# How should I calculate the opportunity cost of using a 401(k) loan?

I've seen a number of financial articles that discuss the "opportunity cost" of using a 401(k) loan; however, I don't seem to recall ever seeing a good formula or calculation that can be done to determine what the opportunity cost - if any - actually is. Does one exist? If not, how should I do this calculation?

As an example, consider the following: if you have \$5,000 of credit card debt with a APR of 8.5%, is it to your advantage to use a \$5,000 401(k) that will be paid back in 12 months with a 6.5% interest rate?

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Consider this situation too – enderland Feb 1 '13 at 17:10

One way to analyze the opportunity cost of using a 401K loan would be to calculate your net worth after using a 401K loan. If your net worth increases then the 401K loan would be advisable. Note that the calculations provided below do not take into account tax considerations.

A net worth calculation is where you add all your assets and then subtract all your liabilities. The resulting number is your net worth.

First, calculate the net worth of not taking the loan and simply paying the credit card interest. This means you only pay the interest on the credit card. In addition to the parameters identified in your question, two additional parameters will need to be considered: Cash and the market rate of return on the 401K.

Scenario 1 (only pay credit card interest):
After 12 months all you have paid is the interest on the credit card. The 401K balance is untouched so it will hopefully grow. The balance on the credit card remains at the end of 12 months.

``````         |---Change in cash----|   |---Change in 401K---|
Assets =  C – (\$5,000 * CCIR)    +   \$5,000 * (1 + MRR)

|--Credit card balance--|
Liabilities =         \$5,000

Net worth = C – 5,000*CCIR + 5,000 + 5000*MRR – 5000
= C – 5,000*CCIR + 5,000*MRR
Where
C   = Cash
CCIR    = Credit Card Interest Rate
MRR     = Market Rate of Return you can earn on your 401K.
``````

Scenario 2 (use 401K loan to pay credit card balance):
You borrow \$5,000 from your 401K to pay the credit card balance. You will have to pay \$5,000 plus the 401K interest rate back into your 401K account.

``````         |---Change in cash----|   |---Change in 401K---|
Assets =  C – \$5,000 * (1 + KIR) +   \$5,000 * (1 + KIR)

|--Credit card balance--|
Liabilities =           \$0

Net worth = C – 5,000 – 5,000*KIR + 5,000 + 5,000*KIR
= C
Where
KIR = 401K Interest Rate
``````

Use the following equation to determine when Scenario 2 increases your net worth more than scenario 1:

``````C > C – 5,000*CCIR + 5,000*MRR

Which simplifies to:

CCIR > MRR
``````

Thus, if your credit card interest rate is greater than the rate you can earn on your 401K then use the 401K loan to pay off the credit card balance.

Another scenario that should be considered: borrow money from somewhere else to pay off the credit card balance.

Scenario 3 (external loan to pay credit card balance):
You borrow \$5,000 from somewhere besides your 401K to pay off the credit card balance.

``````         |---Change in cash----|   |---Change in 401K---|
Assets =  C – \$5,000 * (1 + EIR) +   \$5,000 * (1 + MRR)

|--Credit card balance--|
Liabilities =           \$0

Net worth = C – 5,000 – 5,000*EIR + 5,000 + 5,000*MRR
= C - 5,000*EIR + 5,000*MRR
Where
EIR = External Interest Rate
``````

The following is used to determine if you should use an external loan over the 401K loan:

``````C - 5,000*EIR + 5,000*MRR > C

Which simplifies to:

MRR > EIR
``````

This means you should use an external loan if you can obtain an interest rate less than the rate of return you can earn on your 401K. The same methodology can be used to compare Scenario 3 to Scenario 1.

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There is no equation. Only data that would help you come to the decision that's right for you. Assuming the 401(k) is invested in a stock fund of one sort or another, the choice is nearly the same as if you had \$5K cash to either invest or pay debt. Since stock returns are not fixed, but are a random distribution that somewhat resembles a bell curve, median about 10%, standard deviation about 14%. It's the age old question of "getting a guaranteed X% (paying the debt) or a shot at 8-10% or so in the market." This come up frequently in the decision to pre-pay mortgages at 4-5% versus invest. Many people will take the guaranteed 4% return vs the risk that comes with the market. For your decision, the 401(k) loan, note that the loan is due if you separate from the company for whatever reason. This adds an additional layer of risk and another data point to the mix. For your exact numbers, the savings is barely \$50. I'd probably not do it. If the cards were 18%, I'd lean toward the loan, but only if I knew I could raise the cash to pay it back to not default.

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You did consider, of course, that the "interest" paid to a 401k loan is basically being paid to himself; it goes into the 401k to replace what the principal isn't earning in the market while he has it outstanding. So, if he does this, in net worth terms he's not saving just the 2% between APRs, but the full 8.5% rate of the card. The only caveat is that the 6.5% interest payments are locked up in the 401k. There may also be a one-time percentage fee charged on the money withdrawn, which he does lose. – KeithS Jan 31 '13 at 23:34
@KeithS - There's another level of analysis to apply. First, 'borrow at 6.5 to pay off an 8.5% loan.' No brainer, right? The bigger question becomes 'is a fixed 6.5% in the 401(k) worth it?' Is it S&P index money? Or is it the money market fund, .01%? – JoeTaxpayer Feb 1 '13 at 0:01
Right, but the difference, opportunity-wise, is between 6.5% (by paying off the card), and the current return rate of the 401k minus 8.5% (by keeping the money in the 401k). So the breakeven between the two is a return rate of 15% in the market. Under, pay the card; over, keep the cash in the 401k. It's possible to get that rate, especially when the economy's clawing itself out of a hole, but I don't think you can get that rate long term by just playing "the stock market" as you generally do with an index fund or other diversified fund. – KeithS Feb 1 '13 at 0:29
@KeithS - If the breakeven stock return needed to be 15%, I'd say take the loan, no question. I'm not seeing that. It's between the 6.5 and 8.5, but not the sum of the two. – JoeTaxpayer Feb 1 '13 at 3:37

Make sure that when you have the loan you still contribute enough to get the company match.

For example:

• If you were contributing 6% each pay check, and the company was matching with 3% of each check (the maximum amount they will match) before the loan.
• And if the loan repayment will be \$100 a pay check
• Then you have to up your contribution to 6% plus +\$100 because the company doesn't match the loan repayment.

An inability to maximize the match might need to be figured into the opportunity cost of the loan.

Some companies will suspend your contributions for a specific number of months for a hardship withdraw.

Make sure you understand where the money comes from for the loan. Can you count the money that the company matched but you are not vested with, when determining the maximum amount of the loan? If the money is in what is now a closed fund can you replenish the funds back into that fund if use it to fund the loan? Know what the repayment time period is of the loan.

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