## Monday, November 24, 2008

### VAT calculations

Good old GMTV again you can almost guarantee they'll get things wrong. This morning it was the possibility of a VAT reduction - what would that mean for us?

'Well here's a CD that cost me £9.99', said the reporter. 'If VAT was 15% I'd save 24p'

She repeated this for a toy at £12 a would-be saving of 30p and some perfume/gubbins set at £45 a would-be saving of £1.12 - woo!

Um.

£9.99 is the price of the CD including the 17.5% VAT so the base price is (£9.99/117.5)*100 or about £8.50, VAT being £1.49, if we add 15% to the base price we get VAT of £1.28 a saving of... 21p. How about the others?

Price of £12 - saving of 26p not 30p, price of £45 - saving of 96p not £1.12. What have they done - the same thing so many seem to do nowadays. You take the price you've paid and work out 17.5% of that then work out 15% and compare the two. The result being:

£9.99 saving of 24p
£12 saving of 30p
£45 saving of £1.12

Using simple figures let's see why that happens. I take an item with a base price of £1.00 and add 10% to it making it £1.10 (100/100*10) I then reduce it by 10% which makes it 99p (110/100*10); a penny cheaper then my base price. With a £10 item the price becomes £11 reduce and it becomes £9.90; 10p cheaper. In other words you cannot simply add and subtract percentages and return to where you started from and if you do the bigger the price the more it seems to get cheaper by.

This is what happens when you get art major's doing mathematics.

Anonymous said...

Question: Is it not illegal to make statements such as these which are clearly and demonstratably incorrect?

Anonymous said...

Answer: No. You can't libel maths. Besides, it's the wrong statements that seem reasonable which are the most dangerous.

Anonymous said...

I'm beginning to think it's a good job it's not illegal, as it would be as hard to enforce as prohibition. Today at work our CEO was going round saying that when you buy something 17.5% of the price is tax (no, that's just under 14.9%) and how glad he was that prices would be coming down by 2.5% (no, that's just under 2.2%). I am amazed that someone who runs a business could harbour such a vital misunderstanding about percentages.

FlipC said...

I think what Orphi meant was that it should be illegal to broadcast such inaccuracies and indeed it is if used in official accounting or advertising.

For those trying to get their head around how the tax of the full product isn't 17.5% here's how it's worked out:

For a base price of £100 the VAT@17.5% would be £17.50 making a total of £117.50, however £17.50 is not 17.5% of £117.50:

£17.50/£117.50 * 100 = 14.9%

For VAT@15% the difference is
£115.00/£117.50 * 100 = 97.8% so £115.00 is ~2.2% less then £117.50 not 2.5%

As for your amazement Dan I can't say I'm surprised I'm betting he doesn't actually do the accounts just reads the figures.