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Let's say I have a profit of $50$ and a margin of $50\%$.

Now I know that the revenue is $150$, despite not knowing the cost, because this is the only possibility for the $50\%$ margin i.e.

$Cost * (1 + Margin) = Revenue$

$100 * (1 + 0.5) = 150$

Now, what would the formula be to get the revenue by just knowing the $50\%$ margin and the $50$ profit?

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  • $\begingroup$ Does COGS mean Cost? $\endgroup$
    – lulu
    Commented Jul 9, 2021 at 2:05
  • $\begingroup$ Yes, Cost Of Goods Sold $\endgroup$ Commented Jul 9, 2021 at 2:08
  • $\begingroup$ Ok. Well, letting C=Cost, R=Revenue. Then the Margin is $R-C$ so you'd have $R-C=50$ and $R-C=\frac C2$. Can you finish from there? $\endgroup$
    – lulu
    Commented Jul 9, 2021 at 2:10
  • $\begingroup$ I'm afraid I didn't get what you're aiming at... $\endgroup$ Commented Jul 9, 2021 at 2:19

2 Answers 2

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Let ...

  • $c$ represent Cost
  • $m$ represent Margin
  • $r$ represent Revenue
  • $p =r-c$ represent Profit

Your formula is $$c(1+m)=r$$ you want to express this using $p$ instead of $c$

so substitute $(r-p)$ for $c$ $$(r-p)(1+m) = r$$

now isolate $r$ $$r(1+m)-r = p(1+m) $$ obtain the result $$ r = p\bigg(\frac{1+m}m \bigg ) = p \left ( 1+\frac 1m \right )$$

in your case $m=0.5$ so $\frac 1m = 2$ and you get $$ r = 50(1+2)=150 $$

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  • $\begingroup$ Oh your formula is better than the one I posted. Thank you for the explanation. $\endgroup$ Commented Jul 9, 2021 at 2:37
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I found an old calculation of mine. The formula is:

$$\begin{align} Revenue = \frac{Profit}{1 - \frac{1}{1 + Margin}}\end{align}$$

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    $\begingroup$ That is the same formula that I got in a different form $\endgroup$
    – WW1
    Commented Jul 9, 2021 at 2:37
  • $\begingroup$ Yes, way cleaner than mine. Thank you. $\endgroup$ Commented Jul 9, 2021 at 2:38
  • $\begingroup$ I strongly recommend that whenever you want to do algebra, name your variables as single letters rather than words, it makes it much easier to see the mathematical structure of a formula. I find it quite shocking how much more difficult it is to do algebra with words instead of letters, it feels almost like a right handed person trying to write with their left hand. $\endgroup$
    – WW1
    Commented Jul 9, 2021 at 2:55

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