From: Will Trice 
Newsgroups: misc.invest.financial-plan
Subject: Re: Roth 401K?
Date: Wed, 3 Jan 2007 18:47:28 -0600
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joetaxpayer wrote:
> 
> 
> Tad Borek wrote:
> 
>> joetaxpayer wrote:
>>
>>> And so I'd turn to the spreadsheet, only this one I can do on a napkin.
>>> 401(k) = G * (1.x)^Y * (1-t)
>>> Roth   = G * (1-t) * (1.x)^Y

>> Joe, that's not a complete formula in the Roth-vs-regular 401k 
>> comparison because depending on your value for G, it either knocks 
>> down the Roth contribution below the limit, or allows the 401k to 
>> receive more than the allowed annual limit. Even if you don't 
>> contribute the maximum you need to factor in a different tax rate, 
>> applied to a taxable account, to make it a fair comparison.
> 
> 
> All your points are valid, and well taken. I agree with the approach to 
> diversify among the tax status of accounts. Of course, to simplify the 
> math, and do apples to apples, I needed to assume a G. If one can put 
> $15,000 into the 401(k), then I assume they will net 15000*(1-t) and put 
> that in the Roth. You are right that the Roth guy has an option to 
> invest more, another 15000*t, but the 401(k) had to pay that in taxes, 
> so doesn't my approach provide consistency?

You're both correct.  Joe's formula is accurate until you approach full 
funding, after which you must add the tax-savings of the traditional 
into another account to be fair.  So if instead of just subtracting the 
taxes from the Roth, you also subtract the potential growth from those 
taxes you get:


401(k) = G * (1.x)^Y * (1-t)
Roth   = G * (1.x)^Y - G * t * (1.x)^Y * (1-t')

where t' is the effective tax you pay on the non-401(k) account.

If I can find a tax-free account for my saved taxes (t' = 0) then the 
Roth equation simplifies to the traditional 401(k) equation (Joe's 
original point).

Roth   = G * (1-t) * (1.x)^Y

But if you pay any amount of tax on the Roth (t' > 0), then the Roth 
beats the 401(k) under Joe's assumptions.  Note that t' = 0 when you are 
contributing less than your max contribution * (1-t).

-Will