## Understanding The Break Even Formula

Break Even Formula

Recall the formula to calculate a company's break-even point is;

Break Even in Units        =

Fixed Costs_______
Selling Price - Variable Costs

The difference between the selling price per unit and the variable costs per unit can be considered the profit made on each product sold. This profit made on each unit sold is better known as the product's Contribution Margin.

Selling Price Per Unit  - Variable Cost Per Unit = Contribution Margin

The Contribution Margin for The Cigar Company is simple to calculate;

 Selling price per box of cigars \$50.00 Variable costs per box of cigars \$20.00 Contribution margin on each box of cigars sold \$30.00

In essence, a contribution margin contributes to a company's fixed costs until the fixed costs are absorbed. Moreover, The Cigar Company's contribution margin of \$30, contributes to reducing the fixed costs until these fixed costs are absorbed (paid for). Recall the break-even point for The Cigar Company is 3000 boxes of cigars. Therefore, when 3000 boxes of cigars are sold, the fixed costs of \$90,000 will be paid. In addition, after 3000 units are sold, the company will recognize a full profit of \$30.00 on each additional box it sells. Therefore, if the company sells 5000 units (boxes of cigars), it would have a Net Income Before Taxes of \$60,000 (5,000 units sold - 3,000 unit to break-even point x \$30 profit from each unit = \$60,000).

Lets look at another quick example so that you fully understand the relationship among the components of the break-even formula. Assume, The XYZ Company sells one brand of business calculators. They purchase each calculator from a wholesaler for \$3.00 . The company estimates that each calculator costs \$1.00 to ship. They sell each calculator to customers for \$10.00 . In addition, The XYZ Company forecasts their fixed costs at \$30,000 for the up-coming year.

Based on the information presented above, we can create the following chart.

 Fixed Costs \$30,000 Per unit Selling Price \$10.00 Per unit Variable Costs \$ 4.00 Contribution Margin \$ 6.00

For each calculator sold, the XYZ Company profits \$6.00 (\$10.00 - \$4.00). The profit or contribution margin from each calculator of \$6.00 contributes to paying the company's fixed costs. How many units or calculators would the company have to sell in order to achieve a Net Income Before Taxes of ZERO? In other words, what is the company's break-even point in units?

The Break-even point for the XYZ Company is:

Break Even in Units      =

_____ Fixed Costs________
Selling Price - Variable Costs

___

\$30,000__

\$10.00 - \$ 4.00

\$30,000

\$6.00

=  5,000 calculators

Therefore, the XYZ Company would have to sell 5,000 calculators in order to cover all of the company's expected fixed costs for the year. Remember, if 5,000 calculators were sold, the XYZ Company would have a Net income of zero (\$0.00). To prove this, we can develop the following chart;

 Sales (5000 calculators sold at \$10.00 each) \$50,000 Less: Variable Costs or COGS ( 5000 calculators purchased at \$4.00 each) \$20,000 Contribution Margin (5000 Calculators x \$6.00) \$30,000 Less: Fixed Costs (Marketing & Administrative Expenses) \$30,000 Net Income Before Taxes \$ 0.00

What if the company sold 7,000 calculators during the business year? That is 2,000 calculators above the company's break-even point (7,000 - 5,000). The answer is simple; after 5,000 units have been sold, the company will profit the FULL contribution margin of \$6.00 on each additional product sold. Therefore, the company's net income before taxes would be \$12,000 (2000 calculators above the break-even point multiplied by the contribution margin of \$6.00 = \$12,000).

Categories: Financial