The Difference between Calculating Markup and Profit Margin

Date: 08/11/2006 at 19:01:33
From: Jerry
Subject: How does inverse calculations work with percentage markups

I have a question about how to calculate profit margin.  We have been
calculating this as fixed costs multiplied by whatever the margin
percentage is.  For example, with costs of $50,000 and a desired
margin of 25% we do $50,000 x 1.25 = $62,500, so we would sell the
product for $62,500.

But I am told that the correct way to calculate this is to take the
fixed costs and divide by the desired margin percentage subtracted
from 100%.  So that would be $50,000 / .75 = $66,667.  I am having 
some trouble understanding how this works.  Can you explain this is 
simple layman's terms?

Thank you for your help.

Jerry

Date: 08/11/2006 at 22:42:49
From: Doctor Peterson
Subject: Re: How does inverse calculations work with percentage markups

Hi, Jerry.

You have no idea how common this question is!  You can find some
discussions of this sort of question here (look near the bottom):

  Percentage Increase/Decrease 
   
http://mathforum.org/library/drmath/sets/select/dm_percent_increase.html 

Here's my version:

Profit margin means "what percentage OF THE PRICE is profit?"  That is
different from "what percentage OF COST is the profit?"--that's the
"markup".  When we mark up, we add some percentage of what it costs
us.  Margin is seen from the customer's perspective: how much of what
I'm paying is going into their pockets?

So you want to increase your fixed cost of $50,000 by some amount that
will be 25% of the amount you'll be charging--which you don't know
yet!  You can't just add on 25% of the fixed cost, because that's the
right percentage of the wrong thing.  (You're actually calculating a
25% markup rather than a 25% margin.)

So what can we do?  Well, we think backward.  Suppose we knew the 
price we're going to charge; I'll call it X.  Then the margin would be
25% of that, or 0.25 times X.  The cost would be that much less than X:

  cost = X - 0.25X

But 1 times X, minus 0.25 times X, is 0.75 times X.  That is, 100% -
25% is 75%.  So

  cost = 0.75X

But now we can find X, because we know the cost is $50,000!

  50,000 = 0.75X

  X = 50,000 / 0.75

That is, we undo the multiplication by 0.75, by dividing 50,000 by
0.75. So

  X = $66,666.67

Note that this is more than what you were calculating, because you
were adding 25% of a smaller number--here we're adding 25% of $66,667 
rather than only 25% of $50,000.  By charging only $62,500, you had a 
25% markup but only a 20% margin (12,500/62,500).

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


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