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

Question

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?

Answer 1

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.

Answer 2

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.

Answer 3

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.

Answer 4

The opportunity cost of a 401(k) loan is slightly more complex than your typical investment leveraging scheme. In the short term, a 401(k) loan is very inexpensive, as the interest you pay goes into your 401(k) rather than the banks pockets. That being said, the cost of a 401(k) loan is in terms of loss of growth, and in risk.

The market reliably averages nearly 10% returns before inflation adjustment. This means that, depending on how long between the time of the loan and the time of your retirement, you can place a monetary value on lost growth.

example: 26yo takes $10,000 401(k) loan over 60 months, with the expectation of retiring at 70 the lost growth is the principle times the annual interest times half the time period (as the loan is repaid evenly over the time period). The loss from that period then has to be factored forward into the growth of the account. This gives us: (1.1^5)-1 ~ 0.6 (total interest%) divide by 5 to get annual interest rate of slightly more than 12%. Compared to the 4% interest you pay on the loan (works out to roughly 4 1/3% annually) you're losing 8% of half(for the time period) your principle per year in interest over the 5 year period, or $400 worth.

When the loan is finally paid back, you're sitting at 39 years to retirement. That $400 over 39 years with an average of 10% return is (1.1^39)-1 * 400 , on top of the $400. That works out to roughly $16,500 + $400, or nearly $17,000, compared to the $10,000 principle.

Because there is a cap on how much you can contribute, you can never catch up or scrimp and save to make up the difference(or if you could, you could also do that without the loan, so it's a wash). You're missing out on 1.7 times your principle in accrued interest in a tax exempt account in this particular situation. The numbers get better as you get closer to retirement, and as you pay back the loan in a shorter time frame, but the loss is still higher than even consumer credit card debt in 99% of the cases. The only major difference is your choice to defer the loss to your future self, rather than take it now.

To cap it off, you increase your risk when you take a 401(k) loan, as loss of employment brings the balance due within 60 days, under penalty of early distribution penalties (10% plus the principle remaining is taxed that year as income).

As someone who has taken out a 401(k) loan knowing the potential future loss, I would advise against taking it out as much as possible. The only reason I took one out is that it does not affect the process of a house being underwritten if you are buying. I still feel like I may have made a mistake doing so.