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# Break-Even PointFormula and analysis

## Introduction

The determination of the break-even point is one of the applications of cost-volume-profit (CVP) analysis. In this lesson, you will learn how to calculate the break-even point and appreciate how it works.

In a Nutshell

Break-even point is the level of sales activity at which the business makes zero profit (no gain, no loss). The most common computations are:

For break-even point in number of units: total fixed costs divided by contribution margin per unit.

For break-even point in dollar amount: total fixed costs divided by contribution margin ratio.

Break-even point refers to the level of activity or sales that will yield to zero profit. In other words, it is the level at which the business makes no gain or loss.

If the business operates above the break-even point, it makes profits. If it sells below, then it incurs in losses.

The break-even point is the point where "Sales" is equal to "Total Costs".
(where: Total costs = Total variable costs + Total fixed costs)

The break-even point provides managers with information useful in profit-planning.

## Break-Even Point Formula

Break-even point (BEP) can be determined in terms of number of units or dollar amount. The formula for BEP in units is:

 BEP in Units = Total Fixed Costs CM per Unit

In computing for the BEP in dollars, contribution margin ratio is used instead of contribution margin per unit.

 BEP in Dollars = Total Fixed Costs CM Ratio

## Illustration

To illustrate the concepts of break-even point, consider the following example. The following data summarizes the operations of Company ABC.

 Per Unit Total Sales (5,000 units) \$15 \$75,000 Less: Variable Costs 5 25,000 Contribution Margin \$10 \$50,000 Less: Fixed Costs 20,000 Operating Income \$30,000
 BEP in Units = Total Fixed Costs = \$20,000 CM per Unit \$10 BEP in Units = 2,000 units

Analysis: At 2,000 units, the company will make zero operating income. If the company sells more than 2,000 units, it will make profit. Otherwise, it will incur in losses. To prove, consider the following scenarios.

At 2,000 units (break-even point)

 Per Unit Total Sales (2,000 units) \$15 \$30,000 Less: Variable Costs 5 10,000 Contribution Margin \$10 \$20,000 Less: Fixed Costs 20,000 Operating Income (Loss) \$        0

At 2,001 units (above break-even point)

 Per Unit Total Sales (2,001 units) \$15 \$30,015 Less: Variable Costs 5 10,005 Contribution Margin \$10 \$20,010 Less: Fixed Costs 20,000 Operating Income (Loss) \$      10

At 1,999 units (below break-even point)

 Per Unit Total Sales (1,999 units) \$15 \$29,985 Less: Variable Costs 5 9,995 Contribution Margin \$10 \$19,990 Less: Fixed Costs 20,000 Operating Income (Loss) (\$     10)

The BEP in dollars is \$30,000 as shown in the computation at 2,000 units. Alternatively, it can be computed as total fixed costs divided by contribution margin ratio. The contribution margin ratio is 66.67% (\$10/\$15). Hence, fixed costs of \$20,000 divided by CM ratio of 66.67% results in the BEP in dollars of \$30,000.

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