VAT and how to strip it out

VAT is the most familiar of percentage mark-ups: it is applied to the net price to obtain the final one. The tricky point is the inverse operation, that is, working back from the VAT-inclusive price to the taxable amount.

Definition — VAT and stripping it out

VAT (value added tax, in Italy $22\%$ standard, $10\%$ reduced, $4\%$ super-reduced) is computed on the taxable price: $P_{\text{ivato}} = P_{\text{imponibile}}\cdot(1+i),$ where $i$ is the rate in decimal form ($i=0{,}22$ for $22\%$). To strip out the VAT from a VAT-inclusive price we divide: $P_{\text{imponibile}} = \frac{P_{\text{ivato}}}{1+i}.$

Applying VAT means multiplying by $(1+i)$; stripping it out means dividing by the same factor. It is not the same as taking the rate off the VAT-inclusive price, as the stripping-out example shows.

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Topics: Percentages
Concepts: VAT · Stripping out VAT
Skills: Using formulae