COST-VOLUME-PROFIT ANALYSIS
Profit maximization is one of the most important goals for the management of companies.
Managers can only achieve this goal by analyzing the relationship between costs, volume, and
profits.
Cost-volume-profit analysis can be defined as an analysis that is based on the assumption of
fixed and variable costs in a specific level are equal to the total revenue earned at that level.
This analysis is also called a break-even point analysis.
Break-even point is the volume of activity where total revenues and total costs are equal. Since
it produces equal revenues and costs, there is neither profit nor loss.
The main difference between break-even and cost-volume-profit analyses is that break-even
analysis identifies the number of production where the profit is equal to zero. On the other
hand, cost-volume-profit analysis emphasizes on the factors, which affect the number of
production, at a profit level of zero, or which affect the profit maximization, and so on. It can
be said that cost-volume-profit analysis focuses on the volume and price of products
produced and sold. Moreover, per unit variable cost and total fixed cost are specified for the
purpose of determining the amount of production or creating the product mix.
These analyses can especially be helpful for entrepreneurs. Indeed, if the break-even point of
any investment decision is higher than the expected sales, an entrepreneur should not be made
an investment to that field. In this respect, it can be said that break-even and cost-volumeprofit analyses play a vital role in decision-making processes.
11.1. Formulas For Break-Even Computations
Before giving formulas for break-even computations, the concept of “Contribution
Margin” must be emphasized. Contribution margin is the difference between sales revenue
and variable expenses. Companies can only get a profit when the contribution margin is
sufficient to cover the fixed expenses. A loss occurs if the contribution margin does not cover
the fixed expenses. Accordingly, contribution margin is used in break-even calculations.
The following notations will be used to represent the various items in break-even formulas:
P = Selling price per unit
Q = Number of units
VC = Variable cost per unit
VCp = Variable cost as a percentage
of total sales
FC = Total fixed cost
T = Income tax rate
TVC = Total variable cost
TR = Total revenue
TP = Target Profit
Qe = Expected sales
CM = Contribution Margin per unit
CMR = Contribution Margin Ratio
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TC = Total Cost
Different titles can be given to each formula so these titles are summarized as follows:
The Equation Method:
Sales – Variable Costs – Fixed Costs = Operating Income (Profit)
Operating income is equal to zero at the break-even point, thus
Sales = Variable Costs + Fixed Costs, it can also be showed as follows:
Total Revenue = Variable Cost + Fixed Cost
(Q*P) = (Q*VC) + FC
Note that contribution margin can be
The Contribution Method:
expressed as (P-VC). In addition, the
Total Revenue = Variable Cost + Fixed Cost
fraction “Contribution Margin/ Sales”
is referred to as Contribution Margin
(Q*P) = (Q*VC) + FC
Ratio.
(Q*P) - (Q*VC) – FC = 0
FC
Q=
( P  VC )
The formula above displays that break-even point in units that is found by dividing fixed cost
by unit contribution margin. On the other hand, the contribution margin ratio should be used
in order to compute the break-even point in a local currency. If the break-even quantity is
multiplied by unit sales price, the break-even point in a local currency such as dollars or ¨ is
also obtained. These are summarized as below,
FC
Break-even point in ¨ =
or,
CMR
Break-even point in ¨ = Break-even quantity * Unit sales price
The Graphical Method:
2
¨
Total Revenue
Operating income area
Total Cost
Break-even Point
Variable Cost
Fixed Cost
Fixed Cost
Operating loss area
Number of Units
Figure 11.1. Break-Even Graph
Managers are able to highlight the impact of changes in volume on profit by showing the
break-even point graphically. The various levels of sales volume is represented on the
horizontal axis, and price on the vertical axis. The area up to break-even point is called
operating loss area. Break-even, at the same time, is the starting point (origin) of operating
income area. According to the graph, the total cost is the sum of the total variable, and total
fixed costs. The point at which total revenue is equal to total cost is referred to as a breakeven point. It is compulsory for companies to have higher contribution margin than the total
fixed cost to be incurred. When the graph is analyzed, it can be said that, if managers want to
increase the profit of a company, he or she can increase the number of units sold, or can
enhance the unit-selling price or can follow both of the strategies. Moreover, managers can
also try to discover the ways of diminishing the costs in order to get high profit.
Formulation Of Break-Even Analysis
In this section, the impacts of target profits, and income taxes will be formulated separately.
Afterwards, the margin of safety will also be indicated. Let us look at these in more detail.
The Impact of “Target Profit”
A profit element would be added to formula in order to determine the number of units to be
sold or sales price to be needed to achieve a desired profit. Thus,
Sales to
realize target
profit
(in units)
Sales to
realize target
profit
(in
units)
Sales
to
realize target
profit
(in ¨)
=
T arg et Pr ofit  Total Fixed Costs
Contribution M arg in Per Unit
=
TP  TFC
CM
=
TP  TFC
CMR
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In addition,
On the other hand, additional sales to realize target profit can be found as follows:
TP
Additional=Sales to
=
CM
realize target
profit
(in units)
The Impact of “Income Tax”
The impact of income tax can be formulated as below:
After-tax profit, where taxes are imposed at a constant rate is,
=(Before-tax profit)-( Before-tax profit*Tax rate)
=(Before-tax profit)*(1-Tax rate)
After tax Pr ofit
Before-tax Profit =
(1  Tax Rate)
The information related to before tax profit is important for the reason that managers must
consider the before tax profit for determining the sales amount in units or in ¨ for a desired
profit.
The Margin of Safety
The margin of safety is the difference between the breakeven sales and the budgeted
(expected) or actual sales. Indeed, budgeted sales or actual sales would be used as the base
units of measurement. The margin of safety is measured in units or in ¨ of sales. It points out
the amount of sales that can be declined before profit becomes zero. The formula of the
margin of safety is given as follows:
The Margin of Safety = Budgeted (or Actual) Sales – Break-even Sales
The absolute values cannot be comparable for the companies having different sales volume.
Thus, calculating the margin of safety as a percentage of sales provides insights that are more
reliable than the absolute values do.
Margin of Safety Percentage =
Budgeted (Actual) Sales – Break-even Sales
Total Budgeted (Actual) Sales
It is also important to emphasize that the higher percentage of the margin of safety indicates
the lower level of risk in connection with a product line.
11.2. An Analysis Of Break-Even In A Company Producing A Single Unit Of Product
Let us assume that ABC Company is a manufacturing company producing a single
unit of product. Break-even computations will be showed on the basis of the data given
below:
Sales price per unit = ¨2,000
Variable cost per unit = ¨800
Total fixed cost = ¨360,000
Expected profit after tax = ¨80
The rate of income tax = 20%
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Required
a- Calculate the contribution margin per unit
b- Calculate the contribution margin ratio
c- Calculate the break-even point in units
d- Calculate the break-even point in ¨
e- Calculate the profit before tax
f- Calculate the break-even point in units and ¨ if the profit is expected to be 220,000.
g- Calculate the margin of safety (and its percentage) if the total amount of actual sales is equal
to ¨800,000.
Solution
a- Contribution margin per unit = (P-VC)
= ¨2,000 – ¨800
Contribution margin per unit = ¨1,200
b- Contribution margin ratio
= Contribution Margin = ¨1,200 = 60%
Sales price per unit
¨2,000
It means that the sixty percent of sales provides contributions to company so each sale has
covered the fixed costs of a product.
c- Break-even point in units
FC
360,000
Q=
=
= 300 units
(2,000  800)
( P  VC )
ABC Company must sell 300 units in order to obtain break-even point.
d- Break-even point in ¨
Break-even point in ¨ = Break-even quantity * Unit sales price
Break-even point in ¨ = 300 units * ¨2,000 per unit = ¨600,000
Break-even point in ¨ can also be found as follows:
FC
360,000
Break-even point in ¨ =
=
= ¨600,000
0.60
CMR
Break-even point in ¨ is equal to ¨600,000. It means that when the company sells a total of
¨600,000 goods, its costs and revenues will be equal.
e- Profit before tax
Before-tax Profit =
Aftertax Pr ofit
(1  Tax Rate)
=
80
= ¨100
1  0.20
f- The break-even point in units and ¨ for a target profit of
¨220,000.
Sales to=
realize target
profit
(in units)
=
TP  TFC
220,000  360,000
=
 484 units
CM
1,200
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Sales to
realize target
profit
(in ¨)
=
TP  TFC
220,000  360,000
 ¨968,000
=
0.60
CMR
or 484 units* ¨2000= ¨968,000
g- The margin of safety (and its percentage) at a sales level of ¨800,000.
The Margin of Safety = Budgeted (or Actual) Sales – Break-even Sales
The Margin of Safety = ¨800,000 – ¨600,000 = ¨200,000
Budgeted (Actual) Sales – Break-even Sales
Margin of Safety Percentage =
Total Budgeted (Actual) Sales
Margin of Safety Percentage =
¨800,000
– ¨600,000
¨800,000
Margin of Safety Percentage = 25%
The margin of safety percentage shows that if the sales decline more than 25%, the company
will start to incur a loss.
Analyzing the Effects of Changes in Selling Price, Fixed Costs, and Variable Costs on the
Break-even Point
The effects of changes in selling price, fixed costs, and variable costs on the break-even point
should be analyzed.
Changing in Selling Price: Let us assume that fixed and variable costs remain constant, the
increases of selling price will decrease the break-even volume. This is because the increases of
selling price will also result in the increases of contribution margin. For example, calculate the
break-even point in units when the selling price will increase by 10 percent.
The New Selling Price = ¨2,000 + ¨2,000*10% = ¨2,200
FC
360,000
 258 units
Q=
=
(2,200  800)
( P  VC )
Changing in Fixed Cost: When the selling price and variable costs remain constant, the changes
in fixed costs will increase or decrease the break-even volume. This is because the decreases of
fixed costs will also result in declining the break-even quantity in unit. For example, calculate
the break-even point in units when the fixed cost will increase by 10 percent.
The New Fixed Cost = ¨360,000 + ¨360,000 *10% = ¨396,000
FC
396,000
Q=
=
= 330 units
(2,000  800)
( P  VC )
Changing in Variable Cost: Under the condition of selling price and fixed costs remain constant,
the changes in variable costs will increase or decrease the break-even point. This is because the
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decreases of variable cost will also result in the increases of contribution margin. To illustrate,
calculate the break-even point in units when the variable cost will decrease by 20 percent.
The New Variable Cost = ¨800 - ¨800*20% = ¨640
FC
360,000
 265 units
Q=
=
(2,000  640)
( P  VC )
11.3. Break-Even Computations In A Company Producing Multiple Products
The calculation of break-even points becomes much more difficult when a company
producing and selling multiple products. Indeed, managers must try to determine the sales
mix, which is the relative proportion of products to be planned or actually sold. A weightedaverage unit contribution margin is referred to as the weighted average of each product’s
contribution margin that is used for computing break-even points by considering the relative
proportion of units sold.
Let us look at this issue in more detail by examining the example below:
Assuming that ABC Company produces two types of boxes. The data related to the boxes are
given as follows:
B1
B2
Total
Sales Quantity (units)
150,000 50,000
200,000
Sales price per unit (¨4; ¨6)
600,000 300,000
900,000
Variable cost per unit (¨3; ¨2)
450,000 100,000
550,000
Total fixed cost (¨)
600,000
Required: Calculate the break-even points of boxes.
Solution:
TR = VC + FC or
(Q*P) = (Q*VC) + FC
(Q*P) - (Q*VC) – FC = 0
(4B1+6B2) – (3B1+2B2) – 600,000 = 0
Note that an equation must be generated by examining the sales quantity of boxes:
150,000
B1=3B2
B1=150,000, B2= 50,000 so
= 3 It means that
50,000
The equation can now be reorganized as follows:
(4*3B2+6B2) – (3*3B2+2B2) = 600,000 units
7B2 = 600,000 units so;
B2= 85,715 units
B1= 257,143 units
Summary
Cost-volume-profit analysis can be defined as an analysis that is based on the
assumption of fixed and variable costs in a specific level are equal to the total revenue earned
at that level. This analysis is also called a break-even point analysis.
Break-even point is the volume of activity where total revenues and total costs are equal. Since
it produces equal revenues and costs, there is neither profit nor loss.
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Contribution margin is the difference between sales revenue and variable expenses.
Companies can only get a profit when the contribution margin is sufficient to cover the fixed
expenses. A loss occurs if the contribution margin does not cover the fixed expenses.
Accordingly, contribution margin is used in break-even calculations.
Operating income is equal to zero at the break-even point, thus the equation can be given as;
“Sales = Variable Costs + Fixed Costs”. Accordingly, the break-even point in units is found
by dividing fixed cost by unit contribution margin.
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