Determining your 401(k) Contributions
Friday, 12 January 2007
On January 1, 2006, many companies began to offer the Roth 401(k): an alternative to the traditional 401(k) that allows you to contribute your money in aftertax dollars, rather than pretax dollars. Most (in my opinion incorrectly) summarize the difference as the following choice: "If you think you might be in a higher income tax bracket when you withdraw the funds, invest in the Roth 401(k). Otherwise, invest in a traditional 401(k)." Omar Shahine points to a good summary here: http://www.shahine.com/omar/Roth401k.aspx. (This started as a comment on that article, but quickly grew to a post in of itself.)
Here are some examples, for somebody that is married, filing separately.
Current Income  PostRetirement Income (estimated) 
Current Tax Rate (marginal) 
PostRetirement Tax Rate (effective) * 
Roth or Traditional 
Difference per $1000 

30,000 
30,000 
15%  13%  Traditional  0  
30,000 
60,000 
15%  19%  Roth  40  
30,000 
90,000 
15%  22%  Roth  70  
30,000 
120,000 
15%  25%  Roth  100  
30,000 
200,000 
15%  28%  Roth  130  
60,000 
30,000 
25%  13%  Traditional  120  
60,000 
60,000 
25%  19%  Traditional  60  
60,000 
90,000 
25%  22%  Traditional  30  
60,000 
120,000 
25%  25%  Roth  0  
60,000 
200,000 
25%  28%  Roth  30  
90,000 
30,000** 
28% 
13%  Traditional  150  
90,000 
60,000** 
28%  19%  Traditional  90  
90,000 
90,000 
28%  22%  Traditional  60  
90,000 
120,000 
28%  25%  Traditional  30  
90,000 
200,000 
28%  28%  Roth  0  
120,000 
30,000** 
33%  13%  Traditional  200  
120,000 
60,000** 
33%  19%  Traditional  140  
120,000 
90,000** 
33%  22%  Traditional  110  
120,000 
120,000 
33%  25%  Traditional  80  
120,000 
200,000 
33%  28%  Traditional  50  
200,000 
30,000** 
35%  13%  Traditional  220  
200,000 
60,000** 
35%  19%  Traditional  160  
200,000 
90,000** 
35%  22%  Traditional  130  
200,000 
120,000 
35%  25%  Traditional  100  
200,000 
200,000 
35%  28%  Traditional  70  


* Assumes that tax rates will be the same as they are today. Higher future tax rates would increasingly favour a Roth 401(k), while lower rates would favour a Traditional 401(k) 

** Unlikely, given a mediumtoaggressive savings philosophy that would normally guarantee a higher postretirement income  
Effective tax rates generated by http://www.moneychimp.com/features/tax_brackets.htm 
Notice the "Difference per $1000" column. That shows how many dollars (per $1000) it costs if you make a mistake. Worrying about making a mistake causes people a lot of heartburn, so let's drill into that a bit more. What's the worst mistake you can make? It's the row that shows you earning $200,000 now, contributing to a Roth 401(k), and then withdrawing $30,000 per year during retirement. Over your entire 30year retirement, that would cost 30 years * $30,000 per year / 1,000 * 220 wasted per thousand = $198,000. That's about $6600 per year. Not good, but not the end of the world. Given a mediumtoaggressive savings strategy, this scenario is also highly unlikely.
How should you estimate your postretirement income? It will be based on how much you've managed to save before retirement, which is a dependent on how much you can save per year. Assuming a 6% annual rate of return, this PowerShell calculation shows how to estimate your "nest egg" for retirement, assuming that you contribute $5,000 per year:
PS >$balance = 0
PS >$contribution = 5000
PS >1..30  % { $balance += $contribution; $balance *= 1.06 }
PS >$balance
419008.386940671
Now, for your annual retirement income, you can play around with your withdraw rate on this $419,008 nest egg until the final balance nears zero:
PS >$balance = 419008; 1..30  % { $balance = 28700; $balance *= 1.06 }; $balance
1460.60834058789
So, contributing around $5,000 per year gives you a postretirement income of about $29,000. That will remain $29,000 if the contributions were through a Roth 401(k), but will turn to about $25,000 if the contributions were through a traditional 401(k).
Here's one thing that may play a part in your 401(k) calculations: how much you can hope to retire with. Both the traditional and Roth 401(k) plans have annual contribution limits of $15,500 (expected to increase by $500 per year.) If you are in a position to save the maximum, your choice of 401 vehicle makes a significant difference on your postretirement income if you base it on your 401(k) alone.
If you manage to save the maximum contribution per year, that leaves you with:
PS >$balance = 0
PS >$contribution = 15000
PS >1..30  % { $balance += $contribution; $balance *= 1.06; $contribution += 500 }
PS >$balance
1690372.4723898
Which gives an annual retirement income of about $116,000:
PS >$balance = 1690372; 1..30  % { $balance = 115800; $balance *= 1.06 }; $balance
4402.41939379471
If those funds were contributed through a traditional 401(k), that will shrink to about $87,000 after taxes. If those funds were contributed through a Roth 401(k), they will stay ay $116,000. Given the tax advantage of the Traditional 401(k), though, it may make sense in that situation to maximize your contribution to the Traditional 401(k), and apply the money you would have invested in the Roth 401(k) to other investment vehicles.
The interest earnings on those other vehicles will be taxed at 10%, though, so the answer to this is highly dependent on your personal situation. Take a salary that seems to most highly favour the Traditional IRA, but where that person can afford to max out the Roth 401(k). That is at the 35% tax bracket:
## Scenario 1: Max out Traditional
# A) First, max out Traditional
$balance = 0
$contribution = 15000
1..30  % { $balance += $contribution; $contribution += 500; $balance *= 1.06 }
$balance
1690372$balance = 1690372; 1..30  % { $balance = 115800; $balance *= 1.06 }; $balance
= $115,800 per year minus tax# B) Then, apply your extra (vs. the Roth) to mutual funds
$balance = 0
$contributed = 0
$marginalTaxRate = 1.35
$limit = 15000
$contribution = (($limit * $marginalTaxRate)  $limit) / $marginalTaxRate
1..30  % {
$balance += $contribution; $contributed += $contribution; $balance *= 1.06;
$limit += 500; $contribution = (($limit * $marginalTaxRate)  $limit) / $marginalTaxRate
}
$balance = ($balance  $contributed) * 0.9 + $contributed
$balance
411725.799113175$balance = 411725; 1..30  % { $balance = 36200; $balance *= 1.06 }; $balance
= 28,200 per year (tax free)# C) Then figure out the combination of investments
Total = 144,000 pre tax (A + B) = 25% effective tax rate
= 115,050 per year after tax (0.75 * A + B)## Scenario 2: Max out Roth
$balance = 0
$contribution = 15000
1..30  % { $balance += $contribution; $balance *= 1.06; $contribution += 500 }
$balance
1690372.4723898$balance = 1690372; 1..30  % { $balance = 115800; $balance *= 1.06 }; $balance
= 115,800 per year after tax
Lower tax brackets than 35% (ie all of them) favour the Roth even more heavily if that person can afford to max out their contributions. As always, make your own informed decisions regarding investments, but hopefully this exercise can help clarify some things.
[Edit: Updated table  Brian Kramp reminded me that Roth 401(k) contributions are taxed at your marginal tax rate, not the effective tax rate.]
[Edit2: Added calculations for investing in mutual funds]
No. 1 — January 25th, 2019 at 11:18 pm
[…] done this before (Traditional or Roth 401(k)?,) so let’s do it […]