By Yuriy Smirnov Ph.D.

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:

- 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.
- Determine the relationship between costs and production volume to forecast profit accurately at various levels of operations.
- Define cost structure (the proportion of fixed costs and variable costs at various levels of operations), which is useful in formulating pricing policy.
- Estimate costs at various levels of operation to prepare a flexible budget.

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!

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