Is the Fair Tax Mark mathematically sound this time?

The maths in the original Fair Tax Mark was unsound. In one line of the calculation an “average” (henceforth known as ‘Method B’ for reasons that will become apparent) was effectively calculated by the following formula:

(Rate 1 + Rate 2  + Rate 3 + Rate 4 + Rate 5 + Rate 6) ÷ 6    = “Average” rate of tax over 6 years

Method B was used to average the difference in rate to expected rate average. I have removed the arbitrary annual weighting from the averaging to highlight the principle in question.

Most people should be able to see what is wrong with that. Method B is not how you calculate an average rate. You actually do it like this for rate of tax on profits:

(Tax 1 + Tax 2 + Tax 3 + Tax 4 + Tax 5 + Tax 6) ÷ (Profit 1 + Profit 2 + Profit 3 + Profit 4 + Profit 5 + Profit 6) = Average rate of tax over 6 years

I have tried to find out if there is any legitimate use for Method B. I cannot find an accepted use other than as a shortcut where the denominator in the rate is identical (ie you get the correct answer only if Profits 1 to 6 are identical).

Now, at present, it is not clear from the Fair Tax Mark’s criteria whether they are correctly calculating an average rate this time. So I asked Richard Murphy on Andrew Goodall’s blog which covered this point.


Richard, as yet, hasn’t corrected me on my clarification so I assume that he is unable to disagree. So it appears that the Fair Tax Mark is mathematically sound this time.

But the significance of this point is that both the original Fair Tax Mark and that corporate tax gap estimate contain Method B in their workings (which are both cited on the Fair Tax Mark website).

If you accept that Method B is fundamentally flawed, you have to accept that the corporate tax gap estimate here in Appendix 4 is fundamentally flawed.

And I cannot see how you conclude that Method B is not fundamentally flawed.


About Ben Saunders

I'm a Chartered Tax Adviser and a freelance writer. This is my personal blog about, well, mainly taxation. I might put other stuff in. Who knows.
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