Looking at Expenses of 401k Plans

This article appeared in the September 2001 NAPFA Advisor. NAPFA is the National Association of Personal Financial Advisors. The analytical model is available through my Spreadsheets page. Corrected figures appear in square brackets and bold text. Note that I’m not a financial advisor.

June 2017 comment – small businesses might wish to consider Guideline, a low-cost 401k plan provider.

Companies offer 401k plans to allow employees tax-advantaged investing for their retirement. The contributions and growth aren’t taxed until withdrawn. Unfortunately, in many cases the investment choices have annual expenses comprised of high operating, transaction, and sales costs.

So, at what point does the disadvantage of high expenses outweigh the tax advantages of a 401k plan? As an alternative to a 401k plan investment, I considered a low-expense, tax-managed S&P 500 index fund that minimizes capital gains distributions. The spreadsheet model that I developed calculates the after-tax fund proceeds and then finds the minimum rate of return needed from a hypothetical 401k plan fund to match that amount. Of course, the relevance of this analysis depends on not being able to make additional IRA contributions, not receiving employer matching on the 401k investments, and the appropriateness of a large-capitalization U.S. growth and income fund for a client’s asset allocation.

Starting with the non-401k S&P 500 fund calculations, I assumed an initial investment of $1000 was immediately reduced by the 39.1% highest ordinary income tax rate. For the fund’s return, I used the historical S&P 500 annual total return of 10% (8.5% in unrealized capital gains and 1.5% in dividends). I then reduced the 8.5% by .2% in annual expenses, resulting in an 8.3% unrealized capital gains rate. For this analysis, I also assumed no capital gains distributions would be made, but included this option in the spreadsheet.

The unrealized capital gains rate of 8.3% was applied to the balance at the end of the previous year to obtain the current year’s “unrealized capital gains.” This was assumed to remain in the account for further growth. The 1.5% dividend rate was reduced by the 39.1% tax rate to obtain the “after-tax dividend” available to be reinvested. Note that this new investment becomes part of the tax basis and is excluded from “cumulative unrealized capital gains” when the account is redeemed.

To simplify the analysis, I assumed the entire account would be redeemed at once and calculated the capital gains taxes on the “cumulative unrealized capital gains.” Subtracting the capital gains taxes from the end-of-year balance resulted in the after-tax proceeds for a given year. For a 30 year investment, the after-tax proceeds were $7,251 [$7,396].

The formula for the 401k plan after-tax proceeds is:

$1000 *
(1 + Breakeven 401k Rate)^30 *
(1 – 0.35).

This reflects the tax-deductible investment of $1000, tax-deferred compounding for 30 years, and ordinary income tax rate of 35% upon redemption. Excel’s “Goal Seek” feature can find the breakeven 401k rate, which results in the same after-tax proceeds as the non-401k case. Alternatively, solving for the rate algebraically facilitates calculating values for each year.

The breakeven 401k rate for the 30 year case is 8.54% [8.44%]. Therefore, a 401k plan fund with annual expenses exceeding 1.46% (10% – 8.54%) [1.56% (10% – 8.44%)] might not outperform a tax-managed S&P 500 index fund outside of the 401k.

The spreadsheet that generated the following analysis is available at www.ed-chang.com.

Ed Chang provides quantitative modeling consulting. His experience includes creating mathematical optimization models for complex leases and reviewing the quantitative sections of a personal finance bestseller. He can be reached at www.ed-chang.com.

Bold text items can be changed in the spreadsheet.

————- Tax Rates ———- ————
Initial Investment $1,000 Ordinary Inc. Dividends Cap. Gains 5 Year Gains
Unrealized Capital Gains 8.3% 2001 39.1% 39.1% 20.0% 18.0%
Dividend 1.5% 2002 38.6% 38.6% 20.0% 18.0%
Capital Gains Distribution 0.0% 2003 38.6% 38.6% 20.0% 18.0%
401k Total Return Without Expenses 10.0% 2004 37.6% 37.6% 20.0% 18.0%
Rollover IRA Return After Expenses 9.8% 2005 37.6% 37.6% 20.0% 18.0%
401k Holding Period (maximum of 30) 30 2006 35.0% 35.0% 20.0% 18.0%
First Year (change before Tax Rates) 2001 2007 35.0% 35.0% 20.0% 18.0%

Year Unrealized After-Tax After-Tax End of Cumulative Capital Gains After-Tax Breakeven Breakeven
Capital Dividend Capital Gains Year Unrealized Taxes Upon Proceeds 401k 401k
Gains Distribution Balance Capital Gains Redemption Rate Expenses
2001 $609
2002 $51 $6 $0 $665 $51 $10 $655 6.69% 3.31%
2003 $55 $6 $0 $726 $106 $21 $705 7.18% 2.82%
2004 $60 $7 $0 $794 $166 $33 $760 6.81% 3.19%
2005 $66 $7 $0 $867 $232 $46 $821 7.08% 2.92%
2006 $72 $8 $0 $947 $304 $55 $893 6.55% 3.45%
2007 $79 $9 $0 $1,035 $382 $69 $966 6.83% 3.17%
2008 $86 $10 $0 $1,131 $468 $84 $1,047 7.05% 2.95%
2009 $94 $11 $0 $1,236 $562 $101 $1,135 7.21% 2.79%
2010 $103 $12 $0 $1,351 $665 $120 $1,231 7.35% 2.65%
2011 $112 $13 $0 $1,476 $777 $140 $1,336 7.47% 2.53%
2012 $123 $14 $0 $1,613 $900 $162 $1,451 7.57% 2.43%
2013 $134 $16 $0 $1,762 $1,033 $186 $1,576 7.66% 2.34%
2014 $146 $17 $0 $1,926 $1,180 $212 $1,714 7.74% 2.26%
2015 $160 $19 $0 $2,105 $1,340 $241 $1,863 7.81% 2.19%
2016 $175 $21 $0 $2,300 $1,514 $273 $2,027 7.88% 2.12%
2017 $191 $22 $0 $2,513 $1,705 $307 $2,206 7.94% 2.06%
2018 $209 $25 $0 $2,746 $1,914 $344 $2,402 7.99% 2.01%
2019 $228 $27 $0 $3,001 $2,142 $385 $2,615 8.04% 1.96%
2020 $249 $29 $0 $3,279 $2,391 $430 $2,849 8.09% 1.91%
2021 $272 $32 $0 $3,583 $2,663 $479 $3,104 8.13% 1.87%
2022 $297 $35 $0 $3,916 $2,960 $533 $3,383 8.17% 1.83%
2023 $325 $38 $0 $4,279 $3,285 $591 $3,688 8.21% 1.79%
2024 $355 $42 $0 $4,676 $3,640 $655 $4,021 8.24% 1.76%
2025 $388 $46 $0 $5,109 $4,029 $725 $4,384 8.28% 1.72%
2026 $424 $50 $0 $5,583 $4,453 $801 $4,782 8.31% 1.69%
2027 $463 $54 $0 $6,101 $4,916 $885 $5,216 8.34% 1.66%
2028 $506 $59 $0 $6,667 $5,422 $976 $5,691 8.37% 1.63%
2029 $553 $65 $0 $7,286 $5,976 $1,076 $6,210 8.39% 1.61%
2030 $605 $71 $0 $7,961 $6,581 $1,184 $6,777 8.42% 1.58%
2031 $661 $78 $0 $8,700 $7,241 $1,303 $7,396 8.44% 1.56%

In 2004, I used updated parameters (8% return, 35% ordinary income tax rate, 15% tax rate on capital gains and dividends, etc.) which resulted in a breakeven 401k expense rate of only .85% for a 30 year holding period. However, rolling over to a low-cost IRA after 10 years resulted in a breakeven 401k expense rate of 2.12%. This increased to 4.01% if the 401k is held for only 5 years. Note that all-in costs might be more than twice as much as just the operating costs.

401k Breakeven Expenses
Combined 401k and IRA Holding Period
5 10 15 20 25 30
401k 5 1.26% 2.07% 2.71% 3.23% 3.65% 4.01%
Holding 10 1.14% 1.46% 1.73% 1.94% 2.12%
Period 15 1.04% 1.22% 1.36% 1.49%
20 0.97% 1.07% 1.17%
25 0.90% 0.97%
30 0.85%
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