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

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

• @RScrlli I changed the tag. – saulspatz Oct 30 '19 at 16:03

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 $$S = \boxed{{C\over .8-P}}$$

• thank you @saulspatz – Albert H Nov 1 '19 at 0:03
• @AlbertH My pleasure. – saulspatz Nov 1 '19 at 0:35

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

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

• thank you @rscrlli – Albert H Nov 1 '19 at 0:03