Friday, July 5, 2013

Roth Vs Traditional Analysis

Yet Still over at Bogleheads we read:  

Roth Vs Traditional Analysis


Roth Vs Traditional Analysis

Postby Kalo » Thu Jul 04, 2013 2:31 pm
Can I get suggestions on making this analysis more robust or just tell me what's wrong with it?

I realize I am not taking inflation into account (although arguably neither does the government when it sets tax brackets, except maybe in the long run as they adjust the tables?). My investment earnings assumption is 10%. If inflation was 3% over the same period, I'm thinking the analysis would still hold? Not sure of that.

Also, I held the total contribution made between the two scenarios at 10K per year. I can anticipate the argument that the Traditional investment could have been higher by the amount of the taxes paid in the Roth scenario. I guess I'm assuming the person is able to fully fund all accounts to maximum value for both scenarios.

Sorry if I'm starting a rehash but it seems like every time the subject of Roth Vs Traditional comes up, it's offered as a given that if your tax bracket is the same at contribution time and withdrawal time, then it will be a wash. So I made this spreadsheet to help me see this in black and white.

Assumptions:
Inflation: 0% assumed (not taking it into account in this first pass).
Rate of Return: 10%
Tax Rate: 25%

Image

Doesn't the Roth scenario look like a better deal?

Kalo
Last edited by Kalo on Thu Jul 04, 2013 2:34 pm, edited 1 time in total.
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Re: Roth Vs Traditional Analysis

Postby livesoft » Thu Jul 04, 2013 2:34 pm
First thing I see is that "withdrew all" in the last year does not make sense in the real world. Instead, why not put "Withdrew $30,000 a year tax-free for next 35 years"? After all, 20 years from now the standard deduction will probably creep up to $30,000 a year. :)

Another thing, if you have $12,500 to use, Roth is $10,000 to Roth and $2.5K to taxes, but traditional is $12,500 to IRA and $0 to taxes.
This information has been prepared without taking into account the Sequestration, investment objectives, financial situation and particular needs of any particular person or company.
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Re: Roth Vs Traditional Analysis

Postby Kalo » Thu Jul 04, 2013 2:39 pm
Good point, livesoft. I hadn't thought of that. I was just thinking it didn't matter as long as I held my tax rate at 25%, but I see what you mean. Doesn't effective tax rate already take into account standard deduction? I do see what you mean though if the standard deduction grew enough.

Of course my values were not chosen to account for this. As contributions increase and more time is added, couldn't my payouts grow also to a point where the standard deduction would not be such a large influence?
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Re: Roth Vs Traditional Analysis

Postby Kalo » Thu Jul 04, 2013 2:42 pm
livesoft wrote:First thing I see is that "withdrew all" in the last year does not make sense in the real world. Instead, why not put "Withdrew $30,000 a year tax-free for next 35 years"? After all, 20 years from now the standard deduction will probably creep up to $30,000 a year. :)

Another thing, if you have $12,500 to use, Roth is $10,000 to Roth and $2.5K to taxes, but traditional is $12,500 to IRA and $0 to taxes.


I was assuming the person can fund all accounts to the maximum allowed, as stated. I just stopped at 10K for convenience. (Assume 10k is max allowed, including 401K and IRA, if you will.)

I did show $0 to taxes for the traditional. Am only trying to view the tax effect. Arguably that 2.5K paid to taxes could be invested in a taxable account in the Traditional scenario.
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Re: Roth Vs Traditional Analysis

Postby furwut » Thu Jul 04, 2013 2:48 pm
livesoft wrote:Another thing, if you have $12,500 to use, Roth is $10,000 to Roth and $2.5K to taxes, but traditional is $12,500 to IRA and $0 to taxes.


That's it. OP is comparing apples to oranges by saving more in the Roth since 10000 post-tax beats 10000 pre-tax. If OP reruns the calculation using $7500 for the Roth contribution you will see it is a wash.
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Re: Roth Vs Traditional Analysis

Postby livesoft » Thu Jul 04, 2013 2:54 pm
Kalo wrote:As contributions increase and more time is added, couldn't my payouts grow also to a point where the standard deduction would not be such a large influence?

No. It will always have a large influence even if all the withdrawal is not tax-free because it is larger than the standard deduction (or one's itemized deductions).
This information has been prepared without taking into account the Sequestration, investment objectives, financial situation and particular needs of any particular person or company.
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Re: Roth Vs Traditional Analysis

Postby furwut » Thu Jul 04, 2013 2:56 pm
The Finance Buff has some great posts on Roth versus Traditional:

The Case Against Roth 401(k)
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Re: Roth Vs Traditional Analysis

Postby Kalo » Thu Jul 04, 2013 3:09 pm
furwut wrote:The Finance Buff has some great posts on Roth versus Traditional:

The Case Against Roth 401(k)


Thanks for that link, furwut. That was very informative and had a lot of info I had not thought about. I was forgetting totally about the marginal tax rates (was using a constant effective rate). Plus I learned a lot of other things to consider.

:happy

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Re: Roth Vs Traditional Analysis

Postby Epsilon Delta » Thu Jul 04, 2013 3:13 pm
You are comparing the values of payments in different years, without correcting for the time value.
Would you rather pay $2,500 today or $2,500 in 20 years?
Would you rather pay $2,500 today or $17,652 in 20 years?
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Re: Roth Vs Traditional Analysis

Postby Kalo » Thu Jul 04, 2013 4:18 pm
Epsilon Delta wrote:You are comparing the values of payments in different years, without correcting for the time value.
Would you rather pay $2,500 today or $2,500 in 20 years?
Would you rather pay $2,500 today or $17,652 in 20 years?


I did say I did not take inflation into account (a weakness in my numbers). As for the other components of the time value of money, I only showed the difference in nominal dollars paid, true. I feel intuitively that inflation is the piece that matters since the investment balances grew over the years but I might be wrong on that.

In addition to the link given by furwut above, here is another one by the same author that takes into account maxing out all retirement accounts.

http://thefinancebuff.com/roth-401k-for ... e-max.html

I'm not sure either of the links really tries to account for a potentially higher tax rate on all tax payers in the future, even though it does a good job showing how each additional dollar earned has a different tax rate.

And there is also a ton of great information in both articles. Lots of stuff I did not think about or take into account in my OP spreadsheet.

There is a difference when you are maxing out all retirement accounts, as you will see in the above link. I think it defends (my takeaway) putting some dollars into a Roth 401K if you are maxing out all account types, but it's still complicated to know how much to put in the Roth 401K vs the Traditional 401K.

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Re: Roth Vs Traditional Analysis

Postby livesoft » Thu Jul 04, 2013 4:29 pm
If one is maxing out all retirement accounts, let's say that is traditional 401(k), Roth IRA, and HSA, then a question is whether to put additional money into a taxable account or use the money to replace some of one's tradtional 401(k) contributions with a Roth 401(k) contributions. Not readily apparent is how a taxable account with its tax advantages (tax-loss harvesting, long-term cap gains tax rate as low as 0%) can really help with converting tax-deferred (traditional IRA, traditional 401(k)) to tax-free (Roth IRA) at a very low tax rate ... as low as 0%.

I don't believe this analysis is shown in tfb's well-reasoned blog articles and spreadsheet. Of course, not many people will be able to do that, but if you are one of those folks, a Roth 401(k) makes even less sense, because one can convert from traditional to Roth at a much lower tax rate than one can contribute to a Roth. So for us, it's traditional 401(k)s to the max ($46,000 a year) and Roth IRAs to the max if allowed ($13,000 a year) if we can afford it.
This information has been prepared without taking into account the Sequestration, investment objectives, financial situation and particular needs of any particular person or company.
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Re: Roth Vs Traditional Analysis

Postby Bob's not my name » Thu Jul 04, 2013 5:08 pm
Kalo wrote:it seems like every time the subject of Roth Vs Traditional comes up, it's offered as a given that if your tax bracket is the same at contribution time and withdrawal time, then it will be a wash. So I made this spreadsheet to help me see this in black and white.
Why use a spreadsheet when simple equations prove the "given"? If T is tax rate, G is growth (e.g., 10X), and M is the starting gross income consumed to make the contribution:

Roth(final) = M * (1 - T) * G
Traditional(final) = M * G * (1 - T)

Obviously the result is the same. Only in the saturated case (all accounts maxed in both scenarios) do you need to complicate the choice.

The assumption of tax bracket being the same when working and in retirement is a terrible assumption, of course, because retirees make less money and get more federal and state tax breaks -- the list is extensive, but includes the munificent 0% rate on LTCG and QD, the deductibility of assisted living expenses (putting even multi-millionaires in the 0% bracket), and many states' exemptions of retirement income.
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Re: Roth Vs Traditional Analysis

Postby Bob's not my name » Thu Jul 04, 2013 5:16 pm
livesoft wrote:Another thing, if you have $12,500 to use, Roth is $10,000 to Roth and $2.5K to taxes, but traditional is $12,500 to IRA and $0 to taxes.
Roth would be $9,375.
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