Quick Profit Margin, Multiplier, Currency Conversion Calculator
This is a quick calculator for determining markup multipliers based on desired profit margins and current exchange rates.
| Quick Calc: | |||
| $ | % | ||
| Stash | |||
What is the difference between Profit Margin and Markup?
Too often, the terms Profit Margin and Markup are confused. For instance, if you ask someone what the selling price of an item that costs $100 would be if you set your profit margin at 50%, the odds are (too) good that they will reply $150. This is incorrect. And here is why.
Profit Margin refers to the percentage of the selling price that is profit. So in the example above, an item that costs $100 and sells for $150 has a profit margin of 33.333% (rounded to the nearest hundredth of a percent). That is because 2/3 of the price is cost while only 1/3 is profit. (By the way, for a 50% profit margin you would sell the item at $200, or 2 times the cost, commonly referred to as "keystone". - See the next section.)
Markup refers to the amount you add to cost to get the selling price (sometimes referred to as "cost plus"). As we have already seen, the markup for a 50% Profit Margin is 100%. There are several ways of adding markup to the item cost. Some sellers prefer to use Markup rather than Profit Margin to determine the price of everything. In other words, they will take the cost and add some set percentage to determine the price. In some industries the standard Markup is keystone, or cost + 100%, while in others it is double keystone (cost + 200%) or even triple keystone (cost + 300%). Others prefer to set a Profit Margin to operate on and use that to determine Markup.
How do we tie Markup to Profit Margin?
In order to tie Markup and Profit Margin together (as in to determine one given the other) we need to understand the relationship between the two. In order to make this simpler we will convert all percentages to decimal numbers. (You remember from grade-school math that 40% is the same as 40/100 which is .4, right?)
Determine Selling Price and Profit Margin from Markup
For this section we will start with a 75% Markup.
Determining Selling Price from Markup is simple. A 75% Markup is equal to cost * .75. So you end up with:
cost + (cost * .75) =
(1 * cost) + (cost * .75) =
cost * 1.75
Cost multiplier is simply 1 + markup (as a decimal).
Selling price is cost * multiplier.
Determining Profit Margin from Markup is a bit different. We need to determine the percentage of the selling price that is profit. In order to do that we need to first determine the percentage of the selling price that is cost. We can do this without even knowing the cost (because regardless of cost the amount we are marking up is the same.) We do this by dividing 1 by the Markup. (If you are uncertain about this, think about this, 1 is 25% of 4, which can be expressed by any of the following identical numbers: 25% = .25 = 1/4) So, for a markup of 1.75 we get:
cost percentage = 1/1.75 = 0.57142857 = 57.143%
margin = 100% - 57.143% [cost percentage] = 42.857%
Or in a more compact form: margin = 1 - (1/1.75)
which gives us 0.42857143 or 42.857%.
Cost percentage of selling price is simply 1/multiplier.
Profit Margin is 1 - cost percentage.
margin = 1 - (1/multiplier)
Determine Markup and Selling Price from Profit Margin
For this section we will start with a 40% Profit Margin
For a Profit Margin of 40% (.4) we need to know that 40% (.4) of the selling price is profit. This means that the other 60% (.6) is cost percentage.
To determine a selling price directly from Profit Margin we would simply do cost/(1 - margin), or in this case, cost/ (1 - .4) = cost/.6 This is not always desirable, however, as multipliers are often easier to work with. So how do we turn cost/(1 - margin) into a multiplier?
The quick and easy way to do this is to remember that X/Y = X * (1/Y) (proof? 4/2 = 4 * (1/2)). So our Markup percentage is simply 1/(1 - margin), or in this case .667. And remember from the section on Markup that to determine a multiplier from markup we simply need to add 1
Cost percentage is 1 - profit margin.
Cost multiplier is 1/(1 - profit margin).
Selling price is cost * multiplier.
multiplier = 1 + (1/(1 - margin))
How are the numbers for this calculator determined?
This calculator adds in another layer of complexity, that of currency value vs the dollar. By dividing the results from the formulae above by the currency value versus the dollar we can determine Markup multipliers for a given currency value and profit margin, or profit margins for a given currency value and markup multiplier, or even currency values for a given profit margin and markup multiplier.
The actual formulae used in the script are:
mv = (1/((100 - pm)/100))/cv
cv = (1/((100 - pm)/100))/mv
pm = 100 - (1/(cv*mv))*100
Note that Profit Margin values are passed in and returned like 40 rather .4 so the multiplication and division by 100 in the actual formulae are tied to that. Here are the same formulae in their simplest forms, where m = markup multiplier, c = currency value and p = profit margin, all expressed as decimal numbers.
m = [ 1 / ( 1 - p ) ] / c
c = [ 1 / ( 1 - p ) ] / m
p = 1 - [ 1 / ( c * m ) ]