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I am selling a product and want a $20\%$ margin on the selling price.

To determine the selling price, my plan was to multiply the cost price by $(1+0.2),$ but the salesperson that I'm working with tells me that I should divide the cost price by $(1-0.2)$ instead.

Which formula is right, and why?

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  • $\begingroup$ It depends entirely on what you want "a 20% profit margin" to mean. It could mean you add 20% to your buy-in / production price to set the selling price, so if your "purchase price / production cost" is £100, you'd sell it at £120 for a 20% markup. But it could mean that 20% of your sale price is "profit", in which case you'd sell it for £125. Both those "definitions" of "profit margin" are in use, and it's pointless to argue that either is "better" than the other (except that you as a retailer make more profit with the second definition, obviously! :) $\endgroup$
    – FumbleFingers
    Commented Nov 24 at 19:31
  • $\begingroup$ @FumbleFingers: "it's pointless to argue...". Well, the one that your company accountant tells you your company uses in its own accounts, is "better". It's pointless arguing which one that is if, as you suggest, both are in use by professionally-qualified accountants ;-) AFAIK "gross margin" is universally acclaimed to be "100% - (cost/revenue)", which means £125 is correct, but I might be wrong. And "gross margin" is not the only "profit margin". $\endgroup$
    – Steve Jessop
    Commented Nov 24 at 22:06
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    $\begingroup$ Fundamentally, if this is a question from "algebra pre-calculus" then it should define its terms, not include a sub-question from an accountancy course. If all else fails, explain under what conditions each would be correct, and if you lose marks for not knowing the definition of "profit margin", then hey ho. But since the exercise says a 20% margin "on the selling price", and only the questioner ever mentioned "profit margin" in their paraphrased title, I'd wager that 20% of price is the expected definition. $\endgroup$
    – Steve Jessop
    Commented Nov 24 at 22:18
  • $\begingroup$ @FumbleFingers Both those "definitions" of "profit margin" are in use $\quad$ I just googled, and could find only sources compatible with the second definition. Could you site an example where the term "profit margin" is being used to mean markup percentage? $\endgroup$
    – ryang
    Commented Nov 25 at 4:06
  • $\begingroup$ @ryang: You surprise me. For example, A craftsman makes a chair for $80 and sells it to make a 20% profit on its cost price. It says there Selling Price = Cost Price + Profit = $80 + $16 = $96. But by my second definition above, obviously he's only made 16.6% profit. Drawing a distinction between "profit margin" and "markup percentage" is just nitpicking. $\endgroup$
    – FumbleFingers
    Commented Nov 25 at 4:22

2 Answers 2

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Let $S$ be the selling price and $C$ be the cost price . For a 20% margin , we want the profit ($S-C$) to be 20% So:

$$S-C=0.2S\iff C=S(1-0.2)\iff S=\frac{C}{1-0.2}$$

Your formula is used to mark up the cost by a flat percentage , whereas the salesperson’s formula is used to calculate the selling price so that the profit margin is a specific percentage of the selling price.

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I want a $20\%$ margin on the selling price.

In your computation $$\text{selling price}=1.2\times\text{cost price},$$ the markup percentage (profit $\div$ cost price), or percentage profit, will be $\dfrac{20}{100}=20\%.$

In your coworker's computation \begin{align}\text{selling price}&=\text{cost price}\div(1-0.2)\\&=1.25\times\text{cost price},\end{align} the profit margin (profit $\div$ selling price) will be $\dfrac{25}{125}=20\%,$ as desired.

P.S. While profit margin is the more immediately relevant metric to sellers, markup percentage is the more fundamental concept, at least to analysts and buyers.

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