# Break-even Analysis

Definition

Break-even analysis is a managerial accounting technique that helps to estimate the relationship between sales volume and production costs. It helps to determine how the change in sales will affect the operating profit of a business. The key performance indicator is a break-even point (BEP) that represents such production and sales volume in which revenues of a business are equal to the sum of total variable cost and total fixed cost. At that point, the total contribution margin is also equal to total fixed costs, and the operating profit of a business equals zero.

Assumptions

Break-even analysis implies the following assumptions:

1. The selling price of a unit, the variable cost per unit, and the fixed cost do not change within a relevant time period.
2. All costs can be classified into two categories: fixed and variable.
3. All units produced within a relevant time period are sold, which means that inventories at the beginning of the period are equal to inventories at the end of the period.

Break-Even Point Calculation

BEP can be calculated both “in units” and “in dollars”:

where FC represents fixed costs, P is the selling price of a unit, and VC is the variable cost per unit

where S is total sales, and TVC is total variable costs.

Graphically, the BEP lies at the intersection of the total cost (TC=TVC+TC) curve and the total sales (S) curve.

Sales Mix Break-Even Point

If a company sells two or more products, the proportion of each product in sales must be fixed within a relevant time period. So, the break-even point for each product can be calculated as follows:

where wi is a proportion of a relevant product in total sales, Pi is the selling price per unit of a relevant product, and VCi is the variable cost per unit of a relevant product.

Example 1: Single Product

Company A sells 12,000 units of a single product at \$100 per unit, the variable cost is \$70 per unit, and the total fixed cost is \$270,000. Substituting these values into the formula of “BE in units,” we get 9,000 units:

In turn, “BE in dollars” is \$900,000:

Example 2: Several products

Company B sells three products: X, Y, and Z. Detailed information about the sales mix is presented in the table below.

The break-even point “in units” of Product X will be 18,750 units, Product Y 9,000 units, and Product Z 5,000 units:

The break-even point “in dollars” of Product X will be \$468,750 (18,750×\$25), Product Y \$153,000 (9,000×\$17), and Product Z \$95,000 (5,000×\$19).

Example 3: Break-Even Analysis

Let’s assume that Company XYZ produces only one product and sells it at \$25 per unit, the variable cost per unit is \$15, and the total fixed costs are \$50,000. So, the break-even point will be 5,000 units:

Break-even analysis is based on two alternative scenarios. Under Scenario A, the selling price rises to \$28 per unit, and Scenario B assumes that the selling price drops to \$22 per unit:

If the selling price rises to \$28, Company XYZ needs to produce and sell 3,846 units to cover both total variable costs and fixed costs. In case of a decline in the selling price to \$22, it is necessary to produce and sell 7,143 units to cover total costs.