How can a quick math error—plus faulty logic—cost someone $120,000?

A recent Reddit contributor (wisely) asked the “Bogleheads” forum for investing help. His full question is below. The question highlights are:

- My 401(k) offers me a 2% match. 2% is not great compared to the industry average of 4-5%.
- My 401(k) also has funds with 1% expense ratios (a.k.a. fees). Super high! Yuck!
- This combination—poor employer matching and high fees—makes me want to say, “Screw the 401(k). I’d rather invest in a taxable account.”
- But, I haven’t done the math to backup my gut instinct.

Here’s the full text, if you’re interested:

I recently got my hands on my employer’s 401(k) fund options. They are abysmal. The lowest expense ratio is just about 1%. My employer also gives a 2% match (0.25% of 8% contributed though).

So, the general advice is to contribute up to employer match, but even that I feel like it is not worth the expense ratio.

My argument for saying it is not worth it is related to the compounding effect of 1% exp ratio on the total amount invested vs. only 2% being matched each year. Over time, if I stay in this fund, I will lose much more from the expense ratio than I will gain from employer matching.

Even considering the advantages of the tax-deferred space, I have not done the calculations, but long term, I am pretty sure investing in a taxable account would be better than the 401k with 1% exp ratios.

Full forum post

Let’s quickly highlight some points about this question.

## The Good, Bad, and Ugly About This Question

Open questions about money lead to important lessons. This is a great question to ask!

But we can learn two quick lessons from the “bad/ugly” aspects of this question.

- First, we have to separate what “feels bad” from what “is bad.” It might
*feel*bad to pay a higher expense ratio than standard. And it might*feel*bad to have a low employer match. But the math of the problem holds true irrespective of feelings.** - “I have not done the calculations, but long term, I am pretty sure…”
*Whoa, Nelly!*This is a dangerous statement in personal finance. If you don’t know the calculations,*that’s ok!*Ask for help. The Internet is an amazing resource. But to be “pretty sure” about a mathematical outcome*without*doing any math—that’s unwise.

**Charlie Munger tells a story of when Berkshire Hathaway bought BNSF Railroad. Some Berkshire Hathways shareholders felt that they were only getting a “good” deal, while the BNSF shareholders were getting a “great” deal on the transaction. They wanted Berkshire’s leadership (Warren Buffett and Munger) to negotiate a better deal. And Charlie Munger wisely pointed out, “If you’re getting a good deal, why the hell do you care what the other guy is getting?” Envy is a potent drug.

## The Math

To get a real answer, you’ve got to do real math. So that’s what I did.

Remember, the curious Redditor believed that a 401(k) would *surely* do worse than a taxable account. I’ll give him the benefit of the doubt.

I used **conservative** assumptions for my hypothetical 401(k) investor and compartively **kind** assumptions for my hypothetical taxable investor. I wanted to be extra gracious to the Redditor’s theory—could his gut be correct?

The assumptions and the math can all be found in **this Google Spreadsheet**.

- Both investors contribute the same amount.
- The 401(k) investor receives a 2% company match, but pays a 1% expense ratio.
- The taxable investor pays income tax up front, receives no match, but pays no expense ratio.
- Both investors see the same investment performance (before fees)
- Both investors pay taxes upon withdrawal (30 years), though I assume a 22% income tax rate for the 401(k) investor and only a 10% capital gains rate for the taxable account investor.

Even with my harsh assumptions, the 401(k) investor outperforms the taxable investor by **$120,000** (or about 12%) over a 30-year period.

That’s a *huge* amount. The 2% company match *an**d* tax-deferred nature of the 401(k) is significant.

Not to rub salt in the wound, but recall that this person was “fairly certain” that a taxable account was the smarter choice.

Lesson: **always question your assumptions, especially if math can help you. **I guarantee you know someone who can build this spreadsheet in 15 minutes or less. That’s little time, but much gained.

Thank you for reading! If you enjoyed this article, join **8000+ subscribers** who read my 2-minute weekly email, where I send you links to the smartest financial content I find online every week.

-Jesse

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Plus assumes no tax consequences year over year on the taxable account. Only multiplies the $120,000 spread if you consider dividends, interest, and realized gains trigger immediate tax liability in a taxable account.

Excellent point, Craig!

The taxable account will (most likely) have an annual “drag” on it from taxes.

What’s a rough approximation?

Dividends might be 3% per year.

Tax rate on those…~15%.

So taxes equate to ~0.45% per year (15% of 3%)

That’s a BIG factor!

Before 401K’s were a thing my company had a tax deferred investment vehicle that let you contribute up to 12% of your salary and they matched it 100%! A huge benefit and you could withdraw money at any age with no penalty. It was sweet but only lasted about 7 years when the tax laws ended it. I remember one of my coworkers, an engineer like me, told me he “couldn’t afford” to contribute. He was driving a dream sports car at the time, a 280Z Turbo, brand new. I just shook my head, how can anyone NOT afford to take a free 12% gift from the company that is also tax deferred. Crazy. Of course I’ve been retired for six years and he’s still working.

It’s all about choices 🙂

Sounds like he chose to ignore free money.

That’s a TOUGH choice.

Thanks for putting this together and calculating this problem for us in a way that’s easy and simple to understand!

I agree – I think a lot of times things *feel* one way, but the actual, concrete math says another. And for long-term calculations like this where the math compounds, it’s even more important to actually just take a few minutes to calculate the numbers.

We meet again, Angie 🙂

You’re welcome. And thank you for reading.

If you can do math, you should certainly try. The objective truth is always helpful to know.

Talk soon!

Jesse

would you pay taxes on a taxable account if you make no withdrawls and re-invest dividends and gains ?

Hey Brian, great questions.

Yes – you would pay taxes on dividends on investments held within a taxable account. Even if you plan on reinvesting those dividends, they are taxed first.

Capital gains – i.e. increases in stock price – are taxed too, but not until the investment is sold.

Year 0: Buy $1000 of Stock A.

Year 1: Price goes to $1200, dividend of $30 is paid.

You pay taxes on the $30.

Year 2: Price goes to $1500, div of $50 is paid.

You pay taxes on the $50

Year 3: Price goes to $2000, div of $100 is paid.

You sell the stock.

You pay taxes on the $100.

And you pay taxes on the $1000 ($2000 sale price – $1000 basis cost)