The Best Interest » 15 Minutes of Math = \$120,000

15 Minutes of Math = \$120,000

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

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

1. 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.**
2. “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 and 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 8500+ subscribers who read my 2-minute weekly email, where I send you links to the smartest financial content I find online every week. You can read past newsletters before signing up.

-Jesse

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8 thoughts on “15 Minutes of Math = \$120,000”

1. 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.

1. 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!

2. 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.

1. It’s all about choices 🙂

Sounds like he chose to ignore free money.

That’s a TOUGH choice.

3. 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.

1. 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

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

1. 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)