Cost-Volume-Profit Analysis
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Foundational Assumptions in CVP
 Changes in production/sales volume are the sole cause
for cost and revenue changes.
 Total costs consist only of fixed and variable costs.
 Revenue and costs behave as a linear function (a
straight line).
 Selling price, variable cost per unit, and fixed costs are
all known and constant.
 If multiple products are sold, their relative sales
proportions (sales mix) are known and constant.
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Basic Formulae
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CVP: Contribution Margin
 Manipulation of the basic equations yields an
extremely important and powerful tool extensively
used in cost accounting: contribution margin (CM).
 Contribution margin = revenue less variable cost.
 Contribution margin per unit equals unit selling price
less unit variable costs. For a particular item, assume
Unit Price
Unit VC
Unit CM
$2.50
1.75
$ .75
100%
70% (VC%)
30% (CM%)
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Breakeven Point
 At the breakeven point, a firm has no profit or loss at
the given sales level.
 Sales – Variable Costs – Fixed Costs = 0
 Calculation of breakeven number of units
 Breakeven Units =
Fixed Costs_
_
Contribution Margin per Unit
 Calculation of breakeven revenues
 Breakeven Revenue =
Fixed Costs_
_
Contribution Margin Percentage
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Breakeven Point, extended:
Profit Planning
 The breakeven point formula can be modified to
become a profit planning tool.
 Profit is now added to the BE formula, changing it to a
simple sales volume equation.
 Quantity of Units = (Fixed Costs + Operating Income)
Required to Be Sold
Contribution Margin per Unit
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CVP: Graphically
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Profit Planning, Illustrated (p. 74)
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CVP and Income Taxes
 After-tax profit can be calculated by:
 Net Income = Operating Income * (1-Tax Rate)
 Net income can be converted to operating income for
use in CVP equation
 Operating Income
= II
Net Income
(1-Tax Rate)
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I
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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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 firm’s size from the
output, and expresses itself in the form of a
percentage:
 MOS Ratio = MOS ÷ Budgeted Sales
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Operating Leverage
Results from having fixed costs
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Operating Leverage
 Operating leverage (OL) is the effect that fixed costs
have on changes in operating income as changes 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: Operating Income = CM-FC
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Effects of Sales-Mix on CVP
 To this point we have assumed a single product is
produced and sold.
 A more realistic scenario involves multiple products
sold, in different volumes, with different costs.
 The same formulae are used, but instead use average
contribution margins for “bundles” of products.
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[Remaining slides added by CB]
Decision Models and Uncertainty
 Managers frequently must deal with uncertainty.
 The model presented here represents a rational
approach to decision making under uncertainty,
assuming you are risk-neutral.
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Risk attitudes
 Are you risk-averse?
 Would you toss a coin for $20?
 Would you prefer $100 with .50 probability or $48
certain?
 Managers tend to be risk-averse in general
 But will become risk-seeking when in a loss situation

“Prospect theory” of Tversky & Khaneman
 Compare gamblers in a casino, etc.
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Decision Model Assumptions
 Choice Criterion
 Set of Alternatives (Actions to consider)
Mutually exclusive, Exhaustive
 Set of Events (States of Nature)
 Set of Probabilities associated with the events
 Set of Outcomes (Income, cost, etc., to minimize or
maximize)
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Example of DM under Uncertainty
Action Taken
Buy new Eqpt.
E
v
e
n
t
Keep old Eqpt.
Get Govt
Contract
Income =
$500,000
Income =
$300,000
Not get Govt
Contract
Income =
$10,000
Income =
$200,000
 Which action is best?
Depends on probabilities we assign to the events.
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Decision Models and Uncertainty
 EV=Σ (Outcomei) (Pi)
i.e., summation of each outcome (in this case, income)
times the probability of that outcome.
 Suppose P(getting contract) = .20
[read as “probability of getting contract = .20”]
 Thus P(not getting contract) = .80.
 EV(buying new Eqpt) = $500,000*.20 + $10,000*.80 = $108,000
EV(keeping old Eqpt) = $300,000*.20 + $200,000*.80 = $220,000
 To maximize expected value, we keep old equipment.
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Good decision vs. good outcome
 You take your life savings (assume $100,000) and put it
all on a roulette wheel spin “straight up bet” (any
single number). You win and claim $3,500,000!
 Was it a good decision?
 Was it a rational decision?
 A “good” decision is one made on the information
available at the time, applying one’s values in a rational
way. (Hindsight bias is huge, though!)
 Luck (things outside your control) plays a much bigger
part in business and life than you think!
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