1. COST-VOLUME-PROFIT ANALYSIS
CHAPTER 21
COST-VOLUME-PROFIT
ANALYSIS

2. Cost-Volume-Profit Analysis
You must understand the relationships between costs, volume and “profit”
i.e., costs, volume and revenues
The concept is also known as “Break-Even Analysis”
Focuses on short-run decision making
i.e, time frame during which a company can’t change effects of certain past decisions
Long-run decision making is covered in Chapter 26

3. Cost-Volume-Profit Analysis Assumptions
Throughout the relevant range (range of activity where cost behavior assumptions are valid)
Unit sales price remains constant
Unit variable cost remains constant
Total fixed cost remains constant
All costs may be classified as either fixed or variable

4. Cost Behavior Patterns
Cost behavior means how a cost will react to changes in the level of business activity.
Fixed Costs and
Variable Costs
react differently.

5. Cost Behavior Patterns Fixed Costs
Total fixed costs remain constant over wide ranges of activity/volume.
Per unit fixed costs decrease as volume level increases.
Example: basic monthly telephone charge
Total cost is unchanged regardless of number of local calls.
Cost per local call decreases as number of local calls increases.

6. Total Fixed Cost Example
Your monthly basic telephone bill is probably unchanged as you make more local calls.
Monthly Basic Telephone Bill
Number of Local Calls

7. Per Unit Fixed Cost Example
The average cost per local call decreases as more local calls are made.
Monthly Basic Telephone Bill per Local Call
Number of Local Calls

8. Cost Behavior Patterns Variable Costs
Total variable costs increase and decrease in proportion to increases and decreases in volume.
Per unit variable costs remain constant over wide ranges of volume.
Example: long distance telephone charges
Total cost will increase as a function of minutes talked.
Cost per minute remains unchanged.

9. Total Variable Cost Example
Your total long distance telephone bill is based on how many minutes you talk.
Total Long Distance Telephone Bill
Minutes Talked

10. Per Unit Variable Cost Example
The cost per long distance minute talked is constant. For example, 10 cents per minute.
Per Minute Telephone Charge
Minutes Talked

11. Cost Behavior Patterns

12. Cost Behavior Question
Fixed costs are usually characterized by:
a. Unit costs that remain constant.
b. Total costs that increase as activity decreases.
c. Total costs that increase as activity increases.
d. Total costs that remain constant.

13. Cost Behavior Question
Fixed costs are usually characterized by:
a. Unit costs that remain constant.
b. Total costs that increase as activity decreases.
c. Total costs that increase as activity increases.
d. Total costs that remain constant. a. b. c. d.

14. Cost Behavior Question
Variable costs are usually characterized by:
a. Unit costs that decrease as activity increases.
b. Total costs that increase as activity decreases.
c. Total costs that increase as activity increases.
d. Total costs that remain constant.

15. Cost Behavior Question
Variable costs are usually characterized by:
a. Unit costs that decrease as activity increases.
b. Total costs that increase as activity decreases.
c. Total costs that increase as activity increases.
d. Total costs that remain constant. a. b. c. d.

16. Cost Behavior Patterns Mixed Costs
Contains fixed portion incurred even when facility is unused and a variable portion which increases with usage.
Example: monthly electric utility charge
Fixed service fee
Variable charge per kilowatt hour used

17. Cost Behavior Patterns Mixed Costs
Total Cost $
Activity/Volume Level

18. Cost Behavior Patterns Mixed Costs
Total Cost $
Variable Portion
Fixed Portion
Activity/Volume Level

19. Cost Behavior Patterns Step Costs
Definition: Constant fixed cost over a range of activity with an increase at a certain level to a new, higher fixed cost.
Example: A supervisor’s salary is $30,000 for a process that produces 10,000 units. When volume increased beyond 10,000 units, a second process was added with a second supervisor, increasing total salaries to $60,000.

20. Cost Behavior Patterns Step Costs Salaries in Thousands of Dollars60
Salaries in Thousands of Dollars 30
Activity in Thousands

21. Cost Behavior Patterns Curvilinear Costs
Costs that increase when activity increases, but in a non-linear manner
Total Cost
Activity

22. Cost Behavior Patterns Relevant Range
Definition: Range of activity where the cost behavior assumptions are valid
Total fixed costs remain constant.
Per unit variable costs remain unchanged.
The cost behavior assumptions discussed earlier allow us to use linear relationships.
How does this differ from what you learned in your economics course?

23. Cost Behavior Patterns Relevant Range
Economics (Economies of Scale)
Extremely wide range assumed
e.g., 0 to
Accounting
Relatively narrow range assumed
e.g., 40,000 units to 100,000 units 8

24. The Linearity Assumption and the Relevant Range
Economist’s Curvilinear Total Cost Function
Total Cost
Activity

25. The Linearity Assumption and the Relevant Range
Economist’s Curvilinear Total Cost Function
Total Cost
Accountant’s Straight-Line Approximation (constant unit variable cost)
Activity

26. The Linearity Assumption and the Relevant Range
A straight line closely approximates a curvilinear variable cost line within the relevant range.
Relevant Range
Total Cost
Accountant’s Straight-Line Approximation (constant unit variable cost)
Activity

27. Fixed Costs and Relevant Range
Example: Office space is available at a rental rate of $30,000 per year in increments of 1,000 square feet. As the business grows more space is rented, increasing the total cost.

28. Fixed Costs and Relevant Range
Rent Cost in Thousands of Dollars 30 60 90
Relevant Range
Total cost doesn’t change for a wide range of activity, and then jumps to a new higher cost for the next higher range of activity.
, , , Rented Area (Square Feet)

29. Fixed Costs and Relevant Range
How does this type of fixed cost differ from a step cost?

30. Fixed Costs and Relevant Range
Step costs can be adjusted more quickly and . . .
The width of the activity steps is much wider for the fixed cost.
How does this type of fixed cost differ from a step cost?

31. Methods for Analyzing Costs
We will separate a mixed cost into its fixed and variable components.

32. Methods for Analyzing Costs Two methods will be used:
Scatter Diagram
High-low method

33. Scatter Diagram
A scatter diagram of past cost behavior is helpful in analyzing mixed costs. 20 *
Total Cost in 1,000’s of Dollars 10
Plot the data points on a graph (total cost vs. activity).
Activity, 1,000’s of Units Produced

34. Total Cost in 1,000’s of Dollars
Scatter Diagram
Draw a line through the plotted data points so that about an equal numbers of points fall above and below the line. 20 *
Total Cost in 1,000’s of Dollars 10
Activity, 1,000’s of Units Produced

35. Total Cost in 1,000’s of Dollars
Scatter Diagram
Where line intercepts with cost axis is total fixed cost. 20
Review regression analysis calculations from your statistics class and bring your scientific calculator to the next test. *
Total Cost in 1,000’s of Dollars 10
Estimated fixed cost = $10,000
Activity, 1,000’s of Units Produced

36. Methods for Analyzing Costs
Now, the
High-low method
(You are responsible for knowing how to use it.)

37. Analyzing Mixed Costs High-Low Method
Objective: To separate total cost into fixed and variable portions.
Step 1 - Calculate variable cost per unit.
V.C./unit = in cost ÷ in units
Step 2 - Calculate total variable cost at either high or low volume level and subtract it from total cost at the same volume level to determine total fixed cost at any level.
Objective: To separate total cost into fixed and variable portions.
Step 1 - Calculate variable cost per unit.
V.C./unit = in cost ÷ in units .

38. Using these two levels of activity, compute:
The High-Low Method
WiseCo recorded the following production activity and maintenance costs for two months:
Using these two levels of activity, compute:
the variable cost per unit
the total fixed cost

39. The High-Low Method Unit variable cost = = = $.90 in cost in units
$3,600 $4,000

40. The High-Low Method Unit variable cost = = = $.90
Fixed cost = Total cost – Total variable cost
in cost in units
$3,600 $4,000

41. The High-Low Method Unit variable cost = = = $.90
Fixed cost = Total cost – Total variable cost Fixed cost = $9,700 – ($.90 per unit × 9,000 units) Fixed cost = $9,700 – $8,100 = $1,600
in cost in units
$3,600 $4,000

42. Choosing the low activity level will give the same result.
The High-Low Method
Choosing the low activity level will give the same result.

43. The High-Low Method Unit variable cost = = = $.90
Fixed cost = Total cost – Total variable cost Fixed cost = $6,100 – ($.90 per unit × 5,000 units) Fixed cost = $6,100 – $4,500 = $1,600
in cost in units
$3,600 $4,000

44. Cost-Volume-Profit Analysis
Now that we understand cost behavior, let’s turn our attention to cost-volume-profit analysis.

45. Cost-Volume-Profit Analysis
Objective
Determine the effects that changes in selling prices, costs, and/or volume will have on profits in the short run.

46. Cost-Volume-Profit Chart
Sales
Break-even Point
Income
Costs and Revenue in Dollars
Total costs
Loss
Units of Activity

47. Profit Equations Net income = Revenue – Total costs
At any point on the cost-volume-profit chart the following relationships are valid:
Net income = Revenue – Total costs
Variable costs + Fixed costs
Contribution Margin = Revenue – Variable costs

48. Contribution margin The Cost-Volume-Profit Chart Net income Sales
240
220 -
200 -
180 -
160 -
140 -
120 -
100 -
80 -
60 -
40 -
20 -
Contribution margin
Sales
Sales
Net income
Relevant sales volume range .
Total costs
Fixed costs
Total costs
Variable costs
Variable costs -
Dollars ($000)
Break-even point
Net loss
Fixed costs
Units (000)

49. Cost-Volume-Profit Analysis
Let’s look at the OK Company example.

50. Cost-Volume-Profit Analysis
Contribution margin is amount by which revenue exceeds variable costs of producing the revenue.

51. Cost-Volume-Profit Analysis
Contribution margin goes to cover fixed costs and ...

52. Cost-Volume-Profit Analysis
Contribution margin goes to cover fixed costs and …
after covering fixed costs, any remaining contribution margin contributes to net income.

53. Cost-Volume-Profit Analysis
How much contribution margin does OK need to cover its fixed costs (i.e., break even)?

54. Cost-Volume-Profit Analysis
How much contribution margin does OK need to cover its fixed costs (i.e., break even)?
Answer $30,000

55. Cost-Volume-Profit Analysis
How many units must OK sell to cover its fixed costs (break even)?

56. Cost-Volume-Profit Analysis
How many units must OK sell to cover its fixed costs (break even)?
$30,000 ÷ $20 per unit = 1,500 units

57. Cost-Volume-Profit Analysis
How many units must OK sell to cover its fixed costs (break even)?
$30,000 ÷ $20 per unit = 1,500 units O F

58. Cost-Volume-Profit Analysis
We have just seen one of the basic cost-volume-profit relationships, the break-even computation in units.
Break-even units =
Fixed costs
Contribution margin per unit
Contribution margin per unit is sales price per unit less variable cost per unit. Conceptually, it represents the amount of each sales dollar which “contributes” to fixed costs and profit (net income).

59. Finding the Break-Even Point Break-even (BE) Computation
Fixed costs
BEunits =
Contribution margin per unit

60. Cost-Volume-Profit Analysis
The break-even formula may also be expressed in sales dollars.
Break-even dollars =
Fixed costs
Contribution margin ratio rate
The contribution margin rate is computed either by dividing contribution margin per unit by selling price per unit or by dividing total contribution margin by total revenues.
Conceptually, the contribution margin rate represents the percentage of each sales dollar which “contributes” to fixed costs and profit (net income).

61. Finding the Break-Even Point
The break-even formula may also be expressed in sales dollars:
BE$ =
Fixed costs
Contribution margin rate
OK’s CMR
CMR = contribution margin as a percentage of sales.

62. Finding the Break-Even Point
Total
Unit
Percent
Sales Revenue (1,500 units) $
75,000 $ 50
100%
Less: Variable costs
45,000 30
60%
Contribution margin
30,000 $ 20
40%
OK’s contribution margin per unit is $20.
OK’s CMR is 40% or $20/$50.

63. Cost-Volume-Profit Analysis Question
Tulip Co. sells its plant cartons at $5.00 per unit. If fixed costs are $200,000 and variable costs are $3.00 per unit, how many units must be sold to break even?
a ,000 units
b ,000 units
c ,000 units
d ,667 units

64. Cost-Volume-Profit Analysis Question
Tulip Co. sells its plant cartons at $5.00 per unit. If fixed costs are $200,000 and variable costs are $3.00 per unit, how many units must be sold to break even?
a ,000 units
b ,000 units
c ,000 units
d ,667 units a. =
$200,000 $5.00 – $3.00
= 100,000 units
Fixed costs Unit contribution b. c. d.

65. Cost-Volume-Profit Analysis Question
Use the CMR formula to determine the amount of sales revenue Tulip Co. needs to break even. Fixed costs ($200,000), unit sales price ($5), and per unit variable cost ($3) are unchanged.
a. $200,000
b. $300,000
c. $400,000
d. $500,000

66. Cost-Volume-Profit Analysis Question
Use the CMR formula to determine the amount of sales revenue Tulip Co. needs to break even. Fixed costs ($200,000), unit sales price ($5), and per unit variable cost ($3) are unchanged.
a. $200,000
b. $300,000
c. $400,000
d. $500,000
CMR = ($5.00 – $3.00) ÷ $5.00 = .40
BE$ = $200,000 ÷ .40 = $500,000

67. Forget it! You are not responsible for this concept.
Calculating Break-Even for a Multiproduct Company
Forget it! You are not responsible for this concept.

68. Cost-Volume-Profit Analysis Desired Income
Break-even formulas may be adjusted to show the sales volume needed to earn any amount of income.
Add desired income to fixed costs in the numerator. No other changes are needed.
BE$ =
Fixed costs + Desired income
Contribution margin rate
BEunits =
Contribution margin per unit

69. Cost-Volume-Profit Analysis Question
Tulip Co. sells its plant cartons at $5.00 per unit. If fixed costs are $200,000 and variable costs are $3.00 per unit, how many units must be sold to earn income of $40,000?
a ,000 units
b ,000 units
c ,000 units
d ,000 units

70. Cost-Volume-Profit Analysis Question
Tulip Co. sells its plant cartons at $5.00 per unit. If fixed costs are $200,000 and variable costs are $3.00 per unit, how many units must be sold to earn income of $40,000?
a ,000 units
b ,000 units
c ,000 units
d ,000 units
Fixed costs + Desired income Unit contribution
$200,000 + $40, $5.00 – $3.00
= 120,000 units

71. Let’s calculate the margin of safety for OK Company.
Excess of current sales over the break-even volume of sales. (i.e., the amount by which sales may decline before reaching break-even sales.)
Margin of safety = Current sales – Break-even sales
Let’s calculate the margin of safety for OK Company.

72. Margin of Safety Current sales 100,000 $ Breakeven sales 75,000 -
25,000

73. Margin of Safety
The margin of safety may also be expressed as a percentage of current sales.

74. Margin of Safety
Margin of safety Current sales - Break-even sales percentage Current sales =
$100, $75, $100,000 =
= %

75. THE END