CH 3 ACCOUNTING.pptCost-Volume-Profit Analysis

Cost-Volume-Profit Analysis

1. Chapter 3
Cost-Volume-Profit Analysis

2. After studying this chapter, you should be able to:
Chapter 1: Cost-Volume-Profit
Analysis
1Distinguish between variable and fixed costs.
2Explain the meaning and importance of the
relevant range.
3Explain the concept of mixed costs.
4State the five components of cost-volume-profit
analysis.
5Identify the ways that the break-even point may be
determined.
6Give the formulas for determining sales required to
earn target operating and net income.
7Discern the meaning of the degree of operating
leverage and link the cost-volume-profit analysis to

3. Cost Behavior Analysis
Cost behavior analysisis the study of how
specific costs respond to changes in the level of
activity within a company.
The starting point in cost behavior analysis is
measuring the key activities in the company’s
business.
Activity levelsmay be expressed in terms of
sales dollars (retail company),
miles driven (trucking company),
room occupancy (hotel), or
number of dance classes taught (dance studio).

4. Cost Behavior Analysis
For an activity level to be useful in cost behavior
analysis, there should be correlation between
changes in the level or volume of activity and
changes in the costs.
The activity levelselected is referred to as the
activity (or volume) index.
The activity indexidentifies the activity that causes
changes in the behavior of costs.
Variable costsare costs that vary in total
directly and proportionately with changes in the
activity level.
A variable cost may also be defined as a cost that
remains the same per unitat every level of
activity.

5. Variable Costs
Damon Company manufactures radios that contain a $10
digital clock. The activity indexis the number of radios
produced. As each radio is manufactured, the total cost of
the clocks increases by $10.
$100
80
60
40
20
0
Cost (000)
0246810
Radios produced in (000)
(a) Total Variable Costs
(Digital Clocks)
0
5
$25
20
15
10Cost (per
unit)
0246810
Radios produced in (000)
(b) Unit Variable Costs
(Digital Clocks)

6. Fixed Costs
Fixed costsare costs that remain the same in
totalregardless of changes in the activity level.
Since fixed costs remain constant in total as activity
changes, fixed costs per unitvary inversely with
activity. As volume increases, unit cost declines
and vice versa.

7. Fixed Costs
Damon Company leases all of its productive facilities at a
cost of $10,000 per month. Total fixed costs of the facilities
will remain constant at every level of activity.
$25
20
15
10
5
0
Cost (000)
0246810
Radios produced in (000)
(a) Total Fixed Costs
(Rent Expense)
0
1
$5
4
3
2Cost (per
unit)
0246810
Radios produced in (000)
(b) Fixed Costs Per Unit
(Rent Expense)

8. Nonlinear Behavior of Variable
and Fixed Costs
In the previous two slides, the assumption was made that total
variable costs and total fixed costs were linear, and straight lines
were used to represent both types of costs. A straight-line
relationship does not usually exist for variable costs throughout the
entire range of activity.
In the real world, the relationship between variable cost behavior and
changes in the activity level is often curvilinear.
Operating at zero or at 100% capacity is the exception for most
companies. Companies usually operate over a narrower range –
such as 40-80% of capacity. The relevant rangeof the activity index
is the range over which a company expects to operate during a year.
Within this range a straight-line relationship normally exists for both
fixed and variable costs.

9. Mixed Costs
Mixed costscontain both a variable cost element and a fixed
cost element.
Sometimes called semi-variable costs, mixed costs change
in total but not proportionatelywith changes in the activity
level.
The rental of a U-Haul truck is a good example of a mixed
cost.
Local rental terms for a U-Haul truck are $50 per day plus $.50
per mile. The per diem charge is a fixed costwith respect to
miles driven, while the mileage charge is a variable cost. The
graphic presentation of the rental cost for a one-day rental is
shown below.
150
$200
100
50
Cost
0
Variable Cost Element
Fixed Cost Element
0 50 100150200250300
Miles

10. Mixed Cost Classification for CVP
Analysis
In CVP analysis, it is assumed that mixed costs must
be classified into their fixed and variable elements.
Firms usually ascertain variable and fixed costs on an
aggregate basis at the end of a time period, using the
company’s past experience with the behavior of the
mixed cost at various activity levels.
The mathematical methods of separating total costs into
their fixed and variable components is left for advanced
courses.

11. Cost-Volume Profit Analysis
Cost-volume-profit (CVP)analysisis the study
of the effects of changes of costs and volume on a
company’s profits.
CVP analysisinvolves a consideration of the
interrelationships among the following
components:
Volume or activity level
Unit selling price
Variable cost per unit
Total fixed costs
Sales mix

12. CVP Assumptions
The following assumptions underlie each CVP
application:When these assumptions are not valid,
the results of CVP analysis may be inaccurate.
1The behavior of both costs and revenues is linear
throughout the relevant range of the activity index.
2All costs can be classified as either variable or fixed
with reasonable accuracy.
3Changes in activity are the only factors that affect
costs.
4All units produced are sold.
5When more than one type of product is sold, total sales
will be in a constant sales mix.

13. CVP Analysis
In CVP analysisapplications, the term cost
includes manufacturing costs plus selling and
administrative expenses.
We will use Vargo Video Company as an example.
Relevant data for the VCRs made by this company are
as follows:
Unit selling price
Unit variable costs
Total monthly fixed costs
$500
$300
$200,000

14. Contribution Margin
One of the key relationships in CVP analysis is
contribution margin (CM). Contribution margin is the
amount of revenue remaining after deducting variable
costs. The CM is then available to cover fixed costs and
to contribute income for the company.
For example, assume that VargoVideo sells 1,000 VCRs
in one month, sales are $500,000 (1,000 x$500) and
variable costs are $300,000 (1,000 x$300). Thus,
contribution margin is $200,000, computed as follows:
Sales Variable Costs
Contribution
Margin- =
$500,000 $300,000 $200,000- =

15. Unit Contribution Margin
Views differ as to the best way to express
contribution margin (CM). Some favor a per unit
basis.
At Vargo Video, the contribution margin per unitis
$200.
Unit Selling Price
Unit Variable
Cost
Contribution
Margin per Unit- =
$500 $300 $200- =
CM per unit indicates that for every VCR sold, Vargo
Video will have $200 to cover fixed costs and contribute
to income.

16. Contribution Margin Ratio
Others prefer to use a contribution margin
ratio.
At Vargo Video, the contribution margin ratiois
40%.
Contribution
Margin per Unit
Unit Selling Price
Contribution
Margin Ratio =
$200 $500 40% =
The CM ratio means that 40 cents of each sales dollar
($1 x40%) is available to apply to fixed costs and to
contribute to income.

17. Break-Even Analysis
The second key relationship in CVP analysis is the
break-even point, which is the level of activity
where total revenues equals total costs, both
fixed and variable.
Since no income is involved when the break-even
point is the objective, the analysis is often referred
to as break-even analysis.
The break-even pointcan be:
Computed from a mathematical equation.
Computed by using contribution margin.
The break-even point can be expressed in either
sales dollarsor sales units.

18. Break-Even Analysis: Mathematical Equation
In its simplest form, the equation for
break-even sales is:
Break-even Sales Variable Costs Fixed Costs= +
The break-even point in dollarsis found by
expressing variable costs as a percentage of unit
selling price.
For VargoVideo, the percentage is 60% ($300 $500).
Sales must be $500,000 for VargoVideo to break even.
The computation to determine sales dollars at the break-
even point is:
X = .60X + $200,000
.40X = $200,000
X = $500,000
where:
X = sales dollars at the break-even point
.60 = variable costs as a percentage of unit selling price
$200,000 = total fixed costs

19. Break-Even Analysis:
Mathematical Equation for Units
The break-even point in unitscan be
computed directly from the mathematical
equation by using unit selling prices and unit
variable costs. Vargo must sell 1,000 units to
break even. The computation is:
$500X = $300X + $200,000
$200X = $200,000
X = 1,000 units
where:
X = sales volume
$500 = unit selling price
$300 = variable cost per unit
$200,000 = total fixed costs

20. Break-Even Analysis: CM Technique for Units
Because we know that CM equals total revenues less
variable costs, it follows that at the break-even point,
contribution margin must equal total fixed costs.
When the CM per unit is used, the formula to compute
break-even point in unitsis shown below:
Once again, the CM per unit for VargoVideo is $200.
Fixed Costs
Contribution
Margin per Unit
Break-even Point
in Units =
$200,000 $200 1,000 =

21. Break-Even Analysis: CM Technique for
Dollars
When the CM ratio is used, the formula to
compute break-even point in dollarsis
shown below:
Again, the CM ratio for Vargo Video is 40%.
Fixed Costs
Contribution
Margin Ratio
Break-even Point
in Dollars =
$200,000 40% $500,000 =

22. The CVP Graph
In the graph to
the right, sales
volume is
shown on the
horizontal axis.
This axis needs
to extend to the
maximum level
of expected
sales. Both
total revenues
(sales) and total
costs (fixed plus
variable) are
recorded on the
vertical axis.
Dollars (000)
Units of Sales
$900
700
600
500
400
300
200
100
12002004006008001000 140016001800
Break-even
Point
Profit
Area
Sales
Line
Total Cost
Line
Fixed Cost
Line
Loss
Area

23. Margin of Safety
The margin of safety is another relationship that
may be calculated in CVP analysis. Margin of
safetyis the difference between actual or
expected sales and sales at the break-even point
This relationship measures the “breathing room” or
“cushion” that management has in order to break
even if actual sales fail to materialize.

24. Margin of Safety
The margin of safetymay be expressed in dollars or as a
ratio.Assuming that actual (expected) sales for Vargo Video
are $750,000, the computations are:
Actual (Expected)
Sales
Break-even Sales
Margin of Safety
in Dollars- =
$750,000 $500,000 $250,000- =
Margin of Safety in Dollars
Margin of Safety
in Dollars
Actual (Expected)
Sales
Margin of Safety
Ratio =
$250,000 $750,000 33% =
Margin of Safety Ratio

25. Target Operating Income
Management usually sets an income objective for
individual product lines. This objective, called target
Operating income, is extremely useful to
management because it indicates the sales
necessary to achieve a specified level of income.
The amount of sales necessary to achieve target
operating income can be determined from each of
the approaches used in determining break-even
sales.

26. Target Operating Income: Mathematical
Equation
We know that at the break-even point no profit or loss
results for the company. By adding a factor for target
operating income to the break-even equation, we
obtain the formula shown below for determining
required sales.
Required sales may be expressed in either sales dollars or
sales units.
Required
Sales =
Variable
Costs +
Fixed
Costs +
Target
Operating
Income

27. Target Operating Income: Mathematical
Equation
Assuming the target net income is $120,000 for Vargo
Video, the computation of required sales in dollarsis
as follows:
X = .60X + $200,000 + $120,000
.40X = $320,000
X = $800,000
where:
X = required sales
.60 = variable costs as a percentage of unit selling price
$200,000 = total fixed costs
$120,000 = target operating income
The sales volume in unitsat the target income level is found
by dividing the sales dollars by the unit selling price.
$800,000 $500 = $1,600

28. Target Operating Income: CM Technique
As in the case of break-even sales, the sales
required to meet a target net income can be
computed in either dollars or units.
The formula using the CM ratio for Video Vargo is as
follows:
Required Sales
Fixed Costs +
Target Operating
Income
Contribution
Margin Ratio
$320,000 40% $800,000= 
=

29. CVP and Changes in the Business
Environment
Business conditions change rapidly and
management must respond intelligently to these
changes.
CVP analysiscan be used in responding to
change.
The original VCR sales and cost data for Vargo
Video Company are shown below.Unit selling price$ 500
Unit variable cost$ 300
Total fixed costs$ 200,000
Break-even sales $ 500,000or 1,000 units

30. Fixed Costs÷ Contribution Margin per Unit= Break-even Sales
$ 200,000 ÷ $ 150 = 1,333 units (rounded)
CVP and Changes in the Business Environment:
Case I
A competitor is offering a 10% discount on the selling price of
its VCRs. Management must decide whether or not to offer a
similar discount.
Question: What effect will a 10% discount on selling price
have on the break-even point for VCRs?
Answer: A 10% discount on selling price reduces the selling
price per unit to $450 [$500 –($500 x10%)]. Variable cost per
unit remains unchanged at $300. Therefore, the contribution
margin per unit is $150. Assuming no change in fixed costs,
break-even sales are 1,333 units, calculated as follows:

31. Fixed Costs÷ Contribution Margin per Unit= Break-even Sales
$ 260,000 ÷ ($500 -$210) = 900 units (rounded)
Illustration 5-28
CVP and Changes in the Business
Environment: Case II
Management invests in new robotic equipment that will
significantly lower the amount of direct labor required to make
the VCRs. It is estimated that total fixed costs will increase
30% and that variable cost per unit will decrease 30%.
Question: What effect will the new equipment have on the
sales volume required to break even?
Answer: Total fixed costs become $260,000 [$200,000 +
($200,000 x30%)], and variable cost per unit is now $210
[$300 –($300,000 x30%)]. The new break-even point about
900 units, calculated as follows:

32. CVP and Changes in the Business
Environment: Case III
An increase in the price of raw materials will increase the unit
variable cost of VCRs by an estimated $25. Management is
striving to hold the line on the selling price of the VCRs, and plans
a cost-cutting program that will save $17,500 in fixed costs per
month. Vargo Video Company is currently realizing monthly
income of $80,000 on sales of 1,400 VCRs.
Question: What increase in sales will be needed to maintain the
same level of income?
Answer: The variable cost per unit increases to $325 ($300 +
$25), and fixed costs are reduced to $182,500 ($200,000 –
$17,500). Because of the change in variable cost, the variable cost
becomes 65% of sales ($325 ÷$500). Using the equation for
target net income, required sales are calculated to be $750,000, as
follows:
Required Sales = Variable Costs + Fixed Costs + Target Net Income
X = .65X + $182,500 + $80,000
.35X = $262,500
X = $750,000

33. CVP Analysis with Multiple Products
7-33
For a company with more than one product, sales mix
is the relative combination in which a company’s
products are sold. Different products have different
selling prices, cost structures, and contribution margins.
Let’s assume Curl sells surfboards and sail boards and
see how we deal with break-even analysis.

34. CVP Analysis with Multiple Products
7-34
Curl provides us with the following information:Description
Selling
Price
Unit
Variable
Cost
Unit
Contribution
Margin
Number
of
Boards
Surfboards 500$ 300$ 200$ 500
Sailboards 1,000 450 550 300
Total sold 800 Description
Number
of Boards
% of
Total
Surfboards 500 62.5%(500 ÷ 800)
Sailboards 300 37.5%(300 ÷ 800)
Total sold 800 100.0%

35. CVP Analysis with Multiple Products
7-35
Weighted-average unit contribution marginDescription
Contribution
Margin % of Total
Weighted
Contribution
Surfboards 200$ 62.5% 125.00$
Sailboards 550 37.5% 206.25
Weighted-average contribution margin 331.25$
$200 ×62.5%
$550 ×37.5%

36. CVP Analysis with Multiple Products
7-36
Break-even point
Break-even
point
=
Fixed expenses
Weighted-average unit contribution margin
Break-even
point
=
$170,000
$331.25
Break-even
point
=514 combined unit sales

37. CVP Analysis with Multiple Products
7-37
Break-even point
Break-even
point
=514 combined unit salesDescription
Breakeven
Sales
% of
Total

Individual
Sales
Surfboards 514 62.5% 321
Sailboards 514 37.5% 193
Total units 514

38. CVP Relationships and the Income
Statement
7-38A. Traditional Format
Sales $500,000
Less: 380,000
Gross margin $120,000
Less: Operating expenses:
Selling expenses $35,000
Administrative expenses 35,000 70,000
Net income $50,000
ACCUTIME COMPANY
Income Statement
For the Year Ended December 31, 20x1

39. CVP Relationships and the Income
Statement
7-39B. Contribution Format
Sales $500,000
Less: Variable expenses:
Variable manufacturing $280,000
Variable selling 15,000
Variable administrative 5,000 300,000
Contribution margin $200,000
Less: Fixed expenses:
Fixed manufacturing $100,000
Fixed selling 20,000
Fixed administrative 30,000 150,000
Net income $50,000
Income Statement
For the Year Ended December 31, 20x1
ACCUTIME COMPANY

40. Cost Structure and Operating
Leverage
7-40
The cost structure of an organization is the
relative proportion of its fixed and variable
costs.
Operating leverage is . . .
The extent to which an organization uses
fixed costs in its cost structure.
Higher in companies that have a high
proportion of fixed costs in relation to variable
costs.

41. Measuring Operating Leverage
7-41
Contribution margin
Net income
Operating leverage
factor
=Actual sales
500 Board
Sales 250,000$
Less: variable expenses 150,000
Contribution margin 100,000
Less: fixed expenses 80,000
Net income 20,000$
$100,000
$20,000
= 5

42. Measuring Operating Leverage
A measure of how a percentage change in sales will
affect profits. If a company increases its sales by 10%,
what will be the percentage increase in net income?Percent increase in sales 10%
Operating leverage factor× 5
Percent increase in profits50%

43. Effect of Income Taxes
Target after-tax net income
1 -t
=
Before-tax
net income
Incometaxesaffectacompany’sCVPrelationships.Toearna
particularafter-taxnetincome,agreaterbefore-taxincomewillbe
required.Inordertocomputethesaleslevelorquantitiesthatmustbe
soldtoachieveacertainamountofaftertaxincome,makeuseofthe
followingrelationshipbetweenbeforeandaftertaxincomes.
Exercise: What quantity must be sold by Vargo Video if
it aspires to achieve a TNI of 320,000 assuming a tax rate
of 30%?