How do you calculate profit margin when your price is zero?

Question

I'm just looking for the mathematical answer for this. If I have a source of products that cost me exactly $0, and I sell them for, say, $10 each, what percentage is my profit margin?

But see, I'm not concerned at this point about real world and whether I have any extra costs or not . I just want to the know the MATHEMATICAL solution to: if my cost is $0, and I sell it for $200, what is my profit margin? You can't divide by zero, so most of the equations I found won't work.

Answer 1

I don't see why you need to divide by zero. It's a subtraction problem.
If you sell one unit for $10 and your cost is zero, your profit margin is $10 - $0 = $10.
Now, I suppose, you would divide your profit by your total income (NOT your cost) to get a percentage. In your case:
$10 / $10 = 1.00 or 100%. No division by zero anywhere.

Answer 2

Won't you have other costs, such as admin costs, or taxes? (e.g. your salary managing the sale) I would find that difficult to believe in the real world.

For example, suppose a company produces a loaf of bread and sells it for 10 units of currency. It costs the company 6 units of currency to produce the bread and it also had to pay an additional 2 units of currency in tax.

That makes the company's net income 2 units of currency (10 - 6, before tax, then minus 2 for tax). Since its revenue is 10 units of currency, the profit margin would be (2 / 10) or 20%.

Answer 3

If you dont pay for your product 100% of everything you sell will be profit, whether you sell them for $10 or $1000. But nothing is free.