1. University of Louisiana at Lafayette
Managerial Accounting
Weygandt • Kieso • Kimmel
CHAPTER 5
COST-VOLUME-PROFIT
Prepared by
Dan R. Ward
Suzanne P. Ward
University of Louisiana at Lafayette
John Wiley & Sons, Inc. © 2005

2. CHAPTER 5 COST – VOLUME - PROFIT Study Objectives
Distinguish between variable and fixed costs.
Explain the significance of the relevant range.
Explain the concept of mixed costs.
List the five components of cost-volume-profit analysis.
Indicate what contribution margin is and how it can be expressed.

3. Study Objectives: Continued
Identify the three ways to determine the break- even point.
Give the formulas for determining sales required to earn target net income.
Define margin of safety, and give the formulas for computing it.

4. COST BEHAVIOR ANALYSIS
Definition: The study of how specific costs respond to changes in the level of business activity
Some costs change; others remain the same
Helps management plan operations and make decisions
Applies to all types of businesses and entities

5. COST BEHAVIOR ANALYSIS Continued
Starting point is measuring key business activities
Activity levels may be expressed in terms of
Sales dollars (in a retail company)
Miles driven (in a trucking company)
Room occupancy (in a hotel)
Dance classes taught (by a dance studio)

6. COST BEHAVIOR ANALYSIS Continued
Many companies use more
than one measurement base
For an activity level
to be useful:
Changes in the level or volume of activity should be correlated with changes in cost

7. COST BEHAVIOR ANALYSIS Continued
The activity level selected is called the activity (or volume) index
Identifies the activity that causes changes in the behavior of costs
Allows costs to be classified according to their response to changes in activity as:
Variable Costs
Fixed Costs
Mixed Costs

8. COST BEHAVIOR ANALYSIS VARIABLE COSTS Study Objective 1
Costs that vary in total directly and proportionately with changes in the activity level
If the activity level increases 10 percent, total variable costs increase 10 percent
If the activity level decreases by 25 percent, total variable costs will decrease by 25 percent

9. COST BEHAVIOR ANALYSIS VARIABLE COSTS - Continued
Variable costs also remain constant per unit at every level of activity
Examples of variable costs include
Direct material and direct labor for a manufacturer
Sales commissions for a merchandiser
Gasoline in airlines and trucking companies

10. COST BEHAVIOR ANALYSIS VARIABLE COSTS - Continued
Example
Damon Company manufactures radios that contain a $10 clock
Activity index is the number of radios produced
For each radio produced, the total cost of the clocks increases by $10
If 2,000 radios are made, the total cost of the clocks is $20,000 (2,000 X $10)
If 10,000 radios are made, the total cost of the clocks is $100,000 (10,000 X $10)

11. COST BEHAVIOR ANALYSIS VARIABLE COSTS - Continued
Example: Continued

12. COST BEHAVIOR ANALYSIS FIXED COSTS
Costs that remain the same in total regardless of changes in the activity level.
Per unit cost varies inversely with activity:
As volume increases,
unit cost decline, and vice versa
Examples include
Property taxes
Insurance
Rent
Depreciation on buildings and equipment

13. COST BEHAVIOR ANALYSIS FIXED COSTS - Continued
Example
Damon Company leases its productive facilities for $10,000 per month
Total fixed costs of the facilities remain constant at all levels of activity - $10,000 per month
On a per unit basis, the cost of rent decreases as activity increases and vice versa
At 2,000 radios, the unit cost is $5 ($10,000 ÷ 2,000 units)
At 10,000 radios, the unit cost is $1 ($10,000 ÷ 10,000 units)

14. COST BEHAVIOR ANALYSIS FIXED COSTS - Continued
Example: Continued

15. COST BEHAVIOR ANALYSIS RELEVANT RANGE Study Objective 2
Throughout the range of possible levels of activity, a straight-line relationship usually does not exist for either variable costs or fixed costs
The relationship between variable costs and changes in activity level is often curvilinear
For fixed costs, the relationship is nonlinear – some fixed costs will not change over the entire range of activities, others may

16. COST BEHAVIOR ANALYSIS RELEVANT RANGE - Continued

17. COST BEHAVIOR ANALYSIS RELEVANT RANGE - Continued
Defined as the range of activity over which a company expects to operate during a year
Within this range, a straight-line relationship usually exists for both variable and fixed costs

18. COST BEHAVIOR ANALYSIS MIXED COSTS Study Objective 3
Costs that have both a variable cost element and a fixed cost element
Sometimes called semivariable cost
Change in total but
not proportionately
with changes in
activity level

19. COST BEHAVIOR ANALYSIS MIXED COSTS – High-Low Method
Mixed costs must be classified into their fixed and variable elements
One approach to separate the costs is called the high-low method
Uses the total costs incurred at both the high and the low levels of activity to classify mixed costs
The difference in costs between the high and low levels represents variable costs, since only variable costs change as activity levels change

20. COST BEHAVIOR ANALYSIS MIXED COSTS – High-Low Method - Continued
Steps in Method
STEP 1: Determine variable cost per unit using the following formula:
STEP 2: Determine the fixed cost by subtracting the total variable cost at either the high or the low activity level from the total cost at that level
÷ =
Change in Total Costs
High minus Low Activity Level
Variable Cost per Unit

21. COST BEHAVIOR ANALYSIS MIXED COSTS – High-Low Method - Continued
Example
Data for Metro Transit Company
for the last 4-month period:
High Level of Activity: April $63, ,000 miles
Low Level of Activity: January , ,000 miles
Difference $33, ,000 miles
Step 1: Using the formula, variable costs per unit are
$33,000  30,000 = $1.10 variable cost per mile
Month January February
Miles Driven 20,000 40,000
Total Cost $30,000 $48,000
Month March April
Miles Driven 35,000 50,000
Total Cost $49,000 $63,000

22. COST BEHAVIOR ANALYSIS MIXED COSTS – High-Low Method - Continued
Example: Continued
Step 2: Subtract total variable costs at either the high or low activity level from the total cost at that same level
Total Cost Less: Variable costs (50,000 x $1.10) (20,000 x $1.10) Total fixed costs
High $63, ,000 $ 8,000
Low $30,000
22,000
$ 8,000
Activity Level

23. COST BEHAVIOR ANALYSIS MIXED COSTS – High-Low Method - Continued
Example: Continued
Maintenance costs: $8,000 per month plus $1.10 per mile
To determine maintenance costs at a particular activity level:
multiply the activity level times the variable cost per unit
then add that total to the fixed cost
EXAMPLE: If the activity level is 45,000 miles, the estimated maintenance costs would be $8,000 fixed and $49,500 variable ($1.10 X 45,000 miles) for a total of $57,500.

24. Let’s Review Variable costs are costs that:
Vary in total directly and proportionately with changes in the activity level
Remain the same per unit at every activity level
Neither of the above
Both (a) and (b) above

25. Let’s Review Variable costs are costs that:
Vary in total directly and proportionately with changes in the activity level
Remain the same per unit at every activity level
Neither of the above
Both (a) and (b) above

26. COST-VOLUME-PROFIT ANALYSIS Study Objective 4
Study of the effects of changes of costs and volume on a company’s profits
A critical factor in management decisions
Important in profit planning

27. COST-VOLUME-PROFIT ANALYSIS
Considers the interrelationships among the five components of CVP analysis:

28. ASSUMPTIONS UNDERLYING CVP ANALYSIS
Behavior of both costs and revenues is linear throughout the relevant range of the activity index
All costs can be classified as either variable or fixed with reasonable accuracy
Changes in activity are the only factors that affect costs
All units produced are sold
When more than one type of product is sold, the sales mix will remain constant

29. CVP INCOME STATEMENT Study Objective 5
A statement for internal use
Classifies costs and expenses as fixed or variable
Reports contribution margin in the body of the statement.
Contribution margin –
amount of revenue
remaining after
deducting variable costs
Reports the same net
income as a traditional
income statement

30. CVP INCOME STATEMENT Example Vargo Video Company produces DVD players.
Relevant data for June 2005:
Unit selling price of DVD player $500
Unit variable costs $300
Total monthly fixed costs $200,000
Units sold ,600

31. CVP INCOME STATEMENT Contribution Margin Per Unit
Contribution margin is available to cover fixed costs and to contribute to income
Formula for contribution margin per unit:
Example: Computation for Vargo Video
– =
Unit Selling Price
Unit Variable Costs
Contribution Margin per Unit
– =
Unit Selling Price $500
Unit Variable Costs $300
Contribution Margin per Unit $200

32. CVP INCOME STATEMENT Contribution Margin Ratio
Shows the percentage of each sales dollar available to apply toward fixed costs and profits
Example: Computation for Vargo Video
÷ =
Contribution Margin Ratio
Unit Selling Price
Contribution Margin per Unit
÷ =
Contribution Margin Ratio
40%
Unit Selling Price
$500
Contribution Margin per Unit S200

33. CVP INCOME STATEMENT Contribution Margin Ratio - Example
Ratio helps to determine the effect of changes in sales on net income

34. BREAK-EVEN ANALYSIS Study Objective 6
Process of finding the break-even point
Break-even point
Level of activity at which total revenues equal total costs (both fixed and variable)
Can be computed or derived
from a mathematical equation
by using contribution margin
from a cost-volume-profit (CVP) graph
Expressed either in sales units or in sales dollars

35. BREAK-EVEN ANALYSIS Mathematical Equation
Example using the Vargo Video data:
Where:
Q = sales volume; $500 = selling price; $300 = variable cost per unit; $200,000 total fixed costs
To find sales dollars required to break-even:
1000 units X $500 = $500,000 (break-even sales dollars)
Variable Costs
$300 Q
Fixed Costs
$200,000
Net Income $0
Sales
$500 Q =
$200 Q
$200,000 = Q
1000 units =

36. BREAK-EVEN ANALYSIS Contribution Margin Technique
At the break-even point, contribution margin must equal total fixed costs (CM = total revenues – variable costs)
The break-even point can be computed using either contribution margin per unit or contribution margin ratio
When the break even point in units is desired, contribution margin per unit is used in the following formula
When the break even point in dollars is desired, contribution margin ratio is used in the following formula
÷ =
Fixed Costs
Break-even Point in Units
Contribution Margin per Unit
÷ =
Fixed Costs
Break-even Point in Dollars
Contribution Margin Ratio

37. BREAK-EVEN ANALYSIS Contribution Margin Technique
Example using Vargo Video data:
÷ =
Fixed Costs
$200,000
Break-even Point in Units
1,000 units
Contribution Margin per Unit
$200
÷ =
Fixed Costs
$200,000
Break-even Point in Dollars
$500,000
Contribution Margin per Unit
40%

38. BREAK-EVEN ANALYSIS Graphic Presentation
A cost-volume-profit (CVP) graph shows costs, volume, and profits
Used to visually find the break-even point
To construct a CVP graph,
Plot the total revenue line
starting at the zero activity level
Plot the total fixed cost
by a horizontal line
Plot the total cost line.
(Starts at the fixed cost line
at zero activity)
Determine the break-even point from the intersection of the total cost line and the total revenue line

39. BREAK-EVEN ANALYSIS CVP Graph for Vargo Video

40. BREAK-EVEN ANALYSIS Target Net Income Study Objective 7
Level of sales necessary to achieve a specified income
Can be determined from each of the approaches used to determine break-even sales/units
May be expressed either in sales dollars or sales units

41. BREAK-EVEN ANALYSIS Target Net Income - Example
Using the Contribution Margin Approach
and the Vargo Video Data:
Formula for required sales in units:
Formula for required sales in dollars
÷ =
Contribution Margin Per Unit
$200
Fixed Costs + Target Net Income
$200,000 + $120,000
Required Sales in Units
1,600 units
÷ =
Contribution Margin Ratio
40%
Fixed Costs + Target Net Income
$200,000 + $120,000
Required Sales in Dollars
$800,000

42. Let’s Review Contribution margin:
Is revenue remaining after deducting variable costs
May be expressed as contribution margin per unit
Is selling price less cost of goods sold
Both (a) and (b) above

43. Let’s Review Contribution margin:
Is revenue remaining after deducting variable costs
May be expressed as contribution margin per unit
Is selling price less cost of goods sold
Both (a) and (b) above

44. BREAK-EVEN ANALYSIS Margin of Safety
Difference between actual or expected sales and sales at the break-even point
May be expressed in dollars or as a ratio
Example -
To determine the margin of safety in dollars for Vargo Video assuming that actual (expected) sales are $750,000:
– =
Margin of Safety in Dollars
$250,000
Break-even Sales
$500,000
Actual (Expected) Sales
S750,000

45. BREAK-EVEN ANALYSIS Margin of Safety Ratio Study Objective 8
Computed by dividing the margin of safety in dollars by the actual or expected sales (using Vargo Video data)
Results indicate that Vargo Video’s sales could fall by 33 percent before it would be operating at a loss.
The higher the dollars or the percentage, the greater the margin of safety.
÷ =
Margin of Safety Ratio
33%
Actual (Expected) Sales
$750,000
Margin of Safety in Dollars
$250,000

46. Summary of Study Objectives
Distinguish between variable and fixed costs.
Variable costs:
Costs that vary in total directly and proportionately with changes
in the activity index, but remain constant on a per unit basis
Fixed costs:
Costs that remain the same in total regardless of changes in the
activity index, but, on a per unit basis, vary inversely with
changes in the activity index
Explain the significance of the relevant range.
Relevant range
Range of activity within which the company expects to operate
Cost behavior assumed to be linear through this range

47. Summary of Study Objectives
Explain the concept of mixed costs.
Contains both a variable cost and a fixed cost component
For CVP analysis, must be divided into its fixed and variable amounts
One method used to classify these costs is the high-low method
List the five components of CVP analysis.
Volume or level of activity
Unit selling price
Variable cost per unit
Total fixed costs
Sales mix

48. Summary of Study Objectives
Indicate what contribution margin is and how it can be expressed.
Contribution margin is the excess of revenue over all variable costs
Can be expressed either as a per unit amount or as a ratio
Identify the three ways to determine the break-even point.
Using a mathematical equation
The contribution margin technique
From a CVP graph

49. Summary of Study Objectives
Give the formulas for determining sales required to earn target net income.
General formula:
Required sales = Variable costs + Fixed costs + Target Net Income
Other formulas:
Required sales in units = (Fixed costs + Target Net Income) ÷ Contribution margin per unit
and
Required sales in dollars = (Fixed costs + Target Net Income) ÷ Contribution margin ratio
Define the margin of safety and give the formulas for computing it.
Excess of actual or expected sales over sales at break-even
Formulas:
Actual (expected) sales – Break-even sales = Margin of safety in dollars
Margin of safety in dollars ÷ Actual (expected) sales = Margin of safety ratio

50. COPYRIGHT
Copyright © 2005 John Wiley & Sons, Inc. All rights reserved. Reproduction or translation of this work beyond that permitted in Section 117 of the 1976 United States Copyright Act without the express written consent of the copyright owner is unlawful. Request for further information should be addressed to the Permissions Department, John Wiley & Sons, Inc. The purchaser may make back-up copies for his/her own use only and not for distribution or resale. The Publisher assumes no responsibility for errors, omissions, or damages, caused by the use of these programs or from the use of the information contained herein.