Mark Bole wrote:

- quote -

Right, but...

- quote -

....Bill's point was that a Roth increases its advantage over time vs. a
traditional 401(k). It doesn't.

- quote -

This is not true. As you pointed out, a Roth always beats a taxable
account.

- quote -

Not exactly, because...

- quote -

....that spot is where your retirement marginal tax rate equals your
current marginal tax rate.

-Will

Mark Bole <makbo[at]pacbell.net> writes:

- quote -

It's not. Believing they are the same thing is a common fallacy
and makes people do irrational things like spending money to
create tax deductions for the sake of getting a tax deduction.

--
Rich Carreiro rlcarr[at]animato.arlington.ma.us

Mark Bole wrote:
- quote -

Mark, maybe I am being dense here. Can you give this one more shot?

Roth 401(k) words. Post tax money goes in. Grows, say 5X over time.
Comes out tax free.

401(k) words. Pretax money goes in. Grows, say 5X over time. Taxed upon
withdrawal.

Since both accounts are not taxed while in the account, I don't need to
consider the reinvesting, and can just assume '5X' over whatever time
frame. I also believe it obfuscates the matter to say that one starts
with $20K and continue from that premise, since the limit for either
account is $15,000 in 06. There's an awful lot I get to ignore given I'm
not comparing not retirement accounts and the issues that come with
favorable tax on dividends or cap gain, etc. One can certainly discuss
the other choices, but for this question, I was strictly trying to stick
to "401(k) vs Roth 401(k)" and my conclusion was that the only
difference would be the tax rate differential. And I agree that it's not
knowable what rate you will be in five years hence let alone 10 or 20,
and diversifying among the two types would make sense.

To your point above, I think that you are right for the wrong reason.
Any 20 year old choosing among a Roth or plain 401(k) would likely be an
aggressive saver, one who risks a higher rate at retirement more than
the average Joe. And given the state of the economy is unknown, the risk
is more that income tax rates will rise, not to mention that the 20 year
old is likely in the lower bracket just for the fact that he's just
starting to work.

JOE

Will Trice wrote:

- quote -

Not sure that isn't the same thing... But as one who was a math major,
financial modeler, computer programmer, etc blah blah, I like the
challenge of trying to put this into words rather than equations. (Kind
of like something that vos Savant person in the Sunday newspaper insert
would write...)

In the "normal" case where there are non-zero taxes throughout the
investment period, the Roth would still be better in the end, and the
longer your period, the "more better" it is. This is the original point
I was responding to, namely a Roth investment for a 20-yr old is much
more likely to be a winner than a Roth investment for a 50-yr old,
because the 20-yr old will have thirty additional years of tax-free
earnings. I was agreeing with Bill Woessner's original comment, which
Will Trice was questioning (whew...)

But in an extreme case -- say, your first-year tax rate is 30%, and then
it drops to zero for every year thereafter -- then the trad. IRA/401k
ends up looking a lot like the Roth, and the little extra tax-deferred
(or in this extreme case, tax-free) sweetener from the trad. plan in the
first year makes it overall the better plan. If I were doing a graph, I
would see that as the future tax rate approaches zero, the trad.
IRA/401k approaches the Roth. There will be low enough rate somewhere
out on the graph where the first year "bump" from traditional actually
overcomes the normally better deal of forever tax-free earnings.

After all, when doing these types of analysis, shouldn't regular
tax-free investments be thrown in for comparison as well? With
municipal bonds, the tax benefit has been given to the borrower (state
government), since they pay interest comparable to after-tax interest on
regular investments. With the Roth the tax benefit has been given to the
lender (investor), since they can earn before-tax interest rates but
without ever paying tax on it. With the trad. IRA/401k, it seems to me
one is merely given the ability to treat earned income a lot like a
capital investment, with taxes deferred until the time of "sale" and
hopefully at a lower rate by then.

-Mark Bole

Will Trice wrote:
- quote -

Joe, Will - agreed. I was assuming that given the relatively high tax
bracket & impending retirement, the OP would be making a full deferral.
At lower levels the original formula is fine, you can just mark down the
value of the Roth contribution instead of carrying the side account.
Though really it would depend on exactly what you planned to do with the
$X in pretax dollars.

RE: my (1 + k) - old habits from finance class 20 years ago!

The weakest assumption in all this regards the tax rates. While the math
works when you move that tax term from front to back (because a X b = b
X a), it's unlikely t today will be the same as t at the end of the
pipe. Heck we don't even necessarily know the 07 tax rate -- for several
million taxpayers it's hinging on what this year's version of AMT reform
looks like. And during retirement there's the side issue of Social
Security benefits being taxed, or not, depending on the size of IRA
distributions -- one might consider that a further tax on the IRA
distribution. So seven years out, during distributions...who knows what
the tax rate will be? Hence the fallback to subjective criteria like
"favor immediate tax benefits."

-Tad

Mark Bole wrote:

- quote -

This is Joe's point.

- quote -

It sounds like you are trying to minimize taxes paid rather than
maximize after-tax savings.

-Will

jIM wrote:

- quote -

This is not correct. Your Roth equation uses the contribution amount as
a multiplier against itself. Think of it this way, your equation
suggests phenomenal exponential growth for putting my money under the
mattress (x = 0). After 30 years I'd have [G * (1-t)]^30 dollars. Too
bad it doesn't really work this way...

-Will

joetaxpayer wrote:
- quote -

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


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

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

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

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

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

-Will

Tad Borek wrote:

- quote -

All your points are valid, and well taken. I agree with the approach to
diversify among the tax status of accounts. Of course, to simplify the
math, and do apples to apples, I needed to assume a G. If one can put
$15,000 into the 401(k), then I assume they will net 15000*(1-t) and put
that in the Roth. You are right that the Roth guy has an option to
invest more, another 15000*t, but the 401(k) had to pay that in taxes,
so doesn't my approach provide consistency?

I agree with your remarks about taxes, but I was replying to Mark who
stated the decision had -0- to do with relative tax rates. My point is
that the choice would likely be based 'only' on taxes. BTW, t=tax rate,
Y=years. Not sure where your k came from.

JOE

joetaxpayer wrote:


Whups! Math post-o in my prior reply, last paragraph should read:

For someone paying 40% marginal taxes a full $15,500 Roth 401k deferral
represents $25,833 in pretax income. Scenario B is...deferring $15,500
of that to a regular 401k leaving $10,333 pretax, or $6,200 post-tax,
extra to throw in the taxable side account.

-Tad

joetaxpayer wrote:
- quote -


Joe, that's not a complete formula in the Roth-vs-regular 401k
comparison because depending on your value for G, it either knocks down
the Roth contribution below the limit, or allows the 401k to receive
more than the allowed annual limit. Even if you don't contribute the
maximum you need to factor in a different tax rate, applied to a taxable
account, to make it a fair comparison.

Take 2007 - there's a $15,500 limit on the deferral to a 401k. In a Roth
401k you can defer a full $15,500 and receive no immediate tax benefit.
Or you can defer $15,500 of pretax money. Either way the account
receives $15,500.

In the Roth 401k, assuming say a 35% marginal state + fed tax rate, that
represented $23,846 of pretax earnings. You pay the tax, the balance of
$15.5k goes into the Roth 401k. If you use the regular 401k instead you
defer $15,500 of that pretax, leaving yourself with another $8,346.
Which becomes $5,425 after paying 35% taxes. Now you need to throw that
$5425 into a side account (taxable) and make some assumptions about
annual income, capital gains rates, etc, to run the horse race. After
all if in Scenario A you were deferring the equivalent of $23,846 pretax
for the Roth 401k you should use the same figure for Scenario B right?

So it's not as simple as just shifting the (1 - t) to the beginning or
end of all those (1 + k) years of returns that are applied to G. In
effect you have a G' and a k' and a t' coming along for the ride somewhere.

My view is that these tax-rate assumptions, especially if made over long
time periods, introduce enough "slop" that this could come down to
subjective criteria. Particularly when a comparison relies on a low
capital gains rate (remember - Reagan abolished the capital gains rate
and it's only slowly returned to its current low level).

I like the "hedge future tax rates" approach of splitting the baby. If
someone already has a lot of qualified assets that could mean using the
Roth 401k, simply to get money into that form (despite the immediate tax
cost).

But I also believe in the assumption "take a certain immediate tax
benefit over a potential future one". For someone paying 40% marginal
taxes a full $15,500 Roth 401k deferral represents $38,750 in pretax
income. Scenario B is...deferring $15,500 of that to a regular 401k
leaving $23,250 pretax, or $13,950 post-tax, extra to throw in the
taxable side account. The up-front tax hit of the Roth 401k seems a
tough pill to swallow there - many retirees (including wealthy ones)
aren't in the 40% bracket.

-Tad

jIM wrote:

- quote -

t=.28
x= .10
Y = 10 years

(1000*.72*1.1)^10
(792)^10 ??

You really want to raise 792 to the 10th?

My equation takes the 720 net and then multiplies by (1.1)^Y for
whatever return and years. I admit I shook my head when I ran a spread
sheet, and realized what was happening. Take another peek if you would.
JOE

Mark Bole wrote:
- quote -

You caught a small error from my POV

If you look- the first formula only raises the first variable
exponentially and iss correct as explained
the second forumla raises both exponentially in reality (but it not
shown)... I think there needs to be a second set of () around the
whole thing to show this

401(k) = G * (1.x)^Y * (1-t)
Roth = [G * (1-t) * (1.x)]^Y

Mark Bole wrote:

- quote -

No, it shows the math in order of occurrence. For the 401(k), the tax
(1-t) happens at withdrawal, for the Roth, up front. One year, ten, a
billion, no difference.

The only difference would be due to a change in tax rates. Follow the
math above, and tell me why you would disagree. Keep in mind, Roth
deposits are made with post tax money, so while zero is great, my (1-t)
appears in both equations. I (only) care about high high/low my bracket
goes. Spreadsheets (or in this case, napkins) don't lie. Of course, a
bad equation can mess you up. Elle caught the typos I had on my VA
analysis. You'd be kind to do the same for me above.
JOE

joetaxpayer wrote:
- quote -

Is this a typo? Those two formulas are exactly the same, mathematically.

The answer is pretty simple. Earnings on a 401k/Trad.IRA are
tax-DEFERRED, earnings on a Roth are tax-FREE. The longer your
investment sits around, the greater the portion of the total which is
due to earnings rather than initial investment, hence the greater the
impact of the tax-FREE benefit.

Eliminating taxes altogether on one years' worth of earnings is good,
eliminating it on ten, twenty, or forty years' worth of earnings is
really, really good. I don't care how high or low your tax bracket
goes, nor how much you discount future values, zero taxes always beats
non-zero taxes.

Like others, I believe there is some chance that the promise of the Roth
will someday be broken, so diversify by taxability along with all the
other dimensions. After all, the things you buy with Roth distributions
will still be subject to sales tax, and it wouldn't take much to tweak
the AMT to make earnings in a Roth potentially taxable, at least for
higher-income taxpayers.

-Mark Bole

"thamsenman" <KRamanujam[at]gmail.com> wrote in message
news:1167763184.578704.255050[at]s34g2000cwa.googlegroups.com...
- quote -

and as taxes rise ... and newer, more aggressive taxation is put
in place ... what make you (anyone?) so sure that a Roth will
remain untaxed upon withdrawal? When the situation is dire
(as Medicare, SS, and Uncle Sam in general, will surely be
as the years grind on) -- when it gets bad enough ... are you
sure they wouldn't go after the billions (trillions?) currently
socked away in Roths?

I expect (although I have no basis in fact) that it will go at
least that far, and likely a lot farther.

Hypothetically, think in terms of, say, a wealth tax. Uncle Sam
says "You've got a million-er-two saved up ... we need some.
We're gonna take 5% of that a year ... just for the privelege of
having it when others don't. Give it up or face the FiringSquad(tm)"

It could happen.

Worst case ... the U.S. economy and the Dollar collapse.
Your Roth is now completely worthless.

It *could* happen.

My point is, expectations about what may or may not happen
in the future with regards to taxation (or anything, for that matter)
are nothing more than a guess. Better to have some contingencies
in place.

- quote -

And so I'd turn to the spreadsheet, only this one I can do on a napkin.
401(k) = G * (1.x)^Y * (1-t)
Roth = G * (1-t) * (1.x)^Y

Where Gross is the amount one has available to put in the account,
x is the rate of return (whatever you'd like),
Y= number of years
t is your marginal tax rate.
Doesn't matter when you pay the tax, if the rate is the same in and out,
there's no difference.

The presumption that favors the 401(k) is that more people will be in a
lower bracket at retirement than while working. Of course, this is a
generalization that applies to some percent of retirees. 60%? 80%? I
don't know, but when I hear of the paltry sums that people have saved
who are nearing retirement age, I believe the generalization is accurate.
The above napkin math assumes the same expenses in both accounts.
JOE

woessner[at]gmail.com wrote:
- quote -

Why? It seems that time is immaterial to this decision, all else being
equal.

-Will

To be truthful, I think higher taxes (in the future) are on the way. I
would go for Roth. Medicare and Social Security are more or less going
bankrupt, our government deficit is gigantic an our trade deficit is
huge as well. I don't think there's any way that we can expect a lower
tax rate in the next several years no matter who is in office.


rg wrote:
- quote -

rg wrote:

- quote -

Well, part of the issue is that stuff happens, rates may change.
http://www.fairmark.com/refrence/index.htm is where I recommend to view
tax brackets. If you're that close to retiring, you likely have a good
idea what your taxable income will be, and you can see what bracket
you'd fall into. If you are pretty sure the bracket will drop, you would
be better off sticking with the 401(k) and its tax savings. Then, at
retirement, beginning the process of converting just enough to a Roth
IRA each year to 'top off' the bracket you are in. Fully funding for 20
years means you have quite the balance. RMDs have a way of creaping up
fast as your balance increases with time, and your RMD divisor drops as
you age.
The spreadsheets will show that so close to retirement, if there's a tax
bracket differential (lower rate at retirement) that the advantage leans
toward the regular 401(k).
JOE