# Break-even Point Equation Method

Break-even is the point of zero loss or profit. At break-even point, the revenues of the business are equal its total costs and its contribution margin equals its total fixed costs. Break-even point can be calculated by equation method, contribution method or graphical method. The equation method is based on the cost-volume-profit (CVP) formula:

 px = vx + FC + Profit

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.

## Calculation

### BEP in Sales Units

At break-even point the profit is zero therefore the CVP formula is simplified to:

 px = vx + FC

Solving the above equation for x which equals break-even point in sales units, we get:

 Break-even Sales Units = x = FC p − v

### BEP in Sales Dollars

Break-even point in number of sales dollars is calculated using the following formula:

 Break-even Sales Dollars = Price per Unit × Break-even Sales Units

## Example

Calculate break-even point in sales units and sales dollars from following information:

 Price per Unit \$15 Variable Cost per Unit \$7 Total Fixed Cost \$9,000

### Solution

We have,
p = \$15
v = \$7, and
FC = \$9,000

Substituting the known values into the formula for breakeven point in sales units, we get:

Breakeven Point in Sales Units (x)
= 9,000 ÷ (15 − 7)
= 9,000 ÷ 8
= 1,125 units

Break-even Point in Sales Dollars
= \$15 × 1,125
= \$16,875