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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