Reverse calculation of profit margin and taxes

[_void]

Hello

I need a way to retrieve a profit margin (already applied to) a given amount, knowing that this margin also has taxes apply to it. I'll do an example to expain :

Let's say we have 1000$ base price and need to apply a 10% profit margin :

1000 / (1 - 0.10) = 111.11$

Apply (Quebec, Canada) Taxes :

111.11 * 0.05 = 5.56$
(111.11 + 5.56) * 0.095 = 11.08$ (the provincial tax apply on top of the base price added to the federal tax)

Now, given the amount 1127.75 (base price + margin) and knowing the margin is 10%, how can I extract the margin amount of 127.75 and get that 1000 base price?

Help will be greatly appreciated !

 

[tkhunny]

A little algebra solves your problem quickly.

Margin = 0.10
Base = $1,000.00
Sales = Base / (1 - Margin)
QTaxRate = 0.05
QTax = QTaxRate * Sales

FinalPrice = Sales + QTax
= Base / (1 - Margin) + QTaxRate * Sales
= Base / (1 - Margin) + QTaxRate * Base / (1 - Margin)
= Base * [1 / (1 - Margin) + QTaxRate * 1 / (1 - Margin)]
FinalPrice = [Base / (1 - Margin)] * [1 + QTaxRate]

Solve this equation for "Base" and you have accomplished your task.

\(\displaystyle Base = FinalPrice \cdot \frac{1 - Margin}{1 + QTaxRate}\)

This is why you should have paid better attention in your algebra class. How long ago was that?

 

[_void]

This is why you should have paid better attention in your algebra class. How long ago was that?

Quite long enough indeed and thanks for the reply. This is not the actual problem though...

The tax part is only applied on the profit margin (that is) 111.11 + taxes which are included in the total price. Maybe I wasn't clear enough, I'll try and demonstrate it more clearly :

for a base price of 1000, and a profit margin of 10%, a federal tax of 5% and a provincial tax of 9.5% the calculation goes like this :

(1000 / (1 - 0.10)) - 1000 = 111.11
(111.11 * 0.05) + 111.11 = 116.67
(116.67 * 0.095) + 116.67 = 127.75

giving the profit margin + taxes.

Now, knowing the margin of 10%, the taxes rates (5% and 9.5%) and the final price (1127.75), how can I reverse the calculation to retrieve the 127.75 amount ?

 

[_void]

J'espere que tout est en ordre! :wink:

Yep, that does the job ! un gros merci