# B Gross Profit Margin

#### Puzzled

Hello,

I have recently been given a job in Sales, and I really enjoy it. Math has never been a strong point and I struggle with percentages.

I had an embarrassing experience the other day, where my manager jokingly asked me in front of everyone ‘If our product cost $100 and we want to make 50% Gross profit margin, what the selling price?’ I said ‘$150’ but I am told the answer is $200. I have found online that the calculation is:$100 / 0.5 = $200 I seem to be using a mark-up calculation.$100 x 1.5 = $150 Is there any easy way to calculate margin in your head? Why there is a difference, and businesses don’t just use mark up? Thanks everyone. #### mfb Mentor It depends what the 50% refer to. In your case the profit is 50% of the cost for the company, in the other case the profit is 50% of the (larger) selling price. If the profit is 50% of the selling price then the production cost are 100%-50% = 50% or 0.5 of the final price: cost = 0.5 * price, or price = cost/0.5. For 50% this is easy, just multiply by 2. For other numbers it can be more difficult to calculate it. #### PeroK Science Advisor Homework Helper Gold Member 2018 Award Hello, I have recently been given a job in Sales, and I really enjoy it. Math has never been a strong point and I struggle with percentages. I had an embarrassing experience the other day, where my manager jokingly asked me in front of everyone ‘If our product cost$100 and we want to make 50% Gross profit margin, what the selling price?’ I said ‘$150’ but I am told the answer is$200.

I have found online that the calculation is:

$100 / 0.5 =$200

I seem to be using a mark-up calculation.

$100 x 1.5 =$150

Why there is a difference, and businesses don’t just use mark up?

Thanks everyone.
This is a convention of accountancy. "Gross profit margin" could mean any number of things, but it will have a specific definition that you have to know.

The logical way to look at it is that if you sold your product for $150 and the question is "how much of that is gross profit margin?", then the answer is$50, which is 33.3%.

#### CWatters

Homework Helper
Gold Member
While we are on the subject of percentages here is a neat trick that popped up in my news feed this week...

If you need to calculate say 4% of 25 that's hard to do in your head, however it's the same as 25% of 4 and that's much easier. It works because...

(A/100) * B = (B/100) * A

#### Tom.G

Here is the procedure. It's little complicated to remember, and sometimes hard to do in your head:

Let's say you want 80% profit margin on a product that has $30 cost 100% - {desired profit margin%} == 100 - 80 = 20% convert to decimal 20% = 0.2 divide your cost by that 0.2 == 30/0.2 = 150 selling price If you are moderately comfortable with math, it is sometimes easier to multiply in the last step above: In the above example you could take the reciprocal of the 0.2 (1/0.2 = 5) and multiply that by your cost. For handy use, jot this down and keep it with your calculator. Cheers, Tom #### PeroK Science Advisor Homework Helper Gold Member 2018 Award Here is the procedure. It's little complicated to remember, and sometimes hard to do in your head: Let's say you want 80% profit margin on a product that has$30 cost
100% - {desired profit margin%} == 100 - 80 = 20%
convert to decimal 20% = 0.2
divide
your cost by that 0.2 == 30/0.2 = 150 selling price

If you are moderately comfortable with math, it is sometimes easier to multiply in the last step above:
In the above example you could take the reciprocal of the 0.2 (1/0.2 = 5) and multiply that by your cost.

For handy use, jot this down and keep it with your calculator.

Cheers,
Tom
It's not that complicated.

If you want 80% margin, then the cost of your product is 20% of your selling price. Hence selling price is 5 x £30.

In general: $p = \frac{100}{100-m}c$, where $p, m, c$ are price, margin and cost.

#### Chestermiller

Mentor
Here is what Google says: Gross profit margin is calculated by subtracting cost of goods sold (COGS) from total revenue and dividing that number by total revenue. The top number in the equation, known as gross profit or gross margin, is the total revenue minus the direct costs of producing that good or service.

#### PeroK

Homework Helper
Gold Member
2018 Award
Here is what Google says: Gross profit margin is calculated by subtracting cost of goods sold (COGS) from total revenue and dividing that number by total revenue. The top number in the equation, known as gross profit or gross margin, is the total revenue minus the direct costs of producing that good or service.
And if there is one thing that Google knows about it's gross profit margin!

#### neilparker62

Homework Helper
I would go along with the OP's common sense approach. If I buy goods for R100 and want to make 50% profit on that, then i sell at R150. Quite frankly the whole concept of "gross profit margin" smacks to me of corporates wanting to pretend they've made less percent profit than they actually have. Here for example they would say they've only made a modest 50/150 = 33.3% profit. Garbage which quite frankly makes neither mathematical nor "common" sense!

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#### Chestermiller

Mentor
I would go along with the OP's common sense approach. If I buy goods for R100 and want to make 50% profit on that, then i sell at R150. Quite frankly the whole concept of "gross profit margin" smacks to me of corporates wanting to pretend they've made less percent profit than they actually have. Here for example they would say they've only made a modest 50/150 = 33.3% profit. Garbage which quite frankly makes neither mathematical nor "common" sense!
Sounds like you're espousing a typical liberal conspiracy theory. Why don't you keep your socialist politics out of Physics Forums.

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#### neilparker62

Homework Helper
Sorry to disappoint but just a Maths tutor used to teaching:

$$Percent\,\, increase = \frac{amount\,\, of\,\, increase}{starting\,\, amount}\times 100$$

#### jbriggs444

Sorry to disappoint but just a Maths tutor used to teaching:

$$Percent\,\, increase = \frac{amount\,\, of\,\, increase}{starting\,\, amount}\times 100$$
We can compare and contrast the meanings of "percent increase" and "gross profit margin" without engaging in a debate about which term impugns our moral integrity.

#### Chestermiller

Mentor
Sorry to disappoint but just a Maths tutor used to teaching:

$$Percent\,\, increase = \frac{amount\,\, of\,\, increase}{starting\,\, amount}\times 100$$
In other words, you don't know what you are talking about when you try to accuse corporations of trying to minimize their reported profits for some sinister motive. Do you really think that the manner in which profits are reported would affect in any way the corporate taxes they owe? And, how do you think their shareholders would respond to a report of lower corporate earnings?

#### neilparker62

Homework Helper
I'll go with #12 on this one. At first glance it did not make any mathematical sense to me to alter a perfectly good school level formula for percent increase or percent profit by rather making the denominator of the fraction the increased value. Increase over "already increased" value?? That said I should not ascribe ulterior motives to those who decide to do things that way for whatever reason. Wikipedia indicated so they could measure what percent of sales value the profit is which seems reasonable enough.

#### Tom.G

165 000 000 hits from: https://www.google.com/search?&q=profit+margin
Here is a typical one.

Quoting from: https://www.investopedia.com/terms/p/profitmargin.asp

Profit margin is one of the commonly used profitability ratios to gauge profitability of a business activity. It represents how much percentage of sales has turned into profits. Simply put, the percentage figure indicates how many cents of profit the business has generated for each dollar of sale. For instance, if a business reports that it achieved 35 percent profit margin during the last quarter, it means that it had a net income of \$0.35 for each dollar of sales generated.

A basic course taken in business accounting would have made that clear.

#### StoneTemplePython

Gold Member
I'll go with #12 on this one. At first glance it did not make any mathematical sense to me to alter a perfectly good school level formula for percent increase or percent profit by rather making the denominator of the fraction the increased value. Increase over "already increased" value?? That said I should not ascribe ulterior motives to those who decide to do things that way for whatever reason. Wikipedia indicated so they could measure what percent of sales value the profit is which seems reasonable enough.
To extend what @TomG said a bit:

I'll add that the standard for all of these margins is against sales (sometimes, confusingly, there is a gross vs net sales adjustment issues) -- this includes things like Net Income Margin, EBIT Margin, EBITDA Margin, and so on. Your original suggested approach would not have a common ruler (i.e. denominator amount) for these various margins -- on the other hand common sizing as a percent of sales is homogenous. This is extremely basic financial accounting and reporting statement stuff.

N.B. I have seen language abused and "Gross Profit Margin" or "Gross Margin" referred to mean Gross Profit (i.e. a raw dollar amount). It's unfortunate but these things do happen.

"Gross Profit Margin"

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