Break Even Point AnalysisDefinition, Explanation Formula and
Calculation: BEP
Learning Objectives:
 Define and explain break even point.
 How is it calculated?
 What are its advantages, assumptions,
and limitations?

Definition of Break Even Point

Calculation by
Equation Method

Calculation by Contribution Margin Method

Advantages / Benefits of Break Even Analysis

Assumptions of Break Even Point

Limitations of Break Even Analysis

Review Problem

Break
Even Analysis Calculator

Download Break Even Analysis Notes (Printable)
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.
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
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

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.
The Breakeven Analysis depends
on three key assumptions:

Average perunit
sales price (perunit 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 nonunit based businesses, make the
perunit 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 Breakeven Analysis.

Average perunit
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 UnitsBased 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 perunit
cost of .5, and a perunit revenue of 1.

Monthly fixed costs:
Technically, a breakeven 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 Breakeven 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.
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
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In Business 
Buying on the GoA Dot.com Tale
Star CD is a company set up by two young
engineers, George Searle and Humphrey Chen, to allow customers to order
music CDs on their cell phone. Suppose you hear a cut from a CD on your
car radio that you would like to own. Pick up your cell phone, punch
"*CD." enter the radio stations frequency, and the time you heard the
song, and the CD will soon be on its way to you. Star CD charge about
$17 for a CD, including shipping. The company pays its suppliers about
$13, leaving a contribution margin of $4 per CD. Because the fixed costs
of running the service, Searle expects the company to lose $1.5 million
on sales of $1.5 million in its first year of operations. That assumes
the company sells in excess of 88,000 CDs. What is the company's break
even point? Working backward, the contribution margin per CD is $4, the
company would have to sell over 460,000 CDs per year just to break even.
Source: Peter Kafka, "Pay It Again,"
Forbes, July 26, 1999, P.94

