Optimal Use of Flexible Spending Arrangements: A Marginal Analysis Approach

By Auster, Rolf; Sennetti, John T. | The National Public Accountant, March 1994 | Go to article overview

Optimal Use of Flexible Spending Arrangements: A Marginal Analysis Approach


Auster, Rolf, Sennetti, John T., The National Public Accountant


Flexible Spending Arrangements (FSAs) under Section 125 and Regulation thereunder are employer plans to which employees may contribute before-tax dollars to be spent on medical expenses (medical-care FSAs) or childcare expenses (dependent-care FSAs). While an employee saves taxes (including social security, state and local taxes) on contributions made, amounts not spent for their designated purpose are forfeited. In other words: "Use it or lose it!" Clearly, an employee needs to be reasonably sure that the funds will in fact be needed before parting with a portion of a salary. The marginal analysis approach is shown below to provide a rational method by which an employee may determine just how sure he or she should be about the future need for FSA funds before committing a contribution to the plan.

The Marginal Analysis Approach

Under the traditional marginal analysis approach one more unit should be acquired, stocked or produced until the expected profit from selling or needing the unit equals the expected loss from not selling or needing it.

The expected profit from the next unit needed is pP (read p times P) where

p = the probability of needing at least one more unit

P = the profit derived from needing or selling the extra unit acquired.

The expected loss from the next unit not needed is (1 - p)L |read (1 - p) times L~ where

(1-p) = the probability that at least one more unit is not needed

L = the loss resulting from not needing or selling the extra unit acquired.

The "break even" or indifference point is where

pP = (1-p)L

solving for p

p = L/P + L

Thus, if the decision maker is more than p times 100% sure that at least one more unit is needed where p = L/P+L, the additional unit should be acquired.

Applying Marginal Analysis to FSAs

If an employee takes an additional salary reduction of $1 to be added to an FSA, the potential profit from doing so is the marginal tax saved on the dollar. In this case P = $T where T is the marginal tax rate.

However, if the additional dollar is not used but is forfeited, the loss would be a dollar less the tax not paid on the dollar. Here L = $(1 - T).

Thus, the employee should keep funding the FSA as long as the probability of needing the additional funding equals or exceeds

L/P + L = (1-T)/T + (1-T) = 1-T

Example

The taxpayer is in the 30% marginal tax bracket. Since 1-.30 = .70, the taxpayer should increase the amount in the FSA as long as the taxpayer is more than 70% sure of needing at least the additional amount set aside. At exactly 70% the taxpayer would break even on the additional amount transferred, i.e., the expected benefit would be zero. For a taxpayer who adds $100 to the FSA there are two possibilities, i.e., the amount is used or lost: If used the taxpayer saves tax of $100 x .30 or $30. Since the probability of usage is 70%, the expected tax savings are $30 x .70, or $21.

If lost the taxpayer forfeits $100 less the $30 tax which would have been payable absent the transfer, or $70. Since this has a 30% chance of occurring, the expected after-tax loss is $70 x .30, or $21.

Clearly the higher the employee's marginal tax rate, the less the loss of contributing too much to the FSA and the less confident the employee needs to be to elect additional salary reductions; e.g., if T equals .4, the acceptable risk of losing additional FSA funds is 60%.

Assumptions Made

To maximize the usefulness of the approach presented, the following assumptions are made:

1. The marginal tax rate, T, is constant with respect to the incremental FSA funding amount considered.

2. FSA amounts not used are forfeited. (In practice, an aggregate FSA plan surplus, if any, may in some situations be distributed among plan participants in cash or credited against future contributions the following year).

3. …

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