Flexible Savings Account FSA Plan Paper

A Flexible Savings Account (FSA) plan allows you to put money into an account at the beginning of the calendar year that can be used for medical expenses. This amount is not subject to federal tax as you pay medical expenses during the year, you are reimbursed by the administrator of the FSA until the money is exhausted. From that point on, you must pay your medical expenses out of your own pocket. On the other hand, if you put more money into your FSA than the medical expenses you incur, this extra money is lost to you. The goal of this study is to identify the optimal amount of FSA contribution to maximize the expected salary after tax and medical expenses.

Your annual salary is $70,000 and your federal income tax rate is 30%. Assume that you put $2,000 into your FSA at the beginning of the year and that medical expenses in a year are normally distributed with mean $2,000 and a standard deviation of $500.

A static model is given in the IA5_Q1_FSA_template.xlsx. Note that the output is the amount of money left to you after i) putting money into the FSA, ii) paying tax, iii) paying out of pocket medical expenditure. Make sure you understand all the calculations in the model.

A) Determine the input variables of this problem:

• • What is(are) the input random variable(s)?
  • What is(are) the decision variable(s)?
• B) Add the simulation functionality to the template to output the salary after tax and health care costs (add randomness to any random variables and designate the appropriate outputs). Run the simulation with 1000 replications. Copy and paste the graph of the distribution of salary after tax and health care costs. Explain the shape of the distribution. Particularly, can you explain the spike on the right and the smooth distribution on the left?
• C) Now use RiskSimTable to experiment with the amount of money put in the FSA. Set the range of the amount of FSA contribution to [$0, $4000]. The sections shaded in yellow are intended to assist you organize the information. Also, add RiskSimTable function to the model and update the number of simulations. Copy and paste your table. Based on the simulation results, answer the following questions.
  • If you are risk-neutral, how much would you contribute to your FSA? Explain your answer.
  • If you are risk-averse, how much would you contribute to your FSA? Explain your answer.