VAT Fun

People (including a director from John Lewis and a bank worker interviewed on the news) seem very confused about the new VAT rate. A drop from 17.5% to 15% will not reduced prices by 2.5%. The price reduction will be less than that. Let me use fudge to explain!

Assume I had a 100g slab of fudge and cut it into 100 identical pieces (this is hypothetical fudge so the act is possible and none would be eaten). That would be my “exclusive of VAT” fudge.

Then I clone the fudge pieces and add another 17.5 identical pieces. This would then be my “inclusive of VAT” fudge. I have added 17.5% to it.

I can now squash the fudge together into a slab again. The new slab weighs 117.5g.

And when the VAT rate changes from 17.5% to 15% I need to take some fudge away.

So I could cut my fudge into 100 identical pieces and take away 2.5 of them. But that wouldn’t be right. You can’t just take 2.5 away.

Because…

Each of the 100 pieces of fudge I now have is slightly larger than the pieces I had originally. Remember I added 17.5 extra pieces and squashed those into the slab? So if I took 2.5 pieces away I would be taking away too much. My “new VAT rated slab” would weigh 114.5625g not 115g (117.5g minus (2.5 times 1.175g lumps)).

The discount is not as much as 2.5%.

What you need to do is take the “inclusive of VAT slab” that weighed 117.5g and cut it into 117.5 pieces (not 100 pieces). These 117.5 pieces would each be the same size as the original pieces. You can then take away 2.5 other those and squish it back together. This new slab is the “inclusive of new VAT” fudge and would weigh 115g.

The discount is actually 2.1739%.