Mitt Romney has asked his tax preparers to divulge what
percentage of his income was paid in taxes and in charitable donations for a
number of years. They did so for a period of 20 years but the wording of their
testimony keeps the sought-after facts as obscure as ever. Here is how that
wording was formulated: The average of the annual tax rates as computed based
on the returns as prepared during the period was 20.20%.
It must be understood that there can be a huge difference
between the straight average of a set of numbers, and the weighted average of a
set of paired numbers. To make things simple, we take an example representing
only 2 years instead of the 20 years mentioned above. As far as the math is
concerned, what is true for 2 years will apply just as well for the 20 year
period.
If Romney paid taxes at the rate of 26.74% in one year and
the rate of 13.66% the next year – which is the minimum he says he paid – the
straight average method would yield 20.20% as reported. The way you arrive at
this value is by adding 26.74 to 13.66 which comes to 40.40. You then divide
that result by 2 (because there are 2 years), and this will yield the average
value of 20.20%, what the tax preparers and the Notary Public say Romney paid.
In fact, working with the percentages alone, you do not need
to know how much money Romney made in either year to arrive at that result. But
if you need to compute the weighted average of the taxes he paid, you need to
know how much money he made in each of those years. So then, let us assign a
fictitious number to each year. As far as the math is concerned, what would be
true for these fictitious numbers would be true for the actual numbers should
they be divulged someday.
Let us say Romney made 1,000,000 dollars the first year and
5,000,000 dollars the second year for a total of 6,000,000 dollars. If we go by
what the tax preparers and Notary Public say – which is that Romney paid an
average of 20.20% – without asking further questions, we come to the total
value of 1,212,000 dollars paid in taxes. But did he pay this amount? Probably
not.
And here is why. It is that there is another way to
calculate things. Instead of a set of simple numbers, we work with the weighted
average of the paired numbers. They are the 1,000,000 dollars at 26.74%, and
the 5,000,000 at 13.66%. Computing the yield of the first pair, we obtain
267,400 dollars paid in taxes that year. Computing the yield of the second
pair, we obtain 683,000 dollars that year. The total taxes paid for the two
years would be the sum of the two numbers. That total comes to 950,400 dollars.
And this is below the 1,212,000 dollars computed by the straight average
method.
Now, to compute the average rate in percentage terms using
this method, we divide 950,400 by 6,000,000 and multiply by 100 (to put it in
percentage form) and obtain 15.84% which is the weighted average of the pairs
of numbers. And this is below the 20.20% obtained by the straight average
method. If this is what Romney did, it would indicate that the more money he
made, the more deductions he took in order to lower his taxes. And this poses
the question: What kind of deductions were they?
All in all, what this says in the end is that a true picture
of Romney's tax situation cannot be accurately assessed from the summary that
his tax prepares have produced. When you add to this the fact that he delayed
submitting the tax returns for 2011 to do them over, claim less in charitable
donations and thus remain within the 13.66% minimum he promised he would not
breach, you wonder what else this man would not do to get elected.
Nothing will save his credibility now but the full
disclosure of those 20 years of tax returns. He would be wise to release
everything come what may because the speculation will otherwise never end.