Major caveat! I have no investment training or finance
training and all of my calculations are back of the envelope calculations put
together from what information I can gather online. In addition, given that investment planning usually spans decades, massive uncertainties exist in tax schemes and expected rate of returns. Please consult a professional!
That said, as someone who has an income you are trying to decide if
and how much to invest in your retirement account. Most people have several
options: tax deferred retirement options such as traditional IRA, 401(k), 457, or
403(b). Some employers also offer matching programs
which match contributions at a rate of 50%, 100%, or more to a limit each year. As tax deferred retirement
accounts, money contributed to them are not taxed at the time of contribution
(except for Social Security tax 6.2 and Medicare 2.9).
In addition to these programs there is the option of
investing in a Roth IRA with income that has already been taxed but will suffer
no additional capital gains tax. Finally, there is the option of investing
directly (with pretaxed earnings) such as purchasing stocks, mutual funds etc. While direct investments
give you the freedom to withdraw money at any time, they suffer the penalty of
being liable for capital gains taxes (15% on nominal gains for long term
Each of these investment choices has its relative merits.
One thing to consider is tax bracket.
Each earning level of taxes are paid at a
specific bracket. For example, for a couple the first 19k of earnings is paid
at a 10% rate, while the next 58k of earnings is paid at 12%, while the next
88k is taxed at 22%, and so on with increases to 24%, 32%, 35%, and finally 37%
at total earnings above 600k (see
). Yet the combined effect of these changing marginal tax rates
is to turn the effective tax rate into a globally non-linear function (Figure
For the individual the federal tax rate for a median
household income level $32K or for a married couple making $59k is about 11.5%.
The overall effect of tax bracket structure is to overstate the tax obligation
that most individuals and couples are required to pay. For example, a household
making 103k (75 percentile) while paying 22% on their last dollar earned are
overall only paying only around 14% of their total income in income tax. Even households
making 250k (97 percentile) while their tax bracket is officially 24% on their
last dollar earned are only paying a tax rate a little above 19% on overall
|Figure 1: Overall Federal Income Tax Rate without Social Security and Medicare|
That said, nobody likes to see their income disappear to taxes
so I am not trying to say taxes are too high or too low. I am just noting that
tax brackets alone for the vast majority of the population, are quite inaccurate tools at estimating tax liability. If we
include the social security tax and Medicare (Figure 2), federal taxes become
both more painful overall and less progressive (higher earners paying higher
taxes). This figure is even more non-linear with important portions of the
figure (earnings above 128k) experiencing a lower tax rate growth than earnings
up to that point. Curiously, an individual income earner above 128k actually
experiences a decline in overall tax rate until earning up to the next tax
bracket of 157.5k.
|Figure 2: Overall Federal Income Tax With Medicare and Social Security|
But enough of this! About 75% of households are earning 110k
or less. Those earning above that rate are likely already talking with
financial managers in order to figure out how to plan their futures.
The overall point of the above discussion is that tax
differed savings plans might be quite beneficial for retirees as many retirees
expect to be at a lower income level than they were while working. Income drawn
from such plans is taxed at their current income level rather than the level
they had at the time of saving. Social Security and Medicare tax is always paid
immediately upon all wage earnings (and thus constant under all scenarios) so it will not be included in the following
In order to analyze the benefit of choosing different
investment mechanisms, I looked at three different factors, 1-overall effective lifetime
income, 2-total investment worth at the end of retirement (inheritance available), and 3-annual
effective income. The first two seem like they are pretty important for most
people but arguably annual effective income is probably the most important
factor. Ideally, retirees looking to enjoy their retirement will not suffer a
minimal loss in purchasing power after retirement.
In order to look at different investment strategies, I
simulated two earning levels, 55k per year gross and 110k per year gross. Workers
work for 35 years with real annual salary increases of 0.5%. After 35 years of
work, workers consider the next 20 years as years living on secondary income
sources (1/3 of base income) as well as retirement savings withdrawn at a rate
of 4% per year.
In order to make the numbers make sense, I attempted to
simulate “real” money rather than nominal (including inflation). As a result I
assume that tax brackets remain the same in terms of “real” earnings. Annual
raises are modest as a result as well. In my simulation, I include a real
investment rate of return of 5% and a capital gains tax of 20% on all direct
investment withdraws. This does not take into account in the cost of such investments (which is tax free) while including a higher rate of capital gains tax to take
into account the false effect inflation has on direct investments (and the
corresponding tax on those investments).
In addition of the tax differed retirement accounts
(traditional IRA or a 401k without matching – 401km00), the after tax but not
capital gains taxed retirement accounts (Roth IRA), and the direct investment mechanisms
(Direct), I also included two investment options in which employers match contributions by
either 50% or 100% (401km05 and 401km10).
Generally, all of the investments are considered on the
basis of “investing” a certain amount of money 5.5k or 11k. There was one
scenario in which I allowed for a greater investment quantity in order to allow
the simulation of investing the same amount of after tax income (i401k00b). When the
earning level was 55k and the investment was 5.5k for i401k00b the 401(k) investment level
was instead 6.5k. And when the earning level was
110k and the investment was 11k for i401k00b the 401(k) investment level was instead 14k.
In my analysis I am concerned with "effective
income" which I define as:
effective income = all income –
tax – investment contributions (only made for years working).
Gross Base Income 55k per Year
Under the different investment scenarios, total lifetime
earnings vary between 2.3m and 2.8m in the case when employers provide matching
funds (Table 3). When no matching funds are provided, lifetime earnings are
more similar between scenarios with lifetime earnings between 2.3m and 2.5m. Differences
are more exaggerated when considering total assets at the end of the retirement
period included in total lifetime earnings with the highest level obtained
under scenario i401km00b (no matching but investments made at a rate that are
higher than 5.5k, but instead meant to achieve after tax 5.5k investment per
|Figure 3: Total Lifetime Effective Earning and End of Retirement Assets for Gross Income of 55k per Year|
Rather than look at lifetime effective income and total
assets it might be better to look at per year income (Table 4). Without contribution matching, all of the scenarios result in a significant drop
in effective income. The most dramatic drop is in the "No Saving" scenario in
which the effective income of the worker drops from near the global maximum for
the scenario to the global minimum of the scenario as the worker enters
retirement without any additional income sources outside of the 1/3 base income
(SS income or whatever) provided under all retirement scenarios.
Looking at the effective income while working levels, there are three
levels that the simulated worker experiences. The highest being "No Savings",
which results in the highest possible current effective income level. The
second are the pretax saving schemes such as 401km10, 401km05, and 401km00.
These schemes provide highest effective income during working years because
they reduce the after tax income not by 5.5k but 5.5k after taxes which is 4.8k
in year 1. The scenario in which the highest matching funds are
available is that which produces the highest long run returns. The third
effective income level on working years is the direct investment scenario, the
Roth IRA scenario, and the 401km00b scenario (which is custom calibrated to
achieve this). In this income scenario 401(k) investment even though it is
taxed upon dismemberment produced higher earnings than that of the Roth in retirement
though the difference does not appear to be large in this scenario.
|Figure 4: Annual effective income under different investment mechanisms 55k gross income per year. Note a jitter is added to lines to aid in deciphering overlap.|
Gross Base Income 110k per Year with 11k annual investment
|Figure 5: Total Lifetime Effective Earning and End of Retirement Assets for Gross Income of 55k per Year|
Overall, doubling the household income and the investment
level results very similar relative distributions of Total
Lifetime Effective Earnings or Total Assets at retirement.
|Figure 6: Annual effective income under different investment mechanisms 55k gross income per year. Note a jitter is added to lines to aid in deciphering overlap.|
Likewise when looking at lifetime smoothed effective income,
the overall returns from different investment mechanisms remain similar. That
said the difference between the investment strategy using the Roth IRA and
increased investment using 401km00b (401 tax differed investment without any
match at 11k after tax investment level which is 14k before tax) resulted in
the same level of effective income during working years but significantly
higher effective income in retirement.
That said, Roth IRA funds are more flexible than those of
tax differed funds which suffer a 10% additional penalty if withdrawn before
age 59.5. In addition, if you believe that your current income level
is likely to be lower than your future income level, it probably means that you
should consider investing more in your Roth over that of a tax differed
Comparing 55k to 110k per Year
The 110k per year scenario is basically a doubling of the 55k per year scenario in terms of both income and investment (except in a slight difference with the 401km00b scenario). Comparing the average annual effective income under these two scenarios we can infer the cost of higher income taxes in the 110k scenario. The average ratio is 1.94 which indicates a difference of .06 or 6%. Looking closely at Figures 1 or 2 we can see that the difference in overall tax rates between households making 55k per year and 110k per looks to be about 6% as well. Using larger tax differed investments (401km00b) does appear to be a way to achieve a smaller tax penalty with a decreasing in effective tax rate of closer to 4%.
Table 1: Shows the ratio of average annual effective income (same as total lifetime income). If the ratio were 2 then there would be no tax different between earners at 55k per year and 110k per year.
If there is a 401k or other tax differed investment option
in which matching is available, I would suggest putting the maximum your finances allow. If matching funds are not available, in this
simulation investing pretax income in the 401k equal to that you would invest in
the Roth IRA appears to yield a slightly better outcome. This is generally
because while these funds will be taxed when withdrawn, having that much more funds grows
that much faster than the after tax funds otherwise available.
Finally, in almost all of the scenarios, there is a
significant loss of effective income upon retirement. If you would like to
mitigate the risk of that happening, combining investment mechanisms is likely
to be the best strategy. This might mean relying upon direct investments if for
instance you have already filled your Traditional IRA or Roth IRA and have no other
investment mechanisms provided by your employer.
Feel free to explore the simulation on your own with your own earnings and investment options! Code that produced this analysis can be found on Github