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# Break-even Point Analysis:

## Definition and Explanation:

Break-even point is the level of sales at which profit is zero. At break even point total sales are equal to total cost (variable + fixed).

If a firm cannot manage sales to cover variable as well as fixed costs it will have to bear losses. The following is the further explanation of this concept:

 Profit Sales > Variable Expenses + Fixed Expenses Break-even Point Sales = Variable Expenses + Fixed Expenses Loss Sales < Variable Expenses + Fixed Expenses

There are two methods for the calculation of break-even point. These are:

1. Equation method
2. Contribution margin method

## Equation Method:

We can use the following equation to calculate break-even point:

Profit = Sales - (Variable expenses + Fixed expenses)

or

Sales = Variable expenses + Fixed expenses + Profit

When break-even point is calculated using above equation profit is taken as zero because break-even is that level of sales where sales are equal to total cost (variable + fixed) and profit is zero.

### Example:

We can use the following data to calculate break-even point.

• Sales price per unit = \$500

• variable cost per unit = \$300

• Total fixed expenses = \$70,000

Required: Calculate break-even point using equation method.

Solution:

Sales = Variable expenses + Fixed expenses + Profit

\$500Q* = \$300Q* + \$70,000 + \$0**

\$200Q = \$70,000

Q = \$70,000/\$200

Q = 350 Units

Q* = Number (Quantity) of units sold.
**The break even point can be computed by finding that point where profit is zero

Graphical Representation (Break-even Chart - CVP Graph): The break even point in sales dollars can be computed by multiplying the break even level of unit sales by the selling price per unit.

350 Units × \$500 Per unit = \$175,000

## Contribution Margin Method:

Under this method total fixed cost is divided by unit contribution margin. The resulting figure is number of units to be sold to break-even (no profit, no loss).

### Example:

We can use the following data to calculate break-even point.

• Sales price per unit = \$500

• variable cost per unit = \$300

• Total fixed expenses = \$70,000

Required: Calculate break-even point using contribution margin method.

Solution:

Break-even point in units = Fixed expenses / Unit contribution margin

\$70,000 / \$200*

350 Units

*\$500 (Sales) − \$300 (Variable exp.)

Break even point in sales:

350 Units × \$500 Per unit

= \$175,000

Equation method and contribution margin methods are equivalent. Contribution margin method is actually a shortcut conversion of equation method.

The following formula is also extensively used to calculate break even point:

Break-even Sales in Dollars = [Fixed Cost / 1 – (Variable Cost / Sales)]

This formula produces the same answer:

Break Even Point = [\$70,000 / 1 – (300 / 500)]

= \$70,000 / 1 – 0.6

= \$70,000 / 0.4

= \$175,000

Number of units to be sold to break even:

\$175,000 / \$500

= 350 units

Following are some of the main advantages of break even analysis:

1. It explains the relationship between cost, production, volume and returns.
2. It can be extended to show how changes in fixed cost, variable cost, commodity prices, revenues will effect profit levels and break even points. Break even analysis is most useful when used with partial budgeting, capital budgeting techniques.
3. The major benefits to use break even analysis is that it indicates the lowest amount of business activity necessary to prevent losses.

## Limitations:

Break even analysis is best suited to the analysis of one product at a time. It may be difficult to classify a cost as all variable or all fixed; and there may be a tendency to continue to use a break even analysis after the cost and income functions have changed.

## Review Problem:

Voltar Company manufactures and sells a telephone answering machine. The company's contribution format income statement for the most recent year is given below:

 Total Per unit Percent of sales Sales \$1,200,000 \$60 100% Less variable expenses 900,000 45 ?% Contribution margin 300,000 15 ?% Less fixed expenses 240,000 Net operating income \$60,000

Required: Calculate break-even point both in units and sales dollars. Use the equation method.

### Solution:

Sales = Variable expenses + Fixed expenses +Profit

\$60Q = \$45Q + \$240,000 + \$0

\$15Q = \$240,000

Q = \$240,000 / 15 per unit

Q = 16,000 units; or at \$60 per unit, \$960,000

Alternative solution:

X = 0.75X + 240,000 + \$0

0.25X = \$240,000

X = \$240,000 / 0.25

X = \$960,000; or at \$60 per unit, 16,000 units

## Relevant Articles:

 » Contribution Margin » Contribution Margin Ratio (CM Ratio) » Contribution Margin Income Statement » Break-even Point Analysis » Target Profit Analysis » Margin of Safety (MOS) » Operating Leverage » Break even Analysis with Multiple Products » CVP Consideration in Cost Structure » Importance of Cost Volume Profit (CVP) Analysis

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