Comparing Taxes: Cats and Mice

Comparison of Accounts – After Tax Contribution with Annually Taxable Growth (Savings Account, Money Market, etc.) vs After Tax Contribution With Tax Deferred Growth (After Tax-Tax Deferred IRA, Permanent Life Insurance, etc.) vs After Tax Contribution with Tax Free Growth (Roth, Municipal Bond, etc.) vs. Tax Deductible (Pre-Tax) Contributions with Tax deferred Growth (401K, Tax Deductible IRA, etc.).

Slowing Down and Analyzing Mathematics/Logic. Comparing Taxes.

This can be a difficult topic to understand and, unfortunately, this confusion has led to incorrect information being spread to the consumer by the media and the financial industry. The ultimate result is that consumers, and advisors, and clients of advisors are making decisions based upon faulty information–often the result of a “gimmick” to sell a particular product.

Before we proceed, an analogy might be necessary.

Cats and Mice

Let’s say I need to calculate how much food I will need for new animals I am planning to acquire.  I am getting 6 animals, 3 of one kind and 3 of another.  So my math is correct: 3 + 3 is 6.  Often, this is where financial analysis stops; it is mathematically correct, but totally useless and/or misleading. 

What if the animals are 3 cats and 3 mice?  If the amount of food was calculated based upon 6 mice-sized animals, I will likely be well short of the necessary amount, due to the fact the 3 cats probably eat more than the 3 mice.  If I calculate the amount of food based upon 6 cat-sized animals, I will probably have too much food. 

If all of my calculations were simply based upon cumulative numbers (3 + 3 = 6, as is OFTEN seen in financial calculations and comparisons), I could also conclude I needed a cage big enough to house 6 animals.  Unfortunately, I would very quickly have only 3 animals, as the cats would consume the mice if they were housed together. And I would have way too much food!  How does this happen if the math was correct (3 + 3 = 6)?

The same way it does day in and day out in the financial industry: the pertinent facts are left out of the equation!

The analogy was to prepare you for the sequence of information this “Comparison of Accounts” paper will take.  

  • First, we will look at mathematical truths that may or may not be completely truthful because of a lack of complete information (just “animals”).
  • Second, we will apply a little more “Truth” (the difference in appetites of cats versus mice).
  • And finally, other outside issues that aren’t necessarily mathematical, but vital for the real Truth (how cats and mice “get along” together).

Word to the Wise

WARNING! If you do not continue to the end, you will NOT have accurate or truthful information!

In order to reduce the complexity of the comparison, some assumptions (and we know the true meaning of that word) have to be made up front.  These assumptions we will make for the purpose of the concept are:

  1. A level GROSS (Before Tax) of 10,000 annually to invest (which becomes 7,600 Net for After Tax dollars with a 24% marginal tax bracket).
  2. A level, never-changing, marginal income tax rate of 24%.
  3. An earnings rate of 5%
  4. Distribution of the assets from the accounts at the beginning of the 25th year.
  5. All options are available and have no additional restrictions or benefits (we will however, discuss more reality towards the end of the paper).


References to the 4 different types of accounts from this point forward will be shortened as follows:

  • “Taxable Account” =  After Tax Contribution with Annually Taxable Growth (Savings Account, Money Market, etc.) .
  • “Tax Deferred Account” = After Tax Contribution With Tax Deferred Growth (After Tax-Tax Deferred IRA, Permanent Life Insurance, etc.)
  • “Tax Deductible Account” = Tax Deductible (Pre-Tax) Contributions with Tax deferred Growth (401K, Tax Deductible IRA, etc.)
  • “Tax Free Account” = After Tax Contribution with Tax Free Growth (Roth, Municipal Bond, etc.).

Because of it flexibility, we will be using the “Accumulation” Calculator from Truth Concepts for the calculations.

CUMULATIVE tax differences between the 4 account options with the taxes paid out-of-pocket (from a source other than the account we are examining).

– Taxable Account: – Asset Distribution = $355,126  –  Cumulative Taxes Paid = $41,454
– Tax Deferred Account – Asset Distribution = $355,126  –  Cumulative Taxes Paid = $41,454
Tax Free Account – Asset Distribution = $355,126  –  Cumulative Taxes Paid = $0
Tax Free Account – Asset Distribution = $467,271  –  Cumulative Taxes Paid = $112,145

The compound value of the taxes avoided during accumulation ($2,400/Yr, 25% for 24 Years) = the $112,145 paid in Tax at the end! If you subtract the taxes from the Distribution amount, you get: $467, 271 – $112,145 = $355,126!

That's math, right?

This is all mathematically correct and completely irrelevant (the sum of the animals). It would be easy for an advisor to say, or a consumer to deduce, that all 4 accounts were exactly the same at the end of the 24 years. It’s all provable with calculator and yet completely inaccurate because facts were left out (the types and sizes of the animals).

One of the greatest causes of misleading financial information is removing the “Time Value of Money” from financial calculations.  Additional Cash Flows (Fees, Taxes, Etc.) paid from another source, rather than directly from the account, like the wind are difficult to see.  But just like the devastation that would occur in leaving the impact of wind out of an engineering calculation, so is the devastation when leaving the “Time Value of Money” out of a financial calculation.

Digging Deeper: Analysis

 So lets re-examine the examples above.

With the Taxable Account, the taxes were paid annually from another source (out of income or out of another account). We didn’t get to wait until the end to pay the taxes like the Deferred Account, or pay $0 additional taxes like the Tax Free Account, or have the taxes effectively paid by the tax deduction on the contributions of the Tax Deductible Account. 

Looking back at the “Actual Yield” in the previous examples, we can see some differences.  3.8% for the Taxable Account, 4.15% for the Tax Deferred Account, 5% for the Tax Free Account, and 5% for the Tax Deductible Account.  The “Yield” or “Internal Rate of Return” when calculated correctly puts the comparisons on a level playing field because it takes account of all of the cash flows and the Time Value of Money. 

Why is the Yield different if the results appear to be the same?  Appearances can be deceiving! To make our examples correct, we have to measure the Time Value of Money or in this case the “Opportunity Cost.”  The only way to do this, when the source of the additional cash flows is not the account being examined, is to apply a Cost of Money (“C.O.M.”) rate to the additional cash flows.

The value of this C.O.M. rate can vary based upon many different factors, but a commonly held definition is the “Highest and Best Net Rate you can earn.”  “Highest and Best” is definitely open to interpretation because of factors such as risk, availability, etc.  I feel it relates to what the individual is currently doing (which could be 18% Net in the case of an individual carrying 18% credit card debt). In our Taxable Account example above, the “Actual Yield” is 3.8% Net after tax, so let’s use that.

Let's See…

So by putting 3.8% in the “COM Rate” input and turning on the “Tax and LOC” column in the Taxable Account example, we see a true cost for the taxes of $58,838 rather than the cumulative $41,454.

If we subtract the additional cost we incurred from the asset value, ($355,126 – $58,838 =$296,288 ) we get a much more accurate picture of the results.  A much easier way to see the results is to simply take the taxes from the account directly and seeing the bottom line impact.  In our Taxable Account example, we will turn on the “Net” checkbox in the Tax Data Input box, which gives us an account value of $300,517 (similar to what we saw when adding a “COM Rate” to our “Out-of-Pocket” previously).

To see the correct Net results with the Tax Deferred Asset, we have to eliminate the withdrawal and the interest rate in the 25th year which gives us a net value of $313,672.

So, while the CUMULATIVE Volume of out of pocket tax, with both the Taxable Account and the Tax Deferred Account, are the same, the Tax Deferred Account is a mathematically better when proper accounting is used.

When we look at the Tax Free Account option, there is no Out-of-Pocket or Out-of-the Account tax to pay so the end account value of $355,126 is much better (based upon pure economics) than the previous two.

To correctly level the field for the Tax Deductible Account, we need to do the same thing we did with the Tax Deferred Account: remove the withdrawal and the Earnings Rate in the 25th year.  Doing this, gives us the same Net result at the beginning of the 25th year as the Tax Free Account ($467,271 – $112,145 Tax = $355,126).


From a “pure economics” standpoint, Tax Deductible and Tax Free are both the same end result and both are better than Tax Deferred which is better than Taxable. This can only be seen when the correct calculations are used which must account for the “Time Value of Money”.

In order to determine which Account is actually better in the “Real World,” is dependent on the individual's entire “Big Picture,” and all of the other aspects of the account which may not be purely financial. Here are a few unanswered (and previously unasked) very-important-questions:

  1. Do we have to give up control or use of the money in one account versus another?
  2. Are there restrictions in the type of investment in one account versus another?
  3. Are there additional fees or costs in one account versus another?
  4. Are there additional risks in one account versus another?
  5. Is there a short term need for the money to be saved or invested?
  6. Do we think taxes might be higher in the future because of an increase in tax brackets or an increase in income with the same tax brackets?
  7. Are there additional desired/needed benefits included in one asset which would be an additional cost if another asset were chosen?
  8. Are there penalties if we need to adjust our strategy when “Life Happens?”
  9. Does one asset coordinate better with and/or compliment the other aspects or financial tools in my life?
  10. Is the asset “Exit Plan” better or worse in one account versus another?

Taking it Into the Real World

These are just a few of the questions that need to be addressed but are difficult, if not impossible, to calculate mathematically.  While correct mathematical analysis of a financial decision is important, consideration for the purpose and certainty of the asset STRATEGY is far more important.

Financial Analysis or Advice can, unfortunately, be very wrong even though the math used is correct.

That seems to contradict, but remember: “3 animals plus 3 animals equals 6 animals” is mathematically correct.  However, if three of the animals are cats and three are mice, you might end up with only 3 animals (cats)!

–Todd Langford