## Calculator - pretax vs aftertax plans

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Topic Author
Richard1580
Posts: 47
Joined: Fri Aug 25, 2017 7:53 pm

### Calculator - pretax vs aftertax plans

I am looking for a calculator. Given a starting contribution tax bracket and a withdrawal tax bracket, I want to determine how long before using after tax dollars gives a better return than using pretax dollars.

Example:
Starting tax bracket is 15/25/28%
AGR is x%
Tax bracket at withdrawal is 15/25/28%

How long before using after tax dollars gives a better aftertax return?

I have looked but have not been able to find anything.

Thanks.

patrick013
Posts: 2491
Joined: Mon Jul 13, 2015 7:49 pm

### Re: Calculator - pretax vs aftertax plans

than your accumulation marginal tax bracket then pre-tax is
desirable.

KlangFool
Posts: 12001
Joined: Sat Oct 11, 2008 12:35 pm

### Re: Calculator - pretax vs aftertax plans

Richard1580 wrote:
Sat Oct 21, 2017 9:25 pm
I am looking for a calculator. Given a starting contribution tax bracket and a withdrawal tax bracket, I want to determine how long before using after tax dollars gives a better return than using pretax dollars.

Example:
Starting tax bracket is 15/25/28%
AGR is x%
Tax bracket at withdrawal is 15/25/28%

How long before using after tax dollars gives a better aftertax return?

I have looked but have not been able to find anything.

Thanks.
Richard1580,

n = number of years
Starting tax = S
Ending tax = E
AGR is x%
P= present value
F = Future value

F = P (1 + X)^n

For pretax

F = P*(1+X)^N * (1-E) = P*(1-E)*(1+X)^N

For after tax

F = P*(1-S)* (1+X)^N

If S=E, the result is the same. But, for 90+% of people, E is much smaller than S. Hence, pre-tax is a better deal for 90+% of people. If you do not know how to calculate, pre-tax would be the right answer for you.

KlangFool

avalpert
Posts: 6313
Joined: Sat Mar 22, 2008 4:58 pm

### Re: Calculator - pretax vs aftertax plans

If you mean tax-deferred vs. tax-free (roth) plans then there is no need for a calculator - if the starting and ending tax rates are the same the ending value is always the same, if the tax rates are different the one that is lower is always the better option.

KlangFool
Posts: 12001
Joined: Sat Oct 11, 2008 12:35 pm

### Re: Calculator - pretax vs aftertax plans

avalpert wrote:
Sat Oct 21, 2017 9:36 pm
If you mean tax-deferred vs. tax-free (roth) plans then there is no need for a calculator - if the starting and ending tax rates are the same the ending value is always the same, if the tax rates are different the one that is lower is always the better option.
avalpert,

Sorry to nitpick, Roth is after-tax. It is not tax-free.

KlangFool

avalpert
Posts: 6313
Joined: Sat Mar 22, 2008 4:58 pm

### Re: Calculator - pretax vs aftertax plans

KlangFool wrote:
Sat Oct 21, 2017 9:40 pm
avalpert wrote:
Sat Oct 21, 2017 9:36 pm
If you mean tax-deferred vs. tax-free (roth) plans then there is no need for a calculator - if the starting and ending tax rates are the same the ending value is always the same, if the tax rates are different the one that is lower is always the better option.
avalpert,

Sorry to nitpick, Roth is after-tax. It is not tax-free.

KlangFool
You are right, I meant the returns are tax free - the problem with 'after-tax' is that it also refers to after-tax contributions to traditional 401ks and IRAs where the returns are taxed on withdrawal.

KlangFool
Posts: 12001
Joined: Sat Oct 11, 2008 12:35 pm

### Re: Calculator - pretax vs aftertax plans

avalpert wrote:
Sat Oct 21, 2017 9:44 pm
KlangFool wrote:
Sat Oct 21, 2017 9:40 pm
avalpert wrote:
Sat Oct 21, 2017 9:36 pm
If you mean tax-deferred vs. tax-free (roth) plans then there is no need for a calculator - if the starting and ending tax rates are the same the ending value is always the same, if the tax rates are different the one that is lower is always the better option.
avalpert,

Sorry to nitpick, Roth is after-tax. It is not tax-free.

KlangFool
You are right, I meant the returns are tax free - the problem with 'after-tax' is that it also refers to after-tax contributions to traditional 401ks and IRAs where the returns are taxed on withdrawal.
avalpert,

Contribution to Trad. 401K and Trad. IRA is tax-deferred. It is not after-tax. The terminology matters.

KlangFool

avalpert
Posts: 6313
Joined: Sat Mar 22, 2008 4:58 pm

### Re: Calculator - pretax vs aftertax plans

KlangFool wrote:
Sat Oct 21, 2017 9:53 pm
avalpert wrote:
Sat Oct 21, 2017 9:44 pm
KlangFool wrote:
Sat Oct 21, 2017 9:40 pm
avalpert wrote:
Sat Oct 21, 2017 9:36 pm
If you mean tax-deferred vs. tax-free (roth) plans then there is no need for a calculator - if the starting and ending tax rates are the same the ending value is always the same, if the tax rates are different the one that is lower is always the better option.
avalpert,

Sorry to nitpick, Roth is after-tax. It is not tax-free.

KlangFool
You are right, I meant the returns are tax free - the problem with 'after-tax' is that it also refers to after-tax contributions to traditional 401ks and IRAs where the returns are taxed on withdrawal.
avalpert,

Contribution to Trad. 401K and Trad. IRA is tax-deferred. It is not after-tax. The terminology matters.

KlangFool
You can make non-deductible contributions to both which are not tax-deferred and are referred to by the IRS as 'after-tax contributions' - I don't believe the IRS ever calls Roth contributions 'after-tax' but does refer to distributions of Roth accounts as 'tax-free'.

I agree the terminology matters, but it is more nuanced then you are suggesting.

FiveK
Posts: 6376
Joined: Sun Mar 16, 2014 2:43 pm

### Re: Calculator - pretax vs aftertax plans

Richard1580 wrote:
Sat Oct 21, 2017 9:25 pm
I am looking for a calculator. Given a starting contribution tax bracket and a withdrawal tax bracket, I want to determine how long before using after tax dollars gives a better return than using pretax dollars.
If you are talking small contribution amounts (e.g., \$1000) the answer is "immediately" or "never". See the commutative property of multiplication as it applies here.

If you are talking about maxing out your retirement accounts (i.e., contributing more to a Roth than [(traditional maximum contribution) * (1 - marginal tax rate)]) then see either of the two spreadsheets referenced at the bottom of the wiki section linked here.

Or I may have completely misunderstood the question....

Earl Lemongrab
Posts: 6682
Joined: Tue Jun 10, 2014 1:14 am

### Re: Calculator - pretax vs aftertax plans

It gets a bit tricky when the deferrals lead to extra money invested in non-tax-advantaged accounts. Then you need to look at the ongoing tax drag (if any) and tax on withdrawal (if any).

I can put 18k into traditional or Roth 401(k), but in the former case I have more going into my regular brokerage accounts. I pay tax at 15%-25% (plus state tax of 6%) on dividends ongoing, and will probably be in the 15% capital gains in retirement due to pension.
This week's fortune cookie: "Your financial life will be secure and beneficial." So I got that going for me, which is nice.

FinancialDave
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Joined: Thu May 26, 2011 9:36 pm

### Re: Calculator - pretax vs aftertax plans

Earl Lemongrab wrote:
Mon Oct 23, 2017 5:30 pm
It gets a bit tricky when the deferrals lead to extra money invested in non-tax-advantaged accounts. Then you need to look at the ongoing tax drag (if any) and tax on withdrawal (if any).

I can put 18k into traditional or Roth 401(k), but in the former case I have more going into my regular brokerage accounts. I pay tax at 15%-25% (plus state tax of 6%) on dividends ongoing, and will probably be in the 15% capital gains in retirement due to pension.
Earl,
I'm not sure it is all that tricky, as having money that is put in a taxable account cannot as a rule be better than putting it in either the Traditional 401k or the Roth 401k. It can be "equal" to the Roth if all tax rates in the taxable account are zero however it can never be better.

But let's look at from the amount of earnings you are able to devote to savings:

If it is \$18k and \$18k goes into Trad 401k - no tax due.
If that \$18k is going to be used for the Roth 401k, then you must hold back the tax from the Roth and you have less in the Roth but unless you are assuming some different tax rates the results in retirement are exactly the same.

If on the other hand you want to compare earning \$24k and putting \$18k into the Roth (& \$6k to the taxman), with earning \$24k and putting \$18k in the Traditional and \$6k in the taxable, the Traditional + taxable is never going to win if there is any "tax leakage" from the taxable account.

Dave
I love simulated data. It turns the impossible into the possible!

patrick013
Posts: 2491
Joined: Mon Jul 13, 2015 7:49 pm

### Re: Calculator - pretax vs aftertax plans

FinancialDave wrote:
Mon Oct 23, 2017 7:13 pm

But let's look at from the amount of earnings you are able to devote to savings:

If it is \$18k and \$18k goes into Trad 401k - no tax due.
If that \$18k is going to be used for the Roth 401k, then you must hold back the tax from the Roth and you have less in the Roth but unless you are assuming some different tax rates the results in retirement are exactly the same.
Similar answers are rendered but it actually looks better if both contributions
are equal. So if I put 10,000 in a tax deferred account before matching or
10,000 in an after tax account before matching what is going on ? All income
before investments is taxed with few exceptions so the cost of the Roth is
10,000 and the cost of the tax deferred contribution is 10,000 minus the tax
reduction because of that investment. All cash in/cash out ratios and rates of
return should be based on those 2 contributions as is but the costs of each are
different for the same purpose.

There's no doubt Roth can accumulate many dollars but without the tax benefit.
There's no doubt the tax reduction for tax deferred is highly beneficial for investing
in taxable, or even just paying the rent. But saying there's less in the Roth due to
taxes when all income is rationally taxed shouldn't be standardized. The tax
reduction for a full contribution in tax deferred should be standardized and calc's
for comparison evolved from there, but only on a cost basis for return calculation
not a reduction in the balance of the tax deferred account for computing return or
anything else.

But you can kick a 60 yard field goal with this little proverb however it's calc'd :

than your accumulation marginal tax bracket then pre-tax is
desirable.

FiveK
Posts: 6376
Joined: Sun Mar 16, 2014 2:43 pm

### Re: Calculator - pretax vs aftertax plans

Might be worth perusing maxing out your retirement accounts for a discussion about the tax drag of the taxable "side account."

patrick013
Posts: 2491
Joined: Mon Jul 13, 2015 7:49 pm

### Re: Calculator - pretax vs aftertax plans

FiveK wrote:
Mon Oct 23, 2017 8:12 pm
Might be worth perusing maxing out your retirement accounts for a discussion about the tax drag of the taxable "side account."
Whoever wrote that Wiki gets a D- for presentation skills. No thanks.
Peruse my prior message if you would please.

FiveK
Posts: 6376
Joined: Sun Mar 16, 2014 2:43 pm

### Re: Calculator - pretax vs aftertax plans

patrick013 wrote:
Mon Oct 23, 2017 8:49 pm
FiveK wrote:
Mon Oct 23, 2017 8:12 pm
Might be worth perusing maxing out your retirement accounts for a discussion about the tax drag of the taxable "side account."
Whoever wrote that Wiki gets a D- for presentation skills. No thanks.
Peruse my prior message if you would please.
Because 10,000 is the number used, it isn't clear whether you have addressed the tax drag issue. E.g., someone paying 25% could put the full pre-tax \$10K into traditional, or put \$7500 into Roth. If the withdrawal tax rate is also 25%, the results will be identical either way.

If one has \$24K pre-tax, still assuming 25% tax, \$18K can go into the Roth, while \$18K goes into traditional and \$4500 goes into taxable. For a 25% withdrawal rate, as FinancialDave noted, the spendable amount from the (traditional + taxable) will at best equal the Roth amount. With any taxable tax drag, the Roth will be better, even for equal contribution and withdrawal tax rates.

patrick013
Posts: 2491
Joined: Mon Jul 13, 2015 7:49 pm

### Re: Calculator - pretax vs aftertax plans

FiveK wrote:
Mon Oct 23, 2017 9:15 pm
patrick013 wrote:
Mon Oct 23, 2017 8:49 pm
FiveK wrote:
Mon Oct 23, 2017 8:12 pm
Might be worth perusing maxing out your retirement accounts for a discussion about the tax drag of the taxable "side account."
Whoever wrote that Wiki gets a D- for presentation skills. No thanks.
Peruse my prior message if you would please.
Because 10,000 is the number used, it isn't clear whether you have addressed the tax drag issue.
There's no such thing as tax drag. Your Wiki stinks and I can't use it. Even the
advisor's manual uses cash flow and IRR. Peruse my prior message please.
Your Wiki on this topic is even embarrasing.

FiveK
Posts: 6376
Joined: Sun Mar 16, 2014 2:43 pm

### Re: Calculator - pretax vs aftertax plans

patrick013 wrote:
Mon Oct 23, 2017 9:21 pm
There's no such thing as tax drag.
What is Tax Drag? definition and meaning.

Topic Author
Richard1580
Posts: 47
Joined: Fri Aug 25, 2017 7:53 pm

### Re: Calculator - pretax vs aftertax plans

Getting back to the original question, I was able to find this calculator:
http://www.bankrate.com/calculators/ret ... lator.aspx

After playing with it, it seems that the determining factor is whether your tax rate in retirement is lower than when you make your contribution. If so, it *might* be better to invest in a conventional IRA/401K. Otherwise, the Roth is a clear winner.

FiveK
Posts: 6376
Joined: Sun Mar 16, 2014 2:43 pm

### Re: Calculator - pretax vs aftertax plans

Richard1580 wrote:
Tue Oct 24, 2017 2:19 pm
...the determining factor is whether your tax rate in retirement is lower than when you make your contribution.
Yes, indeed!

avalpert
Posts: 6313
Joined: Sat Mar 22, 2008 4:58 pm

### Re: Calculator - pretax vs aftertax plans

Richard1580 wrote:
Tue Oct 24, 2017 2:19 pm
Getting back to the original question, I was able to find this calculator:
http://www.bankrate.com/calculators/ret ... lator.aspx

After playing with it, it seems that the determining factor is whether your tax rate in retirement is lower than when you make your contribution. If so, it *might* be better to invest in a conventional IRA/401K. Otherwise, the Roth is a clear winner.
The calculator is wrong - I can't reverse engineer to figure out what it is doing wrong. It is something in how it is treating the annual return of the Traditional 401k or the investment of the tax savings - if you set expected return to 0% it rightly shows that Roth and Traditional end balances are equal if the tax rates are equal.

FiveK
Posts: 6376
Joined: Sun Mar 16, 2014 2:43 pm

### Re: Calculator - pretax vs aftertax plans

avalpert wrote:
Tue Oct 24, 2017 4:19 pm
The calculator is wrong - I can't reverse engineer to figure out what it is doing wrong. It is something in how it is treating the annual return of the Traditional 401k or the investment of the tax savings - if you set expected return to 0% it rightly shows that Roth and Traditional end balances are equal if the tax rates are equal.
It assumes one must use a taxable side account in combination with a traditional contribution. That's actually a good comparison if the pre-tax amount going toward the Roth is greater than the IRS maximum for a traditional account. For smaller amounts, however, it makes Roth look better than it should.

avalpert
Posts: 6313
Joined: Sat Mar 22, 2008 4:58 pm

### Re: Calculator - pretax vs aftertax plans

FiveK wrote:
Tue Oct 24, 2017 4:59 pm
avalpert wrote:
Tue Oct 24, 2017 4:19 pm
The calculator is wrong - I can't reverse engineer to figure out what it is doing wrong. It is something in how it is treating the annual return of the Traditional 401k or the investment of the tax savings - if you set expected return to 0% it rightly shows that Roth and Traditional end balances are equal if the tax rates are equal.
It assumes one must use a taxable side account in combination with a traditional contribution. That's actually a good comparison if the pre-tax amount going toward the Roth is greater than the IRS maximum for a traditional account. For smaller amounts, however, it makes Roth look better than it should.
Well no, that isn't the problem with the calculator - it is making some assumption either in sequencing of the taxable contribution or in dividend taxes or something that are unstated and unadjustable.

Beyond that, it is also not the right comparison to make. If you start with \$4000 of free cash flow your choices are either put it all in a pre-tax 401k or pay an additional \$1000 in taxes and put the remaining \$3000 of free cash flow in a Roth 401k - that is the correct comparison. The only exception is when you are talking about the max contribution when you essentially get to put either \$18000 of free cash flow in tax advantaged space with a pre-tax 401k or \$24000 of free cash flow in the Roth as \$6000 in additional tax expenses and \$18000 in the Roth - in that case the correct comparison is to add the \$6000 in additional taxes to a taxable account to compare the traditional with the Roth.

FiveK
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Joined: Sun Mar 16, 2014 2:43 pm

### Re: Calculator - pretax vs aftertax plans

avalpert wrote:
Tue Oct 24, 2017 5:36 pm
FiveK wrote:
Tue Oct 24, 2017 4:59 pm
It assumes one must use a taxable side account in combination with a traditional contribution. That's actually a good comparison if the pre-tax amount going toward the Roth is greater than the IRS maximum for a traditional account. For smaller amounts, however, it makes Roth look better than it should.
Beyond that, it is also not the right comparison to make. If you start with \$4000 of free cash flow your choices are either put it all in a pre-tax 401k or pay an additional \$1000 in taxes and put the remaining \$3000 of free cash flow in a Roth 401k - that is the correct comparison. The only exception is when you are talking about the max contribution when you essentially get to put either \$18000 of free cash flow in tax advantaged space with a pre-tax 401k or \$24000 of free cash flow in the Roth as \$6000 in additional tax expenses and \$18000 in the Roth - in that case the correct comparison is to add the \$6000 in additional taxes to a taxable account to compare the traditional with the Roth.
Yes, we're saying pretty much the same thing about when a taxable account should become part of the comparison.

Topic Author
Richard1580
Posts: 47
Joined: Fri Aug 25, 2017 7:53 pm

### Re: Calculator - pretax vs aftertax plans

Perhaps I am missing something, but the calculator gives you the option of investing the tax savings generated by investing in a traditional 401k into a taxable account (or not). Consequently, the amount going into either the regular or Roth account is the same, but if you contribute to a regular 401k, it allows you to specify whether you will invest and not spend the tax savings.

From the calculator:
Check this box to invest any tax savings generated by contributions to a traditional 401(k). By investing your tax savings each year, you equalize the total cash flow between the two account types. For example, if you have a 25% income tax rate and contribute \$1,000 to your retirement account, the actual cost after taxes would be \$750 for the traditional contribution and \$1,000 for the Roth contribution. If you do not wish to invest the difference, you are actually "spending" more per year with the Roth option and the end result will greatly favor a Roth-type savings plan. You may wish to leave this box unchecked if you have no ability or desire to create an additional investment account outside of your 401(k).

avalpert
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### Re: Calculator - pretax vs aftertax plans

Richard1580 wrote:
Tue Oct 24, 2017 6:07 pm
Perhaps I am missing something, but the calculator gives you the option of investing the tax savings generated by investing in a traditional 401k into a taxable account (or not). Consequently, the amount going into either the regular or Roth account is the same, but if you contribute to a regular 401k, it allows you to specify whether you will invest and not spend the tax savings.

From the calculator:
Check this box to invest any tax savings generated by contributions to a traditional 401(k). By investing your tax savings each year, you equalize the total cash flow between the two account types. For example, if you have a 25% income tax rate and contribute \$1,000 to your retirement account, the actual cost after taxes would be \$750 for the traditional contribution and \$1,000 for the Roth contribution. If you do not wish to invest the difference, you are actually "spending" more per year with the Roth option and the end result will greatly favor a Roth-type savings plan. You may wish to leave this box unchecked if you have no ability or desire to create an additional investment account outside of your 401(k).
If you don't save the tax savings you aren't comparing an equal cash outflow (you have the contribution to the traditional and the contribution plus that additional tax expense to the Roth) - so that isn't helpful. As I argued above, I don't think this comparison is helpful either except in the case where we are maxing all tax-advantages space available (that includes not just the 401k but IRA/backdoor IRA/HSA and any other options that eliminates the tax drag of a taxable account).

And I can't figure out how they are computing the tax drag on the taxable account - my attempts to back it out have resulted in answer that can't possibly be correct.

FiveK
Posts: 6376
Joined: Sun Mar 16, 2014 2:43 pm

### Re: Calculator - pretax vs aftertax plans

Richard1580 wrote:
Tue Oct 24, 2017 6:07 pm
Perhaps I am missing something, but the calculator gives you the option of investing the tax savings generated by investing in a traditional 401k into a taxable account (or not). Consequently, the amount going into either the regular or Roth account is the same, but if you contribute to a regular 401k, it allows you to specify whether you will invest and not spend the tax savings.
With the "invest traditional tax savings" box unchecked, the comparison is wrong - see below. The only way to have \$9000 in the Roth is to have started with \$12K on which \$3K tax was paid. If starting with \$12K, the traditional should also have \$9K after-tax.

The tool may also have problems with non-zero rates of return. Haven't looked in detail at that. Given the problem noted above, why trust anything else coming from this particular black box?

Topic Author
Richard1580
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Joined: Fri Aug 25, 2017 7:53 pm

### Re: Calculator - pretax vs aftertax plans

If you click the "view report" button on those figures, it will show that you started out with a \$9,000 contribution in each account, but since you have to pay 25% tax on the withdrawal from the regular 401k, its value (after tax) drops to \$6,750. That seems correct to me.

avalpert
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### Re: Calculator - pretax vs aftertax plans

Richard1580 wrote:
Tue Oct 24, 2017 6:37 pm
If you click the "view report" button on those figures, it will show that you started out with a \$9,000 contribution in each account, but since you have to pay 25% tax on the withdrawal from the regular 401k, its value (after tax) drops to \$6,750. That seems correct to me.
But to put the 9000 in the Roth account you needed to pay an additional \$3000 in taxes more than the one who put 9000 in the Traditional account - not accounting for that additional spend is not correct.

Topic Author
Richard1580
Posts: 47
Joined: Fri Aug 25, 2017 7:53 pm

### Re: Calculator - pretax vs aftertax plans

True. But in the case of the calculator, instead of taking the tax out of the Roth side of the equation, they are adding the tax saving to the regular 401k side. This is why it is important to put the tax savings into a regular account and include it in the calculation - otherwise the calculation is skewed in favor of the Roth.

avalpert
Posts: 6313
Joined: Sat Mar 22, 2008 4:58 pm

### Re: Calculator - pretax vs aftertax plans

Richard1580 wrote:
Tue Oct 24, 2017 6:44 pm
True. But in the case of the calculator, instead of taking the tax out of the Roth side of the equation, they are adding the tax saving to the regular 401k side. This is why it is important to put the tax savings into a regular account and include it in the calculation - otherwise the calculation is skewed in favor of the Roth.
But why would I save it in a taxable account when I can instead in crease my 401k contribution? Or put it in a Roth IRA (either directly or through a backdoor contribution)? Or an HSA if eligible? Or 529/ESA if I have kids who will have future college/educational expenses? etc.

FiveK
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Joined: Sun Mar 16, 2014 2:43 pm

### Re: Calculator - pretax vs aftertax plans

avalpert wrote:
Tue Oct 24, 2017 6:48 pm
Richard1580 wrote:
Tue Oct 24, 2017 6:44 pm
True. But in the case of the calculator, instead of taking the tax out of the Roth side of the equation, they are adding the tax saving to the regular 401k side. This is why it is important to put the tax savings into a regular account and include it in the calculation - otherwise the calculation is skewed in favor of the Roth.
But why would I save it in a taxable account when I can instead increase my 401k contribution?
+1

E.g., start with \$12K pre-tax: either put all \$12K into a t401k, or \$9K into a R401k. Why compare any other way?

Topic Author
Richard1580
Posts: 47
Joined: Fri Aug 25, 2017 7:53 pm

### Re: Calculator - pretax vs aftertax plans

It is a matter of comparing apples to apples. You need to take the tax advantages into account. What the calculator is doing is comparing equal deposits and then factors in the tax benefit. If you are making the maximum contribution, then it is either \$18K in the Roth or \$18K in the regular 401K, but the later includes a \$4,500 tax savings (in the 25% tax bracket) which must be taken into account.

avalpert
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### Re: Calculator - pretax vs aftertax plans

Richard1580 wrote:
Tue Oct 24, 2017 7:04 pm
It is a matter of comparing apples to apples. You need to take the tax advantages into account. What the calculator is doing is comparing equal deposits and then factors in the tax benefit. If you are making the maximum contribution, then it is either \$18K in the Roth or \$18K in the regular 401K, but the later includes a \$4,500 tax savings (in the 25% tax bracket) which must be taken into account.
No, it would be a \$6,000 tax savings - to put \$18,000 in a Roth it would take \$24,000 of income with 25% paid in taxes.

But the case where we are talking about maxing out is an edge case - and by not allowing for me to put that tax savings in a different tax-advantaged vehicle is a problem. But once we get to someone who is maxing out tax-advantaged space we have to start asking how realistic is the assumption they would be in the same marginal tax bracket in retirement?

Topic Author
Richard1580
Posts: 47
Joined: Fri Aug 25, 2017 7:53 pm

### Re: Calculator - pretax vs aftertax plans

avalpert wrote:
Tue Oct 24, 2017 7:10 pm
No, it would be a \$6,000 tax savings - to put \$18,000 in a Roth it would take \$24,000 of income with 25% paid in taxes.
Putting money in a Roth does not give you a tax advantage. Putting \$18K in a regular 401k (at the 25% bracket) saves you \$4,500 in taxes. If you want to compare the relative tax efficiency between a Roth and a regular 401K, then you need to account for that \$4,500 in your calculations (as well as the tax due at withdrawal). Again, they are comparing putting EQUAL amounts of money into a Roth vs a regular 401K.

You are focusing on the extra tax that is due if you make a contribution to a Roth. The calculator is simply looking at the other side of the equation - the amount of money that you save by taking the deduction. Ultimately, it all balances out.

FiveK
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### Re: Calculator - pretax vs aftertax plans

Richard1580 wrote:
Tue Oct 24, 2017 7:04 pm
It is a matter of comparing apples to apples. You need to take the tax advantages into account.
Agreed - so far so good.
What the calculator is doing is comparing equal deposits and then factors in the tax benefit.
But "equal deposits" is not apples to applies. Equal pre-tax amounts is apples to apples. E.g., start with \$12K pre-tax: either put all \$12K into a t401k, or \$9K into a R401k. Why compare any other way?
If you are making the maximum contribution, then it is either \$18K in the Roth or \$18K in the regular 401K, but the later includes a \$4,500 tax savings (in the 25% tax bracket) which must be taken into account.
Back to agreeing (assuming you mean \$4500 invested in a taxable account, coming from the extra \$6K taxed at 25%).

It doesn't have to be a maximum contribution. Any Roth contribution above (traditional maximum)/(1-tax_rate) has this issue, if comparing equal pre-tax amounts.

Topic Author
Richard1580
Posts: 47
Joined: Fri Aug 25, 2017 7:53 pm

### Re: Calculator - pretax vs aftertax plans

Correction. I have been saying "tax savings" when I meant reductions in AGI. I only wish the former was true.

Topic Author
Richard1580
Posts: 47
Joined: Fri Aug 25, 2017 7:53 pm

### Re: Calculator - pretax vs aftertax plans

FiveK wrote:
Tue Oct 24, 2017 7:28 pm
Equal pre-tax amounts is apples to apples. E.g., start with \$12K pre-tax: either put all \$12K into a t401k, or \$9K into a R401k. Why compare any other way?
You are correct that the tax differential has to be taken into account. The calculator is simply putting it on the other side of the equation. I suspect that they chose the method they did since it makes it simpler to factor in maximum contributions. The end result is the same (provided you chose to account for the growth of tax savings).

Bottom line is that if you think your tax bracket will be lower in retirement than while you are working, then a regular 401K will probably leave you with more money in your pocket at retirement. If you think you will be in an equal (or higher) tax bracket, you are better off paying the taxes up front. And that is the question I was trying to answer.

avalpert
Posts: 6313
Joined: Sat Mar 22, 2008 4:58 pm

### Re: Calculator - pretax vs aftertax plans

Richard1580 wrote:
Tue Oct 24, 2017 7:39 pm
FiveK wrote:
Tue Oct 24, 2017 7:28 pm
Equal pre-tax amounts is apples to apples. E.g., start with \$12K pre-tax: either put all \$12K into a t401k, or \$9K into a R401k. Why compare any other way?
You are correct that the tax differential has to be taken into account. The calculator is simply putting it on the other side of the equation. I suspect that they chose the method they did since it makes it simpler to factor in maximum contributions. The end result is the same (provided you chose to account for the growth of tax savings).

Bottom line is that if you think your tax bracket will be lower in retirement than while you are working, then a regular 401K will probably leave you with more money in your pocket at retirement. If you think you will be in an equal (or higher) tax bracket, you are better off paying the taxes up front. And that is the question I was trying to answer.
Except that answer is incorrect - if you will be in an equal tax bracket then the outcomes are equal, and since you retain the option to convert to a roth at a future point in time you are better off not using up that option now.

FiveK
Posts: 6376
Joined: Sun Mar 16, 2014 2:43 pm

### Re: Calculator - pretax vs aftertax plans

avalpert wrote:
Tue Oct 24, 2017 7:48 pm
Richard1580 wrote:
Tue Oct 24, 2017 7:39 pm
Bottom line is that if you think your tax bracket will be lower in retirement than while you are working, then a regular 401K will probably leave you with more money in your pocket at retirement. If you think you will be in an equal (or higher) tax bracket, you are better off paying the taxes up front. And that is the question I was trying to answer.
Except that answer is incorrect - if you will be in an equal tax bracket then the outcomes are equal, and since you retain the option to convert to a roth at a future point in time you are better off not using up that option now.
Believe It or Not: Roth is better when contribution and withdrawal tax rates are equal and one needs a taxable side account along with a traditional account (for the apples to apples of pre-tax equality) and there is tax drag on the taxable account (e.g., current taxable income is above the 15% bracket).

Both of the calculators mentioned at the bottom of the Maxing out your retirement accounts section get this correct:
Numbers in these examples came from the 'Misc. calcs' tab in the Personal finance toolbox. That spreadsheet can be used to plug in your own numbers.

Another spreadsheet that does similar calculations: Traditional versus Roth (401(k) or IRA)

patrick013
Posts: 2491
Joined: Mon Jul 13, 2015 7:49 pm

### Re: Calculator - pretax vs aftertax plans

FiveK wrote:
Mon Oct 23, 2017 9:15 pm

Because 10,000 is the number used, it isn't clear whether you have addressed the tax drag issue. E.g., someone paying 25% could put the full pre-tax \$10K into traditional, or put \$7500 into Roth. If the withdrawal tax rate is also 25%, the results will be identical either way.
You keep doing the wrong thing the right way. A hundred years ago they would have
called that your own inverted reasoning process. I'd delete it and just move forward.
Also, using the backdoor makes your "equal" comparison inaccurate. It isn't better that
way. Oh well.

FiveK
Posts: 6376
Joined: Sun Mar 16, 2014 2:43 pm

### Re: Calculator - pretax vs aftertax plans

patrick013 wrote:
Sat Oct 28, 2017 1:19 pm
FiveK wrote:
Mon Oct 23, 2017 9:15 pm

Because 10,000 is the number used, it isn't clear whether you have addressed the tax drag issue. E.g., someone paying 25% could put the full pre-tax \$10K into traditional, or put \$7500 into Roth. If the withdrawal tax rate is also 25%, the results will be identical either way.
You keep doing the wrong thing the right way. A hundred years ago they would have
called that your own inverted reasoning process. I'd delete it and just move forward.
Also, using the backdoor makes your "equal" comparison inaccurate. It isn't better that
way. Oh well.
Seems that what we've got here is failure to communicate....

Silly Wabbit
Posts: 91
Joined: Sat Mar 25, 2017 9:54 pm

### Re: Calculator - pretax vs aftertax plans

It's not only the marginal tax rate in retirement that needs examined.

While working, you pay, or save, taxes at your marginal rate on contributions.

During retirement, much of the tax on withdrawals will be at rates under your marginal rate, unless other income fills up the lower brackets.

FiveK
Posts: 6376
Joined: Sun Mar 16, 2014 2:43 pm

### Re: Calculator - pretax vs aftertax plans

Silly Wabbit wrote:
Sat Oct 28, 2017 3:54 pm
It's not only the marginal tax rate in retirement that needs examined.
Yes - if by "the" marginal tax rate you mean the tax on the highest \$1 of taxable income. But that's not the useful marginal tax rate - see below.
While working, you pay, or save, taxes at your marginal rate on contributions.
This is generally understood and agreed. But, to set up the discussion on the next point, what are "your marginal rate"s if you are
- a couple filing MFJ with 2 elementary school kids,
- \$60K AGI if making no 401k contributions
on
a) \$20K split between the couple
b) \$10K split between the couple?

If one looks at (change in tax owed)/(contribution amount), the answers are
a) (\$1733 - (-\$3922))/\$20K = \$5655/\$20K = 28%
b) (\$1733 - (- \$293))/\$10K = \$2026/\$10K = 20%
To emphasize, the useful Marginal tax rate - Bogleheads depends on the amount in the denominator.
During retirement, much of the tax on withdrawals will be at rates under your marginal rate, unless other income fills up the lower brackets.
Note that "other income" can include withdrawals based on traditional contributions made in other years. It would be great if we could use the 0% bracket on withdrawal for each year's traditional contribution, but the IRS won't let us.

When deciding on t vs. R for this year's contribution, one should compare the marginal rate on this year's contribution amount (e.g., see above) with the withdrawal amount based on this year's contribution.

For example, if contributing X, it triples between contribution and retirement, and withdrawing 4% in retirement, the amount would be 12% * X. Add that to the taxable retirement income one would have without this year's traditional contribution, calculate the tax difference and divide by (12% * X) and one gets the useful marginal withdrawal rate.

Silly Wabbit
Posts: 91
Joined: Sat Mar 25, 2017 9:54 pm

### Re: Calculator - pretax vs aftertax plans

FiveK wrote:
Sat Oct 28, 2017 5:08 pm
Silly Wabbit wrote:
Sat Oct 28, 2017 3:54 pm
It's not only the marginal tax rate in retirement that needs examined.
Yes - if by "the" marginal tax rate you mean the tax on the highest \$1 of taxable income. But that's not the useful marginal tax rate - see below.
While working, you pay, or save, taxes at your marginal rate on contributions.
This is generally understood and agreed. But, to set up the discussion on the next point, what are "your marginal rate"s if you are
- a couple filing MFJ with 2 elementary school kids,
- \$60K AGI if making no 401k contributions
on
a) \$20K split between the couple
b) \$10K split between the couple?

If one looks at (change in tax owed)/(contribution amount), the answers are
a) (\$1733 - (-\$3922))/\$20K = \$5655/\$20K = 28%
b) (\$1733 - (- \$293))/\$10K = \$2026/\$10K = 20%
To emphasize, the useful Marginal tax rate - Bogleheads depends on the amount in the denominator.
I get different numbers than you.

Standard deduction = 12700
Child deduction = 4,050 *2 = 8100

60,000 - 12700 - 4050*2 = 39200

2017 tax brackets:
10% \$0 to \$9,325 10% of Taxable Income
15% \$9,325 to \$37,950 \$932.50 plus 15% of the excess over \$9325
25% \$37,950 to \$91,900 \$5,226.25 plus 25% of the excess over \$37,950

With no contributions:
Taxable income = 39200
TaxesPaid = 5226.25+ (39200-37950)*.25 = 5538
Effective tax rate = 5538/60000 = 9.2%

With 10k contribution, taxes become..
Taxable Income = 39200-10000 = 29200
TaxesPaid = 932.50 + (29200-9325)*.15 = 3913
Effective tax rate = 3913/60000 = 6.5%
Effective rate on contributions = ((37950-29100)*.15 + (39200-37950)*.25)/10000 = 16.5%
Marginal rate on additional contributions = 25%

With 20k contribution, taxes become..
Taxable Income = 39200-20000 = 19200
TaxesPaid = 932.50 + (19200-9325)*.15 = 2413
Effective tax rate = 2413/60000 = 5%
Effective rate on contributions = ((37950-19200)*.15 + (39200-37950)*.25)/20000 = 15.6%
Marginal rate on additional contributions = 25%
During retirement, much of the tax on withdrawals will be at rates under your marginal rate, unless other income fills up the lower brackets.
Note that "other income" can include withdrawals based on traditional contributions made in other years. It would be great if we could use the 0% bracket on withdrawal for each year's traditional contribution, but the IRS won't let us.

When deciding on t vs. R for this year's contribution, one should compare the marginal rate on this year's contribution amount (e.g., see above) with the withdrawal amount based on this year's contribution.

For example, if contributing X, it triples between contribution and retirement, and withdrawing 4% in retirement, the amount would be 12% * X. Add that to the taxable retirement income one would have without this year's traditional contribution, calculate the tax difference and divide by (12% * X) and one gets the useful marginal withdrawal rate.
I think we agree.. it's just math.

I don't think most people do the actual math using realistic deductions and credits. I see people comparing their personal tax bracket now and as predicted in retirement. It seems to me that this can lead to the inappropriate conclusion that Roth is the correct choice.

The definition you cite says, "The marginal tax rate is often the same as the individual's tax bracket, but not always." For purposes of comparing retirement contribution types, the marginal tax rate on the withdrawals is mostly NOT equivalent to the individuals tax bracket. If all, most, of my income comes from withdrawals, the marginal tax rate on the withdrawal is == to my effective tax rate and much less than my tax bracket.

FiveK
Posts: 6376
Joined: Sun Mar 16, 2014 2:43 pm

### Re: Calculator - pretax vs aftertax plans

Silly Wabbit wrote:
Sat Oct 28, 2017 7:08 pm
I get different numbers than you.
Appears the difference is whether the saver's, earned income, and child tax credits are considered. See the tax calculations in the personal finance toolbox spreadsheet (or any other 2017 calculation that considers all of those).
I think we agree.. it's just math.

I don't think most people do the actual math using realistic deductions and credits. I see people comparing their personal tax bracket now and as predicted in retirement. It seems to me that this can lead to the inappropriate conclusion that Roth is the correct choice.

The definition you cite says, "The marginal tax rate is often the same as the individual's tax bracket, but not always." For purposes of comparing retirement contribution types, the marginal tax rate on the withdrawals is mostly NOT equivalent to the individuals tax bracket. If all, most, of my income comes from withdrawals, the marginal tax rate on the withdrawal is == to my effective tax rate and much less than my tax bracket.
The last sentence seems so obvious - but it is not correct.

A common misunderstanding about traditional accounts is "contributions are taken from the top while withdrawals come from the bottom": in other words, that one saves a marginal rate when contributing but pays only an average rate (starting at 0% for the first dollar withdrawn) when withdrawing. That is true in a limited sense - limited, that is, to the very first traditional contribution one makes. After that, subsequent contributions will be withdrawn on top of the withdrawals due to previous contributions. One must therefore calculate the marginal withdrawal tax rate due to those subsequent contributions.
There is a subtle but very important point: one does not have to choose traditional vs. Roth once and forever for an entire working career - agreed?

If one did have to make such a choice, the use of effective withdrawal rate (and, for that matter, average marginal contribution rate over a career) would be correct because all the contributions and withdrawals get lumped together.

Because the choice can be made anew each year (for that matter, each paycheck or even each dollar), the effects of each year's contribution should be considered, well, each year. For example, assume you
- have contributed enough to traditional in previous years that a 4% withdrawal rate in retirement from the traditional balance alone would put you in the 25% bracket, with an 11% effective rate.
- are currently in the 15% bracket (and that is your current marginal rate).

Knowing that any traditional contribution will save you 15% this year, but you will pay 25% on any extra withdrawals because of it, would you still use traditional because your effective retirement rate is 11%?

Silly Wabbit
Posts: 91
Joined: Sat Mar 25, 2017 9:54 pm

### Re: Calculator - pretax vs aftertax plans

FiveK wrote:
Sat Oct 28, 2017 8:05 pm
Silly Wabbit wrote:
Sat Oct 28, 2017 7:08 pm
I get different numbers than you.
Appears the difference is whether the saver's, earned income, and child tax credits are considered. See the tax calculations in the personal finance toolbox spreadsheet (or any other 2017 calculation that considers all of those).
I think we agree.. it's just math.

I don't think most people do the actual math using realistic deductions and credits. I see people comparing their personal tax bracket now and as predicted in retirement. It seems to me that this can lead to the inappropriate conclusion that Roth is the correct choice.

The definition you cite says, "The marginal tax rate is often the same as the individual's tax bracket, but not always." For purposes of comparing retirement contribution types, the marginal tax rate on the withdrawals is mostly NOT equivalent to the individuals tax bracket. If all, most, of my income comes from withdrawals, the marginal tax rate on the withdrawal is == to my effective tax rate and much less than my tax bracket.
The last sentence seems so obvious - but it is not correct.

A common misunderstanding about traditional accounts is "contributions are taken from the top while withdrawals come from the bottom": in other words, that one saves a marginal rate when contributing but pays only an average rate (starting at 0% for the first dollar withdrawn) when withdrawing. That is true in a limited sense - limited, that is, to the very first traditional contribution one makes. After that, subsequent contributions will be withdrawn on top of the withdrawals due to previous contributions. One must therefore calculate the marginal withdrawal tax rate due to those subsequent contributions.
There is a subtle but very important point: one does not have to choose traditional vs. Roth once and forever for an entire working career - agreed?

If one did have to make such a choice, the use of effective withdrawal rate (and, for that matter, average marginal contribution rate over a career) would be correct because all the contributions and withdrawals get lumped together.

Because the choice can be made anew each year (for that matter, each paycheck or even each dollar), the effects of each year's contribution should be considered, well, each year. For example, assume you
- have contributed enough to traditional in previous years that a 4% withdrawal rate in retirement from the traditional balance alone would put you in the 25% bracket, with an 11% effective rate.
- are currently in the 15% bracket (and that is your current marginal rate).

Knowing that any traditional contribution will save you 15% this year, but you will pay 25% on any extra withdrawals because of it, would you still use traditional because your effective retirement rate is 11%?
Thanks for illuminating!

Each contribution event is independent and may push further contributions, that year, to be taxed at a lower rate or push withdrawals to be taxed at a higher rate.

Let's see if I can correctly define post-facto whether the correct choices were made.

If taxes on a withdrawal occur at a higher rate than an early years potential contribution, or conversion tax rate, a non-optimal contribution decision was made. In an earlier year, the dollars could have been contributed, or converted, at a lower rate than in withdrawal.

FiveK
Posts: 6376
Joined: Sun Mar 16, 2014 2:43 pm

### Re: Calculator - pretax vs aftertax plans

Silly Wabbit wrote:
Sun Oct 29, 2017 11:41 am
Thanks for illuminating!
No problem. First time I heard "contribute at marginal, withdraw at effective" it sounded correct to me too, but the math shows it isn't.
Each contribution event is independent and may push further contributions, that year, to be taxed at a lower rate or push withdrawals to be taxed at a higher rate.
That would be exactly true if looking only at the tax brackets. Due to quirks of the tax code, notably credits on the contribution side and SS benefit taxation on the withdrawal side, there are exceptions. E.g., the \$60K-earning couple example, in which the marginal saving rate increased with higher contributions.
Let's see if I can correctly define post-facto whether the correct choices were made.

If taxes on a withdrawal occur at a higher rate than an early years potential contribution, or conversion tax rate, a non-optimal contribution decision was made. In an earlier year, the dollars could have been contributed, or converted, at a lower rate than in withdrawal.
Not exactly sure how the words "potential" and "decision" interact, but I think you have the gist.

Note also that the more one contributes to either traditional or Roth, the more likely that decision becomes incorrect. Fortunately it takes a lot of overcontribution "the wrong way" to matter.