Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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?

share|improve this question
1  
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

2 Answers 2

up vote 2 down vote accepted

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 $z = \frac{5}{0.85} + 0.25 = \$6.13$.

share|improve this answer
    
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.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.