1. Cost-Volume-Profit Analysis
CHAPTER 3
Cost-Volume-Profit Analysis
© 2012 Pearson Prentice Hall. All rights reserved.

2. A Five-Step Decision-Making Process in Planning and Control Revisited
Identify the problem and uncertainties
Obtain information
Make predictions about the future
Make decisions by choosing between alternatives, using cost-volume-profit (CVP) analysis
Implement the decision, evaluate performance, and learn

3. 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.

4. Basic Formulae

5. 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 % (VC%)
Unit CM $ % (CM%)

6. CVP uses VC income equation
Revenue – Variable Costs – Fixed Costs = Operating Income
Selling
Price
Sales
Quantity * ( ) -
Unit
Variable
Costs
Fixed =
Operating
Income

7. Breakeven Point Calculation of breakeven revenues
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_ _
Calculation of breakeven revenues
Breakeven Revenue = Fixed Costs_ _
Contribution Margin per Unit
Contribution Margin Percentage

8. 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

9. CVP: Graphically

10. Profit Planning, Illustrated (p. 74)

11. 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 = I I Net Income I
(1-Tax Rate)

12. 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.

13. 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

14. Operating Leverage Results from having fixed costs

15. 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

16. 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.

17. Alternative Income Statement Formats

18. [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.

19. 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.

20. 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)

21. Example of DM under Uncertainty
Action Taken
Buy new Eqpt. Keep old Eqpt.
E Get Govt Income = Income =
v Contract $500, $300,000 e
n Not get Govt Income = Income =
t Contract $10, $200,000
Which action is best?
Depends on probabilities we assign to the events.

22. 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.

23. 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!