Calculating Percentage Markup Versus Profit

Date: 01/23/2004 at 15:57:26
From: Lisa
Subject: Explanation of profit percentage

In order to figure a profit of 10% I would normally take the amount 
and then multiply by 1.1 to find the selling price.  For example, 800 
x 1.1 = 880 so I say we should charge $880 to make a 10% profit. 
However my employer tells me that in order to find a 10% profit I 
should divide by .9 to get 800/.9 = $888.89.  I do not understand how
this is 10%.  Can you please explain?  Thank you very much.

Date: 01/23/2004 at 23:34:22
From: Doctor Peterson
Subject: Re: Explanation of profit percentage

Hi, Lisa.

You and your employer are calculating two subtly different things: a 
markup versus a profit.

Your calculation is correct when you are given the cost and want to 
find a sale price that will give you a profit of 10% OF THE COST TO 
YOU.  If the cost to you is C and you sell it for 1.1C, your profit is 

  1.1C - C = 0.1C, or 10% of C.

which is 10% of what you paid for the item, or a 10% markup. 

But your employer is calculating the price that will give you a profit
of 10% OF THE SELLING PRICE.  If you sell the item for C/0.9, then 
your profit is

  C/0.9 - C = (C - 0.9C)/0.9 = 0.1 * C/0.9, or 10% of C/0.9.

which is 10% of the selling price, C/0.9.  What he is doing is solving 
the equation

  P - C = 0.1P

which says the profit (price minus cost) is 10% of the price, this 
way:

  P - 0.1P = C

  0.9P = C

  P = C/0.9

You method solves the equation

  P - C = 0.1C

Your employer's method is correct for what he is calling it, a 10% 
profit on the sale.  Your method is correct for a 10% markup over the 
cost.  It's all a matter of words.

You can see similar issues here:

  Duelling Percentages
    http://mathforum.org/library/drmath/view/60803.html 

  Markups and Discounts
    http://mathforum.org/library/drmath/view/58077.html 

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 01/24/2004 at 09:03:22
From: Lisa
Subject: Explanation of profit percentage

Thanks!  I can follow this now that I see the mathematical equations
written out.  This has been a great help.

I have another similar question for you, if I could, again involving
us buying and then selling an item, but now figuring tax in as well.

For example, the price we pay is $250.00 (tax not included).  We would
then figure in 7% tax (250 * 1.07 = 267.50) to find our total cost.  
We then proceed to figure out our selling price by calculating
267.50/0.9 = 297.22.  This selling price will give us 10% profit.

Other people believe that we should do it the following way.  Take 
250.00 (our cost)/0.93 = 268.82 (price with tax) and then calculate
268.82/0.9 = 298.69 for the selling price with 10% profit. 

I have always figured sales tax as a multiplication factor but then 
again I had never thought about the difference between a markup of 10% 
and a selling price with a 10% profit either, so I wanted to verify
that I truly am understanding everything correctly.  

Date: 01/25/2004 at 22:28:15
From: Doctor Peterson
Subject: Re: Explanation of profit percentage

Hi, Lisa.

There could be tax issues that are beyond my knowledge, but the math 
aspect seems straightforward.

You would divide by 0.93 if, as in the case of the profit, you wanted 
7% of the price you charge to go for tax.  But that isn't how tax 
works.  The tax part of the transaction, as I understand it, is simply 
your payment when you buy the item, based on the amount charged to 
you, so your calculation is clearly correct, and the fact that the 
other version gives a different answer shows that it is wrong.

You can always check something like this (assuming you have defined 
clearly what you want to do) by seeing how much the actual tax and 
profit are based on the number you calculate.  If you charge $297.22; 
10% of that is $29.72, which leaves $267.50.  That is $250 plus the 
7% tax.  The other number will not check out this way.

To put it simply, you multiply by 1.07 because the tax is calculated 
forward, from the cost to you; you divide by 0.9 because the profit 
is calculated backward, from the price to your customer.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 01/27/2004 at 14:31:12
From: Lisa
Subject: Thank you (Explanation of profit percentage)

Thank you so much for all your help.  All of this actually makes sense
to me now!  I appreciate it very much.