# Formula to calculate final profit

I'm using SmugMug to host and sell my photography images, and I'm looking to set my prices. I can't seem to figure out a formula to simply calculate my final profit after all deductions.

Example:

The printing company charges $\$0.25$for a$4\times 6$image. I want to make a$\$5$ profit off of the images but the hosting site charges $15\%$ of my profit for their expenses.

If I charge $\$5.25$for a print, my final profit will be$\$4.85$
$((\$5.25 - \$0.25)-15\%)$ $=$ $\$4.85$If I charge$\$5.40$ for a print, my final profit will be $\$5$(which is what I want).$((\$5.40 - \$0.25)-15\%)=\$5.00$

What would the formula look like to set my prices in such a way that I will always make a $\$5$profit off of an image? - I'm a bit confused by your question - do you mean 15% or 15 cents? Since in the first case, where you charge$\$5.25$, your initial profit is $\$5.25 - \$0.25 = \$5.00$, and it seems like they take \$0.15. 15% of \$5.00 would be \$0.75, so your final profit in that case would be \$4.25 – Gautam Kamath Jul 20 '11 at 3:02 They take 15% of the profit. ^^ did I screw that up? – Chase Florell Jul 20 '11 at 3:10 Say I go to the store, and there's a sweater that's usually \$50, but it's 25% off. You wouldn't just do \$50 - 25%, since that would be \$49.75. Like mixedmath said, you'd subtract 25%*\$50, making the final price \$50 - (25%*\$50) = \$37.50 –  Gautam Kamath Jul 20 '11 at 3:31

I'm going to assume that they deduct some percentage of your profit, rather than a fixed amount, since that's more intuitive.

Suppose you pay $x$ dollars for a print. The hosting site takes a fraction $p$ of your profit. You want to make $y$ dollars per sale. The price that you sell the image for is $z$ dollars.

We then have the following relationships. Your initial profit is given by $z - x$. The hosting site takes the fraction $p$ away from this profit, so you're left with the fraction $(1-p)$. This means the profit you're left with, after Smugmug's deduction is $(1-p)*(z-x)$. You want this to be equal to $d$, so $d = (1-p)(z-x)$. Since what we really care about here is $z$, the price that you sell for, we can rearrange, and get $z = \frac{d}{1-p} + x$.

Just to make it clear, let's substitute some numbers in, like the example you gave above. You want to make $\$5.00$, so$d = 5$. They take 15%, so$p = 0.15$. Finally, it costs you 25 cents for a print, so$x = 0.25$. If we substitute this in, we get$z = \frac{5}{0.85} + 0.25 = \$6.13$.

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This makes sense, thank you. –  Chase Florell Jul 20 '11 at 3:54

The formula looks like this.

If you charge C amount, the printing company will always take \$0.25 away. So gross profit is$P = C - 0.25$. You get a final profit of$P - 0.15 P = 0.85 P$, as 15% is taken away from you by the host. So you want$0.85P = \$5.00$. Solving this yields $P = \$5.89$. And so you need to charge$\$6.14$.

Let's check. $6.14 - 0.25 = 5.89$. That's good. $0.85 \cdot 5.89 = 5.0065$. Great.

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