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