# How to derive a simple profit equation. Kinda embarrassing.

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1. Nov 15, 2014

### AcousticBruce

I made this excel file that is basically a calculator. It needs to create a Total price after fees, profit and supplier cost. Most profit margin calculators have you add a percentage for profit... this is not what I want. I have a hard dollar amount.

You must know that the entire transaction includes supplier cost, profit and fee. The fee is charged from the total of the Transaction. I do not want to brute force until I find a total price that equals 5 bucks in profit.

For instance...

Supplier Cost : $50 Profit I want to make :$5
10% Transaction Fee : ?
Total to charge : Some unknown without brute force.

Currently you put the Supplier cost and a GUESS of the Total price. And keep adjusting while watching your profit until it gets to $5 bucks. So here is an example.... Enter Supplier cost..... ___$50___
Enter Profit to make.... ___$5____ With this info I need it to spit out the total to charge so that the money left in the account is enough to *pay supplier *Pay transaction fee *And exact profit of$5 is what is left.

In this case...
*Fee is: $6.11 *Total price is$61.11

Customer is charged 61.11 and we pay a transaction fee and a profit. It should zero out.

Does this make sense?

2. Nov 15, 2014

### SteamKing

Staff Emeritus
Have you tried algebra?

You know:

T = total price

X = transaction cost

F = transaction fee = 0.1 * X

F + X = T or 0.1 * X + X = T, which means

1.1 * X = T

X = T / 1.1

X = Cost + Profit = T / 1.1

So Profit = (Total Price / 1.1) - Cost

Something like this?

3. Nov 15, 2014

### AcousticBruce

The problem is we have 2 unknowns: Transaction fee and Total Price.

Fee can be derived from Total Price.
Total price can be derived from Fee + Cost + Profit

We only have Cost and Profit

Basically, I could write a brute force method in Java, but I just think there is some math I do not understand. Probably because there is 2 missing variables. Fee and Total.

Edit: I looked at your math and I am unsure it does what I am trying to do. Maybe I am missing something. Thank you.

4. Nov 15, 2014

### Mentallic

You have two variables, but you also have two equations that relate those variables.

S = supplier cost
P = profit to make
F = transaction fee
T = total price

So we have that

T = S+F+P

We know S and P, so they're constants, so we have two variables in that equation, T and F.
The other equation is:

0.1*T = F

So then if we plug 0.1*T for F into the first equation, then we get

T = S + 0.1*T + P

solving for T,

T - 0.1*T = S+P
(1-0.1)T = S+P
T = (S+P)/0.9

and then plugging this value for T back into the second equation, we get

0.1*(S+P)/0.9 = F

T = 10/9*(S+P)
F = 1/9*(S+P)

You can easily generalize this procedure so that you can use any % in your transaction fee that you wish.

5. Nov 15, 2014

### AcousticBruce

Wonderful! Thank you both for the time and effort not only does this work, but I understand it completely. I also added a way to change the percentage on the calculator. Wonderful!

6. Nov 15, 2014

### Mentallic

Well of course it works, it's Math ;)

That's good to hear!