 # Break-Even Analysis By Yuriy Smirnov Ph.D.

## Definition

Break-even analysis is a technique widely used by management accountants to determine the sales volume, also known as the break-even point, that allows restoration of all the variable costs and fixed costs and earn zero profit. The break-even point can be defined both in units of production or dollar amount.

## Objectives

The objectives of break-even analysis are as follows:

1. The key objective of break-even analysis is to calculate the minimum sales level (called break-even point) sufficient to cover all fixed and variable costs.
2. Determine the relationship between costs and production volume to forecast profit accurately at various levels of operations.
3. Define cost structure (the proportion of fixed costs and variable costs at various levels of operations), which is useful in formulating pricing policy.
4. Estimate costs at various levels of operation to prepare a flexible budget.

## Break-Even Analysis Methods

### Equation Method

Break-even analysis can be performed using the equation method:

Sales = Fixed Cost + Variable Cost + Profit

It can also be written as:

n × Price per Unit = Fixed Cost + n × Variable Cost per Unit + Profit

where n is a number of units.

As far as profit sets equal zero, the break-even point (BEP) in units can be calculated using the following formula:

 BEP in Units = Fixed Costs Price per Unit - Variable Cost per Unit

The dollar amount of break-even sales volume can be computed by either multiplying the units break-even sales volume by price per unit or by using the formula below.

 BEP in Dollars = Fixed Costs × Sales Sales - Variable Cost

### Contribution Margin Method

The contribution margin method of break-even analysis is a modification of the equation method discussed above. The units break-even sales volume can be calculated as follows:

 BEP in Units = Fixed Costs Contribution Margin per Unit

where the contribution margin per unit is the difference between the price per unit and the variable cost per unit.

The break-even sales volume in dollars can be computed as follows:

 BEP in Dollars = Fixed Costs Contribution Margin Ratio

In turn, the contribution margin ratio can be calculated as follows:

 Contribution Margin Ratio = Sales - Variable Costs Sales

or

 Contribution Margin Ratio = Price per Unit - Variable Cost per Unit Price per Unit

### Graphical Method

The results of break-even analysis can also be presented graphically. The break-even point is at the intersection of the total cost line and the sales line. The projection of the break-even point on the X-axis is in units break-even sales volume and projection on the Y-axis is in dollars break-even sales volume.

## Calculation Examples

### Example 1 – Equation Method

Winsdor House LLC prepares financial statements on a quarterly basis. The quarterly amount of fixed cost is expected to be \$500,000, the price per unit \$120, and the variable cost per unit \$70. Company management expects to sell 12,000 units during the relevant quarter.

 BEP in Units = \$500,000 = 10,000 Units \$120 - \$70
 BEP in Dollars = \$500,000 × [12,000 × \$120] = \$1,200,000 12,000 × \$120 - 12,000 × \$70

### Example 2 – Contribution Margin Method

Let’s perform break-even analysis under the contribution margin method using the data from the example above. The contribution margin per unit of \$50 is the difference between the sales price of \$120 and the variable cost per unit of \$70.

 BEP in Units = \$500,000 = 10,000 Units \$50

We should calculate the contribution margin ratio first to compute in dollars the break-even sales volume.

 Contribution Margin Ratio = 12,000 × \$120 - 12,000 × \$70 = 0.3 12,000 × \$120
 BEP in Dollars = \$500,000 = \$1,200,000 0.3

Please note that the results of break-even analysis are the same regardless of the method used!