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If a company has a 45600 in sales and their margins are 50%.

How do I calculate the costs?

I thought the margins were defined as $$ \text{margins} = \frac{\text{profit}}{\text{revenue}} = \frac{\text{revenue}-\text{costs}}{\text{revenue}} $$

So I get $$ \frac{45600-\text{costs}}{45600} = 1 - \frac{\text{costs}}{45600} = 50\% \Leftrightarrow \text{costs} = 45600 - 50\% \cdot 45600 = 22800 $$

But I have also seen people simply saying that if their margins are $50\%$ then their costs are $50\% \cdot \text{revenue}$. Is this exactly the same?

I can see that $22800 = 50\% \cdot 45600$, so it seems to be the same, but it's a little hard for me to understand the concept of margins.

Jamgreen
  • 809

1 Answers1

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... if their margins are $50\%$ then their costs are $50 \%⋅\text{revenue}$.

That is true. It can be shown mathematically

$\text{margin}=1 - \frac{\text{costs}}{\text{revenue}} $

Now we say that the costs are the half of the revenue. We can replace costs by $0.5\cdot revenue$

$\text{margin}=1 - \frac{0.5\cdot \text{revenue}}{\text{revenue}} $

The revenue is cancelling out

$\text{margin}=1 - \frac{0.5}{1}=1-0.5=0.5 $

The margin is indeed $50\%$.

callculus42
  • 30,550