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Patent entertaining: the maths behind patent box profits

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Think of a number, multiply it by three, add one, multiply this by three, add the number you first thought of, take away three, divide by ten, and the answer is …

Surprising results can emerge from a multi-step formula.

The patent box consultation issued by HM Treasury & HMRC in June has a ‘three step model’ to determine how much of a company’s profits will be ‘patent box’ profits.

The complexity makes it difficult to identify factors that will increase and those that will decrease the amount of profits in the box.

Re-expressed as a formula

Condensing the three step model to a formula allows us to more easily spot the practical effects of the proposal and implications for companies seeking to benefit from this proposed tax relief.

The three step model can be re-expressed as:

Amount in patent box = (p – 0.15e) x 

r x q
  r+b    q+o 


  • p is the company’s tax adjusted profit for the year (excluding R&D tax credit enhancement, financing income and financing expenses);
  • e are the trading expenses for the year (excluding certain costs such as raw materials);
  • r are expenses on research (R&D charged in the accounts, and costs relating to patent filing, renewal and protection as set out in para 4.22 of the consultation paper);
  • b are brand expenses (marketing, selling, promotion, trademark development, again as per para 4.22 of the consultation paper);
  • q is turnover (sales) from patented products; and
  • o is other trading turnover.

In narrative form:

  • take the tax adjusted trading profit for the period;
  • increase this by any R&D tax credit enhancement and financing expense, and exclude any financing income;
  • reduce this amount by 15% of certain trading expenses;
  • next take a fraction of this amount: the fraction is sales from patented product divided by total trading turnover; and
  • finally, take a fraction of that amount, the fraction being direct patent expenses divided by patent and brand expenses.

The formula makes evident the items that cause reductions in the amount of profits in the patent box.

With the 15% reduction for certain trading costs, a company that spends to develop and expand its business will suffer a greater reduction than a company with the same taxable profit that does not incur such expenses.

Also, companies that spend on promotion of their products will have lower patent box profits.

And these two restrictions compound, leading to some doubling of the reduction.

The compounding effect is evident in the worked examples in the consultation paper.

In the simple example, Example A on page 35 of the paper, 70% of the company’s turnover is from patented products and the company has a trading profit of £225.

However the calculated amount in the patent box is £44 – much lower that the straight proportion by reference to turnover, which would be £158.

Surprising results

The hidden surprising aspect concerns entertaining and other disallowable costs.

The consultation proposes using tax adjusted figures.

Entertaining expenditure is not tax allowable and hence the patent box will effectively give tax relief for a part of companies’ entertaining expense.

To illustrate, let’s use Example A in the consultation paper.

Suppose that the £75 of marketing expenditure in the example was disallowable entertaining.

Reworking the patent box calculation would produce a patent box profit of £137 rather than £44, an increase of £93 of profits in the box.

If we assume that the year in question is after the patent box transition period, and assuming a corporation tax rate of 23%, its entertaining disallowance is in effect reduced from £75 to £22 (the patent box gives a computational deduction of 13/23 of the amount in the box; so an additional £93 in the box produces a computational deduction of £53).

Is this intended?

The bigger picture

On the bigger picture, do these proposals align with the government’s desire for tax simplification? Should the Office for Tax Simplification be asked to review these legislative provisions before enactment? It gives the appearance of two steps forward, one back; the OTS simplify one area, only for complexity to be added elsewhere.

I would suggest that the complexity of the ‘three step model’, and what I suspect are unintended side effects, not to mention the relief that will actually be delivered is much less than businesses are expecting will require substantial revision of the proposals.

This would not be the first occasion that far too complex rules are simplified – recall the initial worldwide debt cap proposals.

Another aside on the maths and for those with a long enough memory is that the patent box will be delivered in the same way as pre-1987 chargeable gains of companies were taxed at a lower rate.

There will not actually be a patent box with a 10% rate – rather there will be a reduction to taxable profits in respect of the patent profits.

The answer to the number puzzle should be the number you first thought of.

The consultation paper is available on HM Treasury's website.

Richard Service, Tax Director, Mazars

This comment is a personal view, not one of Mazars. If you would like to see the algebra linking the consultation paper three step process to his formula, e-mail Richard at