1. business and industrial

Managerial accounting
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COST definition and classifications
Concept of Cost
In general, cost means the amount of expenditure (actual or notional) incurred on, or
attributable to a given thing. However, the term cost cannot be exactly defined. Its
interpretation depends upon the following factors:


The nature of business or industry
The context in which it is used
In a business where selling and distribution expenses are quite nominal the cost of an article
may be calculated without considering the selling and distribution overheads. At the same
time, in a business where the nature of a product requires heavy selling and distribution
expenses, the calculation of cost without taking into account the selling and distribution
expenses may prove very costly to a business. The cost may be factory cost, office cost, cost
of sales and even an item of expense. For example, prime cost includes expenditure on
direct materials, direct labour and direct expenses. Money spent on materials is termed as
cost of materials just like money spent on labour is called cost of labour and so on. Thus, the
use of term cost without understanding the circumstances can be misleading.
Different costs are found for different purposes. The work-in-progress is valued at factory
cost while stock of finished goods is valued at office cost. Numerous other examples can be
given to show that the term “cost” does not mean the same thing under all circumstances
and for all purposes. Many items of cost of production are handled in an optional manner
which may give different costs for the same product or job without going against the
accepted principles of cost accounting. Depreciation is one of such items. Its amount varies
in accordance with the method of depreciation being used. However, endeavour should be,
as far as possible, to obtain an accurate cost of a product or service.
Elements of Cost
Following are the three broad elements of cost:
1. Material
The substance from which a product is made is known as material. It may be in a raw or a
manufactured state. It can be direct as well as indirect.
2. Labour
For conversion of materials into finished goods, human effort is needed and such human
effort is called labour. Labour can be direct as well as indirect.
3. Expenses
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Classification of Cost
Cost may be classified into different categories depending upon the purpose of
classification. Consider some ways of classifying costs:
A. Based on business function (R&D, Design, Production, Marketing, Distribution,
Customer service)
B. Based on financial statement presentation (capitalized, noncapitalized,
inventoriable, non-inventoriable: product vs. period)
C. Based on assignment to cost object (direct vs. indirect)
D. Based on behavior in relation to cost driver (variable vs. fixed)
E. Based on aggregation (total vs. unit)
Some of the important categories in which the costs are classified are as follows:
First. Direct and Indirect Costs
The expenses incurred on material and labor which are economically and easily traceable
for a product, service or job is considered as direct costs. In the process of manufacturing of
production of articles, materials are purchased, laborers are employed and the wages are
paid to them. Certain other expenses are also incurred directly. All of these take an active
and direct part in the manufacture of a particular commodity and hence are called direct
costs. The expenses incurred on those items which are not directly chargeable to production
are known as indirect costs. For example, salaries of timekeepers, storekeepers and
foremen. Also certain expenses incurred for running the administration are the indirect
costs. All of these cannot be conveniently allocated to production and hence are called
indirect costs.
Second.
Avoidable or Escapable Costs and Unavoidable or Inescapable Costs
Avoidable costs are those which will be eliminated if a segment of a business (e.g., a product
or department) with which they are directly related is discontinued. Unavoidable costs are
those which will not be eliminated with the segment. Such costs are merely reallocated if
the segment is discontinued. For example, in case a product is discontinued, the salary of a
factory manager or factory rent cannot be eliminated. It will simply mean that certain other
products will have to absorb a large amount of such overheads. However, the salary of
people attached to a product or the bad debts traceable to a product would be eliminated.
Certain costs are partly avoidable and partly unavoidable. For example, closing of one
department of a store might result in decrease in delivery expenses but not in their
altogether elimination. It is to be noted that only avoidable costs are relevant for deciding
whether to continue or eliminate a segment of a business.
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Third. Differentials, Incremental or Decrement Cost
The difference in total cost between two alternatives is termed as differential cost. In case
the choice of an alternative results in an increase in total cost, such increased costs are
known as incremental costs. While assessing the profitability of a proposed change, the
incremental costs are matched with incremental revenue. This is explained with the
following example:
Example
A company is manufacturing 1,000 units of a product. The present costs and sales data are
as follows:
Selling price per unit
Variable cost per unit
Fixed costs
$. 10
$. 5
$. 4,000
The management is considering the following two alternatives:
a. To accept an export order for another 200 units at $. 8 per unit. The expenditure of the
export order will increase the fixed costs by $. 500.
b. To reduce the production from present 1,000 units to 600 units and buy another 400
units from the market at $. 6 per unit. This will result in reducing the present fixed costs
from $. 4,000 to $. 3,000.
Which alternative the management should accept?
Solution
Statement showing profitability under different alternatives is as follows:
Particulars
Present situation
$.
$.
Sales.
Less:
5,000
Variable purchase costs 4,000
Fixed costs Profit
10,000
9,000
1,000
Proposed situations
11,600
10,000
6,000
5,400
10,500
8,400
4,500
3,000
1,100
1,600
Observations
i.
ii.
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In the present situation, the company is making a profit of $. 1,000.
In the proposed situation (a), the company will make a profit of $. 1,100. The incremental
costs will be $. 1,500 (i.e. $. 10,500 - $. 9,000) and the incremental revenue (sales) will be
[COST-VOLUME-PROFIT ANALYSIS]
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$. 1,600. Hence, there is a net gain of $. 100 under the proposed situation as compared
to the existing situation.
In the proposed situation (b), the detrimental costs are $. 600 (i.e. $. 9,000 to $. 8,400) as
there is no decrease in sales revenue as compared to the present situation. Hence, there
is a net gain of $. 600 as compared to the present situation.
Thus, under proposal (b), the company makes the maximum profit and therefore it should
adopt alternative (b). The technique of differential costing which is based on differential
cost is useful in planning and decision-making and helps in selecting the best alternative. In
case the choice results in decrease in total costs, this decreased costs will be known as
detrimental costs.
cost behavior
The most important building block of both microeconomic analysis and cost accounting is
the characterization of how costs change as output volume changes. Output volume can
refer to production, sales, or any other principle activity that is appropriate for the
organization under consideration (e.g.: for a school, number of students enrolled; for a
health clinic, number of patient visits; for an airline, number of passenger miles). The
following discussion examines the volume of production in a factory, but the same
principles apply regardless of the type of organization and the appropriate measure of
activity. Costs can be variable, fixed, or mixed.
1st. Variable Costs:
Variable costs vary in a linear fashion with the production level. However, when stated on a
per unit basis, variable costs remain constant across all production levels within the relevant
range. The following two charts depict this relationship between variable costs and output
volume.
Total variable cost
12000
10000
8000
6000
4000
2000
90
0
50
0
10
0
0
Production level (units produced)
.
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variable cost per unit
12
10
8
6
4
2
0
100
500
900
Production Level (units produced)
A good example of a variable cost is materials. If one pair of pants requires $10 of fabric,
then every pair of pants requires $10 of fabric, no matter how many pairs are made. The
fabric cost is $10 per unit at every level of production. If one pair is made, the total fabric
cost is $10; if two pairs are made, the total fabric cost is $20; and if 1,000 pairs are made,
the total fabric cost is $10,000. Hence, the total cost is increasing and linear in the
production level.
2nd. Fixed Costs:
Fixed costs do not vary with the production level. Total fixed costs remain the same, within
the relevant range. However, the fixed cost per unit decreases as production increases,
because the same fixed costs are spread over more units. The following two charts depict
this relationship between fixed costs and output volume.
Total fixed cost
60000
50000
40000
30000
20000
10000
0
100
500
900
Production level (units produced)
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Fixed cost per unit
1000
800
600
400
200
0
50 100 150 200 250 300 350 400 450 500
Production level (units produced)
In this example, fixed costs are $50,000. The first chart shows that fixed costs remain
$50,000 at all production levels from 100 units to 1,000 units. The second chart shows that
the fixed cost per unit decreases as production increases. Hence, when 100 units are
manufactured, the fixed cost per unit is $500 ($50,000 ÷ 100). When 500 units are
manufactured, the fixed cost per unit is $100 ($50,000 ÷ 500).
Relevant Range:
The relevant range is the range of activity (e.g., production or sales) over which these
relationships are valid. For example, if the factory is operating at capacity, increasing
production requires additional investment in fixed costs to expand the facility or to lease or
build another factory. Alternatively, production might be reduced below a threshold at
which point one of the company’s factories is no longer needed, and the fixed costs
associated with that factory can be avoided. With respect to variable costs, the company
might qualify for a volume discount on fabric purchases above some production level. The
relevant range for characterizing fabric as a variable cost ends at that production level,
because the fabric cost per unit of output is different when the factory produces above that
threshold than when the factory produces below that threshold.
3rd. Mixed Costs:
If, within a relevant range, a cost is neither fixed nor variable, it is called semi-variable or
mixed. Following are two common examples of mixed costs.
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Total cost
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14000
12000
10000
8000
6000
4000
2000
90
0
50
0
10
0
0
Production level (units produced)
7000
6000
5000
4000
3000
2000
1000
0
10
0
20
0
30
0
40
0
50
0
60
0
70
0
80
0
90
0
10
00
Total cost
In this example, although the total cost line increases in production, it does not pass
through the origin because there is a fixed cost component. An example of a cost that fits
this description is electricity. A fixed amount of electricity is required to run the factory air
conditioning, computers and lights. There is also a variable cost component related to
running the machines on the factory floor. The fixed component in this example is $3,000
per month. The variable cost component is $10 per unit of output. Hence, at a production
level of 500 units, the total electric cost is $8,000 [$3,000 + ($10 x 500)].
Production level (units produced)
The mixed cost illustrated in the above chart is called a step function. An example of such
cost behavior would be the total salary expense for shift supervisors. If the factory runs one
shift, only one shift supervisor is required. In order for the factory to produce above the
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maximum capacity of a single shift, the factory must add a second shift and hire a second
shift supervisor, so that total shift supervisor salary expense doubles. If the factory runs
three shifts, three shift supervisors are required.
Methods for separating mixed costs into fixed and variable
The common three methods for separating mixed costs into their fixed and variable cost
components:
 Prepare a scattergraph by plotting points onto a graph.
 High-low method.
 Regression analysis.
It is wise to prepare the scattergraph even if you use the high-low method or regression
analysis. The benefit of the scattergraph is that it allows you to see if some of the plotted
points are simply out of line. These points are referred to as outliers and will need to be
reviewed and possibly adjusted or eliminated. In other words, you don’t want incorrect data
to distort your calculations under any of the three methods.
Let’s assume that a company uses only one type of equipment and it wants to know how
much of the monthly electricity bill is a constant amount and how much the electricity bill
will increase when its equipment runs for an additional hour. The scattergraph’s vertical or
y-axis will indicate the dollars of total monthly electricity cost. Its horizontal or x-axis will
indicate the number of equipment hours. For each monthly electricity bill, a point will be
entered on the graph at the intersection of the dollar amount of the total electricity bill and
the equipment hours occurring between the meter reading dates shown on the electricity
bill. If you plot this information for the most recent 12 months, you may see some type of
pattern, such as a line that rises as the number of equipment hours increase. If you draw a
line through the plotted points and extend the line through the y-axis, the amount where
the line crosses the y-axis is the approximate amount of fixed costs for each month. The
slope of the line indicates the variable cost per equipment hour. The slope or variable rate is
the increase in the total monthly electricity cost divided by the change in the total number
of equipment hours.
The high-low calculation is similar but it uses only two of the plotted points: the highest
point and the lowest point.
Regression analysis uses all of the monthly electricity bill amounts along with their related
number of equipment hours in order to calculate the monthly fixed cost of electricity and
the variable rate for each equipment hour. Software can be used for regression analysis and
it will also provide statistical insights.
If a scattergraph of data shows no clear pattern, you should not place much confidence in
the calculated amount of the fixed cost and variable rate regardless of the method used.
The high-low method
The high-low method is a simple technique for computing the variable cost rate and the
total amount of fixed costs that are part of mixed costs. Mixed costs are costs that are
partially variable and partially fixed. The cost of electricity used in a factory is likely to be a
mixed cost since some of the electricity will vary with the number of machine hours, while
some of the cost will not vary with machine hours. Perhaps this second part of the
electricity cost is associated with circulating and chilling the air in the factory and from the
public utility billing its large customers with a significant fixed monthly charge not directly
tied to the kilowatt hours of electricity used.
The high-low method uses two sets of numbers:
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The total number of the mixed costs occurring at the highest volume of activity, and
The total number of the mixed costs occurring at the lowest volume of activity.
It is assumed that at both points of activity the total amount of fixed costs is the same.
Therefore, the change in the total costs is assumed to be the variable cost rate times the
change in the number of units of activity. Prior to using the high-low method, it is important
to plot or graph all of the data available to be certain that the two sets of numbers being
used are indeed representative.
To illustrate the high-low method, let’s assume that a company had total costs of electricity
of $18,000 in the month when its highest activity was 120,000 machine hours. (Be sure to
match the dates of the machine hours to the electric meter reading dates.) During the
month of its lowest activity there were 100,000 machine hours and the total cost of
electricity was $16,000. This means that the total monthly cost of electricity changed by
$2,000 when the number of machine hours changed by 20,000. This indicates that the
variable cost rate was $0.10 per machine hour.
Continuing with this example, if the total electricity cost was $18,000 when there were
120,000 machine hours, the variable portion is assumed to have been $12,000 (120,000
machine hours times $0.10). Since the total electricity cost was $18,000 and the variable
cost was calculated to be $12,000, the fixed cost of electricity for the month must have been
the $6,000. If we use the lowest level of activity, the total cost of $16,000 would include
$10,000 of variable cost (100,000 machine hours times $0.10) with the remainder of $6,000
being the fixed cost for the month.
Example
Suppose that the maintenance cost and volume of production for some months are:
Production volume 5o
11o 180 160 170 190
Costs
2200 2440 2720 2640 2680 2760
Required: separating maintenance costs into their fixed and variable cost components
Solution
Determine the highest volume of activity (volume of production) and its costs and
the lowest volume of activity (volume of production) and its costs as the following.
volume of activity (production) costs
highest 190
2760
lowest 50
2200
Calculate the variable cost rate
Costs at the highest level
highest volume of activity
- Costs at the lowest level
- lowest volume of activity
2760 - 2200
190 - 50
= 4 SR/unit (that is mean that variable cost for each production unit is 4 SR).
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At any level of production (suppose that level of 110 units):
Variable cost = variable cost rate × number of units
= 4 × 11o units = 440 SR
Fixed cost = total cost at this level – variable cost
= 2440 – 440 = 2000 SR
Summary Cost Concepts & Definitions
CONCEPT
DEFINITION
Direct costs
Costs directly related to cost object.
Indirect costs
Costs not directly related to a cost object.
Cost Concepts Used in Decision Making
Variable costs
Cost that vary with the volume of activity.
Fixed costs
Costs that do not vary with volume of activity over a specified time span.
Differential
Costs that change in response to a particular course of action.
Costs
Sunk Costs
Costs that result from an expenditure made in the past and that cannot be
changed by present or future decisions.
Opportunity
The return that one could realize from the best foregone alternative use of a
cost:
resource.
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Questions
Variable costs are those costs that:
A) vary inversely with changes in activity.
B) vary directly with changes in activity.
C) remain constant as activity changes.
D) decrease on a per-unit basis as activity increases.
E) increase on a per-unit basis as activity increases.
As activity decreases, unit variable cost:
A) increases proportionately with activity.
B) decreases proportionately with activity.
C) remains constant.
D) increases by a fixed amount.
E) decreases by a fixed amount.
Fixed costs are those costs that:
A) vary directly with changes in activity.
B) vary inversely with changes in activity.
C) remain constant on a per-unit basis.
D) increase on a per-unit basis as activity increases.
E) remain constant as activity changes.
The fixed costs per unit are $10 when a company produces 10,000 units of product.
What are the fixed costs per unit when 12,500 units are produced?
A) $4.
B) $6.
C) $8.
D) $10.
E) $12.
Total costs are $80,000 when 8,000 units are produced; of this amount, variable costs
are $48,000. What are the total costs when 10,000 units are produced?
A) $80,000.
B) $92,000.
C) $98,000.
D) $100,000.
E) $108,000.
Costs that can be easily traced to a specific department are called:
A) direct costs.
B) indirect costs.
C) product costs.
D) manufacturing costs.
E) processing costs.
Midwest Motors manufactures automobiles Which of the following would not be
classified as direct materials by the company?
A) Sheet metal used in the automobile's body.
B) Tires.
C) Interior leather.
D) CD player.
E) Wheel lubricant.
Selling and administrative expenses would likely appear on the balance sheet of:
A) American Airlines.
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B) Wal-Mart Corporation.
C) Dell Computer.
D) all of the above firms.
E) none of the above firms.
The relationship between cost and activity is termed:
A) cost estimation.
B) cost prediction.
C) cost behavior.
D) cost analysis.
E) cost approximation.
Which of the following costs changes in direct proportion to a change in the activity level?
A) Variable cost.
B) Fixed cost.
C) Semi variable cost.
D) Step-variable cost.
E) Step-fixed cost.
Costs that remain the same over a wide range of activity, but jump to a different amount
outside that range, are termed:
A) step-fixed costs.
B) step-variable costs.
C) semi variable costs.
D) curvilinear costs.
E) mixed costs.
A cost that has both a fixed and variable component is termed a:
A) step-fixed cost.
B) step-variable cost.
C) semi variable cost.
D) curvilinear cost.
E) discretionary cost.
The relevant range is that range of activity:
A) where a company achieves its maximum efficiency.
B) where units produced equal units sold.
C) where management expects the firm to operate.
D) where the firm will earn a profit.
E) where expected results are abnormally high.
A variable cost that has a definitive physical relationship to the activity measure is called a(n):
A) discretionary cost.
B) engineered cost.
C) managed cost.
D) programmed cost.
E) committed cost.
Controllable costs, as used in a responsibility accounting system, consist of:
A) only fixed costs.
B) only direct materials and direct labor.
C) those costs that a manager can influence in the time period under review.
D) those costs about which a manager has some knowledge.
E) those costs that are influenced by parties external to the organization.
A common cost is:
A) not easily related to a segment's activities
B) easily related to a segment's activities.
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C) avoidable.
D) unavoidable.
E) applicable only to manufacturing organizations.
Which of the following statements is true?
A) The word "cost" has the same meaning in all situations in which it is used.
B) Cost data, once classified and recorded for a specific application, can then be used in any
application.
C) Different cost concepts and classifications are used for different purposes.
D) All organizations incur the same types of costs.
E) Costs incurred in one year are always meaningful in the following year.
Which of the following is not an example of a variable cost?
A) Straight-line depreciation on a machine expected to last five years.
B) Piece-rate wages paid to manufacturing workers.
C) Tires used to produce tractors.
D) Lumber used to make patio furniture.
E) Commissions paid to sales personnel.
The tuition that is paid this semester by a college student who pursues a degree is a(n):
A) sunk cost.
B) out-of-pocket cost.
C) opportunity cost.
D) average cost.
E) marginal cost.
The variable costs per unit are $4 when a company produces 10,000 units of product. What are
the variable costs per unit when 8,000 units are produced?
A) $4.00.
B) $4.50.
C) $5.00.
D) $5.50.
E) $6.00.
Costs that can be easily traced to a specific department are called:
A) direct costs.
B) indirect costs.
C) product costs.
D) manufacturing costs.
E) processing costs.
Which of the following employees of a commercial printer/publisher would be classified as
direct labor?
A) Book binder.
B) Plant security guard.
C) Sales representative.
D) Plant supervisor.
E) Payroll supervisor.
Indirect costs:
A) can be traced to a cost object.
B) cannot be traced to a particular cost object.
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C) are not important.
D) are always variable costs.
E) may be indirect with respect to Disney World but direct with respect to one its major
components, Epcot Center.
Quality Appliance produces washers and dryers in an assembly-line process. Labor costs
incurred during a recent period were: corporate executives, $100,000; assembly-line workers,
$60,000; security guards, $11,000; and plant supervisor, $18,000. The total of Quality's direct
labor cost was:
A) $60,000.
B) $71,000.
C) $78,000.
D) $89,000.
E) $189,000.
Conversion costs are:
A) direct material, direct labor, and manufacturing overhead.
B) direct material and direct labor.
C) direct labor and manufacturing overhead.
D) prime costs.
E) period costs.
The salary of the president of a manufacturing company would be classified as which of
the following?
A) Manufacturing overhead.
B) Direct labor.
C) Direct material.
D) Period cost.
E) Sunk cost.
The relationship between cost and activity is termed:
A) cost estimation.
B) cost prediction.
C) cost behavior.
D) cost analysis.
E) cost approximation.
Atlanta, Inc., which uses the high-low method to analyze cost behavior, has determined
that machine hours best explain the company's utilities cost. The company's relevant
range of activity varies from a low of 600 machine hours to a high of 1,100 machine
hours, with the following data being available for the first six months of the year:
Month
January
February
March
April
May
June
Utilities
Machine Hours
$8,700
8,360
8,950
9,360
9,625
9,150
1st. The variable utilities cost per machine hour is:
A) $0.18.
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800
720
810
920
950
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B) $4.50.
C) $5.00.
D) $5.50.
E) none of these.
2nd.
The fixed utilities cost per month is:
A) $3,764.
B) $4,400.
C) $4,760.
D) $5,100.
E) none of these.
3rd.
Using the high-low method, the utilities cost associated with 980 machine
hours would be:
A) $9,510.
B) $9,660.
C) $9,700.
D) $9,790.
E) none of these.
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COST-VOLUME-PROFIT analysis
Cost volume profit analysis (CVP analysis) is one of the most powerful tools that managers
have at their command. It helps them understand the interrelationship between cost,
volume, and profit in an organization by focusing on interactions among the following five
elements:
1.
2.
3.
4.
5.
Prices of products
Volume or level of activity
Per unit variable cost
Total fixed cost
Mix of product sold
Because cost-volume-profit (CVP) analysis helps managers understand the interrelationships
among cost, volume, and profit it is a vital tool in many business decisions. These decisions
include, for example, what products to manufacture or sell, what pricing policy to follow,
what marketing strategy to employ, and what type of productive facilities to acquire.
The Basic Profit Equation
Cost-Volume-Profit analysis (CVP) relates the firm’s cost structure to sales volume and
profitability. A formula that facilitates CVP analysis can be easily derived as follows:
Profit
=
Sales – Costs

Profit
=
Sales – (Variable Costs + Fixed Costs)

Profit + Fixed Costs =
Sales – Variable Costs

Profit + Fixed Costs =
Units Sold x (Unit Sales Price – Unit Variable Cost)
This formula is henceforth called the Basic Profit Equation and is abbreviated
P + FC = Q x (SP – VC)
Typically, the Basic Profit Equation is used to solve one equation in one unknown, where the
unknown can be any of the elements of the equation. For example, given an understanding
of the firm’s cost structure and an estimate of sales volume for the coming period, the
equation predicts profits for the period. As another example, given the firm’s cost structure,
the equation indicates the required sales volume Q to achieve a targeted level of profits P. If
targeted profits are zero, the equation simplifies to
Q = FC ÷ Unit Contribution Margin
In this case, Q indicates the required sales volume to break even, and the exercise is called
breakeven analysis.
Assumptions in CVP Analysis
The Basic Profit Equation relies on a number of simplifying assumptions.
1. Only one product is sold. However, multiple products can be accommodated by using an
average sales mix and restating Q, SP and VC in terms of a representative bundle of
products. For example, a hot dog vendor might calculate that the “average” customer
buys two hot dogs, one bag of chips, and two-thirds of a beverage. Q is the number of
customers, and SP and VC refer to the sales price and variable cost for this “average”
customer order.
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2. If the equation is applied to a manufacturer, beginning inventory is assumed equal to
zero, and production is assumed equal to sales. Relaxing these assumptions requires
additional structure on the equation, including specifying an inventory flow assumption
(e.g., FIFO or LIFO) and the extent to which the matching principle is honored for
manufacturing costs.
3. The analysis is confined to the relevant range. In other words, fixed costs remain
unchanged in total, and variable costs remain unchanged per unit, over the range of Q
under consideration.
Contribution Margin and Basics of Cost Volume Profit
(CVP) Analysis
Contribution margin is the amount remaining from sales revenue after variable expenses
have been deducted. Thus it is the amount available to cover fixed expenses and then to
provide profits for the period. Contribution margin is first used to cover the fixed expenses
and then whatever remains go towards profits. If the contribution margin is not sufficient to
cover the fixed expenses, then a loss occurs for the period. This concept is explained in the
following equations:
Sales revenue − Variable cost* = Contribution Margin
*Both Manufacturing and Non Manufacturing
Contribution margin − Fixed cost* = Net operating Income or Loss
*Both Manufacturing and Non Manufacturing
Example:
Assume that Omar’s company has been able to sell only one unit of product during the
period. If company does not sell any more units during the period, the company's
contribution margin income statement will appear as follows:
Total
Per Unit
Sales (1 Unit only)
$250
$250
Less Variable expenses
150
150
Contribution margin
100
100
Less fixed expenses
35,000
======
--------Net operating loss
$(34,900)
For each additional unit that the company is able to sell during the period, $100 more in
contribution margin will become available to help cover the fixed expenses. If a second unit
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is sold, for example, then the total contribution margin will increase by $100 (to a total of
$200) and the company's loss will decrease by $100, to $34800. If enough units can be sold
to generate $35,000 in contribution margin, then all of the fixed costs will be covered and
the company will have managed to at least break even for the month-that is to show neither
profit nor loss but just cover all of its costs. To reach the break even point, the company will
have to sell 350 units in a period, since each unit sold contribute $100 in the contribution
margin. This is shown as follows by the contribution margin format income statement.
Total
Per Unit
Sales (350 Units)
$87,500
$250
Less variable expenses
52,500
150
---------
---------
Contribution margin
35,000
$100
Less fixed expenses
35,000
======
---------Net operating profit
$0
Once the break even point has been reached, net income will increase by unit contribution
margin by each additional unit sold. For example, if 351 units are sold during the period
then we can expect that the net income for the month will be $100, since the company will
have sold 1 unit more than the number needed to break even. This is explained by the
following contribution margin income statement.
Total
Per Unit
Sales (351 Units)
$87,750
$250
Less Variable expenses
52,500
150
----------
----------
Contribution margin
35,100
100
Less fixed expenses
35,000
======
---------Net operating loss
$100
If 352 units are sold then we can expect that net operating income for the period will be
$200 and so forth. To know what the profit will be at various levels of activity, therefore,
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manager do not need to prepare a whole series of income statements. To estimate the
profit at any point above the break even point, the manager can simply take the number of
units to be sold above the breakeven and multiply that number by the unit contribution
margin. The result represents the anticipated profit for the period. Or to estimate the effect
of a planned increase in sale on profits, the manager can simply multiply the increase in
units sold by the unit contribution margin. The result will be expressed as increase in
profits. To illustrate it suppose company is currently selling 400 units and plans to sell 425
units in near future, the anticipated impact on profits can be calculated as follows:
Increased number of units to be sold
25
Contribution margin per unit
×100
Increase in the net operating income
2,500
======
To summarize these examples, if there were no sales, the company's loss would equal to its
fixed expenses. Each unit that is sold reduces the loss by the amount of the unit
contribution margin. Once the break even point has been reached, each additional unit sold
increases the company's profit by the amount of the unit contribution margin.
Difference between Gross Margin and Contribution Margin
Gross Margin is the Gross Profit as a percentage of Net Sales. The calculation of the Gross
Profit is: Sales minus Cost of Goods Sold. The Cost of Goods Sold consists of the fixed and
variable product costs, but it excludes all of the selling and administrative expenses.
Contribution Margin is Net Sales minus the variable product costs and the variable period
expenses. The Contribution Margin Ratio is the Contribution Margin as a percentage of Net
Sales.
Example
Let’s illustrate the difference between gross margin and contribution margin with the
following information: company had Net Sales of $600,000 during the past year.
Its inventory of goods was the same quantity at the beginning and at the end of year. Its
Cost of Goods Sold consisted of $120,000 of variable costs and $200,000 of fixed costs. Its
selling and administrative expenses were $40,000 of variable and $150,000
of fixed expenses.
The company’s Gross Margin is: Net Sales of $600,000 minus its Cost of Goods Sold of
$320,000 ($120,000 + $200,000) for a Gross Profit of $280,000 ($600,000 - $320,000). The
Gross Margin or Gross Profit Percentage is the Gross Profit of $280,000 divided by $600,000,
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or 46.7%.
The company’s Contribution Margin is: Net Sales of $600,000 minus the variable product
costs of $120,000 and the variable expenses of $40,000 for a Contribution Margin of
$440,000. The Contribution Margin Ratio is 73.3% ($440,000 divided by $600,000).
Cost Volume Profit (CVP) Relationship in Graphic
Form
The relationships among revenue, cost, profit and volume can be expressed graphically by
preparing a cost-volume-profit (CVP) graph or break even chart. A CVP graph highlights
CVP relationships over wide ranges of activity and can give managers a perspective that can
be obtained in no other way.
Preparing a CVP Graph or Break-Even Chart
In a CVP graph sometimes called a break even chart unit volume is commonly represented
on the horizontal (X) axis and dollars on the vertical (Y) axis. Preparing a CVP graph involves
three steps.
The graph below shows total revenue (SP x Q) as a function of sales volume (Q),
when the unit sales price (SP) is $12.
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1433
10
00
50
0
10
0
14000
12000
10000
8000
6000
4000
2000
0
0
Total Revenue
[COST-VOLUME-PROFIT ANALYSIS]
Units produced and sold
The following graph shows the total cost function when fixed costs (FC) are $4,000
and the variable cost per unit (VC) is $5.
10000
Total cost
8000
6000
4000
2000
10
00
50
0
10
0
0
0
Units produced and sold
The following graph combines the revenue and cost functions depicted in the
previous two graphs into a single graph.
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14000
12000
10000
8000
6000
4000
2000
0
Revenue
10
00
50
0
Total cost
10
0
0
Total dollars
[COST-VOLUME-PROFIT ANALYSIS]
Units produced and sold
The intersection of the revenue line and the total cost line indicates the breakeven volume,
which in this example, occurs between 571 and 572 units. To the left of this point, the
company incurs a loss. To the right of this point, the company generates profits. The amount
of profit or loss can be measured as the vertical distance between the revenue line and the
total cost line.
Contribution Margin Ratio (CM Ratio)
The contribution margin as a percentage of total sales is referred to as contribution margin
ratio (CM Ratio).
Formula of CM Ratio:
[CM Ratio = Contribution Margin / Sales]
This ratio is extensively used in cost-volume profit calculations.
Example
Consider the following contribution margin income statement of Omar’s company in which
sales revenues, variable expenses, and contribution margin are expressed as percentage of
sales.
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Total
Per Unit
Percent of
Sales
Sales (400 units)
$100,000
$250
100%
Less variable expenses
60,000
150
60%
------------
------------
------------
$40,000
$100
40%
======
======
Contribution margin
Less fixed expenses
35,000
------------
Net operating income
$5,000
======
According to above data of Omar’s company the computations are:
Contribution Margin Ratio = (Contribution Margin / Sales) × 100
= ($40,000 / $100,000) × 100
= 40%
In a company that has only one product such as Omar’s company CM ratio can also be
calculated as follows:
Contribution Margin Ratio = (Unit contribution margin / Unit selling price) × 100
= ($100 / $250) × 100
= 40%
Importance of Contribution Margin Ratio
The CM ratio is extremely useful since it shows how the contribution margin will be affected
by a change in total sales. To illustrate notice that Omar’s company has a CM ratio of 40%.
This means that for each dollar increase in sales, total contribution margin will increase by
40 cents ($1 sales × CM ratio of 40%). Net operating income will also increase by 40 cents,
assuming that fixed cost do not change.
The impact on net operating income of any given dollar change in total sales can be
computed in seconds by simply applying the contribution margin ratio to the dollar change.
For example if the A Omar’s company plans a $30,000 increase in sales during the coming
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month, the contribution margin should increase by $12,000 ($30,000 increased sales × CM
ratio of 40%). As we noted above, Net operating income will also increase by $12,000 if fixed
cost do not change. This is verified by the following table:
Sales Volume
Percent
Expected
Increase
Percent of
Sales
Sales
$100,000
$130,000
$30,000
10%
Less variable expenses
60,000
78,000
18,000
60%
---------
--------
--------
------
Contribution margin
40,000
52,000
12,000
40%
Less fixed expenses
35,000
35,000
0
======
---------
--------
--------
5,000
17,000*
12,000
======
======
======
Net operating income
*Expected net operating income of $17,000 can also be calculated directly by using the
following formula:
[P*= (Sales × CM ratio) – Fixed Cost]
P* = Profit
Review Problems
Problem 1
Sales = $5,000,000
CM = 0.40
Fixed cost = $1,600,000
Calculate Profit.
Solution
P = (Sales × CM ratio) – Fixed Cost
P = ($5,000,000 × 0.4) – $1,600,000
P = $2,000,000 – $1,600,000
= $400,000
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Problem 2
A company has budgeted sales of $200,000, a profit of $60,000 and fixed expenses of
$40,000.
Calculate contribution margin ratio.
Solution:
P = (Sales × CM ratio) – Fixed Cost
$60,000 = ($200,000 × CM ratio) – $40,000
$60,000 + $40,000 = ($200,000 × CM ratio)
CM ratio = $100,000 / $200,000
= 0.5
Some managers prefer to work with the contribution margin ratio rather than the unit
contribution margin. The CM ratio is particularly valuable in situations where trade-offs
must be made between more dollar sales of one product versus more dollar sales of
another. Generally speaking, when trying to increase sales, products that yield the greatest
amount of contribution margin per dollar of sales should be emphasized.
Target Costing
A relatively recent innovation in product planning and design is called target costing. In the
context of the Basic Profit Equation, target costing sets a goal for profits, and solves for the
unit variable cost required to achieve those profits. The design and manufacturing engineers
are then assigned the task of building the product for a unit cost not to exceed the target.
This approach differs from a more traditional product design approach, in which design
engineers (possibly with input from merchandisers) design innovative products,
manufacturing engineers then determine how to make the products, cost accountants then
determine the manufacturing costs, and finally, merchandisers and sales personnel set sales
prices. Hence, setting the sales price comes last in the traditional approach, but it comes
first in target costing.
Target costing is appropriate when SP and Q are predictable, but are not choice variables,
such as might occur in well-established competitive markets. In such a setting,
merchandisers might know the price that they want to charge for the product, and can
probably estimate the sales volume that will be achieved at that price. Target costing has
been used successfully by a number of companies including Toyota, which redesigned the
Camry around the turn of the century as part of a target costing strategy.
Examples
Breakeven: Omar owns a service station in Walnut Creek. Steve is considering leasing a
machine that will allow him to offer customers the mandatory California emissions test.
Every car in the state must be tested every two years. The machine costs $6,000 per month
to lease. The variable cost per test (i.e., per car inspected) is $10. The amount that Steve can
charge each customer is set by state law, and is currently $40.
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How many inspections would Steve have to perform monthly to break even from this part of
his business?
Q = FC ÷ Unit Contribution Margin
Q = $6,000 ÷ ($40  $10) = 200 inspections
Targeted profits, solving for volume: Refer to the information in the previous question.
How many inspections would Steve have to perform monthly to generate a profit of $3,000
from this part of his business?
P + FC = Q x (SP – VC)
$3,000 + $6,000 = Q x ($40  $10)
Q = 300 inspections
Targeted profits, solving for sales price: Alice Waters (age 9) runs a lemonade stand in the
summer in Palo Alto, California. Her daily fixed costs are $20. Her variable costs are $2 per
glass of ice-cold, refreshing, lemonade. Alice sells an average of 100 glasses per day. What
price would Alice have to charge per glass, in order to generate profits of $200 per day?
P + FC = Q x (SP – VC)
$200 + $20 = 100 x (SP - $2)
SP = $4.20 per glass
Contribution margin: Refer to the previous question. What price would Alice have to charge
per glass, in order to generate a total contribution margin of $200 per day?
Total CM = Q x (SP – VC)
$200 = 100 x (SP - $2.00)
SP = $4.00 per glass
Target costing: Refer to the information about Alice, but now assume that Alice wants to
charge $3 per glass of lemonade, and at this price, Alice can sell 110 glasses of lemonade
daily. Applying target costing, what would the variable cost per glass have to be, in order to
generate profits of $200 per day?
P + FC = Q x (SP – VC)
$200 + $20 = 110 x ($3 – VC)
VC = $1
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Questions
The unit contribution margin is calculated as the difference between:
A) selling price and fixed cost per unit.
B) selling price and variable cost per unit.
C) selling price and product cost per unit.
D) fixed cost per unit and variable cost per unit.
E) fixed cost per unit and product cost per unit.
The break-even point is that level of activity where:
A) total revenue equals total cost.
B) variable cost equals fixed cost.
C) total contribution margin equals the sum of variable cost plus fixed cost.
D) sales revenue equals total variable cost.
E) profit is greater than zero.
The contribution margin ratio is:
A) the difference between the selling price and the variable cost per unit.
B) fixed cost per unit divided by variable cost per unit.
C) variable cost per unit divided by the selling price.
D) unit contribution margin divided by the selling price.
E) unit contribution margin divided by fixed cost per unit.
Cost-volume-profit analysis is based on certain general assumptions. Which of the following is
not one of these assumptions?
A) Product prices will remain constant as volume varies within the relevant range.
B) Expenses can be categorized as fixed, variable, or semi variable.
C) The efficiency and productivity of the production process and workers will change to reflect
manufacturing advances.
D) Total fixed expenses remain constant as activity changes.
E) Unit variable expense remains constant as activity changes.
The contribution income statement differs from the traditional income statement in which of
the following ways?
A) The traditional income statement separates costs into fixed and variable components.
B) The traditional income statement subtracts all variable expenses from sales to obtain the
contribution margin.
C) Cost-volume-profit relationships can be analyzed from the contribution income statement.
D) The effect of sales volume changes on profit is readily apparent on the traditional income
statement.
E) The contribution income statement separates costs into product and period categories.
A company that desires to lower its break-even point should strive to:
A) decrease selling prices.
B) reduce variable costs.
C) increase fixed costs.
D) sell more units.
E) pursue more than one of the above actions.
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The extent to which an organization uses fixed costs in its cost structure is measured by:
A) financial leverage.
B) operating leverage.
C) fixed cost leverage.
D) contribution leverage.
E) efficiency leverage.
A company, subject to a 40% tax rate, desires to earn $300,000 of after-tax income. How much
should the firm add to fixed expenses when figuring the sales revenues necessary to produce
this income level?
A) $120,000.
B) $180,000.
C) $300,000.
D) $500,000.
E) $750,000.
Which of the following would take place if a company were able to reduce its variable
cost per unit?
A)
B)
C)
D)
E)
511
Contribution Margin
Increase
Increase
Decrease
Decrease
Increase
Breakeven Point
Increase
Decrease
Increase
Decrease
No effect
[COST-VOLUME-PROFIT ANALYSIS]
1433
Break Even Point Analysis
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 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.
For example we can use the following data to calculate break even point.



Sales price per unit = SR250
variable cost per unit = SR150
Total fixed expenses = SR35,000
Calculate break even point
Sales = Variable expenses + Fixed expenses + Profit
SR 250Q* = SR 150Q* + SR 35,000 + SR 0**
SR100Q = SR35000
Q = SR35,000 /SR100
Q = 350 Units
Q* = Number (Quantity) of units sold.
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**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 × SR250 Per unit = SR87,500
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
SR35,000 / SR100* per unit
350 Units
*S250 (Sales) − SR150 (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 value= Fixed expenses / CM ratio
SR35,000 / 0.40
= SR87,500
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 = [SR35,000 / 1 – (150 / 250)]
= SR35,000 / 1 – 0.6
= SR35,000 / 0.4
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= SR87,500
Benefits / Advantages of Break Even Analysis
The main advantage 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 SR1 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.
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Review Problem:
Dima’s 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
SR 1,200,000
SR 60
100%
Less variable expenses
900,000
45
?%
--------
--------
--------
Contribution margin
300,000
15
?%
Less fixed expenses
240,000
======
======
-------Net operating income
SR60,000
======
Calculate break even point both in units and sales value. Use the equation method.
Solution:
Sales = Variable expenses + Fixed expenses +Profit
SR 60 Q = SR 45 Q + SR 240,000 + SR 0
SR 15 Q = SR 240,000
Q = SR 240,000 / 15 per unit
Q = 16,000 units; or at SR60 per unit, SR960,000
Alternative solution:
X = 0.75 X + 240,000 + SR 0
0.25 X = SR 240,000
X = SR 240,000 / 0.25
X = SR 960,000; or at SR60 per unit, 16,000 units
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Target Profit Analysis
Target profit is the amount of net operating income or profit that management desires to
achieve at the end of a business period. Management needs to know the required level of
business activities to get target profits.
Cost volume profit (CVP) equations and formulas can be used to determine the sales volume
needed to achieve a target profit. The explanation of target profit analysis requires an
example.
Example





Sales price per unit = SR250
Variable cost per unit = SR150
Total fixed expenses = SR35,000
Target Profit = SR40,000
Q = Number (Quantity) of units sold
Required:
How many units will have to be sold to earn a profit of SR40,000?
Solution
The CVP Equation Method
Under CVP equation approach, we can find the number of units to be sold to obtain target
profit by solving the equation where profits are equal to target profit (that is SR 40,000).
Sales = Variable expenses + Fixed expenses + Profit
SR250Q = SR150 + SR35,000 + SR40,000
SR100Q = SR75,000
Q = SR75,000 / SR100 per unit
Q = 750 Units
Thus the target profit can be achieved by selling 750 units per month, which represents SR
187,500 in total sales (SR 250 × 750 units). This equation is also extensively used to calculate
break even point. When break even point is calculated the value of profit in the equation is
taken equal to ZERO.
The Contribution Margin Approach:
A second approach involves expanding the contribution margin formula to include the
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1433
target profit.
[Unit sales to attain target profit = (Fixed expenses + Target Profit) ÷ Unit contribution
margin]
This approach gives the same answer as the equation method since it is simply a short cut
version of the equation method. similarly the dollar sales needed to attain the target profit
can be computed as follows:
Dollar sales to attain the target profit = [(Fixed expenses + Target profit) ÷ CM ratio]
= (SR35,000 + SR40,000) ÷ 0.40
= SR187,500
No. of units to be sold = SR187,500 / SR250
=750 units
Review Problem:
Dima’s Company manufactures and sells a telephone answering machine. The Company's
contribution margin format income statement for the most recent year is given below:
Total
Per Unit
Percent of
Sales
Sales (20,000 units)
SR1,200,000
SR60
100%
Less variable expenses
900,000
45
?%
-----------
-----------
-----------
Contribution margin
300,000
SR15
?%
Less fixed expenses
240,000
======
======
-----------Net operating income
SR60,000
======
Management is anxious to improve the company's profit performance. Assume that next
year management wants the company to earn a minimum profit of SR90,000. How many
units will have to be sold to meet the target profit figure?
Solution:
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1433
Equation Method:
Sales = Variable expenses + Fixed expenses + Profits
SR60Q = SR45Q + SR240,000 + SR90,000
SR15Q = SR3330,000
Q = SR3330,000 / SR15 Per unit
Q = 22,000 Units
Contribution Margin Method:
[(Fixed expenses + Target profit) / Contribution margin per unit]
[(SR240,000 + SR90,000) / SR15 Per unit]
22,000 Units
Margin of Safety (MOS)
Margin of safety (MOS) is the excess of budgeted or actual sales over the break even volume
of sales. It stats the amount by which sales can drop before losses begin to be incurred. The
higher the margin of safety, the lower the risk of not breaking even.
Formula of Margin of Safety:
The formula or equation for the calculation of margin of safety is as follows:
[Margin of Safety = Total budgeted or actual sales − Break even sales]
The margin of safety can also be expressed in percentage form. This percentage is obtained
by dividing the margin of safety in dollar terms by total sales. Following equation is used for
this purpose.
[Margin of Safety = Margin of safety in dollars / Total budgeted or actual sales]
Example
Sales(400 units @ SR250)
SR100,000
Break even sales
SR87,500
Calculate margin of safety
solution
Sales(400units @SR 250)
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SR100,000
[COST-VOLUME-PROFIT ANALYSIS]
1433
Break even sales
SR 87,500
---------
Margin of safety in dollars
SR 12,500
=======
Margin of safety as a percentage of sales:
12,500 / 100,000
= 12.5%
It means that at the current level of sales and with the company’s current prices and cost
structure, a reduction in sales of SR12,500, or 12.5%, would result in just breaking even. In a
single product firm, the margin of safety can also be expressed in terms of the number of
units sold by dividing the margin of safety in dollars by the selling price per unit. In this case,
the margin of safety is 50 units (SR12,500 ÷ SR 250 units = 50 units).
Review Problem:
Dim’s company manufactures and sells a telephone answering machine. The company's
contribution margin income statement for the most recent year is given below:
Total
Per unit
Percent of Sales
Sales (20,000 units)
SR 1,200,000
SR60
100%
Less variable expenses
900,000
SR45
?%
---------
--------
--------
Contribution margin
300,000
SR15
?%
Less fixed expenses
240,000
======
=====
Description
--------Net operating income
60,000
======
Required: margin of safety of safety both in dollars and percentage form.
Solution to Review Problem:
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Margin of safety = Total sales – Break even sales*
= SR1,200,000 – SR960,000
= SR240,000
Margin of safety percentage = Margin of safety in dollars / Total sales
= SR240,000 / SR1,200,000
= 20%
*The break even sales have been calculated as follows:
Sales = Variable expenses + Fixed expenses + Profit
SR60Q = SR45Q + SR240,000 + SR0**
SR15Q = SR240,000
Q = SR240,000 / SR15 per unit
Q = 16,000 units; or at SR60 per unit. SR960,000
**We know that break even is the level of sales where profit is zero
Break Even Analysis With Multiple Products
Sale mix--Definition and Explanation of the Concept
The term sale mix refers to the relative proportion in which a company's products are sold.
The concept is to achieve the combination, that will yield the greatest amount of profits.
Most companies have many products, and often these products are not equally profitable.
Hence, profits will depend to some extent on the company's sales mix. Profits will be greater
if high margin rather than low margin items make up a relatively large proportion of total
sales.
Changes in sales mix can cause interesting variation in profits. A shift in sales mix from high
margin items to low margin items can cause profits to decrease even though total sales may
increase. Conversely, a shift in sales mix from low margin items to high margin items can
cause reverse effect-total profit may increase even though total sales decrease. It is one
thing to achieve a particular sales volume; it is quite a different thing to sell most profitable
mix of products.
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Sales Mix and Break Even Analysis
If a company sells multiple products, break even analysis is somewhat more complex than
discussed in the topic break even point calculation. The reason is that the different products
will have different selling prices, different costs, and different contribution margins.
Consequently, the break even point will depend on the mix in which the various products are
sold
Example
Omar’s Company
Sales
Product A
SR20,000 100%
Product B
80,000 100%
Total
100,000 100%
75%
40,000
50%
55,000 55%
-------
-----
------
-----
------
5,000
25%
40,000
50%
45,000 45%
=====
=====
=====
=====
Less Variable expenses15,000
Contribution margin
Less fixed expenses
----
27,000
-------
Net operating income
18,000
=====
Computation / Calculation of break even point:
Fixed expenses / Overall contribution margin
27,000 / 0.45
SR60,000
SR60,000 sales represent the break even point for the company as long as the sales mix does
not changes. If the sales mix changes, then the break even point will also change. This is
illustrated below.
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Example
Omar’s Company
Product A
Sales
Total
80,000 100% 20,000 100% 100,000100%
Less
variable
60,000 75%
expenses
Contribution
margin
Product B
10,000 50%
70,000 70%
------- -----
------
------
20,000 25%
10,000 50%
-----
30,000 30%
================== ======
Fixed expenses
-----
======
27,000
------
Net
operating
income
3,000
======
Computation / Calculation of break even point:
Fixed expenses / Overall contribution margin
SR27,000 / 0.3
SR90,000
Although sales have remained unchanged at SR100,000, the sales mix is exactly the reverse
of what it was in example1, with the bulk of sales now coming from the less profitable
product A. Notice that this change in the sales mix has caused both the overall contribution
margin and total profits to drop sharply. The overall contribution margin ratio (CM ratio) has
dropped from 45% to 30% and net operating income has dropped from SR18,000 to SR3,000.
The company's break even point is no longer SR60,000 in sales. Since the company is now
realizing less contribution margin per dollar of sales, it takes more sales to cover the same
amount of fixed costs. Thus the break even point has increased from SR60,000 to SR90,000 in
sales per year.
Example
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Omar’s company produce two products A and B. sale price and variable cost for each
product are:
A
B
Price
100 160
Variable cost
70 90
Contribution margin 30 70
Sales mix
3
1
Fixed cost for the company 600000.
Calculate:
Break-even point
Sales that achieve target profit 200000.
Solution
The percent of sales mix for each product:
A = 3/4=0.75
B = 1/4=0. 25
Weighted contribution margin = contribution margin for each product × sales mix percent
for each product.
Weighted contribution margin = (30 × 0.75) + (70 × 0.25)
= 40
Break-even point = fixed cost / Weighted contribution margin
= 600000/40= 15000 units
Volume of sales to achieve target profit = (fixed cost + target profit) / Weighted contribution
margin
= (600000 + 200000) / 40= 20000 units
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Questions
first
Edco Company produced and sold 45,000 units of a single product last year, with
the following results:
Sales revenue
Manufacturing costs:
Variable
Fixed
Selling costs:
Variable
Fixed
Administrative costs:
Variable
Fixed
$1,350,000
$585,000
$270,000
$40,500
$54,000
$184,500
$108,000
Edco's break-even point in unit sales for the previous year was:
A) 15,882.
B) 24,000.
C) 25,411.
D) 26,832.
E) 36,000.
The break-even point is that level of activity where:
A) total revenue equals total cost.
B) variable cost equals fixed cost.
C) total contribution margin equals the sum of variable cost plus fixed cost.
D) sales revenue equals total variable cost.
E) profit is greater than zero.
A company that desires to lower its break-even point should strive to:
A) decrease selling prices.
B) reduce variable costs.
C) increase fixed costs.
D) sell more units.
E) pursue more than one of the above actions.
Omar has a break-even point of 40,000 units. If the firm's sole product sells for $24 and
fixed costs total $240,000, the variable cost per unit must be:
A) $6.
B) $10.
C) $18.
D) an amount that cannot be derived based on the information presented.
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E) an amount other than those in choices "a," "b," and "c" but one that can be derived
based on the information presented.
If a company desires to increase its safety margin, it should:
A) increase fixed costs.
B) decrease the contribution margin.
C) decrease selling prices, assuming the price change will have no effect on demand.
D) stimulate sales volume.
E) attempt to raise the break-even point.
Dima sells a single product for $60 that has a variable cost of $40. Fixed costs at the
break-even point amount to $5 per unit. If the company sells one unit in excess of its
break-even volume, the bottom-line profit will be:
A) $15.
B) $20.
C) $60.
D) an amount that cannot be derived based on the information presented.
E) an amount other than those in choices "a," "b," and "c" but one that can be derived
based on the information presented.
The difference between budgeted sales revenue and break-even sales revenue is the:
A) unit contribution margin.
B) contribution margin ratio.
C) safety margin.
D) target net profit.
E) operating leverage.
Second (true – false)
511
1. Fixed Expenses do not change in total when there is a modest change in
sales.
True False
2. An example of a fixed expense would be a 5% sales commission.
True False
3. Property taxes and rent are often fixed expenses.
True False
4. Variable expenses change in total as volume changes.
True False
5. An example of a variable expense is an office manager's monthly salary.
True False
6. A retailer's cost of goods sold is an example of a variable expense.
True False
7. Contribution margin is defined as sales (or revenues) minus variable
expenses.
True False
8. Break-even point is the point where revenues equal the total of all
expenses including the cost of goods sold.
True False
[COST-VOLUME-PROFIT ANALYSIS]
9. The break-even point in dollars of revenues is equal to the total of the
fixed expenses divided by the contribution margin per unit.
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True False
10. If a company requires a profit of $30,000 (instead of breaking even), the
$30,000 should be combined with the fixed expenses in order to compute
the point at which the company will earn $30,000.
True False
11. If a company has mixed expenses, the fixed component can be combined
with the company's fixed expenses and the variable component can be
combined with the company's variable expenses.
True False
12. Decreasing a company's fixed expenses should reduce the break-even
point.
True False
13. The contribution margin per unit is the selling price per unit minus the
fixed expenses per unit.
True False
14. Break-even analysis is useful for companies that sell products, but it is not
useful for companies that provide services.
True False