My company is doing open enrollment again for next year (for more info on what to choose in open enrollment, see previous posts). I’m not going to make any changes except I have to re-enroll for flexible spending account (FSA).
If you use flexible spending account, you should be familiar with the use-it-or-lose-it rule. If you put too much in the FSA, you will lose what you can’t use. In the past I always estimated conservatively. I’ve never lost any money to the FSA. However there is also a cost to that approach. After the money in the FSA is used up, any additional expenses must be paid with after-tax dollars. There has to be a point where losing a little pre-tax money in the FSA is less expensive than paying a lot with after-tax money.
This becomes an interesting math problem.
Suppose your best estimate for next year’s FSA-eligible expenses is $1,000, plus or minus $500 because you can never be sure what your actual expenses will be. Your marginal tax rate for FSA contributions is 32% (you have to include the Social Security and Medicare taxes if your income is below the Social Security Wage Base, $106,800 in 2009). How much should be put in your FSA?
So your expenses will range from $500 to $1,500 next year. We can divide it up into ten smaller intervals: $500-600, $600-700, …, $1,400-1,500. For each interval, we use the mid-point as the proxy and calculate the total after-tax cost. The total after-tax cost is:
FSA Contributions * (1 – Marginal Tax Rate) + Expenses Above & Beyond FSA
For example, if you contribute $1,000 to FSA, and your actual eligible expenses are:
|From||To||Midpoint||Total After-Tax Cost|
Over the full range of likely expenses, your average total after-tax cost is $805 if you contribute $1,000 to your FSA. After calculating the same for other contribution amounts, we get this nice graph.
The graph shows that putting in the most conservative amount ($500) isn’t the best strategy. Putting in your best estimate ($1,000) isn’t the best either. The lowest average total after-tax cost over the full range of the estimated expenses is achieved when you put in somewhere in between those two numbers, around $800 in our example.
If you’d like to play with your own numbers, here’s the spreadsheet I created.
Math-minded readers probably noticed that by taking a straight average of the total after-tax costs for all ten intervals, I’m giving each interval equal weight. In math terms, it’s called a uniform distribution. In real life, the intervals at either end of the range ($500-600 and $1,400-1,500) will be less likely than the intervals in the middle. So here’s the challenge question for interested readers:
If you assume your next year’s FSA-eligible expenses follow a normal distribution with a mean of $1,000 and a standard deviation of $250 (same $500 to $1,500 range with 95% confidence), how much should you put into the flexible spending account in order to minimize your expected total after-tax cost?
Who knew a flexible spending account involves this much math?
Finally, if you are married and one of you earns an income above the Social Security Wage Base and another earns below, you should have the spouse with the lower income contribute to the FSA. This was explained by indexfundfan.
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