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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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Ivan
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2 Answers2

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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 $$ r = 50(1+2)=150 $$

WW1
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I found an old calculation of mine. The formula is:

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

Ivan
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    That is the same formula that I got in a different form – WW1 Jul 09 '21 at 02:37
  • Yes, way cleaner than mine. Thank you. – Ivan Jul 09 '21 at 02:38
  • 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.

     – WW1 Jul 09 '21 at 02:55