Remedy Update: Grossing up

Grossing up (incorrectly!) in Hall v Durham County Council & Ors UKEAT/0256/14/MC

In [this case]() the EJ and representatives of the parties (and the parties themselves!) had clearly forgotten GCSE/'O' level maths. A typical grade B question might go something like this:

"A car is worth £4,500 after having lost 10% of its value. How much was it worth BEFORE the decrease in value?"

Now, the numbers have been chosen deliberately so that the maths is relatively easy. The car was initially worth £5,000, because 10% of £5,000 is £500, and when taken off makes £4,500. But we need to be able to do this when the numbers are more difficult.

Many students (and the ET in this case!) would work out 10% of £4,500 (which is £450) and add this amount back to £4,500 to get £4,950. Although not a million miles away from the correct answer of £5,000, it can, and did in this case, make a lot of difference to the amount the respondent has to pay if the grossing up is done incorrectly.

A grossing up calculation is directly analogous to the question above. What we are trying to calculate is the amount the respondent needs to pay which is equivalent to the amount the car was worth before the decrease in value. The amount of money in the claimant's hands after they have paid tax is equivalent to the amount the car is worth now.

So how does grossing up work? The calculation is in fact an example of a 'reverse percentage', where we know the amount AFTER a percentage has been applied rather than before.

If the net sum to be received by the claimant is, say, £50,000, all of which will be taxed at, say, 25%, the gross amount to be awarded is 50,000/0.75 = £66,666.66.

Why? Well, the £50,000 is only 75% of what the claimant will actually receive because they have to pay 25% of what they receive in tax.

So, 75% of something (let's call it A) = £50,000

Translated into algebra: 75% x A = 50,000 where A is the amount payable by the respondent (the word 'of' in maths can be replaced by a multiplication sign).

0.75 x A = 50,000 (remember that 75% = 0.75)

Now A is 50,000 divided by 0.75 (remember that division is the opposite to multiplication) = £66,666.66

Working forwards again, if the claimant receives £66,666.66 and pays tax @ 25% on this amount she will receive 66,666.66 x 0.75 = 50,000 which is correct.

What the Tribunal had done was calculate 25% of £50,000 = 50,000 x 0.25 = 12,500 and then added it back on to get £62,500. But 25% of £62,500 = £15,625 so the claimant would end up with only £46,875.

In the car example, we would write: 0.9 x A = 4,500, therefore A = 4,500/0.9 = £5,000

The general rule is that if the claimant should receive in her hand £x, and the marginal tax rate is y%, you divide £x by (1 - y%) to get the gross amount to be paid by the respondent.

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Published: 23/06/2015 15:00