1. Cost-Volume-Profit Analysis
Chapter 3
Cost-Volume-Profit Analysis

2. Introduction Feature story:
Mary Frost sells Do-All software, a home-office software package, at booths rented at software conventions.
There’s a new computer convention coming up that she views as critical for exposure to new clients and growth.
The convention organizer has different booth-rental plan.
Pay a fixed amount.
Pay nothing up front and then pay a fixed percentage on whatever revenues she earn.
The management accountant recommends doing Cost-Volume-Profit (CVP) analysis to help evaluate the risks and rewards of the options.

3. Introduction
Cost-volume-Profit (CVP) analysis examines the behavior of total revenues, total costs, and operating income as changes occur in the output level (the volume), the selling price, the variable cost per unit, or the fixed costs of the product.
An important feature of CVP analysis is distinguishing fixed from variable costs.

4. 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) with volume.
Selling price, variable cost per unit, and fixed costs 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 and constant.
The time value of money (interest) is ignored.

5. Basic Formulae

6. Essentials of CVP analysis
Example:
Mary Frost is considering selling Do-All software at a new computer convention.
Mary can purchase this software at $120 per package (with privilege of returning unsold packages).
The packages would be sold at $200 each
She would pay a fixed rental cost: $2,000. Assume no other costs.
Mary is uncertain about how many packages she would be able to sell.
She wants to know what profits she would make for different quantities of packages that she might sell.

7. Example (contd.) Contribution income statement
The only numbers that change from selling different quantities of packages are total revenues and total variable costs.
The difference between total revenues and total variable costs is called contribution margin.
contribution margin per unit is the difference between selling price and variable cost per unit. ($200-$120=$80)
contribution margin percentage = contribution margin per unit divided by selling price ($80/$200 = 0.40, or 40%)

8. Methods to Express CVP Relationships
Equation Method:

9. Methods to Express CVP Relationships (contd.)
Contribution Margin Method:
Contribution Margin
Per unit

10. Methods to Express CVP Relationships (contd.)
Graph Method:

11. Breakeven Point
The breakeven point (BEP) is that quantity of output sold at which total revenues equal total costs – that is the quantity of output sold at which the operating income is $0.
Recall the equation method:
Using Do-All software data: the breakeven point (Q) when operating income is zero.
[$200 X Q] – [$120 X Q ] – [$2,000] = $0
$80 X Q = $2,000
Q = 25 units

12. Breakeven Point (contd.)
Breakeven point can also be expressed in terms of Revenues:
Breakeven revenue = Breakeven point X selling price
Do-All software example:
Breakeven revenue = 25 units X $200 = $5,000
Also Contribution margin method can be used:
Contribution margin per unit X Breakeven point = Fixed cost
Breakeven point = Fixed cost/ Contribution margin
= $2,000/ $80 per unit = 25 unit

13. Target Operating Income
How many units must Do-All software sell to earn an operating income of $1,200?
Using equation method:
[$200 X Q] – [$120 X Q ] – [$2,000] = $1,200
$80 X Q = $2,000 + $1,200 = $3,200
Q = 40 units
The revenue needed to earn $1,200 =
40 X $200 = $8,000

14. Profit-Volume Graph
PV graph shows how change in volume affect operating income.

15. Using CVP analysis for Decision Making
“What if” theme.
Introduce additional features for existing product
Advertise
Expand into new market
Reducing selling price
CVP analysis helps managers make decisions by estimating the expected profitability of these choices, and evaluating the risk.
Example: Do-All software :
Decision to advertise
Decision to reduce selling price

16. Using CVP analysis for Decision Making (contd.)
Decision to Advertise:
Suppose Mary anticipates selling 40 units. Operating income would be $1,200.
Mary is considering placing an advertisements.
Advertisements cost is $500 (fixed cost)
She anticipate that the advertising will increase sales by 10% to 44 packages.
Should Mary Advertise?

17. Using CVP analysis for Decision Making (contd.)
40 packages sold with No advertising
44 packages sold with advertising
Difference
Revenues
($200 X…)
$8,000
$8,800
$800
Variable costs
($120 X…)
4,800
5,280
480
Contribution margin ($80 X..)
3,200
3,520
320
Fixed cost
2,000
2,500
500
Operating income
$1,200
$1,020
$(180)

18. Using CVP analysis for Decision Making (contd.)
Decision to Reduce Selling Price:
Mary is contemplating whether to reduce the selling price to $175.
At this price, she thinks she will sell 50 units.
At this quantity, the software wholesaler will sell the packages to Mary for $115 per unit instead of $120.
Should Mary reduce the selling price?

19. Using CVP analysis for Decision Making (contd.)
Lowering price to $175, 50 packages sold
Maintaining price ,40 packages sold
Difference
Revenues
$8,750
$8,000
$750
Variable costs
$5,750
$4,800
$950
Contribution
$3,000
$3,200
$200
Fixed cost
$2,000
Operating income
$1,000
$1,200
$(200)

20. Using CVP analysis for Decision Making (contd.)
Mary could also ask “ At what price can I sell 50 units (purchased at $115 per unit) and continue to earn an operating income of $1,200?
The answer is $179.
Target operating income $1,200
Add fixed cost $2,000
Target contribution margin $ 3,200
Divided by number of units sold ÷ 50 units
Target contribution margin/unit $64
Add variable cost/unit $115
Target selling price $179

21. Sensitivity Analysis
Sensitivity analysis is a “what-if” technique that managers use to examine how an outcome will change if the original predicted data are not achieved or if an underlying assumption changes.
“What” happens to profit (operating income) “if”:
Selling price changes
Volume changes
Cost structure changes
Variable cost per unit changes
Fixed cost changes
Spreadsheets, such as Excel, enable managers to conduct CVP-based sensitivity analysis in a systematic and efficient way.

22. Sensitivity Analysis (contd.)

23. Margin of Safety One indicator of risk
The amount by which budgeted (or actual ) revenues exceed breakeven revenues.
Margin of safety = Budgeted Revenue – Breakeven Revenue
Expressed in units, margin of safety is the sales quantity minus the breakeven quantity.
The higher margin of safety gives the company confidence that it is unlikely to suffer a loss.

24. Alternative Fixed-Cost / Variable-Cost Structures
CVP-based sensitivity analysis highlights the risks and returns as fixed costs are substituted for variable costs in a company’s cost structure.
Suppose Computer Convention offers Mary three rental alternatives:
Option 1: $2,000 fixed fee
Option 2: $800 fixed fee plus 15% of revenues
Option 3: no fixed fee with 25% of revenues.
Mary interested in how her choice of a rental agreement will affect the income she earns and the risks she faces.

25. Alternative Fixed-Cost / Variable-Cost Structures (contd.)
Contribution margin /unit
(Selling price – Variable costs per unit)
Option 1
$2,000
$80
($200 - $120)
Option 2
$800
$50
($200 - $120 – (0.15 X $200))
Option 3 $0
$30
($200 - $120 – (0.25 X $200))

26. Alternative Fixed-Cost / Variable-Cost Structures (contd.)
If Mary sells 40 units, she should be indifferent across the three options. Each option results in operating income of $1,200.(see Exhibit 3-5)
Option 1 has the higher risk of loss because of its higher fixed cost which result in a higher breakeven point (25 units) an a lower margin of safety (40-25=15 units) relative to other options.
Also, option 1 has the higher contribution margin per unit ($80) because of its low variable costs.
At low demand levels option 3 is preferable.
At high levels of demand option 1 is preferable.
Mary choice will depend on her attitude to accept risk.

27. Alternative Fixed-Cost / Variable-Cost Structures (contd.)

28. 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 simplicity’s sake, only two products will be presented, but this could easily be extended to even more products

29. Effects of Sales-Mix on CVP (contd.)
A weighted-average CM must be calculated (in this case, for two products)
This new CM would be used in CVP equations

30. Effects of Sales-Mix on CVP (contd.)
Mary plans to sell two different software products: Do-All and Superword.
We assume the budgeted sales mix ( 3 units of Do-All sold for every 2 units of Superword sold) will not change.
What is the breakeven point?
Do-All
Superword
Total
Units sold 60 40
100
Revenues ($200, and $100/unit)
$12,000
$4,000
$16,000
Variable costs ($120, and $70)
7,200
2,800
10,000
Contribution margin ($80,$30)
$4,800
$1,200
6,000
Fixed costs
4,500
Operating income
$1,500

31. Effects of Sales-Mix on CVP (contd.)
WA contribution margin =( [$80 X 60] + [$30 X 40]) / ( ) = $ 60 /unit
Breakeven point = Fixed costs/ WA contribution margin per unit
= $4,500/ $60 = 75 unit
Because the ratio of Do-All sales to Superword sales is 3:2 (60:40), the breakeven point is 45 units of Do-All and 30 units of Superword.
Try to find the Breakeven revenue. How you split the total breakeven revenue between the different products?

32. Multiple Cost Drivers HW # 6 (chapter 3): [20, 24, 41, 44]
Variable costs may arise from multiple cost drivers or activities. A separate variable cost needs to be calculated for each driver.
Suppose Mary will incur a variable cost of $10 for preparing documents for each customer who buys Do-All software.
Operating income = Revenues – (cost of each package X Number of packages) – (Cost of preparing doc. X number of customers) – Fixed costs.
If Mary sells 40 packages to 15 customer, then OI= $1,050
If Mary sells 40 packages to 40 customer, then OI= $800
No unique breakeven point. Mary will breakeven if she sells 26 packages to 8 customers, or 27 packages to 16 customer.
The simple formula cannot be used.
HW # 6 (chapter 3): [20, 24, 41, 44]