfeited?

c. Suppose she thinks that a beta distribution (using the min and max values above and the α and β parameters from the PowerPoint) is a more accurate representation of reality. What would be the revised value for the optimum contribution?