To start, the "Breakeven point” is the stage at which the income from sale of a product or service equals the invested costs of that product. In short, it is the stage at which income equals expenditure, resulting in neither profit nor loss (as shown on the picture above). Companies use this number to identify how many of their products they should sell in order to earn profit.

In this Instructable, to calculate the Breakeven point of a company, you are going to learn how to use the Breakeven Formula stated below:

(SPu - VCu)x - FC = 0

Note: Some people write "Break-even" and others "Breakeven." Both are correct. Choose the spelling you prefer.

Step 1: What You Need

Supplies:

A blank piece of paper
A pencil or pen at your preference
A simple calculator. If you do not have a calculator as the one on the picture, it is OK to use the calculator app on your smartphone
Finally, make sure that the following operation signs are visible and functional on your calculator:

(+) : addition
(-) : subtraction
(÷ or /) : division
(×) : multiplication
(= or Enter) : equality sign

Time: 20 - 30 minutes

Step 2: Read the Problem : Chad's Chocolates Company Example

For this Instructable, I am going to use the example of Chad's Chocolate company to illustrate the steps needed to find the Breakeven point in units.

Note: Each company has their own data, so the final result will be different from one to another. However, the steps remain the same.

Step 3: Organize the Information Given in the Problem

On the top of your piece of paper, draw three columns with the following titles : Sales price per unit , Variable cost per unit and Fixed cost; as shown on the picture above.

Sales price: this is the price that a single unit is sold for.
Variable costs: they are costs that vary depending on a company's production volume; they rise as production increases and fall as production decreases
Fixed costs: they are expenses that have to be paid by a company, independent of any business activity

Step 4: Fill Out the Previous Table

Next, looking back at the Chad's Chocolate company example (step two), fill out the table above by putting each dollar amount in their corresponding columns. And then calculate the total amount of each section.

Hint: Look for the sales price per unit in the first paragraph. However, the picture above is just an example, you do not have to find four different prices in each column. You can find only one price in one column and five in another. It depends on the information given in the problem.

Step 5: Set Up the Breakeven Formula

As stated in the introduction, to resolve this type of problem, out of many other methods, I am going to show you how to use the Breakeven Formula above where :

SPu = Sales price per unit

VCu = Variable cost per unit

x = number of units that needs to be sold to break even (this is the number you are trying to solve the equation for)

and, FC = Fixed costs

In fact, your goal is to be able to write x in terms of SPu, VCu and FC. To do so, you are going to use two rules of transformation, to transform the Breakeven Formula above. They are the Addition and the Division rules.

Write down the Breakeven Formula, exactly as shown on the picture, below the table on your piece of paper.

Step 6: Addition : Write SPu, VCu and X in Terms of FC

For this step, follow the example of the Addition rule illustrated in the picture above.

To solve, consider "(SPu - VCu)x" as Y, "FC" as a and 0 is b

From step five, you have:

(SPu - VCu)x - FC = 0, to move FC on the other side of the equation, you need to add FC on both sides.

Hint: -FC + FC = 0 because mathematically the sum of a number and its opposite always equals 0. FC here is treated as a number.

Step 7: Division : Write X in Terms of FC, SPu and VCu

After step six, you should have on your paper : (SPu - VCu)x = FC

Now, use the Division rule to perform the next transformation.

This time, consider "(SPu - VCu)" as d, x is the same in both the equation and the example, and FC is c.

To avoid confusion, do not try to link the letters in the Division rule example to the ones used in step six. This is a different transformation, and that is why I used different letters.

Using (SPu - VCu)x = FC, to solve for x, you need to divide each side of the equation by (SPu - VCu).

Hint: (SPu - VCu) / (SPu - VCu) = 1 because a number divided by itself always equals 1.

Step 8: Replace Each Variable by Its Corresponding Amount Into the Final Equation

After the transformations done in the two previous steps, you should have on your paper the equation shown on the picture above. This is the final equation.

Now, go back to step four, and plug in each total amount you found there in this final equation.

Final result : x = 15,000 boxes

Step 9: Write a Conclusion

As mentioned in the introduction, the Breakeven point is the number of units of a product that a company should sell to earn neither profit nor loss.

In the case of Chad's Chocolates company, from your calculations, you can conclude that to break even, they should sell 15,000 boxes of their special collection of chocolates.

Any sale above 15,000 boxes will be considered as profit, and any sale below will be a loss.