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I kept searching for the logic of the vat calculations, but i still can't understand a few things,maybe you can help me out.

If i want to extract the price without tva,i'll be using this formula:

  1. PriceWithoutTva = PriceWithTva / 1.19(for a tva rate of 19%),which i can't understand because for something like this: 100/1.19 = 84.02521008403361 , and that makes the TVA value to be almost 16 , but 19% of 100 is clearly 19.

If i want to extract the TVA from a price with tva,some say to use the above formula and simply decrease it from the PriceWithTva,which makes sense. Other says to multiply with the VAT percentage like this:

  1. PriceWithTva * 0.19(for a tva rate of 19%) ,which makes sense because if i have 100 *0.19 it will give 19 which it's logical.

But then,i came across a formula which is widely used if i want to extract the TVA from a PriceWithTva:

  1. PriceWithoutTVA = 100/(100+19) * PriceWithTVA , and the result is 84.02521008403361 which makes the TVA value almost 16 again for a PriceWithTVA of 100

Another formula which i can't understand is:

4.TVA = PriceWithoutTVA * 0.19(tva rate) , which again gives almost 16 for the PriceWithoutTVA of 84.02521008403361

Thanks for help.

Peter Cos
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  • For a question with the reverse approach (percentage of the larger amount), see https://math.stackexchange.com/questions/2746372/find-the-total-amount-from-a-given-percentage-and-x-amount-which-on-substraction – Henry May 16 '18 at 00:36

1 Answers1

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Your (4) is the theory of how this tax is applied, implying your (1) and (3), while your (2) is wrong. The tax rate is applied to the before-tax price

You have the underlying application of value added tax (I will call this VAT rather than TVA) $$\text{ VAT amount }= \text{ Price before VAT }\times \frac{19}{100}$$

so adding these two together

$$\text{ Price after VAT }= \text{ Price before VAT }\times \frac{119}{100}$$

and multiplying both sides by $\frac{100}{119}$

$$\text{ Price before VAT } = \text{ Price after VAT }\times \frac{100}{119} $$

and with substitution

$$\text{ VAT amount }\times \frac{100}{19} = \text{ Price after VAT }\times \frac{100}{119} $$

which, by multiplying both sides by $\frac{19}{100}$, simplifies to

$$\text{ VAT amount } = \text{ Price after VAT }\times \frac{19}{119}$$

Henry
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