In this article, we’ll explore the formula for Break Even point, including what it is and how it works. Let’s get into it.
What is the Formula for Break Even Point?
There are actually 2 main types of Break Even formulas, and we’ll cover both, starting with the more popular and most commonly used one in CVP Analysis – Break Even units.
By the way, if you’re wondering what “CVP Analysis” is, it’s Cost Volume Profit Analysis.
That’s a tad bit outside the scope of this article, but at this stage, it’ll suffice if you know that break even analysis falls under CVP Analysis.
Formula for Break Even Point (Number of Units)
The Break Even formula (for the number of units) is equal to Fixed Costs (“FC”) divided by Contribution:
![\[BEP = \frac{FC}{Contribution}\]](https://www.ferventlearning.com/wp-content/ql-cache/quicklatex.com-b7377af927ce1e6389599fd41bf30ebe_l3.svg?495a33&495a33 "Rendered by QuickLaTeX.com")
This particular Break Even point formula gives you the number of units that you’d need to sell in order to break even.
Here, 
represents the Break Even Point, 
reflects Fixed Costs (aka Total Fixed Cost), and 
just refers to Contribution; we’ll explore what it is in just a bit.
Fixed Costs or are, as the name suggests, costs that are fixed. These costs do not change with outputs. If a company’s fixed costs are, say, $1,000,000 then it’ll incur that full cost regardless of whether it produces 1 unit or 1,000,000 units.
Examples of fixed costs include rent, rates, depreciation, salaries, etc.
Contribution () is the difference between the Selling Price (
) and the Variable Cost (
) per unit. In other words, 
.
It’s kinda like Gross Profit in the Profit and Loss / Income Statement, but strictly speaking, it’s not the same thing.
Example of Contribution: suppose the Selling Price of an item is $10, and the Variable Cost for the same item is $4. The Contribution will then be 
We’ll touch on the individual parts, and further down.
Alternative Expression for Break Even Units
The formula for Break Even point (in terms of the number of units) can also be written in a slightly different way, like this:
![\[BEP = \frac{FC}{SP - VC}\]](https://www.ferventlearning.com/wp-content/ql-cache/quicklatex.com-9737c462a5df093940314daa0456b241_l3.svg?495a33&495a33 "Rendered by QuickLaTeX.com")
Here and continue to denote the Break Even Point and Fixed Costs (or Total Fixed Cost) respectively. And the new terms and reflect the Selling Price and the Variable Cost per unit.
Selling Price or refers to the price at which you would sell the product to your customer.
Variable Cost or typically reflects costs directly involved in creating the product. It’s a little bit more tricky than that in reality, but this simplified explanation should do for now.
The main thing you want to take away right now is that both the Selling Price and Variable Cost are stated on a per-unit basis. The Fixed Costs, on the other hand, apply across all units.
There is an alternative formula for Break Even, which gives you the total revenue needed in order to break even. This is sometimes referred to as the “breakeven revenue”. Let’s now take a look at this alternative formula.
Formula for Break Even Point (Revenue Required)
The Break Even formula (for revenue) is equal to Fixed Costs (“FC”) divided by Contribution Margin (or “CM”):
![\[BER = \frac{FC}{CM}\]](https://www.ferventlearning.com/wp-content/ql-cache/quicklatex.com-042e9aae1e42afa28655c67e90dc3236_l3.svg?495a33&495a33 "Rendered by QuickLaTeX.com")
Here, 
reflects the Break Even Revenue and represents Fixed Costs.
The new term 
denotes Contribution Margin, which is calculated as follows…
![\[CM = \frac{SP - VC}{SP}\]](https://www.ferventlearning.com/wp-content/ql-cache/quicklatex.com-3057e6fe2b659077f04ebaa9f907c09f_l3.svg?495a33&495a33 "Rendered by QuickLaTeX.com")
The Contribution Margin is just the Contribution, expressed as a percentage of the Selling Price.
So really, we could write out the Break Even formula (for revenue) like this…
![\[BER = \frac{FC}{\frac{SP - VC}{SP}}\]](https://www.ferventlearning.com/wp-content/ql-cache/quicklatex.com-d375a453c2c3b95aa37c71020c192793_l3.svg?495a33&495a33 "Rendered by QuickLaTeX.com")
And this itself can be rewritten like so…
![\[BER = \frac{FC \times SP}{SP - VC}\]](https://www.ferventlearning.com/wp-content/ql-cache/quicklatex.com-9bf19437f5a87449f0a1f90a0e1f2b7f_l3.svg?495a33&495a33 "Rendered by QuickLaTeX.com")
Now, since we know that 
is in fact the Contribution, we can rewrite this equation like so…
![\[BER = \frac{FC \times SP}{Contribution}\]](https://www.ferventlearning.com/wp-content/ql-cache/quicklatex.com-fde69218dce16dd13b1003d16498fdc7_l3.svg?495a33&495a33 "Rendered by QuickLaTeX.com")
Okay, now that you know the formula for Break Even in is two forms – units and revenue – let’s apply these equations in examples.
Examples of Break Even Point
Question #1
Rode Island Inc. is exploring the possibility of launching a new product, “Pro Master” that they expect to sell for $19.99 a piece. The accountants estimate the product’s variable costs to be equal to $5.55 per unit. They also confirmed that the company’s annual fixed costs are $350,000.
Assuming this is the only product they will sell, approximately how many units of the Pro Master will Rode Island Inc. need to sell in order to break even?
Please round up your answer to the nearest whole number.
Try solving this on your own before exploring the solution!
Solution
Rode Island Inc. will need to sell approximately 24,239 Pro Masters in order to break even.
How did we get this?
Well, we know that the formula for Break Even point (in terms of the number of units) is the following…
And we know that . In this example, the selling price is $19.99 and the variable cost per unit is $5.55. Thus, the Contribution must be equal to 
We’re told that the Fixed Costs are equal to $350,000 so all we need to do now is plug in our numbers!
![\[BEP = \frac{\$350,000}{\$14.44} \approx 24,238.23\]](https://www.ferventlearning.com/wp-content/ql-cache/quicklatex.com-67b79296726739ba30c92c4feea5bcfe_l3.svg?495a33&495a33 "Rendered by QuickLaTeX.com")
If we round off the answer to the nearest whole number, we have 24,238. But strictly speaking, Rode Island Inc would not break even if they sold 24,238 units. They’d still be at a loss! And since we’d rather be in profit than in loss, we round up to the nearest whole number, taking us to 24,239
Let’s now take a look at another example.
Question #2
Let’s continue working with Rode Island Inc. How much revenue will the company need to earn in order to break even? Here’s the information about the scenario again:
Rode Island Inc. is exploring the possibility of launching a new product, “Pro Master” that they expect to sell for $19.99 apiece. The accountants estimate the product’s variable costs to be equal to $5.55 per unit. They also confirmed that the company’s annual fixed costs are $350,000.
As before, please round up your answer to the nearest whole number.
Can you try solving it on your own? Go on, give it a shot!
Solution
The Break Even revenue is approximately equal to $484,523
How did we get that?
Well, we know that the formula for Break Even point (in revenue terms) is the following…
Plugging in our numbers, we have…
![\[BER = \frac{\$350,000 \times \$19.99}{\$14.44} \approx \$484,522.16\]](https://www.ferventlearning.com/wp-content/ql-cache/quicklatex.com-2a99f5d8c1d2c6b6da9483899994199c_l3.svg?495a33&495a33 "Rendered by QuickLaTeX.com")
Alternatively, we could use the other expression for the equation, like so…
And we can calculate the Contribution Margin as…
This will give us…
![\[CM = \frac{\$19.99 - \$5.55}{\$19.99} = 0.7223611806\]](https://www.ferventlearning.com/wp-content/ql-cache/quicklatex.com-149e4cb3aea6ab321182a8ccf5506943_l3.svg?495a33&495a33 "Rendered by QuickLaTeX.com")
Plugging in the figures into the alternative formula for Break Even point (in revenue terms), we have…
![\[BER = \frac{\$350,000}{0.7223611806} \approx \$484,522.16\]](https://www.ferventlearning.com/wp-content/ql-cache/quicklatex.com-f8e4ddd87253254d23ae4b98148ff3be_l3.svg?495a33&495a33 "Rendered by QuickLaTeX.com")
And since as before, we’re rounding up and not rounding off, we have a final answer of $484,523
Nice and simple, isn’t it? 🙂
Hopefully, all of that makes sense, and you now know the formula for Break Even point inside out.
At the time of writing, we don’t have a course on Accounting explicitly, but we do have a variety of related finance and investing courses. The one that’s probably most relevant for you is our Investment Appraisal Mastery course, so do check it out.
Related Course: Investment Appraisal Mastery
Do you want to become a PRO at Investment Appraisal / Capital Budgeting?
Leave a Reply
You must be logged in to post a comment.