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.
The objectives of break-even analysis are as follows:
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 |
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 |
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.
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 |
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!