Tuesday, 2 December 2008

Dodgy Maths Special Edition: On Calculating Prices Following The VAT Decrease

Right, I'm only going to explain this once, so please listen carefully.

The UK Government has reduced VAT by 2.5%. So how much of a saving does this represent?

Let us suppose, for ease of calculation, that an item cost £100 on Friday.

Now, we wish to determine how much it will cost today, having had VAT reduced by 2.5%.

Many people have supposed that it will now cost £97.50 - in other words, 2.5% of £100 is £2.50, so you pay £2.50 less.

But this is not correct, because it corresponds to a price reduction of 2.5%, not a VAT reduction of 2.5%.

Instead, we must calculate how much VAT is currently being paid on the £100 item, and then reduce that, and recalculate the total.

So:
£100 = full price
= cost of item + 17.5% of cost of item
= 117.5% of cost of item (because 'cost of item' = '100% of cost of item')

Hence:
cost of item = £(100/117.5)*100
= £85.11

So, if an item cost £100 on Friday, then that price was made up of £85.11 for the item, plus £14.89 for VAT.

However, the VAT is now 15%, instead of 17.5%. This means that the total cost of the item is now:
total cost of item = cost of item + 15% of cost of item
= £85.11 + (£85.11*15)/100
= £85.11 + £12.77
= £97.88

And thus we see that the saving is, in fact £2.12, and not £2.50 as has been proposed.

I think.

7 comments:

vanishing point said...

I made it £97.87, giving a saving of £2.13. However, the point you made is correct. Although, in reality the cost to business of these changes (lets not forget its temporary and will revert at the end of next year), may result in smaller businesses recalculating their costs and repricing higher. Fiscal stimulus? Bah, nothing but vote buying.

bresker said...

I agree. It's a saving of £2.13 in the pound.

So Poundstretcher must change its name to (100p-2.3p)stretcher

vanishing point said...

Its a rounding up thing. Anyhoo, 2 things:
1. If we get deflation then it will be Poundshrinker
and
2. How strange that I should bump into you on the net in 2 places within the space of weeks

Apologies to Miss Smile for the short hijack.

andmilestogobeforeisleep said...

you were always so much better at this than me.

bresker said...

Ah, but surely it will be Poundstretchevenfurther, because deflation will mean that the money in your pocket will buy more goods & services, not less. The pound may shrink in value but it will have the power to buy more.

I think.

whynotsmile said...

The £2.13/£2.12 is just a rounding thing, it depends how you calculate it. I did it in steps, whereas if you do it all in one go, you'd get £2.13, but you wouldn't have shown your working out, which is not so good for Educational Purposes.

Vanishing Point, when did we bump into each other on the web before? Who are you?!!

vanishing point said...

Apologies, I was referring to Bresker.