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What is the formula to determine "profitability" in the inflated art appraisal tax evasion scheme?

Personal Finance & Money Asked on May 23, 2021

An often talked about form of tax evasion in the last several years is donation of works of art that have a grossly inflated appraised value. A rich person buys some piece of art for thousands, possibly tens of thousands of dollars, and then they manage to get it appraised at hundreds of thousands or possibly even millions. Then they donate the art to some organization and get to write off that inflated value from their taxes.

As a concept this makes sense, but I want to know what formula can be used to represent this scheme so that one can calculate the break points for profitability. I’m not terrible at math, but there are enough values involved, and possibly tax law that I don’t know, that make it hard for me to know if I’ve got it right.

C = **C**ost of art.
A = **A**ppraised value of art.
W = How much can be **W**ritten off (if different from 'A').
T = Rate of the highest **T**ax bracket that applies to the person.
L = The **L**ower limit of the bracket.
E = The **E**arnings realized in unpaid taxes.
G = **G**ross income of the person.

My assumptions are:

  • The write off affects the AGI, and isn’t just a straight reduction in final taxes.
  • The write off is not large enough to knock the person into the lower tax bracket.
  • The person in question is filing single.

I’m thinking the formula is something like: E = ((G - L) * T) - ((G - L - W) * T) - C

Is that right? With that calculation, I come out to around 270% markup on the art in order to be almost even. It becomes noteworthy profit after you reach extreme numbers like C = 10 million

And if W does not equal A, is there some generally applicable formula to determine what W would be?

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