# Break-even Point Contribution Margin Approach

The contribution margin approach to calculate the break-even point (i.e. the point of zero profit or loss) is based on the CVP analysis concepts known as contribution margin and contribution margin ratio. Contribution margin is the difference between sales and variable costs. When calculated for a single unit, it is called unit contribution margin. Contribution margin ratio is the ratio of contribution margin to sales.

In this method simple formulas are derived from the CVP analysis equation by rearranging the equation and then replacing certain parts with Contribution Margin formulas.

## Contribution Approach Formulas

### BEP in Sales Units

We learned that, at break-even point, the CVP analysis equation is reduced to:

 px = vx + FC

Where p is the price per unit, x is the number of units, v is variable cost per unit and FC is total fixed cost.

Solving the above equation for x (i.e. Break-even sales units ):

 Break-even Sales Units = x = FC ÷ ( p − v )

Since unit contribution margin (Unit CM) is equal to unit sale price (p) less unit variable cost (v), So,

 Unit CM = p − v

Therefore,

 Break-even Sales Units = x = FC ÷ Unit CM

### BEP in Sales Dollars

Break-even point in dollars can be calculated via:

 Break-even Sales Dollars = Price per Unit × Break-even Sales Units ; or
 Break-even Sales Dollars = FC ÷ CM Ratio

## Example

Calculate the break-even point in units and in sales dollars when sales price per unit is \$35, variable cost per unit is \$28 and total fixed cost is \$7,000.

### Solution

Contribution Margin per Unit = ( \$35 − \$28 ) = \$7
Contribution Margin Ratio = \$7 ÷ \$35 = 20%
Break-even Point in Units = \$7,000 ÷ \$7 = 1,000
Break-even Point in Sales Dollars = 1,000 × \$35 or \$7,000 ÷ 20% = \$35,000