Break Even Point Formula Analysis and Calculation

Break Even Formula ,analysis, definition and Calculation:

Learning Objectives:

1. Define and explain break even point equation.
2. How break even point is calculated by formula or methods of estimating break even point?
3. What are its advantages, assumptions, characteristics and limitations?
4. What are the three approaches of break even computations ?

Definition of Break Even point:

Break even point is the level of sales at which profit is zero. According to this definition, at break even point sales are equal to fixed cost plus variable cost. This concept is further explained by the the following equation:

[Break even sales = fixed cost + variable cost]

The break even point can be calculated using either the equation method or contribution margin method. These two methods are equivalent.

Equation Method:

The equation method centers on the contribution approach to the income statement. The format of this statement can be expressed in equation form as follows:

Profit = (Sales − Variable expenses) − Fixed expenses

Rearranging this equation slightly yields the following equation, which is widely used in cost volume profit (CVP) analysis:

Sales = Variable expenses + Fixed expenses + Profit

According to the definition of break even point, break even point is the level of sales where profits are zero. Therefore the break even point can be computed by finding that point where sales just equal the total of the variable expenses plus fixed expenses and profit is zero.

Example:

For example we can use the following data to calculate break even point.

 Sales price per unit = \$250 variable cost per unit = \$150 Total fixed expenses = \$35,000 Calculate break even point

Calculation:

 Sales = Variable expenses + Fixed expenses + Profit \$250Q* = \$150Q* + \$35,000 + \$0** \$100Q = \$35000 Q = \$35,000 /\$100 Q = 350 Units Q* = Number (Quantity) of units sold. **The break even point can be computed by finding that point where profit is zero

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 × \$250 Per unit = \$87,500

Contribution Margin Method:

The contribution margin method is actually just a short cut conversion of the equation method already described. The approach centers on the idea discussed earlier that each unit sold provides a certain amount of contribution margin that goes toward covering fixed cost. To find out how many units must be sold to break even, divide the total fixed cost by the unit contribution margin.

 Break even point in units = Fixed expenses / Unit contribution margin  \$35,000 / \$100* per unit  350 Units *S250 (Sales) − \$150 (Variable exp.)

A variation of this method uses the Contribution Margin ratio (CM ratio) instead of the unit contribution margin. The result is the break even in total sales dollars rather than in total units sold.

 Break even point in total sales dollars = Fixed expenses / CM ratio \$35,000 / 0.40 = \$87,500

This approach is particularly suitable in situations where a company has multiple products lines and wishes to compute a single break even point for the company as a whole.

The following formula is also used to calculate break even point

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

This formula can produce the same answer:

 Break Even Point = [\$35,000 / 1 – (150 / 250)] = \$35,000 / 1 – 0.6 = \$35,000 / 0.4 = \$87,500

Benefits / Advantages of Break Even Analysis:

The main advantages of break even point analysis is that it explains the relationship between cost, production, volume and returns. 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. The major benefits to use break even analysis is that it indicates the lowest amount of business activity necessary to prevent losses.

Assumption of Break Even Point:

The Break-even Analysis depends on three key assumptions:

1. Average per-unit sales price (per-unit revenue):
This is the price that you receive per unit of sales. Take into account sales discounts and special offers. Get this number from your Sales Forecast. For non-unit based businesses, make the per-unit revenue \$1 and enter your costs as a percent of a dollar. The most common questions about this input relate to averaging many different products into a single estimate. The analysis requires a single number, and if you build your Sales Forecast first, then you will have this number. You are not alone in this, the vast majority of businesses sell more than one item, and have to average for their Break-even Analysis.

2. Average per-unit cost:
This is the incremental cost, or variable cost, of each unit of sales. If you buy goods for resale, this is what you paid, on average, for the goods you sell. If you sell a service, this is what it costs you, per dollar of revenue or unit of service delivered, to deliver that service. If you are using a Units-Based Sales Forecast table (for manufacturing and mixed business types), you can project unit costs from the Sales Forecast table. If you are using the basic Sales Forecast table for retail, service and distribution businesses, use a percentage estimate, e.g., a retail store running a 50% margin would have a per-unit cost of .5, and a per-unit revenue of 1.

3. Monthly fixed costs:
Technically, a break-even analysis defines fixed costs as costs that would continue even if you went broke. Instead, we recommend that you use your regular running fixed costs, including payroll and normal expenses (total monthly Operating Expenses). This will give you a better insight on financial realities. If averaging and estimating is difficult, use your Profit and Loss table to calculate a working fixed cost estimate—it will be a rough estimate, but it will provide a useful input for a conservative Break-even Analysis.

Limitations of Break Even Analysis:

It 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 ======

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