What is the correct way to calculate a selling price from margin and a cost?

Question

There seems to be two formula to calculate a selling price.

The first formula that I came upon would be

Cost * (1+Margin) = Selling price
Example : 10 * (1+0.25) = 12.5

However, a lot of people uses the following :

Cost / (1 - Margin) = Selling price
Example : 10 / (1-0.25) = 13.33...

This gives a very different number.

As far as I know, the margin and selling prices can be anything you want for most products.

Also note that the second formula fails if you have a margin of more dans 100%.

My question is why is the second formula the most popular ? Is it only a gimmick to get a bigger price?

Am I missing something subtle at work here ?

Also, what should I do if the wanted margin is more than 100% ?

Thanks!

Answer 1

The "margin" is a portion of the selling price. It is defined as

$$\text {margin} \equiv \frac {P-C}{P}$$

From the above definition, we see that the margin cannot exceed $100\%$.

If one has the cost and he wants to calculate the price in order to have a specific margin, one must calculate

$$P(\text {margin}^*) = \frac {C}{1-\text {margin}^*}$$

The first formula written in the question is wrong, because it uses "margin", but it would become correct if instead one used the concept of "markup".

The "markup" is defined as the percentage increase of cost in order to determine the selling price:

$$\text {markup} \equiv \frac {P-C}{C}$$

It is easy to obtain that the relation between them is

$$\text {margin} = \frac {\text {markup}}{1+\text {markup}}$$