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### Re: Help me with the Trad vs Roth 401k Math

Posted: **Sun Feb 17, 2019 11:03 am**

by **willthrill81**

KlangFool wrote: ↑Sun Feb 17, 2019 11:00 am

willthrill81 wrote: ↑Sun Feb 17, 2019 10:43 am

nick evets wrote: ↑Sun Feb 17, 2019 9:25 am

Whoa...that IS interesting. Thanks all -- I'm not sure my wife and I would be able to live for a year, yet, w/out taxable income, but the idea is cool.

Many, probably most, of those who employ this strategy have significant taxable accounts as well. These can provide significant tax-free income (remember that long-term capital gains taxes can be 0%) while you're doing Roth conversions.

Using a combination of filling up the standard deduction with withdrawals from tax-deferred accounts, paying for medical expenses tax-free via HSA withdrawals, and covering the rest with withdrawals from taxable and Roth accounts, it's pretty easy to craft a realistic scenario where a married-filing-jointly couple has $100k of

income expense in retirement that they pay no taxes on at all.

willthrill81,

I would like to change one word in your post.

KlangFool

Only one?

### Re: Help me with the Trad vs Roth 401k Math

Posted: **Sun Feb 17, 2019 11:03 am**

by **aristotelian**

OP, in addition to the advice you have received, you are welcome to try this spreadsheet. You will see that it is very difficult for Roth to come out ahead.

https://docs.google.com/spreadsheets/d/ ... 1374797127

### Re: Help me with the Trad vs Roth 401k Math

Posted: **Sun Feb 17, 2019 11:10 am**

by **willthrill81**

The appeal at first glance of the prospect of never having to pay taxes again on Roth contributions and growth is very strong. I've even heard numerous financial pundits pontificate about the superiority of Roth accounts to tax-deferred for the average person.

### Re: Help me with the Trad vs Roth 401k Math

Posted: **Sun Feb 17, 2019 11:21 am**

by **MathIsMyWayr**

justsomeguy2018 wrote: ↑Sat Feb 16, 2019 7:52 pm

Help me understand how the tax rate in retirement vs current marginal rate is all that matters when thinking of tax efficiency of Roth vs Trad.

...

Can someone show me mathematically how maxing out a Roth vs Trad 401k would generate the same final net value if the tax rate stayed exactly the same?

Your net after-tax during retirement
- a: pre-tax amount to invest
- a0: max. (Roth) 401k (currently $19,000)
- G: investment gain factor for 401k or Roth
- G3: investment gain factor for taxable
- t1: ordinary tax rate now
- t2: ordinary tax rate during retirement
- t3: LT CG tax rate during retirement

case 1) a=<a0

- 401k: a*G*(1-t2)
- Roth: (1-t1)*a*G

case 2) a>a0

- 401k: a0*G*(1-t2)+(1-t1)*(a-a0)*G3*(1-t3)
- Roth: min((1-t1)*a,a0)*G+min((1-t1)*a-a0,0)*G3*(1-t3)

In case 2, you have after-tax (1-t1)*(a-a0) remaining for investing in taxable after maxing 401k. If you choose Roth, you have after-tax (1-t1)*a for Roth and taxable.

### Re: Help me with the Trad vs Roth 401k Math

Posted: **Sun Feb 17, 2019 11:43 am**

by **02nz**

willthrill81 wrote: ↑Sun Feb 17, 2019 11:10 am

The appeal at first glance of the prospect of never having to pay taxes again on Roth contributions and growth is very strong. I've even heard numerous financial pundits pontificate about the superiority of Roth accounts to tax-deferred for the average person.

It's especially bad when these pundits claim that taking the tax hit now with is "worth it" if you have a long time for the money to grow tax-free. Which is of course nonsense when the alternative is to defer taxes. (In cases of maxing the contribution limit, yes 19K of Roth space is effectively more than 19K of tax-deferred + putting the tax savings into taxable, but even this advantage isn't usually enough to overcome the lower tax rates most people have in retirement.)

### Re: Help me with the Trad vs Roth 401k Math

Posted: **Sun Feb 17, 2019 11:51 am**

by **nick evets**

KlangFool wrote: ↑Sun Feb 17, 2019 10:24 am

nick evets wrote: ↑Sun Feb 17, 2019 9:25 am

Whoa...that IS interesting. Thanks all -- I'm not sure my wife and I would be able to live for a year, yet, w/out taxable income, but the idea is cool. Please forgive the interruption.

nick evets,

A) If you early retire, you should keep 1 to 2 years of the emergency fund. So, if you only spend from your emergency fund, what is your taxable income? Aka, spending cash.

B) If you are married, you have 10K to 12K of Roth IRA contribution every year. After 10 to 20 years, you have 100K to 200K worth of IRA contribution that you can spend without generating taxable income. So, how many years can you live on 100K to 200K worth of Roth IRA's contribution?

KlangFool

Hmm....All of our savings is basically in 401k IRA's and virtually nothing in Roth IRA's, to date. One year we tried the back-door ROTH approach and it was a huge hassle; another year our AGI dipped down and I was able to contribute, but...there is maybe $25k total in our Roth IRA's combined.

If we need $100k of income a year, that's not going to get us very far. With our current situation as we near retirement (I am 54, my wife 59), I'm able to max out my 401k at 24k, and my wife contributes up to her match %6, but that's it...I feel like Roth's offer a huge advantage, but that ship is sailing by.

### Re: Help me with the Trad vs Roth 401k Math

Posted: **Sun Feb 17, 2019 12:00 pm**

by **justsomeguy2018**

KlangFool wrote: ↑Sun Feb 17, 2019 10:30 am

justsomeguy2018 wrote: ↑Sun Feb 17, 2019 8:59 am

rkhusky wrote: ↑Sun Feb 17, 2019 8:15 am

justsomeguy2018 wrote: ↑Sat Feb 16, 2019 10:14 pm

Final thought: the math only works if you actually invest the $3800 tax savings in similar growth investment, right? if you invest the $3800 in a 2% Savings Account, e.g., then the Roth might still come out ahead, right?

That's definitely not an apple to apple comparison. The reverse is also true - if you put the Roth in a MM account and invest taxable in Total Stock Market, Roth probably does much worse.

Sorry my point may not have been very clear - as someone else mentioned earlier in this thread,

**I am skeptical most people have the discipline to say "Hey this $x tax dollars I am saving from Traditional, I am going to invest it in a taxable account at the same AA/growth rate as my Traditional to be sure I come out ahead vs if I had invested in Roth instead, and to ensure I capitalize on my lower tax rate in retirement vs current Roth tax rate"**

justsomeguy2018,

This is a strawman that you created in order to support your point. The best combination is Trad. 401K and Roth IRAs. If someone can save beyond that, they are not normal people. Then, you do not need to worry about their discipline of investing in the taxable account.

For a single Trad. 401K + 2 X Roth IRAs = 19K + 12K = 31K

2 X 401K + 2 Roth IRAs = 38K + 12K = 50K

KlangFool

How is it a straw man? Show me how someone who maxes out traditional but doesn't invest the tax savings comes out ahead vs maxing out the Roth.

A $19,000 80/20 AA investment made in 1989 yielded $288,806 according to Portfolio Visualizer. Assume a 20% tax on $19k = $3,800 in taxes paid .

The retirement break even nominal tax rate is 1.3% ($3800/$288806).

Even assuming a 5% retirement tax rate, you pay $14.4k taxes in retirement vs the $3800 now.

And yes, sure, you can do the things you mentioned and pay the 0% rate. But that is not what I am talking about.

To be clear - I am not advocating for the Roth or saying that is the route people should take.

Just saying for your average Joe that may be financially unsavvy and spends their tax savings rather than invests it, the tax-free growth of the Roth would likely outweigh the tax-deferred status of the Traditional.

### Re: Help me with the Trad vs Roth 401k Math

Posted: **Sun Feb 17, 2019 12:13 pm**

by **willthrill81**

justsomeguy2018 wrote: ↑Sun Feb 17, 2019 12:00 pm

KlangFool wrote: ↑Sun Feb 17, 2019 10:30 am

justsomeguy2018 wrote: ↑Sun Feb 17, 2019 8:59 am

rkhusky wrote: ↑Sun Feb 17, 2019 8:15 am

justsomeguy2018 wrote: ↑Sat Feb 16, 2019 10:14 pm

Final thought: the math only works if you actually invest the $3800 tax savings in similar growth investment, right? if you invest the $3800 in a 2% Savings Account, e.g., then the Roth might still come out ahead, right?

That's definitely not an apple to apple comparison. The reverse is also true - if you put the Roth in a MM account and invest taxable in Total Stock Market, Roth probably does much worse.

Sorry my point may not have been very clear - as someone else mentioned earlier in this thread,

**I am skeptical most people have the discipline to say "Hey this $x tax dollars I am saving from Traditional, I am going to invest it in a taxable account at the same AA/growth rate as my Traditional to be sure I come out ahead vs if I had invested in Roth instead, and to ensure I capitalize on my lower tax rate in retirement vs current Roth tax rate"**

justsomeguy2018,

This is a strawman that you created in order to support your point. The best combination is Trad. 401K and Roth IRAs. If someone can save beyond that, they are not normal people. Then, you do not need to worry about their discipline of investing in the taxable account.

For a single Trad. 401K + 2 X Roth IRAs = 19K + 12K = 31K

2 X 401K + 2 Roth IRAs = 38K + 12K = 50K

KlangFool

How is it a straw man? Show me how someone who maxes out traditional but doesn't invest the tax savings comes out ahead vs maxing out the Roth.

A $19,000 80/20 AA investment made in 1989 yielded $288,806 according to Portfolio Visualizer. Assume a 20% tax on $19k = $3,800 in taxes paid .

The retirement break even nominal tax rate is 1.3% ($3800/$288806).

Even assuming a 5% retirement tax rate, you pay $14.4k taxes in retirement vs the $3800 now.

And yes, sure, you can do the things you mentioned and pay the 0% rate. But that is not what I am talking about.

To be clear - I am not advocating for the Roth or saying that is the route people should take.

Just saying for your average Joe that may be financially unsavvy and spends their tax savings rather than invests it, the tax-free growth of the Roth would likely outweigh the tax-deferred status of the Traditional.

It comes across as a strawman argument because you started the discussion by looking at the math, but then you switched to behavioral considerations. Behavior is definitely a valid consideration, but it's distinct from the math, which clearly indicates that in normal situations, tax-deferred beats Roth.

The "average Joe" isn't coming to this forum for financial advice, and there's little to nothing we can do to help such people.

### Re: Help me with the Trad vs Roth 401k Math

Posted: **Sun Feb 17, 2019 12:20 pm**

by **KlangFool**

nick evets wrote: ↑Sun Feb 17, 2019 11:51 am

KlangFool wrote: ↑Sun Feb 17, 2019 10:24 am

nick evets wrote: ↑Sun Feb 17, 2019 9:25 am

Whoa...that IS interesting. Thanks all -- I'm not sure my wife and I would be able to live for a year, yet, w/out taxable income, but the idea is cool. Please forgive the interruption.

nick evets,

A) If you early retire, you should keep 1 to 2 years of the emergency fund. So, if you only spend from your emergency fund, what is your taxable income? Aka, spending cash.

B) If you are married, you have 10K to 12K of Roth IRA contribution every year. After 10 to 20 years, you have 100K to 200K worth of IRA contribution that you can spend without generating taxable income. So, how many years can you live on 100K to 200K worth of Roth IRA's contribution?

KlangFool

Hmm....All of our savings is basically in 401k IRA's and virtually nothing in Roth IRA's, to date. One year we tried the back-door ROTH approach and it was a huge hassle; another year our AGI dipped down and I was able to contribute, but...there is maybe $25k total in our Roth IRA's combined.

If we need $100k of income a year, that's not going to get us very far. With our current situation as we near retirement (I am 54, my wife 59), I'm able to max out my 401k at 24k, and

**my wife contributes up to her match %6, but that's it**...I feel like Roth's offer a huge advantage, but that ship is sailing by.

nick evets,

You could contribute to your wife's Roth 401K.

KlangFool

### Re: Help me with the Trad vs Roth 401k Math

Posted: **Sun Feb 17, 2019 12:21 pm**

by **teen persuasion**

OP, another thing to consider is whether contributing to pre-tax 401k can lower AGI enough to make you eligible for credits that phaseout. One example is the Retirement Saver's credit. Another is EITC. They are both also credits one can likely not claim in retirement (as they both require earned income, and EITC requires dependent children for significant credits).

We contribute to DH's 401k, to reduce our line 7 wages and AGI (EITC tests both) to increase this refundable credit. It has a 21% phaseout. Our state matches EITC at 30%, so an additional effective 6.3%. That would be on top of our 10-12% federal plus 4-5% state tax rates. Lowering our AGI also drops us thru the Saver's credit bands from zero credit to 50% credit * 2.

Contributing to pre-tax not only saves us 14-17% in taxes plus nonrefundable credits we become eligible for, it also nets us refundable credits (that would otherwise be phased out at 27.3% combined). It makes for a very high marginal rate, compared to a similar income level in retirement. We are choosing to optimize these credits while the conditions exist for us (have dependents, have earned income), because it's not a level field (accumulation years vs withdrawal years).

The refundable credits and tax savings are used to contribute to Roth IRAs. It's a significant increase in the amount we can save annually.

### Re: Help me with the Trad vs Roth 401k Math

Posted: **Sun Feb 17, 2019 12:56 pm**

by **justsomeguy2018**

willthrill81 wrote: ↑Sun Feb 17, 2019 12:13 pm

justsomeguy2018 wrote: ↑Sun Feb 17, 2019 12:00 pm

KlangFool wrote: ↑Sun Feb 17, 2019 10:30 am

justsomeguy2018 wrote: ↑Sun Feb 17, 2019 8:59 am

rkhusky wrote: ↑Sun Feb 17, 2019 8:15 am

That's definitely not an apple to apple comparison. The reverse is also true - if you put the Roth in a MM account and invest taxable in Total Stock Market, Roth probably does much worse.

Sorry my point may not have been very clear - as someone else mentioned earlier in this thread,

**I am skeptical most people have the discipline to say "Hey this $x tax dollars I am saving from Traditional, I am going to invest it in a taxable account at the same AA/growth rate as my Traditional to be sure I come out ahead vs if I had invested in Roth instead, and to ensure I capitalize on my lower tax rate in retirement vs current Roth tax rate"**

justsomeguy2018,

This is a strawman that you created in order to support your point. The best combination is Trad. 401K and Roth IRAs. If someone can save beyond that, they are not normal people. Then, you do not need to worry about their discipline of investing in the taxable account.

For a single Trad. 401K + 2 X Roth IRAs = 19K + 12K = 31K

2 X 401K + 2 Roth IRAs = 38K + 12K = 50K

KlangFool

How is it a straw man? Show me how someone who maxes out traditional but doesn't invest the tax savings comes out ahead vs maxing out the Roth.

A $19,000 80/20 AA investment made in 1989 yielded $288,806 according to Portfolio Visualizer. Assume a 20% tax on $19k = $3,800 in taxes paid .

The retirement break even nominal tax rate is 1.3% ($3800/$288806).

Even assuming a 5% retirement tax rate, you pay $14.4k taxes in retirement vs the $3800 now.

And yes, sure, you can do the things you mentioned and pay the 0% rate. But that is not what I am talking about.

To be clear - I am not advocating for the Roth or saying that is the route people should take.

Just saying for your average Joe that may be financially unsavvy and spends their tax savings rather than invests it, the tax-free growth of the Roth would likely outweigh the tax-deferred status of the Traditional.

It comes across as a strawman argument because you started the discussion by looking at the math, but then you switched to behavioral considerations. Behavior is definitely a valid consideration, but it's distinct from the math, which clearly indicates that in normal situations, tax-deferred beats Roth.

The "average Joe" isn't coming to this forum for financial advice, and there's little to nothing we can do to help such people.

I think you have it the other way around.

The "math" being used to justify traditional 401k beating Roth 401k involves behavioral considerations; it requires behavior of the contributor to invest in a taxable account with similar growth rates/investments.

So behavioral considerations have entered the discussion by default. It's the only way the math works.

That being said - at this point I think we're probably talking in circles. I was only making an observation/thinking-out-loud - not really trying to defend Roth as the superior choice - just observing the outcome depends on the additional behavior of the contributor.

### Re: Help me with the Trad vs Roth 401k Math

Posted: **Sun Feb 17, 2019 12:57 pm**

by **FiveK**

MathIsMyWayr wrote: ↑Sun Feb 17, 2019 11:21 am

Your net after-tax during retirement
- a: pre-tax amount to invest
- a0: max. (Roth) 401k (currently $19,000)
- G: investment gain factor for 401k or Roth
- G3: investment gain factor for taxable
- t1: ordinary tax rate now
- t2: ordinary tax rate during retirement
- t3: LT CG tax rate during retirement

case 1) a=<a0

- 401k: a*G*(1-t2)
- Roth: (1-t1)*a*G

Yes.

case 2) a>a0

- 401k: a0*G*(1-t2)+(1-t1)*(a-a0)*G3*(1-t3)
- Roth: min((1-t1)*a,a0)*G+min((1-t1)*a-a0,0)*G3*(1-t3)

That's close. Reinvested dividends increase the basis in the taxable account, thus lowering the amount of capital gain subject to tax.

See

viewtopic.php?f=10&t=150516#p2773840

### Re: Help me with the Trad vs Roth 401k Math

Posted: **Sun Feb 17, 2019 1:12 pm**

by **KlangFool**

justsomeguy2018 wrote: ↑Sun Feb 17, 2019 12:56 pm

willthrill81 wrote: ↑Sun Feb 17, 2019 12:13 pm

justsomeguy2018 wrote: ↑Sun Feb 17, 2019 12:00 pm

KlangFool wrote: ↑Sun Feb 17, 2019 10:30 am

justsomeguy2018 wrote: ↑Sun Feb 17, 2019 8:59 am

Sorry my point may not have been very clear - as someone else mentioned earlier in this thread,

**I am skeptical most people have the discipline to say "Hey this $x tax dollars I am saving from Traditional, I am going to invest it in a taxable account at the same AA/growth rate as my Traditional to be sure I come out ahead vs if I had invested in Roth instead, and to ensure I capitalize on my lower tax rate in retirement vs current Roth tax rate"**

justsomeguy2018,

This is a strawman that you created in order to support your point. The best combination is Trad. 401K and Roth IRAs. If someone can save beyond that, they are not normal people. Then, you do not need to worry about their discipline of investing in the taxable account.

For a single Trad. 401K + 2 X Roth IRAs = 19K + 12K = 31K

2 X 401K + 2 Roth IRAs = 38K + 12K = 50K

KlangFool

How is it a straw man? Show me how someone who maxes out traditional but doesn't invest the tax savings comes out ahead vs maxing out the Roth.

A $19,000 80/20 AA investment made in 1989 yielded $288,806 according to Portfolio Visualizer. Assume a 20% tax on $19k = $3,800 in taxes paid .

The retirement break even nominal tax rate is 1.3% ($3800/$288806).

Even assuming a 5% retirement tax rate, you pay $14.4k taxes in retirement vs the $3800 now.

And yes, sure, you can do the things you mentioned and pay the 0% rate. But that is not what I am talking about.

To be clear - I am not advocating for the Roth or saying that is the route people should take.

Just saying for your average Joe that may be financially unsavvy and spends their tax savings rather than invests it, the tax-free growth of the Roth would likely outweigh the tax-deferred status of the Traditional.

It comes across as a strawman argument because you started the discussion by looking at the math, but then you switched to behavioral considerations. Behavior is definitely a valid consideration, but it's distinct from the math, which clearly indicates that in normal situations, tax-deferred beats Roth.

The "average Joe" isn't coming to this forum for financial advice, and there's little to nothing we can do to help such people.

I think you have it the other way around.

**The "math" being used to justify traditional 401k beating Roth 401k involves behavioral considerations; **it requires behavior of the contributor to invest in a taxable account with similar growth rates/investments.

justsomeguy2018,

Only if you pick your strawman of Trad. 401K + taxable account. If it is Trad. 401K + Roth IRA, Roth 401K lose all the time.

KlangFool

### Re: Help me with the Trad vs Roth 401k Math

Posted: **Sun Feb 17, 2019 1:18 pm**

by **FiveK**

KlangFool wrote: ↑Sun Feb 17, 2019 1:12 pm

Only if you pick your strawman of Trad. 401K + taxable account. If it is Trad. 401K + Roth IRA, Roth 401K lose all the time.

One can fill the Roth IRA regardless of what one does with the 401k. If we assume that the Roth IRA contribution limit has already been reached, then "trad 401k + taxable" vs. "Roth 401k" is indeed the fair comparison.

### Re: Help me with the Trad vs Roth 401k Math

Posted: **Sun Feb 17, 2019 1:24 pm**

by **justsomeguy2018**

KlangFool wrote: ↑Sun Feb 17, 2019 1:12 pm

justsomeguy2018 wrote: ↑Sun Feb 17, 2019 12:56 pm

willthrill81 wrote: ↑Sun Feb 17, 2019 12:13 pm

justsomeguy2018 wrote: ↑Sun Feb 17, 2019 12:00 pm

KlangFool wrote: ↑Sun Feb 17, 2019 10:30 am

justsomeguy2018,

This is a strawman that you created in order to support your point. The best combination is Trad. 401K and Roth IRAs. If someone can save beyond that, they are not normal people. Then, you do not need to worry about their discipline of investing in the taxable account.

For a single Trad. 401K + 2 X Roth IRAs = 19K + 12K = 31K

2 X 401K + 2 Roth IRAs = 38K + 12K = 50K

KlangFool

How is it a straw man? Show me how someone who maxes out traditional but doesn't invest the tax savings comes out ahead vs maxing out the Roth.

A $19,000 80/20 AA investment made in 1989 yielded $288,806 according to Portfolio Visualizer. Assume a 20% tax on $19k = $3,800 in taxes paid .

The retirement break even nominal tax rate is 1.3% ($3800/$288806).

Even assuming a 5% retirement tax rate, you pay $14.4k taxes in retirement vs the $3800 now.

And yes, sure, you can do the things you mentioned and pay the 0% rate. But that is not what I am talking about.

To be clear - I am not advocating for the Roth or saying that is the route people should take.

Just saying for your average Joe that may be financially unsavvy and spends their tax savings rather than invests it, the tax-free growth of the Roth would likely outweigh the tax-deferred status of the Traditional.

It comes across as a strawman argument because you started the discussion by looking at the math, but then you switched to behavioral considerations. Behavior is definitely a valid consideration, but it's distinct from the math, which clearly indicates that in normal situations, tax-deferred beats Roth.

The "average Joe" isn't coming to this forum for financial advice, and there's little to nothing we can do to help such people.

I think you have it the other way around.

**The "math" being used to justify traditional 401k beating Roth 401k involves behavioral considerations; **it requires behavior of the contributor to invest in a taxable account with similar growth rates/investments.

justsomeguy2018,

Only if you pick your strawman of Trad. 401K + taxable account. If it is Trad. 401K + Roth IRA, Roth 401K lose all the time.

KlangFool

If it's Trad 401k + spend all the tax savings instead of invest them, it doesn't.

Trad 401k + Roth IRA still requires behavioral actions on the part of contributor to make the decision to invest the tax savings in the Roth IRA.

All I am saying is the Trad 401k vs Roth 401k math outcome is completely dependent on the behavior of the contributor in regards to what they do with the tax savings.

It isn't a strawman, it's just an observational fact.

### Re: Help me with the Trad vs Roth 401k Math

Posted: **Sun Feb 17, 2019 1:26 pm**

by **KlangFool**

FiveK wrote: ↑Sun Feb 17, 2019 1:18 pm

KlangFool wrote: ↑Sun Feb 17, 2019 1:12 pm

Only if you pick your strawman of Trad. 401K + taxable account. If it is Trad. 401K + Roth IRA, Roth 401K lose all the time.

One can fill the Roth IRA regardless of what one does with the 401k. If we assume that the Roth IRA contribution limit has already been reached, then "trad 401k + taxable" vs. "Roth 401k" is indeed the fair comparison.

FiveK,

I disagreed. Then, it is Trad. 401K + Roth IRA+ Taxable versus Roth 401K + Roth IRA. It comes back to my statement that this is no longer a normal person. Hence, the behavioral consideration of a normal person no longer applies.

A) This person's income is low enough to directly contributing to Roth IRA.

B) This person's saving rate is high enough to save far exceed a normal person.

C) With a combination of Trad. 401K + Roth IRA + Taxable account, this person get to choose whatever amount of taxable income to generate.

D) This person's saving rate is very high as compared to his annual expense. Hence, this person can early retire.

I know this. I am one of those persons.

KlangFool

### Re: Help me with the Trad vs Roth 401k Math

Posted: **Sun Feb 17, 2019 1:30 pm**

by **KlangFool**

justsomeguy2018 wrote: ↑Sun Feb 17, 2019 1:24 pm

**If it's Trad 401k + spend all the tax savings instead of invest them, it doesn't.**
Trad 401k + Roth IRA still requires behavioral actions on the part of contributor to make the decision to invest the tax savings in the Roth IRA.

All I am saying is the Trad 401k vs Roth 401k math outcome is completely dependent on the behavior of the contributor in regards to what they do with the tax savings.

It isn't a strawman, it's just an observational fact.

justsomeguy2018,

<<

**If it's Trad 401k + spend all the tax savings instead of invest them, it doesn't.**>>

This is the behavior of a normal person.

<<All I am saying is the Trad 401k vs Roth 401k math outcome is completely dependent on the behavior of the contributor in regards to what they do with the tax savings.>>

A normal person saves less than 5% of their gross income. They do not max up their Trad. 401K.

That is my whole point. You cannot have it both ways.

A) It takes an abnormal person to max up their Trad. 401Ks.

B) So, you cannot assume that this person will behave like a normal person and spend all the tax savings instead of putting the tax saving into the Roth IRAs.

KlangFool

### Re: Help me with the Trad vs Roth 401k Math

Posted: **Sun Feb 17, 2019 1:34 pm**

by **FiveK**

KlangFool wrote: ↑Sun Feb 17, 2019 1:26 pm

Then, it is Trad. 401K + Roth IRA+ Taxable versus Roth 401K + Roth IRA.

Agreed.

Subtract Roth IRA from both sides and we have Trad. 401K + Taxable versus Roth 401K.

### Re: Help me with the Trad vs Roth 401k Math

Posted: **Sun Feb 17, 2019 1:47 pm**

by **KlangFool**

FiveK wrote: ↑Sun Feb 17, 2019 1:34 pm

KlangFool wrote: ↑Sun Feb 17, 2019 1:26 pm

Then, it is Trad. 401K + Roth IRA+ Taxable versus Roth 401K + Roth IRA.

Agreed.

Subtract Roth IRA from both sides and we have Trad. 401K + Taxable versus Roth 401K.

Then, we have a highly inaccurate way to predict and calculate the future retirement tax rate. The whole calculation becomes pointless since future retirement tax rate is a key consideration.

There is a significant difference between

A) Trad. 401K + Roth IRA + Taxable versus Roth 401K + Roth IRA

versus

B) Trad. 401K + Taxable versus Roth 401K

KlangFool

### Re: Help me with the Trad vs Roth 401k Math

Posted: **Sun Feb 17, 2019 2:08 pm**

by **aristotelian**

OP, if your position is that you know that Roth is inferior but it works for you behaviorally, there is no reason for this thread. You have already made up your mind and your assumptions preclude a rational discussion. Personally, my presumption is that I am a rational investor.

### Re: Help me with the Trad vs Roth 401k Math

Posted: **Sun Feb 17, 2019 2:58 pm**

by **02nz**

aristotelian wrote: ↑Sun Feb 17, 2019 2:08 pm

OP, if your position is that you know that Roth is inferior but it works for you behaviorally, there is no reason for this thread. You have already made up your mind and your assumptions preclude a rational discussion. Personally, my presumption is that I am a rational investor.

+1. The original post actually explicitly asks the question mathematically. It contains not a single reference to anything behavioral. So, maybe it's not a strawman argument, but it's definitely moving the goalposts.

### Re: Help me with the Trad vs Roth 401k Math

Posted: **Sun Feb 17, 2019 4:04 pm**

by **FiveK**

KlangFool wrote: ↑Sun Feb 17, 2019 1:47 pm

FiveK wrote: ↑Sun Feb 17, 2019 1:34 pm

KlangFool wrote: ↑Sun Feb 17, 2019 1:26 pm

Then, it is Trad. 401K + Roth IRA+ Taxable versus Roth 401K + Roth IRA.

Agreed.

Subtract Roth IRA from both sides and we have Trad. 401K + Taxable versus Roth 401K.

Then, we have a highly inaccurate way to predict and calculate the future retirement tax rate. The whole calculation becomes pointless since future retirement tax rate is a key consideration.

There is a significant difference between

A) Trad. 401K + Roth IRA + Taxable versus Roth 401K + Roth IRA

versus

B) Trad. 401K + Taxable versus Roth 401K

KlangFool

Probably best to let this side conversation die, as I think we are using different perspectives and the main thread topic has become confusing enough.

### Re: Help me with the Trad vs Roth 401k Math

Posted: **Sun Feb 17, 2019 4:19 pm**

by **justsomeguy2018**

aristotelian wrote: ↑Sun Feb 17, 2019 2:08 pm

OP, if your position is that you know that Roth is inferior but it works for you behaviorally, there is no reason for this thread. You have already made up your mind and your assumptions preclude a rational discussion. Personally, my presumption is that I am a rational investor.

That isn't my "position".

My "position" (if you even want to call it a "position") is that if someone (anyone, not necessarily myself) isn't going to bother investing the tax savings, then it might make more sense to just do the Roth.

Why is this so hard to understand?

I am not trying to make an argument, I am just making a statement of fact. Is my statement of fact incorrect?

### Re: Help me with the Trad vs Roth 401k Math

Posted: **Sun Feb 17, 2019 4:32 pm**

by **willthrill81**

aristotelian wrote: ↑Sun Feb 17, 2019 2:08 pm

OP, if your position is that you know that Roth is inferior but it works for you behaviorally, there is no reason for this thread. You have already made up your mind and your assumptions preclude a rational discussion. Personally, my presumption is that I am a rational investor.

That's my conclusion as well.

### Re: Help me with the Trad vs Roth 401k Math

Posted: **Sun Feb 17, 2019 4:33 pm**

by **justsomeguy2018**

02nz wrote: ↑Sun Feb 17, 2019 2:58 pm

aristotelian wrote: ↑Sun Feb 17, 2019 2:08 pm

OP, if your position is that you know that Roth is inferior but it works for you behaviorally, there is no reason for this thread. You have already made up your mind and your assumptions preclude a rational discussion. Personally, my presumption is that I am a rational investor.

+1. The original post actually explicitly asks the question mathematically. It contains not a single reference to anything behavioral. So, maybe it's not a strawman argument, but it's definitely moving the goalposts.

Not true, I mention this in my original post:

*Is the assumption that the $3,800 paid in taxes on Roth, would have been invested in a Taxable account, so the growth would be equivalent? If so, expound on that for me. *
There was some fruitful discussion around this (tax drag, future 0% LTCG rates, etc.) and after reading the Wiki FiveK linked to and some other user comments, I got the mathematical explanations I was looking for. And they all primarily revolved around

*investing the tax savings elsewhere* as I alluded to in my post. Which is fine, makes sense, I am on board with that and agree with the logic.

After all was said and done, all I did was observe that

*if someone does not bother investing the tax saving elsewhere*, then the Roth 401k would likely be the winner. I wasn't saying that to try and justify the Roth 401k as superior, just merely observing that

*certain behavioral considerations are implicit in the superiority of the Trad 401k*. It's ironic that I am being accused of "injecting behavioral considerations into this discussion", when the entire premise of the math revolves around behavioral considerations. It's impossible to do the math you want to apply without using behavioral considerations.

### Re: Help me with the Trad vs Roth 401k Math

Posted: **Sun Feb 17, 2019 4:33 pm**

by **JustinR**

justsomeguy2018 wrote: ↑Sun Feb 17, 2019 4:19 pm

aristotelian wrote: ↑Sun Feb 17, 2019 2:08 pm

OP, if your position is that you know that Roth is inferior but it works for you behaviorally, there is no reason for this thread. You have already made up your mind and your assumptions preclude a rational discussion. Personally, my presumption is that I am a rational investor.

That isn't my "position".

My "position" (if you even want to call it a "position") is that if someone (anyone, not necessarily myself) isn't going to bother investing the tax savings, then it might make more sense to just do the Roth.

Why is this so hard to understand?

I am not trying to make an argument, I am just making a statement of fact. Is my statement of fact incorrect?

**Original Poster:** "B is better than A"

**Forum:** "No, A is better than B. Here's why."

**OP:** "But if person doesn't do the thing that makes A better than B, then B is clearly better."

**Forum:** "..."

### Re: Help me with the Trad vs Roth 401k Math

Posted: **Sun Feb 17, 2019 4:54 pm**

by **justsomeguy2018**

JustinR wrote: ↑Sun Feb 17, 2019 4:33 pm

justsomeguy2018 wrote: ↑Sun Feb 17, 2019 4:19 pm

aristotelian wrote: ↑Sun Feb 17, 2019 2:08 pm

OP, if your position is that you know that Roth is inferior but it works for you behaviorally, there is no reason for this thread. You have already made up your mind and your assumptions preclude a rational discussion. Personally, my presumption is that I am a rational investor.

That isn't my "position".

My "position" (if you even want to call it a "position") is that if someone (anyone, not necessarily myself) isn't going to bother investing the tax savings, then it might make more sense to just do the Roth.

Why is this so hard to understand?

I am not trying to make an argument, I am just making a statement of fact. Is my statement of fact incorrect?

**Original Poster:** "B is better than A"

**Forum:** "No, A is better than B. Here's why."

**OP:** "But if person doesn't do the thing that makes A better than B, then B is clearly better."

**Forum:** "..."

More like...

**Original Poster:** "B appears to be better than A. Help me understand why...is it because of C? Show me how that works"

**Forum:** "No, A is better than B. It's because when you add in Behavior C + A, the combined is better than B"

**OP:** "<after some discussions> Ok, that makes sense. So if the person doesn't do Behavior C at the time they do A, then B would probably be better"

**Forum:** "Stop injecting behavior into this discussion!!"

### Re: Help me with the Trad vs Roth 401k Math

Posted: **Sun Feb 17, 2019 5:14 pm**

by **Momus**

justsomeguy2018 wrote: ↑Sat Feb 16, 2019 7:52 pm

Help me understand how the tax rate in retirement vs current marginal rate is all that matters when thinking of tax efficiency of Roth vs Trad. Here is how I see math if I max out the 401k at a fictional 20% current tax bracket vs 10% retirement bracket:

Trad: $19,000 contribution, grows to $190,000 in retirement. Taxes in retirement = .10 x $190,000 = $19,000. Net = $171,000

Roth: $19,000 contribution, grows to $190,000 in retirement. Taxes currently paid = .20 x $19,000 =$3,800. Net = $186,200

What am I missing here? Is the assumption that the $3,800 paid in taxes on Roth, would have been invested in a Taxable account, so the growth would be equivalent? If so, expound on that for me.

Most of the time I see this example explained as the Roth contribution would end up equal with equal tax rates because it would only be $15,200 after you paid $3,800 in taxes, but what if you paid those $3800 taxes, and still maxed out at the $19,000 rate? How could the Trad possibly be better, assuming an extremely high growth rate in the Roth?

Can someone show me mathematically how maxing out a Roth vs Trad 401k would generate the same final net value if the tax rate stayed exactly the same?

https://thefinancebuff.com/case-against-roth-401k.html

### Re: Help me with the Trad vs Roth 401k Math

Posted: **Sun Feb 17, 2019 5:40 pm**

by **MathIsMyWayr**

FiveK wrote: ↑Sun Feb 17, 2019 12:57 pm

MathIsMyWayr wrote: ↑Sun Feb 17, 2019 11:21 am

Your net after-tax during retirement
- a: pre-tax amount to invest
- a0: max. (Roth) 401k (currently $19,000)
- G: investment gain factor for 401k or Roth
- G3: investment gain factor for taxable
- t1: ordinary tax rate now
- t2: ordinary tax rate during retirement
- t3: LT CG tax rate during retirement

case 1) a=<a0

- 401k: a*G*(1-t2)
- Roth: (1-t1)*a*G

Yes.

case 2) a>a0

- 401k: a0*G*(1-t2)+(1-t1)*(a-a0)*G3*(1-t3)
- Roth: min((1-t1)*a,a0)*G+min((1-t1)*a-a0,0)*G3*(1-t3)

That's close. Reinvested dividends increase the basis in the taxable account, thus lowering the amount of capital gain subject to tax.

See

viewtopic.php?f=10&t=150516#p2773840

Yes, as FiveK pointed out and also showed in his link, tax drag on dividend reinvestment makes it a little more complicated.

Basis (B) and Appreciation (A) at year n+1 are related to those at year n

- d: dividend rate
- g: appreciation rate
- T: tax rate on dividend
- B(n+1)=B(n)+(1-T)*d*[B(n)+A(n)]
- A(n+1)=A(n)+g*[B(n)+A(n)]
- B(0)=(1-t1)*a-a0
- A(0)=0

The above may be easily evaluated recursively or by using matrix algebra.

### Re: Help me with the Trad vs Roth 401k Math

Posted: **Sun Feb 17, 2019 7:19 pm**

by **LadyGeek**

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