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CHAPTER 3
Cost-Volume-Profit
(CVP)Analysis
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3-2To accompanyCost Accounting 12e, by Horngren/Datar/Foster. Copyright 2006 by Pearson Education. All rights reserved.
Basic Assumptions
Changes in production/sales volume are the
sole cause for cost and revenue changes
Total costs consist of fixed costs and variable
costs Revenue and costs behave and can be
graphed as a linear function (a straight line)
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3-3To accompanyCost Accounting 12e, by Horngren/Datar/Foster. Copyright 2006 by Pearson Education. All rights reserved.
Basic Assumptions, continued
Selling price, variable cost per unit, and fixedcosts are all known and constant
In many cases only a single product will be
analyzed. If multiple products are studied,their relative sales proportions are known andconstant
The time value of money (interest) is ignored
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3-4To accompanyCost Accounting 12e, by Horngren/Datar/Foster. Copyright 2006 by Pearson Education. All rights reserved.
Basic Formulae
Total Cost Pretax
Operating Revenues of Operating
Income from Goods Expenses
Operations Sold
=
Net Operating Income
Income Income Taxes=
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3-5To accompanyCost Accounting 12e, by Horngren/Datar/Foster. Copyright 2006 by Pearson Education. All rights reserved.
Contribution Margin
Contribution Margin equals sales less
variable costs
CM = S VC
Contribution Margin per unit equals unitselling price less variable cost per unit CMu = SP VCu
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3-6To accompanyCost Accounting 12e, by Horngren/Datar/Foster. Copyright 2006 by Pearson Education. All rights reserved.
Contribution Margin
Contribution Margin also equals contribution
margin per unit multiplied by the number of
units sold
CM = CMu x Q Contribution Margin Ratio (percentage)
equals contribution margin per unit divided by
selling price
CMR = CMu SP
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3-7To accompanyCost Accounting 12e, by Horngren/Datar/Foster. Copyright 2006 by Pearson Education. All rights reserved.
Contribution Margin
Income Statement Derivations
A horizontal presentation of the ContributionMargin Income Statement:
Sales VC FC = Operating Income (OI)
(SP x Q) (VCu x Q) FC = OI
Q (SP VCu) FC = OI
Q (CMu) FC = OI Remember this last equation, it will be used
again in a moment
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3-8To accompanyCost Accounting 12e, by Horngren/Datar/Foster. Copyright 2006 by Pearson Education. All rights reserved.
CVP, Graphically
Total
costs
line
Operatingloss area
Breakeven point = 25 units
$10,000y
$8,000
$6,000
$5,000
$4,000
$2,000
Dollars
10 20 25 30 40 50
x
Units Sold
Total
costs
line
Operatingloss area
Operating
income area
Breakeven
point
= 25 units
Total
revenues
line
Operating
income
Variable
costs
Fixed
costs
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3-9To accompanyCost Accounting 12e, by Horngren/Datar/Foster. Copyright 2006 by Pearson Education. All rights reserved.
Breakeven Point
Recall the last equation in an earlier slide: Q (CMu) FC = OI
A simple manipulation of this formula, and
setting OI to zero will result in the BreakevenPoint (quantity): BEQ = FC CMu
At this point, a firm has no profit or loss at
a given sales level
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3-10To accompanyCost Accounting 12e, by Horngren/Datar/Foster. Copyright 2006 by Pearson Education. All rights reserved.
Breakeven Point, continued
If per-unit values are not available, the
Breakeven Point may be restated in its
alternate format:
BE Sales = FC CMR
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3-11To accompanyCost Accounting 12e, by Horngren/Datar/Foster. Copyright 2006 by Pearson Education. All rights reserved.
Breakeven Point, extended:
Profit Planning
With a simple adjustment, the Breakeven
Point formula can be modified to become a
Profit Planning tool
Profit is now reinstated to the BE formula,changing it to a simple sales volume equation
Q = (FC + OI)
CM
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3-12To accompanyCost Accounting 12e, by Horngren/Datar/Foster. Copyright 2006 by Pearson Education. All rights reserved.
CVP and Income Taxes
From time to time it is necessary to move back and forth
between pre-tax profit (OI) and after-tax profit (NI),
depending on the facts presented
After-tax profit can be calculated by: OI x (1-Tax Rate) = NI
NI can substitute into the profit planning equation
through this form:
OI = I I NI I
(1-Tax Rate)
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3-13To accompanyCost Accounting 12e, by Horngren/Datar/Foster. Copyright 2006 by Pearson Education. All rights reserved.
Sensitivity Analysis
CVP provides structure to answer a variety of
what-if scenarios
What happens to profit if:
Selling price changes Volume changes
Cost structure changes
Variable cost per unit changes Fixed cost changes
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3-14To accompanyCost Accounting 12e, by Horngren/Datar/Foster. Copyright 2006 by Pearson Education. All rights reserved.
Margin of Safety
One indicator of risk, the Margin of Safety
(MOS) measures the distance between
budgeted sales and breakeven sales:
MOS = Budgeted Sales BE Sales The MOS Ratio removes the firms size from
the output, and expresses itself in the form of
a percentage:
MOS Ratio = MOS Budgeted Sales
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3-15To accompanyCost Accounting 12e, by Horngren/Datar/Foster. Copyright 2006 by Pearson Education. All rights reserved.
Operating Leverage
Operating Leverage (OL) is the effect that fixedcosts have on changes in operating income aschanges occur in units sold, expressed as
changes in contribution margin OL = Contribution Margin
Operating Income Notice these two items are identical, except for
fixed costs
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3-16To accompanyCost Accounting 12e, by Horngren/Datar/Foster. Copyright 2006 by Pearson Education. All rights reserved.
Effects of Sales-Mix on CVP
The formulae presented to this point have assumed a
single product is produced and sold
A more realistic scenario involves multiple products
sold, in different volumes, with different costs
For simplicitys sake, only two products will be
presented, but this could easily be extended to even
more products
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3-17To accompanyCost Accounting 12e, by Horngren/Datar/Foster. Copyright 2006 by Pearson Education. All rights reserved.
Effects of Sales-Mix on CVP
A weighted-average CM must be calculated (in this
case, for two products)
This new CM would be used in CVP equations
Weighted ( Product #1 CMu x Product #1 Q ) + ( Product #2 CMu x Product #2 Q )
Average
CMu
=
Total Units Sold (Q) for Both Products
Multi- Fixed Costs
Product Weighted Average CM per unit
BE
=
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3-18To accompanyCost Accounting 12e, by Horngren/Datar/Foster. Copyright 2006 by Pearson Education. All rights reserved.
Multiple Cost Drivers
Variable costs may arise from multiple cost
drivers or activities. A separate variable cost
needs to be calculated for each driver.
Examples include: Customer or patient count
Passenger miles
Patient days
Student credit-hours
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3-19To accompanyCost Accounting 12e, by Horngren/Datar/Foster. Copyright 2006 by Pearson Education. All rights reserved.
Contribution Margin vs.
Gross Profit Comparative Statements
Revenues: $200Less:
Variable Cost of Goods Sold $120Variable Operating Costs 45 165
Contribution Margin 35Fixed Operating Costs 20
Operating Income $15
Contribution Margin Income Statement(Internal-Use Only)
Revenues: $200Less:
Cost of Goods Sold $120
Gross Margin (Profit) 80Fixed & Variable Operating Costs 65
Operating Income $15
Financial Accounting Income StatementGAAP - Based