Calculate pre-royalty sell price based on Cost and target Gross Profit %

Question

I'm having trouble figuring out how to calculate a sell price based on an established cost and a target Gross profit % margin.

The complicating factor for me is that there's a royalty deducted from the gross sell price (to get to a net sell price). GP% is calculated as:

$$((\text{gross sell price}*(1-\text{royalty}\%))- \text{cost})/\text{gross sell price}$$

So for example: something costs me $\$5$, I sell it for $\$10$ gross. But there's a $20$% royalty I owe on the sell price, so my effective net sell price is $\$8$.

$\$8-\$5 = \$3$ profit. $3/$10 = 30%

NET sell price is used to calculate profit, not gross sell price.

Now, i want to work backwards without knowing the sell price. I know the cost ($\$5$) i know the margin i want to reach ($30$%), what equation gives me $\$10$?

Going backwards, we need the profit amount to calculate the net sell price, but since the royalty % (that gets us to net sell price) comes off the gross sell price (which is what we're trying to calculate in the first place) it's like a circular reference

Answer 1

Let $S$ be the sales price, $C$ the cost and $P$ the profit. We are given$$P={.8S-C\over S}=.8-{C\over S},$$ so that $$(P-.8)S=-C$$ Therefore $$S = \boxed{{C\over .8-P}}$$

Answer 2

Following your example I will assume that you don't actually know the gross sell price and I'll call it $X$ for the sake of simplicity.

Then your equation takes the form

$$\text{profit}=(X*(1-0,2)-5)$$ and you also know that

$$\frac{\text{profit}}{X}=0.3$$ $$\text{profit}=0.3 X$$

Putting all together $$ (X*(1-0,2)-5)=0.3X$$

$$(0.8-0.3)X=5$$ $$0.5X=5$$ $$X=10$$