The coalition government has announced that VAT will increase from 17.5% to 20% on January 4^th 2011.

Problem

A TV is advertised at £1000 including VAT at 17.5%.

VAT is increased to 20%.  What will the new price tag be?

Solution

The immediately apparent answer is £1025, because we’ve “added 2.5%”.  But that’s not quite right…

The TV’s advertised price was £1000.  This included VAT at 17.5%.  What was the wholesale price before VAT was added?

To get from the wholesale price to the advertised price, a percentage increase operation was performed:

The shopkeeper took the wholesale price and multiplied it by 1.175, which gave the answer £1000.

To get back from £1000 to the wholesale price, just do the opposite of multiplying by 1.175, i.e. divide by 1.175:

So the wholesale price was £851.06.  Now, how do we add the new VAT at 20%?  Easy!  Just multiply it by 1.20:

So the new price would be £1021.28, not £1025 as might be assumed.

Discussion

So it transpires the 2.5% increase in VAT actually only increases the prices you pay by about 2.1%.  So is it worth panic buying for the sake of 2.1%?  In my experience, half an hour spent shopping around on the Internet will almost always reveal a better deal somewhere.  Prices of electronic goods are falling all the time, so wait another month and that telly you had your eye on might even be superseded by a newer model, meaning the price of your prized telly might drop anyway.

My recommendation is to be patient.  Plan ahead, but it’ll be January sales anyway and people will all be going shopping mental.

(I mention the “wholesale” price above just for clarity.  In real life the shop would have already added on another percentage reflecting their profit margin, to reach £851.06, so the true wholesale price would actually be less than £851.06)