Thursday, March 2, 2017

Introduction to a Mathematical Analysis of Tax Preparation

Warning: This post is not for the faint of heart. Or for 99.873% of mankind. Nor is it for anyone driving, operating heavy machinery, or in need of their mental faculties within the next hour.

Last night a young woman came in to get her taxes done. At first, it seemed simple. Just her, no dependents, two W-2s, no other income. Then it got more complicated. Seems that for the first six weeks of 2016, she lived and worked in New York, out in Long Island. Then she got a job over here in Jersey, in her chosen field, so she moved mid-February and began her new work. So though her federal is not affected and remains a 1040EZ, she now has to file a New York non-resident return as well as a New Jersey return, and both prorated for the amount of time she spent living and working in each.

It became a little embarrassing because I couldn’t find where to establish her residency dates in New York via the software we use. Plus the fact that a New York return contains two dozen forms doesn’t help. The clock was ticking and I was, in all honesty, getting a little frazzled (it was only my second New York return of the season, so I’m far from comfortable with them). I asked her if I could work on the returns over the next couple of days since she has until April 18 anyway. She said yes.

This morning I got to thinking about all this as I was shampooing and shaving in the shower. Doing a tax return is like solving a jigsaw puzzle. The more complicated the return, the more numerous the pieces and the more exotic the picture. The more returns you do, the more familiar these jigsaw puzzles become, and solving them almost becomes second nature. So I asked myself, how many patterns of returns are there? How many set types of a return? In the case above, my client had the return type of [Federal 1040EZ + NJ resident + NY nonresident + zero adjustments / credits / deductions].

At first I guessed 50, but then, recalling the class on finite math I took in 1989 which covered permutations and combinatorics, I realized it had to be much more.

Rinsing out conditioner, I mentally made a very rough list that determines the option for most major variables when doing a tax return:

Type of Federal return (1040, 1040A, 1040EZ) = 3

NJ resident vs NJ nonresident = 2

NY resident vs NY nonresident or no NY = 3

Has child / child dependent care credits Y/N = 2

Has capital gains/losses Y/N = 2

Has substantial interest income Y/N = 2

Has retirement income Y/N = 2

Has education adjustments/credits Y/N = 2

Has health care penalties/PTC adjustments Y/N = 2

Has other deductions or credits Y/N = 2

Has anything out of the blue Y/N (such as another State) = 2

Multiplying everything out, we have

3 x 2 x 3 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 =

3^2 x 2^9 =

9 x 512 = 4,608

Or 4,608 different sets/patterns of returns.

But that’s somewhat of an overestimate. In fact, if you are on a 1040EZ, you most likely do not have all the credits and deductions and alternative income listed. So if we just calculate the 1040EZ permutations with the state return(s), if any, and add that to the 1040/1040A option combined with all the permutations of the credits, deductions, etc., we get something like:

3 x 2^10 + (1 x 2 x 3) =

3 x 1024 + 6 =

3072 + 6 = 3,078

3,078 different sets of sets/patterns of returns.

Even that overstates the number of sets though, because some of those credits/deductions/etc. merely involve clicking a YES or NO button in our software, while others involving inputting a completely new form or forms. So each would have to be weighted somehow in some way, in terms of effort needed, as well as typical frequency of occurrence.

Out of fear of driving you comatose, I shall not do that. But my very inexperienced gut tells me that the result of this further weighting will yield an approximate number of

150 different sets of sets/patterns of returns.

Me, I’ve only done around 15, or 10% of the jigsaw puzzles.

Full proficiency expected sometime the beginning of February 2018.

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