Calculating VAT

Question

I have a customer who is disputing a (UK 20%) VAT total, but not sure how they are calculating this. This is their comment:

"The RRP is £225. Then minus the 10% discount which is £202.50. £202.50/1.2 = £168.75"

So they are saying 20% VAT of £202.50 leaves £168.75

I thought you simply take 20% from £202.50 which would be £40.50 leaves £162

So which is correct & why!

Answer 1

If you take a number and you first add the 20% and then take the 20% you don't obtain the original number. In fact $100 + 20\% = 120$ and $120 - 20\% = 96$.

So, since VAT is "adding $20\%$" the inverse is not "subtract $20\%$".

Since "adding $20\%$" is equivalent to multiply by $1.2$ then dividing by the same quantity is correct.

If you want to subtract a percentage then the right percentage is $$ 100 \cdot \left( 1- \frac{1}{1.2} \right) = 100 \cdot 1.\bar 6 = 16.\bar 6 \% \approx 16.67\% $$

Answer 2

I calculate VAT in these ways of two different (most common) contexts:

X = Cost.
Y = VAT Calculation Basis.

1) Expanding a number by Y:

  X * Y / 100 == costsVAT (Add it to the cost to get sum).
  X * Y %     == costsVAT (Add it to the cost to get sum).
  X * 1.Y     == ES (End Sum).

2) Decerment VAT from a number:

  X * Y / 100 == Only VAT (decerment it from the charging sum to get end sum).
  X * Y %     == Only VAT (decerment it from the charging sum to get end sum).
  X / 1.Y     == cost decermented by costsVAT