# Cost Profit Volume _ Analaysis

Document Sample

```					Cost-Volume-Profit
Relationships

1
Introduction
• Cost-volume-profit analysis examines the
behavior of
– total revenues,
– total costs, and
– operating income
• as changes occur in
–   the output level,
–   selling price,
–   variable costs per unit, or
–   fixed costs.

2
Learning Objectives
1 Understand basic cost-volume-profit
(CVP) assumptions
2 Explain essential features of CVP analysis
3 Determine the breakeven point and target
operating income using the equation,
contribution margin, and graph methods

3
Learning Objectives
4 Incorporate income tax considerations into
CVP analysis
5 Explain the use of CVP analysis in
decision making and how sensitivity
analysis can help managers cope with
uncertainty
6 Use CVP analysis to plan costs

4
Learning Objectives
7 Apply CVP analysis to a multi-product
company
8 Distinguish between contribution margin
and gross margin
9 Adapt CVP analysis to multiple cost driver
situations

5
Learning Objective 1

Understand basic cost-
volume-profit (CVP)
assumptions

6
Definitions
• Variable Costs: Costs that vary in total,
directly and proportionately, with changes
in production (also called activity level).
• If the activity level increases by 50%,
variable costs increase by 50%.

7
Examples of Variable Costs
• Direct labor
• Direct materials
• Variable overhead

8
Definitions
• Mixed Costs: costs that contain both a
fixed and a variable element.
• Mixed cost change in total, but not
proportionately, with changes in the
activity level.
• An example of a mixed cost might be
maintenance cost on a taxi.
– Maintenance costs increase as miles increase.
Even if the truck is never driven, however, it is a
good idea to change the oil every three months to
keep it from degenerating.
9
Separating Fixed and Variable
Costs
• If you will look at a general ledger, you will
never find accounts labeled “variable
labor” or “fixed labor” or “variable
overhead” or “fixed overhead.”
• In order to perform cost volume profit
analysis, therefore, it is usually necessary
to separate fixed and variable costs.
• There are three methods best method is the
The to do this:
– Scatter graph method   least squares method,
but since the author
– High-low method
does not teach it we will
– Least squares method   not cover it either.        10
Definitions
• Fixed Costs: Costs that do not change with
increases or decreases in production volume.
• It is important to add, there is usually a
relevant range.
• For example, a plant may be built to
manufacture 1 to 10,000 shoes per month.
• Fixed costs would not change within this
“relevant range.”
• If a company wanted to manufacture 12,000
shoes per month, however, there of course
would be a new relevant range and the fixed11
Examples of Fixed Costs
•   Rent on a factory
•   Depreciation – straight-line method
•   Heating and air-conditioning expense
•   Housekeeping
It is important to emphasize that what might be a fixed
cost in one factory, could be a variable cost in another,
depending upon the way the firm does business.

12
Other Definitions
• Contribution Margin: Revenue (or unit
price) minus total variable costs (or unit
variable costs).
• Example:
Contribution Margin
Note that
Income Statement
contribution
Sales            \$100,000           margin is what
Less variable      60,000           is left after
costs                               paying
variable costs.
Contribution      \$40,000
margin
Less fixed costs   30,000                        13
Other Definitions

Contribution Margin
After fixed
Income Statement
costs are paid,
Sales             \$100,000   where does the
Less variable       60,000   contribution
costs                        margin go? To
the bottom line!
Contribution       \$40,000
margin
Less fixed costs    30,000                14
Cost-Volume-Profit
Assumptions and Terminology
1 Changes in the level of revenues and
costs arise only because of changes in the
number of product (or service) units
produced and sold.
2 Total costs can be divided into a fixed
component and a component that is
variable with respect to the level of output.

15
Cost-Volume-Profit
Assumptions and Terminology
3 When graphed, the behavior of total
revenues and total costs is linear (straight-
line) in relation to output units within the
relevant range (and time period).
4 The unit selling price, unit variable costs,
and fixed costs are known and constant.

16
Cost-Volume-Profit
Assumptions and Terminology
5 The analysis either covers a single product
or assumes that the sales mix when
multiple products are sold will remain
constant as the level of total units sold
changes.
6 All revenues and costs can be added and
compared without taking into account the
time value of money.

17
Cost-Volume-Profit
Assumptions and Terminology
• Operating income = Total revenues from
operations – Cost of goods sold and
operating costs (excluding income taxes)
• Net Income = Operating income +
Nonoperating revenues (such as interest
revenue) – Nonoperating costs (such as
interest cost) – Income taxes

18
Learning Objective 2

Explain essential features of
CVP analysis

19
Essentials of Cost-Volume-
Profit (CVP) Analysis
• Assume that Dresses by Mary can
purchase dresses for \$32 from a local
factory; other variable costs amount to \$10
per dress.
• Because she plans to sell these dresses
overseas, the local factory allows Mary to
return all unsold dresses and receive a full
\$32 refund per dress within one year.

20
Essentials of Cost-Volume-
Profit (CVP) Analysis
• Mary can use CVP analysis to examine
changes in operating income as a result of
selling different quantities of dresses.
• Assume that the average selling price per
dress is \$70 and total fixed costs amount
to \$84,000.
• How much revenue will she receive if she
sells 2,500 dresses?

21
Essentials of Cost-Volume-
Profit (CVP) Analysis
• 2,500 × \$70 = \$175,000
• How much variable costs will she incur?
• 2,500 × \$42 = \$105,000
• Would she show an operating income or
an operating loss?
• An operating loss
• \$175,000 – 105,000 – 84,000 = (\$14,000)

22
Essentials of Cost-Volume-
Profit (CVP) Analysis
• The only numbers that change are total
revenues and total variable cost.
• Total revenues – total variable costs
= Contribution margin
• Contribution margin per unit
= selling price – variable cost per unit
• What is Mary’s contribution margin per
unit?

23
Essentials of Cost-Volume-
Profit (CVP) Analysis
• \$70 – \$42 = \$28 contribution margin per
unit
• What is the total contribution margin
when 2,500 dresses are sold?
• 2,500 × \$28 = \$70,000

24
Essentials of Cost-Volume-
Profit (CVP) Analysis
• Contribution margin percentage
(contribution margin ratio) is the
contribution margin per unit divided by the
selling price.
• What is Mary’s contribution margin
percentage?
• \$28 ÷ \$70 = 40%

25
Essentials of Cost-Volume-
Profit (CVP) Analysis
• If Mary sells 3,000 dresses, revenues will
be \$210,000 and contribution margin
would equal 40% × \$210,000 = \$84,000.

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26
Learning Objective 3

Determine the breakeven
point and target operating
income using the equation,
contribution margin, and
graph methods

27
Breakeven Point...
– is the sales level at which operating
income is zero.
• At the breakeven point, sales minus
variable expenses equals fixed expenses.
• Total revenues = Total costs

28
Abbreviations
•   USP = Unit selling price
•   UVC = Unit variable costs
•   UCM = Unit contribution margin
•   CM% = Contribution margin percentage
•   FC = Fixed costs

29
Abbreviations
• Q = Quantity of output (units sold or
manufactured)
• OI = Operating income
• TOI = Target operating income
• TNI = Target net income

30
Methods for Determining
Breakeven Point
• Breakeven can be computed by using
either the equation method, the
contribution margin method, or the graph
method.

31
Equation Method
• With the equation approach, breakeven
sales in units is calculated as follows:
• (Unit sales price × Units sold) – (Variable
unit cost x units sold) – Fixed expenses =
Operating income

32
Equation Method
• Using the equation approach, compute the
breakeven for Dresses by Mary.
• \$70Q – \$42Q – \$84,000 = 0
• \$28Q = \$84,000
• Q = \$84,000 ÷ \$28
• Q = 3,000 units

33
Contribution Margin Method
• With the contribution margin method,
breakeven is calculated by using the
following relationship:
• (USP – UVC) × Q = FC + OI
• UCM × Q = FC + OI
• Q = FC + OI ÷ UCM
• \$84,000 ÷ \$28 = 3,000 units

34
Contribution Margin Method
• Using the contribution margin percentage,
what is the breakeven point for Dresses by
Mary?
• \$84,000 ÷ 40% = \$210,000

35
Graph Method
• In this method, we plot a line for total
revenues and total costs.
• The breakeven point is the point at which
the total revenue line intersects the total
cost line.
• The area between the two lines to the right
of the breakeven point is the operating
income area.

36
Graph Method
Dresses by Mary

\$ (000)
245
Revenue Break-even

231                   Total
expenses
210
84

37
Target Operating Income...
– can be determined by using any of three
methods:
1 The equation method
2 The contribution margin method
3 The graph method

38
Target Operating Income
• Insert the target operating income in the
formula and solve for target sales either in
dollars or units.
• (Fixed costs + Target operating income)
divided either by Contribution margin
percentage or Contribution margin per unit

39
Target Operating Income
• Assume that Mary wants to have an
operating income of \$14,000.
• How many dresses must she sell?
• (\$84,000 + \$14,000) ÷ \$28 = 3,500
• What dollar sales are needed to achieve
this income?
• (\$84,000 + \$14,000) ÷ 40% = \$245,000

40
Learning Objective 4

Incorporate income tax
considerations into CVP
analysis

41
Target Net Income
and Income Taxes
• When managers want to know the effect of
their decisions on income after taxes, CVP
calculations must be stated in terms of
target net income instead of target
operating income.

42
Target Net Income
and Income Taxes
• Management of Dresses by Mary would
like to earn an after tax income of
\$35,711.
• The tax rate is 30%.
• What is the target operating income?
• Target operating income
= Target net income ÷ (1 – tax rate)
• TOI = \$35,711 ÷ (1 – 0.30)
• TOI = \$51,016                          43
Target Net Income
and Income Taxes
• How many units must she sell?
• Revenues – Variable costs – Fixed costs =
Target net income ÷ (1 – tax rate)
• \$70Q – \$42Q – \$84,000 = \$35,711 ÷ 0.70
• \$28Q = \$51,016 + \$84,000
• Q = \$135,016 ÷ \$28
• Q = 4,822 dresses

44
Target Net Income
and Income Taxes
Proof:
Revenues: 4,822 × \$70
\$337,540
Variable costs: 4,822 × \$42
202,524 Contribution margin
135,016       Fixed costs
84,000      Operating income
51,016 Income
taxes: \$51,016 × 30%           15,305 Net
income                      \$ 35,711    45
Learning Objective 5

Explain the use of CVP
analysis in decision making
and how sensitivity analysis
can help managers cope
with uncertainty

46
Using CVP Analysis
• Suppose the management of Dresses by
Mary anticipates selling 3,200 dresses.
• Management is considering an advertising
campaign that would cost \$10,000.
• It is anticipated that the advertising will
increase sales to 4,000 dresses.
• Should Mary advertise?

47
Using CVP Analysis
• 3,200 dresses sold with no advertising:
• Contribution margin         \$89,600
Fixed costs                  84,000
Operating income            \$ 5,600
• 4,000 dresses sold with advertising:
• Contribution margin         \$112,000
Fixed costs                    94,000
Operating income            \$ 18,000

48
Using CVP Analysis
• Mary should advertise.
• Operating income increases by \$12,400.
• The \$10,000 increase in fixed costs is
offset by the \$22,400 increase in the
contribution margin.

49
Using CVP Analysis
• Instead of advertising, management is
considering reducing the selling price to
\$61 per dress.
• It is anticipated that this will increase sales
to 4,500 dresses.
• Should Mary decrease the selling price per
dress to \$61?

50
Using CVP Analysis
• 3,200 dresses sold with no change in the
selling price:
• Operating income                 \$ 5,600
• 4,500 dresses sold at a reduced selling
price:
• Contribution margin: (4,500 × \$19)
\$85,500 Fixed costs
84,000 Operating income
\$ 1,500
51
Using CVP Analysis

• The selling price should not be reduced to
\$61.
• Operating income decreases from \$5,600
to \$1,500.

52
Sensitivity Analysis and
Uncertainty
• Sensitivity analysis is a “what if “ technique
that examines how a result will change if
the original predicted data are not
achieved or if an underlying assumption
changes.

53
Sensitivity Analysis and
Uncertainty

• Assume that Dresses by Mary can sell
4,000 dresses.
• Fixed costs are \$84,000.
• Contribution margin ratio is 40%.
• At the present time Dresses by Mary
cannot handle more than 3,500 dresses.

54
Sensitivity Analysis and
Uncertainty
• To satisfy a demand for 4,000 dresses,
management must acquire additional
space for \$6,000.
• Should the additional space be acquired?

55
Sensitivity Analysis and
Uncertainty
• Revenues at breakeven with existing
space are \$84,000 ÷ .40 = \$210,000.
• Revenues at breakeven with additional
space are \$90,000 ÷ .40 = \$225,000.

56
Sensitivity Analysis and
Uncertainty
• Operating income at \$245,000 revenues
with existing space = (\$245,000 × .40) –
\$84,000 = \$14,000.
• (3,500 dresses × \$28) – \$84,000 =
\$14,000

57
Sensitivity Analysis and
Uncertainty
• Operating income at \$280,000 revenues
with additional space = (\$280,000 × .40) –
\$90,000 = \$22,000.
• (4,000 dresses × \$28 contribution margin)
– \$90,000 = \$22,000

58
Learning Objective 6

Use CVP analysis to plan
costs

59
Alternative Fixed/Variable
Cost Structures
• Suppose that the factory Dresses by Mary
is using to obtain the merchandise offers
Mary the following:
• Decrease the price they charge Mary from
\$32 to \$25 and charge an annual
administrative fee of \$30,000.
• What is the new contribution margin?

60
Alternative Fixed/Variable
Cost Structures

• \$70 – (\$25 + \$10) = \$35
• Contribution margin increases from \$28 to
\$35.
• What is the contribution margin
percentage?
• \$35 ÷ \$70 = 50%
• What are the new fixed costs?
• \$84,000 + \$30,000 = \$114,000
61
Alternative Fixed/Variable
Cost Structures
• Management questions what sales volume
would yield an identical operating income
regardless of the arrangement.
• 28X – 84,000 = 35X – 114,000
• 114,000 – 84,000 = 35X – 28X
• 7X = 30,000
• X = 4,286 dresses

62
Alternative Fixed/Variable
Cost Structures
• Cost with existing arrangement = Cost with
new arrangement
• .60X + 84,000 = .50X + 114,000
• .10X = \$30,000
• X = \$300,000
• (\$300,000 × .40) – \$ 84,000 = \$36,000
• (\$300,000 × .50) – \$114,000 = \$36,000

63
Operating Leverage...
– measures the relationship between a
company’s variable and fixed expenses.
• It is greatest in organizations that have
high fixed expenses and low per unit
variable expenses.

64
Operating Leverage
• The degree of operating leverage shows
how a percentage change in sales
volume affects income.
• Degree of operating leverage =
Contribution margin ÷ Operating income
• What is the degree of operating leverage
of Dresses by Mary at the 3,500 sales
level under both arrangements?

65
Operating Leverage
• Existing arrangement:
• 3,500 × \$28 = \$98,000 contribution margin
• \$98,000 contribution margin – \$84,000
fixed costs = \$14,000 operating income
• \$98,000 ÷ \$14,000 = 7.0

66
Operating Leverage
• New arrangement:
• 3,500 × \$35 = \$122,500 contribution
margin
• \$122,500 contribution margin
– \$114,000 fixed costs = \$8,500
• \$122,500 ÷ \$8,500 = 14.4

67
Learning Objective 7

Apply CVP analysis to a
multi-product company

68
Effects of Sales Mix on Income
• Sales mix is the combination of products
that a business sells.

69
Effects of Sales Mix on Income

• Assume that Dresses by Mary is
considering selling blouses.
• This will not require any additional fixed
costs.
• It expects to sell 2 blouses at \$20 each for
every dress it sells.
• The variable cost per blouse is \$9.
• What is the new breakeven point?
70
Effects of Sales Mix on Income
• The contribution margin per dress is \$28
(\$70 selling price – \$42 variable cost).
• The contribution margin per blouse is
\$20 – \$9 = \$11.
• The contribution margin of the mix is
\$28 + (2 × \$11) = \$28 + \$22 = \$50.

71
Effects of Sales Mix on Income
• \$84,000 fixed costs ÷ \$50 = 1,680
packages
• 1,680 × 2 = 3,360 blouses
1,680 × 1 = 1,680 dresses
Total units = 5,040
• What is the breakeven in dollars?

72
Effects of Sales Mix on Income
• 1,680 × 2 = 3,360 blouses × \$20 =    \$
67,200
1,680 × 1 = 1,680 dresses × \$70 =
117,600
\$184,800
• What is the weighted average budgeted
contribution margin?

73
Effects of Sales Mix on Income
• Dresses      Blouses
1 × \$28 + 2 × \$11 = \$50 ÷ 3 = \$16.667
• Breakeven point for the two products is:
\$84,000 ÷ \$16.667 = 5,040 units
• 5,040 × 1/3 = 1,680 dresses
• 5,040 × 2/3 = 3,360 blouses

74
Effects of Sales Mix on Income

• Sales mix can be stated in sales dollars:

Dresses Blouses
Sales price                  \$70     \$40
Variable costs                    42
18       Contribution margin     \$28
\$22 Contribution margin ratio
40%       55%
75
Effects of Sales Mix on Income
• Assume the sales mix in dollars is 63.6%
dresses and 36.4% blouses.
• Weighted contribution would be:
40% × 63.6% = 25.44% dresses
55% × 36.4% = 20.02% blouses
45.46%

76
Effects of Sales Mix on Income
• Breakeven sales dollars is \$84,000 ÷
45.46% = \$184,778 (rounding).
• \$184,778 × 63.6% = \$117,519 dress sales
• \$184,778 × 36.4% = \$67,259 blouse sales

77
CVP Analysis in Service and
Nonprofit Organizations
• CVP can also be applied to decisions by
manufacturing, service, and nonprofit
organizations.
• The key to applying CVP analysis in
service and nonprofit organizations is
measuring their output.

78
Learning Objective 8

Distinguish between
contribution margin
and gross margin

79
Contribution Margin versus
Gross Margin

• Contribution income statement emphasizes
contribution margin.
• Revenues – Variable cost of goods sold –
Variable operating costs = Contribution
margin
• Contribution margin – Fixed operating costs
= Operating income

80
Contribution Margin versus
Gross Margin

• Financial accounting income statement
emphasizes gross margin.
• Revenues – Cost of goods sold = Gross
margin
• Gross margin – Operating costs =
Operating income

81
Learning Objective 9

Adapt CVP analysis to
multiple cost driver
situations

82
Multiple Cost Drivers
• Some aspects of CVP analysis can be
adapted to the more general case of
multiple cost drivers.
• Suppose that Dresses by Mary will incur
an additional cost of \$10 for preparing
documents associated with the sale of
dresses to various customers.

83
Multiple Cost Drivers
• Assume that she sells 3,500 dresses to
100 different customers.
• What is the operating income from this
sale?
• Operating income = Revenues –
(Variable cost per dress × No. of
dresses) – (Cost of preparing documents
× No. of customers) – Fixed costs

84
Multiple Cost Drivers

• Revenues: 3,500 × \$70          \$245,000
Variable costs:
Dresses: 3,500 × \$42 147,000
Documents: 100 × \$10 1,000
Total                           148,000
Contribution margin              97,000
Fixed costs                      84,000
Operating income               \$ 13,000
85
Multiple Cost Drivers
• Would the operating income of Dresses
by Mary be lower or higher if Mary sells
dresses to more customers?
• Mary’s cost structure depends on two
cost drivers:
1 Number of dresses
2 Number of customers

86
Bye for now!      I’m ready for
some leisure time.

Please ensure you
Prepare for next session

87

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