A break-even analysis consists of calculating how many units of a product you need to sell at a given price, to cover all your costs.

In other words, it tells you **how many units you need to sell to have a profit of zero (that is, to break even)**. If you sell one unit more, you start making a profit.

So, the first thing we must do in order to perform a break even analysis, is to make sure that we understand our cost structure.

Because our goal here, is to analyze how our costs and profits vary, depending on our production and sales volume.

That is, we need to perform what is usually referred to as a cost-volume-profit analysis (or CVP). And to do that, it’s obviously fundamental that first we understand how our costs change as our production volume changes.

**What is the break even point?** The break-even point (or BEP) is the sales volume at which you sell enough units of your product or service to cover all your costs. Above that sales volume you start making a profit.

Anyway, to illustrate all these concepts, let’s use the bakery example you may already be familiar with if you read the cost structure or contribution margin posts.

In this case, let’s imagine that we’re making birthday cakes, which we sell for $50 each.

Making each of those cakes has a total variable cost of $15 (that’s for ingredients, packaging, electricity to bake it, etc.). And, we have total fixed costs of $5,000 per month (that’s for salaries, rent, equipment depreciation, etc.).

As we've seen in the post about the cost structure, variable costs increase with each additional unit of product you manufacture, while fixed costs remain constant despite variations in production amount (within a relevant range of production, of course).

In the case of our example, whenever we make an additional cake, our variable costs increase by $15. If we bake 1 cake our total variable costs are $15, if we bake 2, our total variable costs are $30, if we bake 10, $150… and so on.

## How to calculate the break-even point using the break even chart

Variable costs can be represented graphically by an upward-sloped line. And we can calculate our total variable costs of producing birthday cakes (let’s say for a month), by multiplying the number of cakes we produce per month, by the $15 of variable cost per unit that we have with each of those cakes that we make.

Note that frequently as production volume increases, the variable cost per unit decreases. That’s because we start getting quantity discounts, or economies of scale. That’s not being considered here for simplicity reasons, but in real life you may want to (the upward-sloped line wouldn't be a straight one in that case).

When it comes to fixed costs, because they’re fixed, regardless of the number of cakes we produce, we’ll always have a cost per month of $5,000. So, they can be represented by a horizontal line.

To get to our total costs per month of producing birthday cakes, we need to add the total variable cost per month, and the total fixed cost per month.

Graphically, we would get a line with the same slope as the variable costs one, but instead of starting at a cost of 0, it starts at the level of fixed costs that we have. (Basically, the variable costs line shifts upwards, by the amount of fixed costs per month).

If you prefer to see it mathematically, we would add our total variable costs (that we’ve seen before), to the total fixed costs per month of $5,000.

And that’s it for the cost part. By now we know how costs change as our production volume changes.

So, if we want to calculate our break even point in units, that is, at what unit sales volume we break even (and above which we start making a profit), we need to calculate how our revenue increases with each sale. But that’s the easy one, right?

If we sell each birthday cake for $50, our revenue increases by $50 whenever we sell a cake.

If we represented our revenue graphically, we would get an upward-sloped line, similar to the variable costs one, but steeper. Since the price at which we sell each unit of our product is higher than what it costs us to make it, when we multiply it by the number of units sold, total revenue grows faster than total costs.

Note that there are couple of important simplifications here:

- One, is that our selling price remains constant regardless of how many units we sell.
- And the other, and the most important one, is that we’re assuming that we sell every unit we produce. If that’s not the case, to avoid this assumption, we would have to factor in the cost of the wasted resources in our total costs.

Anyway, moving on, since the total cost and total revenue lines have different slopes, if we represent them in the same graphic, they will intersect. After all, costs start at a higher level, but because revenues grow faster than costs, at some point total revenue will surpass total costs.

At that point at which total costs and total revenues are equal, is what we call break-even point. To the left of that point, our business is running at a loss. To the right of it, revenues are higher than costs, and you’re making a profit.

So, **at the breakeven point, your sales and your costs are the same**. And we know that:

## Calculating the break even point formula

Total sales = price per unit x number of units sold

Total cost = variable cost per unit x number of units sold + fixed costs

This means that our profit will be zero when both sides are equal.

Since we’re assuming that the number of cakes made and the number of cakes sold is the same, I’ll replace it for Q (to represent quantity, and make it shorter).

If we solve this equation, we get to the conclusion that we need to sell 143 cakes every month for $50 each, to break even. Above that, we start making a profit.

And this is one of the reasons why the cost-volume-profit analysis is such a great tool. Because while it may be very difficult to estimate how many units of a product you will sell, if you turn that question into “is it feasible to sell X units of my product at a price of Y?”, it becomes a lot easier to answer.

And if the answer to that is “no”, you have a problem. But at least you know it, and can take measures to solve it.

So one of the points of this analysis is to help us understanding whether it is realistic to expect to make a profit if we sell at a given price.

Anyway, we can write the above equations in a simplified way to get to the general break-even point formula:

**What is the break even point formula?**

P x Q | = | VCu x Q | + | FC |

In which:

P = unit sales price

Q = number of units sold

VCu = variable costs per unit

FC = total fixed costs

Or, if we solve for Q in case you want to calculate the break-even point in units:

Q | = | FC P - VCu |

It makes sense, right? The total number of units you would need to sell to cover all costs would be equal to the total fixed costs divided by the contribution margin you get from each unit you sell.

**Building cost-volume-profit scenarios**

Finally, keep in mind that we know that our profit is equal to total revenue minus total costs, which can be represented as selling price minus variable cost per unit (also known as contribution margin), times the number of units sold, minus total fixed costs.

Since we know our costs, we can use this simple equation to do a cost-volume-profit analysis, and build scenarios considering different target profits, sales prices, and sales volumes, and see how they affect each other.

And this is what’s great about a **break-even or**** a c****ost-volume-profit analysis,** and the reason I use it for anything I do.

It not only turns the difficult to answer “what is my expected sales volume?” into a much easier to answer “is it reasonable to achieve this particular sales volume?”, but also allows us to create different scenarios of expected prices, costs, and required unit sales to reach a target profit, that help us therefore understanding the impact of our possible decisions.

And that’s it for the break-even and cost-volume-profit analysis. I hope you found the post useful.

In my next post I’ll go over the impact of discounts on profit, particularly about how seemingly small discounts can get you in the red if you fail to make an important calculation I’ll explain. So, if you’re considering offering discounts or even cutting your prices, I would encourage you to watch that one.

Bye!