I am trying to prove to myself that incurring expenses just for the purpose of writing them off never saves money. It is always better to not incur the expense at all if you can avoid it. This is my calculation. IS it correct?

I: income  
E: expense  
r: tax rate  

So, to actually 'save' money by incurring an expense and then writing it off:

E + (I - E)r <= Ir // left hand side represents total expense + tax,
                      right hand side represents tax without any expenses(write off)

E + Ir - Er < = Ir

E < = Er

1 <= r

But 0 < r < 1, hence disproved.

  • 3
    what is true: if you discover an expense you have made or must make is deductible, then you should deduct it. – mhoran_psprep Sep 30 '13 at 1:47
  • You spend ten dollars
  • You get back six dollars in tax relief
  • Total loss of four dollars.

This will always be the case unless the tax relief is more than the expenditure, which it never is.

There are some ways in which this can become worth it: if the thing you are spending the money on would actually be useful, of it you might be able to sell it for more than four dollars later - or if you can claim a government grant or similar for more than four dollars. And at the level of corporate finance it can get more complicated. But otherwise, No.

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  • 2
    Good answer, and your first statement is exactly what the math in the question proved: you suffer a loss unless the marginal tax rate is greater than 100%, which it never is. – John Bensin Sep 30 '13 at 13:35
  • @JohnBensin does that episode in france a couple years ago due to a one-time levy count? – im so confused Sep 30 '13 at 20:33
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    @JohnBensin - There are anomalies within the tax code where a credit doesn't slowly "phase" away, but has a step function. When I look at the healthcare credit, if one (family) is at 400% of poverty MAGI, they can get a credit, $4500 or so. 400.01% of poverty level, the credit goes to zero. The instantaneous marginal rate is near infinite, (well, the $1 loses $4500, so not quite) and there are other quirks that one can uncover, usually MAGI based. – JTP - Apologise to Monica Sep 30 '13 at 20:48
  • @JoeTaxpayer Great point. My original comment shouldn't have been so unequivocal (and I'm ashamed that I didn't immediately think of the healthcare credit, seeing as healthcare is my job...) – John Bensin Sep 30 '13 at 21:33
  • @JohnBensin - To circle back, I wonder if there's anything in a business tax return that has any similar step functions? Or is my remark above limited to individual's personal returns? – JTP - Apologise to Monica Sep 30 '13 at 21:56

Firstly assumption is that

E - Expense is a part of Income ( i.e you are spending from your income ).
so the equation becomes

( I - E )r <= Ir  // always true.

Now if expense is from your savings

E is not exactly an expense, its an investment - it holds value
( it could be insurance , deposits or even a commodity )
it is an asset that has value, even if it is depreciating 

on R.H.S --> I * r is amount lost, it holds no value.

well except if E is donation to charity
Only in such case where E is lost, is your equation correct
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