I am trying to figure out how to get the breakeven price of a product where there is a fee charged based on the selling price of the item.
I know how to get the breakeven price if the fee is a fixed percentage:
(cost) x 100 / (100-(fee percentage + desired margin))
Example:
Cost $10
Desired Margin: %5
Fixed Fee: %15
$10 \times 100 / (100-(15 + 5)) = $12.5$
The issue I am having is that the fee is based on the final price of the product, for example if the product is under 15, the fee is 8%. If the products final price is over 15 the fee is 15%.
Is there a way I could calculate the final price of the product with a desired margin if the fee is not fixed?
Best Answer
I don't know anything about the topic, but if the provided formula is correct and we need to find out the price, using an uknown fee, then the equation should look like this:
$$p=\frac{100c}{100-f(p)-m}$$
Where $p$ is the price, $c$ the cost, $f(p)$ a variable fee, which is a function depending on price, and finally $m$ is the margin.
In your example we have:
$$f(p)=\begin{cases} 8, p<15 \\ 15, p \geq 15 \end{cases}$$
Solving the equation is a little bit tricky in this case, but possible.
The easiest way is simply to substitute whatever fee into the right hand side and see if the condition is fulfilled.
In this case setting $f=15$ gives $p=12.5<15$, while $f=8$ gives $p\approx 11.5$, which satisfies the condition, and so is the correct answer.