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Subject:  Re: Roth IRA Contriubtions & Conversions Date:  2/2/1998  4:33 AM
Author:  Kilmarnoch Number:  1570 of 76406

is it done yet?

  this is kinda long... (547 lines).  if you think this takes a while 
to read, think about how long it took to write.  =)  I should have 
prolly broken this up into 3 parts... i'll do that next time If
I get a bunch of flak about the size of this.

  hopefully there are enough errors to spark at least one reply.
and hopefully someone else understand something I wrote here.

========================================== 
to summarize (and fan the fires :) this is what I think is true:

general statements of fact: 
  - always max out your IRA options, every year!

  - if you are not eligible for a tax deductible IRA, then a roth is *the*
    best option.
  - if you are eligible for a tax deductible IRA then a traditional IRA
    *only* makes sense if you will retire in less than 20 years.
  - if you are not eligible for a Roth (lucky you), put your money into
    a traditional IRA... then evaluate a rollover to Roth when you stop
    making so much money.

MAJOR DISCLAIMER:
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
  I expect people to not believe these numbers... there is prolly
also going to be some misunderstanding.  Who knows all my numbers
might be completely bogus?  Please ask questions about how I
calculated a particular table if it looks fishy, and please
point out any place that my rates are bogus.  (But explain what
about them is bogus, and how you think the numbers are fishy so
I can correct them =)
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
END OF MAJOR DISCLAIMER.

now for the post...
=============================
TMFPixy wrote everything quoted like '>'

[tangent 1...
>Investments will earn a 9% annual rate of return...
  
  why not pick an easier number say like 10%... as long as the number
stays the same in all charts it doesn't hurt the comparison.  10% 
is a *whole bunch* easier to visually verify.  (note: even though I am
whining about it over here I will continue to use 9% in my reply ;P )
  
  all math was done to an insane number of decimal places.
...end tangent]

>Scenario 1.
>----------
>  John makes a tax-deductible contribution of $2,000 per year to a
>traditional IRA. He is considering the new Roth IRA, but must maintain
>the same net income he has today using the traditional IRA.  John is
>in the 28% marginal tax bracket, which means he may only contribute
>$1,440 to a Roth IRA to keep his net income the same as it is by using
>the traditional IRA.
  
  Okay... here is a problem.  Remember that bit about the difference
between effective tax rates and tax brackets rates?

I rambled something about: 
:The main point of this is that just because you are "in the 28% tax
:bracket" does *NOT* mean you pay 28% in taxes. being at the very top of
:the 28% tax bracket you only actually pay 22% in taxes... the lower in
:the bracket you are the lower the percent of your income you pay to tax,
:(tax ranges from 15% upto 22% in the "single's 28% bracket", and 22%
:upto 26% in the "single's 31% bracket", etc...).
  
  I really really suggest that for chart purposes people use 15.0% 
and 22.6% as the two tax rates... and maybe something in the middle
like 19.99%.  the idea that "being in the 28% tax bracket means that
you pay 28% tax" is so plain wrong, the most you will *ever* pay in the
28% bracket is effectively 22.6% and that is only if you are earning at
the _very_ top of the bracket!

---------------------------------------------------

  The "most" refund he would get for a deductible IRA contribution is
somewhere between 15% and 22% of the amount invested... that is if you
still *qualify* for a full deduction:

             your effective     $2000 deduction
you make ... tax rate is    ... is worth
==================================================
  $20000 ... 15.00000000%   ... $300.00
  $25000 ... 15.18200000%   ... $303.64
  $30000 ... 17.31833333%   ... $346.37
  $35000 ... 18.84428571%   ... $376.89
  $40000 ... 19.98875000%   ... $399.78
  $45000 ... 20.87888888%   ... $417.58
  $50000 ... 21.59100000%   ... $431.82
  $55000 ... 22.17363636%   ... $443.47
  $59750 ... 22.63682008%   ... $452.74
... the more you make the bigger the tax rebate ...

example 1:

  John makes $40k per year, so his effective tax rate is 19.99%....
if he put 2000 into a traditional IRA he would get $399.78 back in a
tax refund.

    - so he puts $2000.00 yearly into a traditional IRA
      *or*
    - so he puts $1600.22 yearly into a Roth IRA

example 2:

  John makes $20k per year, so his effective tax rate is 15.00%....
if he put 2000 into a traditional IRA he would get $300.00 back in a
tax refund.

    - so he puts $2000.00 yearly into a traditional IRA
      *or*
    - so he puts $1700.00 yearly into a Roth IRA

  so the following is my revision of Table 1, assuming that John *can*
make a fully deductible contribution and choices to make a 2000 dollars
worth of "pre tax" dollars into both types.  This uses effective tax rates
to calculate the amount put into a Roth IRA (see examples above).
(in the end: bigger numbers are better *=)

Kilmarnoch's Table 1:
      Annual Contributions to Roth IRA
  As Compared to Traditional IRA (After Taxes)

            effectively put         |
      2000 pre-tax $ into Roth IRA  |            Trad IRA
                you make            | before     after effective tax
     50,000  40,000  30,000  20,000 |   tax     15.0%   18.8%   22.6%
=========================================================================
5     10229   10438   10787   11089 |  13046 |  11089   10591   10093
10    25969   26500   27384   28152 |  33120 |  28152   26887   25623
15    50187   51212   52921   54405 |  64006 |  54405   51961   49517
20    87448   89235   92214   94799 | 111529 |  94799   90541   86282
25   144780  147739  152670  156950 | 184647 | 156950  149900  142849
30   232992  237753  245688  252577 | 297150 | 252577  241231  229885
35   368717  376252  388810  399712 | 470249 | 399712  381755  363799
                                      ^^^^^^
                            this column does not count

  Notice that the 20K per year and the 15.0% traditional IRA case match
identically... because the effective rates are the same going in and
coming out.
  So what's the result of using the effective rate?  It makes the
Roth IRA look *MUCH* less of a bad choice if your effective rate
is 15% in retirement (compared to the non-logic of the 28% -> 15%
charts).

[tangent 2...
  ...think of the chart above as a "snapshot in time"...

  Effective rates are show removing from the traditional IRA...
this is a little bogus, because it assumes either:
  - the money is taken out as one lump sum (which isn't possible at
    some of the effective rates show)
    *or*
  - the money stops earning any interest (right ;) and is taken out over a
    series of years at the effective rate show

  To *really* do the this right I need an estimated life span over
which to spread the withdrawals (from both the Roth and traditional IRA)
accounts... this would allow me to calculate the *real* effective rates
on the withdrawals from the traditional IRA each year as they are withdrawn.

tangent 3...
  how many people who make 50K and still qualify for a full deduction???
maybe 2% of the population?  ;)
... end tangents]


MAJOR DISCLAIMER:
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
[this was the original location of the disclaimer it applies
a *whole bunch* to the following, post]
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
END OF MAJOR DISCLAIMER.


Scenario 2.
----------
>  Assume John's circumstances are the same as before except that he will
>deposit $2,000 annually into the Roth IRA.  To do so, he will forego
>contributions he was making to a regular investment account that has
>an after-tax return of 8.244% per year.  (Note: The total return on
>this account is 9%, of which 30% comes from taxable dividends and 70%
>comes from long term capital appreciation.)

  I think the 8.244% return per year on the after tax account is
bogus... here's my math:

return = (rate * 70%) ... taxed at capital gains rate +
         (rate * 30%) ... taxed at effect tax rate

return = (rate * 70% * [percent that you keep after capital gains tax]) +
         (rate * 30% * [percent that you keep after max effective tax])

for someone in the 28% bracket return would be:
  7.1288058578 = (9.0 * .7 * .8) + (9 * .3 * .7736317992)

for someone in the 15% bracket return would be:
  7.965 = (9.0 * .7 * .9) + (9 * .3 * .85)

  did I miss something here?  does this make sense?

>For fairness, the lost
>principal and growth on this additional $560 deposit must be added to
>traditional IRA proceeds because the foregone investment would have
>been available for withdrawal in later years.  Assume growth in this
>investment account will be taxed at a long-term capital gain rate of
>20% on withdrawal for a taxpayer in the 28% marginal bracket and at 10%
>for one in the 15% bracket.

So in my version of table 2...
  - He is going to max out his Roth contributions, (2000 a year).
Which means to be fair to the traditional IRA...
  - he needs to put 2000 into the traditional *and*
  - then put his entire tax refund into a taxable account earning
    the "post tax" return rate.  ;)

Kilmarnoch's Table 2a:

  So what would happen if you are paying 22.6% effective taxes and
you max out as above, *then* move to the 15% effective rate at
retirement?...  *this* is the interesting part ;P

notes:
  while working the individual account earns 7.1288058578% after tax
  all other accounts earn 9%.

  while working the individual account receives 452.73 a year

  at retirement the tax rate shifts instantly to 15% effective.

     |        |  Deduc  Indiv         | Deduc  Indiv
     |        |   IRA    Acct         |  IRA    Acct
     |        | Before  Before        | After   After
Year |  Roth  |   Tax     Tax   Total |  Tax     Tax    Total
=============================================================
5    |  13047 |  13047   2796   15843 |  11090   1613   13466
10   |  33121 |  33121   6742   39863 |  28152   3981   33883
15   |  64007 |  64007  12309   76316 |  54406   7454   64868
20   | 111529 | 111529  20165  131694 |  94800  12549  111939
25   | 184648 | 184648  31249  215897 | 156951  20023  183512
30   | 297150 | 297150  46890  344040 | 252578  30988  292434
35   | 470249 | 470249  68958  539207 | 399712  47072  458325

  So this table assumes the *worst possible* tax rate (in the 28% bracket)
over the working career, then the *best possible* tax rate at retirement.
Notice how the Roth wins after 20 years?  also notice how the the
traditional wins only by $800 dollars at it's peak?  But after
35 years Roth is ahead by $12000???
  ___With___the___current___tax___scheme___ long term Roth is a no brainer.


  The higher the effective tax rate the larger the differences are
at the ends of the time spectrum.  It takes the *same* amount of time
for the Roth to "pull ahead".  (the top end of the 31% tax bracket has
an effective tax rate of 26.99117529%)... doing everything the same as
above moves the return on the taxable account to 5.7687617328%, and
moves the tax rebate to 539.82 per year.  We are still going to
assume the retiree moves straight into the 15% effective tax rate.

Kilmarnoch's Table 2c:

  post tax return rate:
    5.7687617328 = (9.0 * .7 * .8) + (9 * .3 * .2699117529)
  tax rebate:
    539.8235058000 = 2000 * .2699117529

     |        |  Deduc  Indiv         | Deduc  Indiv
     |        |   IRA    Acct         |  IRA    Acct
     |        | Before  Before        | After   After
Year |  Roth  |   Tax     Tax   Total |  Tax     Tax    Total
=============================================================
5    |  13047 |  13047   3203   16250 |  11090   2723   13812
10   |  33121 |  33121   7444   40565 |  28152   6327   34480
15   |  64007 |  64007  13058   77065 |  54406  11099   65505
20   | 111529 | 111529  20488  132017 |  94800  17415  112214
25   | 184648 | 184648  30324  214972 | 156951  25775  182726
30   | 297150 | 297150  43343  340493 | 252578  36842  289419
35   | 470249 | 470249  60577  530826 | 399712  51491  451202

note:
  - short term the difference is more in favor of traditional IRAs.
  - long term the difference is more in favor of Roth IRAs

  Also, people at the top of the 31% tax bracket aren't even eligible
for a Roth IRA... so continuing this series of graphs any higher is moot.

[tangent 4...
  I don't know the exact number of years it takes for Roth to pull ahead
but I'm interested in what it is... I'm guessing it's about 22.5 years
can any math types out there explain why that is the case?

...end tangent]


>Conclusions Regarding IRA Contributions.
>---------------------------------------
>  In choosing between a tax deductible traditional IRA and a Roth IRA,
>our marginal tax rate today versus that of tomorrow is important.
>If the tax rate declines when the money is withdrawn, those who end
>up in a 15% tax bracket will not benefit from Roth IRA contributions.

  *IF* my tables above are not completely wrong, then you need to
rewrite that conclusion.  ;P


  ahhhh... now what _about_ those conversions?
[you might want to take a break at this point... I *need* to switch
music, perhaps it's time for a drink? ;]


>Traditional IRA Conversions to a Roth IRA.
>-----------------------------------------
>  TRA 97 allows taxpayers to convert traditional IRAs to Roth IRAs provided
>their AGI is under $100,000 in the year of conversion.  (Note: Based
>on 1997 tax brackets, this means only those with a 15% or 28% marginal
>rate are eligible for a Roth IRA conversion.)  No penalty applies, but
>ordinary income taxes must be paid on previously untaxed IRA proceeds.
>If the conversion occurs in 1998, the income from the IRA must be spread
>equally over four years for taxation.  Conversions made in 1999 or later
>will be fully taxed in the year they occur.  If money is withdrawn from
>the converted IRA to pay taxes, the 10% early withdrawal penalty will
>apply for those younger than age 59 ½.

some more general statements of fact:
  - if must use IRA funds to convert don't even think about it
    (the tax twits will slap you hard).
  - if you can convert to a Roth IRA with outside funds do it.


  Thanks to those "facts" above I'm tossing out Scenario 3... which has
someone trying to use IRA funds for the rollover.  Most people who
"should" rollover must save money outside the IRA to do the rollover
with, the rollover is not worth it otherwise.


  I would prefer to stick to lump sum rollover examples, because provided
that you stay in the same tax bracket you will *always* pay more on a
lump sum rollover than a 4 year spread out rollover and the spread rollover
is only available in this one year.  So if a lump sum rollover makes sense
then a spread out rollover will always make "more" sense.  I will also
assume that *all* of the amount is taxable, simply because that is the
worst case example for the Roth.  Despite both disadvantages the Roth
rollover is a no brainer...

[tangent 6...
  I would like for all of the following examples to use 2000 per year
contributions to the resulting Roth ... and 2000 + rebate to the
non-rolled over traditional IRA (but my head is beginning to hurt ;)
so I'm going to keep it simple: no contributions to any account after
roll over (i think donations might give the traditional account an slight
short term advantage).
...end tangent]


>Scenario 4.
>----------
>  Jane is in the 28% tax bracket and has a $50,000 traditional IRA she
>wants to convert to a Roth IRA.  She will pay all taxes due on the
>conversion from other assets. To do so, she will withdraw the taxes due
>each year from a regular investment account.
  [the after 8.244% tax return rate was bogus in the example above]

side note:
  Jane is currently about 34 years old... (starting at 21, 13 years of
max contributions with a 9% return results in $50k), so 25 year forecasts
put her at the "penalty free withdrawals" age.  35 years puts her at the
point that she *must* start making withdrawals from a traditional IRA.

Kilmarnoch's Table 4a:
      Roth IRA Conversions
   Taxes and Penalty Paid from Taxable Investment Account

  taxable account returns 7.1288058578%  (worst 28% bracket return)

             22.6% effective at conversion
              |   Ded      Inv      IRA  |  22.6% |  15.0%
              |   IRA      Acct      &   |  Total |  Total
              |  Before   Before    Inv  |  After |  After
Year    Roth  |   Tax      Tax     Total |   Tax  |   Tax
===========================================================
0       50000 |   50000   14630    64630 |  50000 |   54935
5       76931 |   76931   20643    97574 |  75486 |   82937
10     118368 |  118368   29127   147495 | 114106 |  125370
15     182124 |  182124   41099   223223 | 172692 |  189739
20     280221 |  280221   57992   338213 | 261652 |  287481
25     431154 |  431154   81827   512981 | 396858 |  436033
30     663384 |  663384  115460   778844 | 602538 |  662017
35    1020698 | 1020698  162915  1183613 | 915680 | 1006071


  Roth is a no brainer win after 10 years for level, and 30 years
for 22.6 -> 15.0 % changes in tax rates.


  Well now... 50000 as a lump sum is going to really raise the AGI...
which means it might "push" this poor person into the higher 31% bracket!
So let's do the math as if it does:


Kilmarnoch's Table 4b:
      Roth IRA Conversions
   Taxes and Penalty Paid from Taxable Investment Account

notes:
  taxable account still returns 7.1288058578%  (worst 28% bracket return)

  but the effective tax rate when the conversion happens is 26.99117529%
this is the *highest effective tax rate* in the 31% tax bracket!
  that means that she needs $18484.87 at the time of the rollover.

the math:
  needed to rollover = [desired in roth] / [portion you keep after tax]
  68484.8717926992 =  50000 / (1.0 - .2699117529)

to check the math:
  [amount in roth] = [amount taxed] * [amount you keep after tax]
  50000 =  68484.8717926992 * .7300882471


             27.0% effective at conversion
              |   Ded      Inv      IRA  |  22.6% |  15.0%
              |   IRA      Acct      &   |  Total |  Total
              |  Before   Before    Inv  |  After |  After
Year    Roth  |   Tax      Tax     Total |   Tax  |   Tax
===========================================================
0       50000 |   50000   18484    68484 |  52981 |   58211
5       76931 |   76931   26081   103012 |  79693 |   87560
10     118368 |  118368   36800   155168 | 120042 |  131892
15     182124 |  182124   51926   234050 | 181068 |  198942
20     280221 |  280221   73269   353490 | 273471 |  300466
25     431154 |  431154  103383   534537 | 413534 |  454356
30     663384 |  663384  145876   809260 | 626069 |  687871
35    1020698 | 1020698  205833  1226531 | 948883 | 1042551


  wow?!?  Notice the traditional beats Roth hands down over time
for the 27% conversion -> 15% retirement?  how is that?


[tangent 5...
  the test mentioned here was discovered as I was writing my reply
    I've developed a headache and don't want to test all these numbers
    with a different rate of return, but I suspect that the higher
    the return rate the more a Roth helps you (because it saves
    you more in tax each year)
...end tangent]

the 35 year test:
  [convert test] = [conversion effective rate] -
                   [retirement effective rate] - [investment growth rate]

  if convert test is less than zero you should do the conversation.
  if convert test is grater than zero you should not convert.

in the first 22.6 -> 15.0 example:
  convert test = -1.36317992 = 22.63682008 - 15.0 - 9.0
  difference between roth and traditional = 1.0145387353 = 1020698 / 1006071
  a roth IRA earns 101.45387353% of what a traditional would (winning).

in the second 27.0 -> 15.0 example:
  2.99117529 = 26.99117529 - 15.0 - 9.0
  difference between roth and traditional = .9790389151 = 1020698 / 1042551
  a roth IRA earns 97.90389151% of what a traditional would (lossing).


  You should notice that the roth is favored more over time... because
my little "covert test" formula is off by some factor in favor of the
roth.  if a math type would like to explain how/why that is I'm all
ears.  =)


  I'm sure that my test as described above is not 100% correct.  But I am
also *SURE* there is some formula that takes into account the short term
and long term periods and answers one of the following questions (the
formula *must* exisit):

  "How many years will it take, with an effective conversion rate of [A],
    with a tax able account growth rate of [B] and a non-taxable growth
    of [C], for a roth IRA to beat a traditional IRA, if at retirement
    my effective tax rate is [D]?"

    *or*

  "After [A] years, how much does a roth beat a traditional, when the
    effective conversion rate of was [B], a tax able account growth
    rate is [C], non taxable growth is [D], and at retirement my
    effective tax rate is [E]?"

  anyone like word problems?  *=)

Later,
  -- Kilmarnoch


ps.
  What I would really like to talk about is what people think congress
is going to do about the SS and debt problems in the future... how they
handle that is going to have a major effect on what the best place to
store our money is.

  If the simply crank up the tax rates but mostly keep the current system
(highest bracket in the mid-50's ... 45%, 35%, 30%, lowest bracket at
20%)... Roth will win hands down.  (provided it retains it tax free nature =)
  If they add a national sales tax of some sort, and do away with income
tax (right next pipe dream), traditional wins.  If they don't do away
with income tax and add a sales tax, roth wins.

  I know it's alot of speculation, but I also know *SOMETHING* is going to
happen before I reach 50... and I'm concerned.  =)


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