1. Prepared by Debby Bloom-Hill CMA, CFM

2. CHAPTER 4
Cost-Volume-Profit Analysis
Slide 4-2

3. Management Questions Planning Control Decision making
What level of profit should be in the budget for the coming year?
Control
Did the manager responsible for production costs do a good job of controlling costs?
Decision making
Should the price be increased?
Slide 4-3
Learning objective 1: Identify common cost behavior patterns

4. Common Cost Behavior Patterns
Variable Costs
Costs which change directly in proportion to changes in quantity or activity
Fixed Costs
Costs which do not change when quantity or activity volume changes
Slide 4-4
Learning objective 1: Identify common cost behavior patterns

5. Common Cost Behavior Patterns
Mixed Costs
Costs that have both variable and fixed elements
Step Costs
Fixed for a range of output, but increase when upper bound of range is exceeded
Slide 4-5
Learning objective 1: Identify common cost behavior patterns

6. Variable Costs
Costs that change in proportion to changes in volume or activity
An automobile manufacturer will need 400 tires to make 100 cars, but 4,000 tires to make 1,000 cars
A bakery will need 2 eggs to make 1 cake and 20 eggs to make 10 cakes
If activity increases by a certain percentage, cost increases by that same percentage
Slide 4-6
Learning objective 1: Identify common cost behavior patterns

7. Test Your Knowledge 1
A company has decided that direct labor costs are 100% variable. Last month total direct labor costs were $125,000 and total direct labor hours worked were 10,000.
What is the direct labor cost per hour?
$125,000 / 10,000 hours = $12.50 per hour
Predict labor costs in a month when 12,000 labor hours are worked
$12.50 per hour × 12,000 hours = $150,000
Slide 4-7
Learning objective 1: Identify common cost behavior patterns

8. Variable Costs Total Variable Cost = $91 × Units produced Slide 4-8
Learning objective 1: Identify common cost behavior patterns

9. Fixed Costs Do not change in response to changes in activity level
Typical fixed costs are depreciation, supervisory salaries, and building maintenance
Rent for a bakery will not double if output increases from 100 to 200 cakes
If activity increases by a certain percentage, costs remain unchanged
Slide 4-9
Learning objective 1: Identify common cost behavior patterns

10. Fixed Costs Total fixed cost = $94,000 Slide 4-10
Learning objective 1: Identify common cost behavior patterns

11. Fixed Costs Discretionary fixed costs Committed fixed costs
Management can easily change, e.g. advertising, research & development
Many companies cut back on these costs when sales drop. This can be shortsighted
A cut in research & development can have a negative effect on long run profitability
A cut in repair and maintenance can have a negative effect on the life of valuable assets
Committed fixed costs
Cannot be easily changed, e.g. rent, insurance
Slide 4-11
Learning objective 1: Identify common cost behavior patterns

12. Mixed Costs Contain both variable and fixed cost elements
Can separate mixed costs into variable and fixed components
Salesperson with base salary (fixed) and commission on sales (variable)
Base salary included with fixed costs
Commission included with variable costs
Slide 4-12
Learning objective 1: Identify common cost behavior patterns

13. Mixed Costs Total cost = ($91 × Units produced) + $94,000 Slide 4-13
Learning objective 1: Identify common cost behavior patterns

14. Step Costs Fixed cost for a specific range of volume
Increases to higher level when upper bound of range is exceeded
At that point, costs again remain fixed until another upper bound is exceeded
Step costs are often classified as either:
Step variable costs, if the range of activity where the cost is fixed is small, or
Step fixed costs, if the range of activity where the cost is fixed is large
Slide 4-14
Learning objective 1: Identify common cost behavior patterns

15. Step Costs Total step costs =
$7,000 for relevant range 0 – 3,000 units produced
$14,000 for relevant range 3,001 – 6,000 units
$21,000 for relevant range 6,001 – 9,000 units
Slide 4-15
Learning objective 1: Identify common cost behavior patterns

16. Relevant Range
The relevant range is the range of activity for which assumptions as to how costs behave are reasonably valid
If it is known that production is going to be within the relevant range, we can use assumptions about the fixed and variable costs
Making assumptions about fixed and variable costs at production levels well above or below this range would not be valid
Slide 4-16
Learning objective 1: Identify common cost behavior patterns

17. The Relevant Range Slide 4-17
Learning objective 3: Perform cost-volume profit analysis for single products

18. Cost Estimation Methods
Account Analysis
Classify costs into variable and fixed pools
Scattergraphs
Can see cost relationships visually
High-Low Method
Linear estimation connects high and low volume observations
Regression Analysis
Linear estimation is best fit to observed values
Slide 4-18
Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method

19. Account Analysis Most common approach
Requires professional judgment of management
Management classifies costs as fixed, variable, or mixed
Total variable costs divided by activity equals variable cost per unit
Variable cost per unit and total fixed costs can be used in cost equation
Slide 4-19
Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method

20. Account Analysis Slide 4-20
Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method

21. Scattergraphs
Utilization of cost information from several previous periods
Weekly, monthly, or quarterly cost reports are useful
Plot the actual costs at the observed activity levels
Look for relationship between cost and activity, linear is ideal
Use relationship to predict future costs
Slide 4-21
Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method

22. Scattergraphs
Is there a relationship between units produced and production costs? Describe the relationship.
Slide 4-22
Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method

23. High-Low Method Utilization of cost information from previous periods
Fits a straight line from lowest activity level to highest activity level
Slope of the line is the estimate of the unit variable cost
The slope measures the change in cost per unit change in activity level
Total cost at lowest or highest activity level minus variable cost at that level equals fixed cost
Slide 4-23
Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method

24. High-Low Method Total cost at high activity level
Total cost at low activity level
Slide 4-24
Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method

25. High-Low Method Slide 4-25
Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method

26. High-Low Method Slide 4-26
Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method

27. Test Your Knowledge 2
During the past year, Island Air flew 15,000 miles in August (its busiest month) and had total costs of $300,000. In November (its least busy month) the company flew 5,000 miles and had $200,000 of costs. Using the high-low method, estimate variable cost per mile and fixed cost per month.
$20 of variable cost and $100,000 fixed
$15 of variable cost and $250,000 fixed
$10 of variable cost and $150,000 fixed
$5 of variable cost and $250,000 fixed
Answer: c
Slide 4-27
Learning objective 1: Identify common cost behavior patterns

28. Test Your Knowledge 2
During the past year, Island Air flew 15,000 miles in August (its busiest month) and had total costs of $300,000. In November (its least busy month) the company flew 5,000 miles and had $200,000 of costs. Using the high-low method, estimate variable cost per mile and fixed cost per month.
Estimate of variable cost = (𝟑𝟎𝟎,𝟎𝟎𝟎 −𝟐𝟎𝟎,𝟎𝟎𝟎) (𝟏𝟓,𝟎𝟎𝟎 −𝟓,𝟎𝟎𝟎) = 𝟏𝟎𝟎,𝟎𝟎𝟎 𝟏𝟎,𝟎𝟎𝟎 = $10
Variable cost at low level = $10 * 5,000 miles = $50,000
Fixed cost = $200,000 total – $50,000 variable = $150,000
Slide 4-28
Learning objective 1: Identify common cost behavior patterns

29. Regression Analysis Statistical technique
Estimates the slope and intercept of a cost equation
Finds the best straight line fit to the observations
Typically statistical software packages are utilized
Spreadsheet applications like Excel® typically include statistical operations
See appendix fox Excel® example
Slide 4-29
Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method

30. Cost-Volume-Profit Analysis
The Profit Equation
Profit = SP(x) – VC(x) – TFC
Where:
x = Quantity of units produced and sold
SP = Selling price per unit
VC = Variable cost per unit
TFC = Total fixed cost
Fundamental to CVP analysis
Slide 4-30
Learning objective 3: Perform cost-volume profit analysis for single products

31. Cost-Volume-Profit Analysis
Break-Even Point
Number of units sold that allow the company to neither earn a profit nor incur a loss
$0 = SP(x) – VC(x) – TFC
CodeConnect has the following cost structure
Selling price $ per unit
Variable cost $90.83 per unit
Total fixed cost $160,285
Find CodeConnect’s break-even point
Slide 4-31
Learning objective 3: Perform cost-volume profit analysis for single products

32. Cost-Volume-Profit Analysis
Break-Even Point
$0 = SP(x) – VC(x) – TFC
$0 = $ (x) – $90.83(x) – $160,285
$0 = $109.17(x) – $160,285
$109.17(x) = $160,285
x = $160,285 / $109.17
x = 1, units
Break-even point is 1,469 units (always round up)
Slide 4-32
Learning objective 3: Perform cost-volume profit analysis for single products

33. Break-Even Point Slide 4-33
Learning objective 3: Perform cost-volume profit analysis for single products

34. Test Your Knowledge 3
Gabby’s Wedding Cakes creates elaborate wedding cakes. Each cake sells for $500. The variable cost of baking the cakes is $200 and the fixed cost per month is $6,000. What is the break-even point in number of units?
200 20 12
100
Answer: b
Slide 4-34
Learning objective 3: Perform cost-volume profit analysis for single products

35. Test Your Knowledge 3
Gabby’s Wedding Cakes creates elaborate wedding cakes. Each cake sells for $500. The variable cost of baking the cakes is $200 and the fixed cost per month is $6,000. What is the break-even point in number of units?
0 = SP(x) – VC(x) – TFC
0 = (SP – VC)(x) – TFC
0 = (500 – 200)(x) – 6,000
0 = 300(x) – 6,000
300(x) = 6,000
x = 6,000 / 300 = 20
Slide 4-35
Learning objective 3: Perform cost-volume profit analysis for single products

36. Margin of Safety
The margin of safety is the difference between the expected level of sales and break-even sales
If breakeven sales for Model DX375 is $293,600 and expected sales are $350,000, calculate the margin of safety
The margin of safety is:
$350,000 - $293,600 = $56,400
Slide 4-36
Learning objective 3: Perform cost-volume profit analysis for single products

37. Margin of Safety Ratio
The margin of safety can also be expressed as a ratio
Called the margin of safety ratio
Equal to the margin of safety divided by expected sales
Shows what percentage sales would have to drop before the product shows a loss
= 𝐌𝐚𝐫𝐠𝐢𝐧 𝐨𝐟 𝐬𝐚𝐟𝐞𝐭𝐲 𝐄𝐱𝐩𝐞𝐜𝐭𝐞𝐝 𝐬𝐚𝐥𝐞𝐬 = $𝟓𝟔,𝟒𝟎𝟎 $𝟑𝟓𝟎,𝟎𝟎𝟎 = 0.16
Margin of
safety ratio
Slide 4-37
Learning objective 3: Perform cost-volume profit analysis for single products

38. Contribution Margin Difference between revenue and variable costs
Contribution margin = total revenue minus total variable costs
Contribution margin per unit = selling price minus variable cost per unit
For CodeConnect’s Model DX375, the contribution margin is the $ selling price less the variable cost of $90.83
$ – $90.83 = $109.17
Slide 4-38
Learning objective 3: Perform cost-volume profit analysis for single products

39. Contribution Margin
The contribution margin per unit measures the amount of incremental profit generated by selling an additional unit
For CodeConnect, how much incremental profit would be generated by selling 100 more units?
Incremental profit = number of units sold * contribution margin per unit
Incremental profit = 100 * $ = $10,917
Slide 4-39
Learning objective 3: Perform cost-volume profit analysis for single products

40. Contribution Margin
The profit equation in terms of the contribution margin
Profit = SP(x) – VC(x) – TFC
Profit = (SP – VC)(x) – TFC
Profit = Contribution margin per unit(x) - TFC
Slide 4-40
Learning objective 3: Perform cost-volume profit analysis for single products

41. Units Needed for Target Profit
Solve the profit equation for the sales quantity in units
Unit sales (x) needed to attain a specified profit =
𝐏𝐫𝐨𝐟𝐢𝐭+𝐓𝐅𝐂 𝐒𝐏 −𝐕𝐂 = 𝐏𝐫𝐨𝐟𝐢𝐭+𝐓𝐅𝐂 𝐂𝐨𝐧𝐭𝐫𝐢𝐛𝐮𝐭𝐢𝐨𝐧 𝐦𝐚𝐫𝐠𝐢𝐧 𝐩𝐞𝐫 𝐮𝐧𝐢𝐭
Slide 4-41
Learning objective 3: Perform cost-volume profit analysis for single products

42. Test Your Knowledge 4
Gabby’s Wedding Cakes creates elaborate wedding cakes. Each cake sells for $500. The variable cost of baking the cakes is $200 and the fixed cost per month is $6,000
Calculate the break-even point in units
𝐏𝐫𝐨𝐟𝐢𝐭+𝐓𝐅𝐂 𝐒𝐏 −𝐕𝐂 = 𝟎+𝟔,𝟎𝟎𝟎 𝟓𝟎𝟎 −𝟐𝟎𝟎 = 𝟔,𝟎𝟎𝟎 𝟑𝟎𝟎 = 20 cakes
How many cakes must be sold to earn a profit of $9,000?
𝐏𝐫𝐨𝐟𝐢𝐭+𝐓𝐅𝐂 𝐒𝐏 −𝐕𝐂 = 𝟗,𝟎𝟎𝟎 +𝟔,𝟎𝟎𝟎 𝟓𝟎𝟎 −𝟐𝟎𝟎 = 𝟏𝟓,𝟎𝟎𝟎 𝟑𝟎𝟎 = 50 cakes
Slide 4-42
Learning objective 3: Perform cost-volume profit analysis for single products

43. Contribution Margin Ratio
The unit contribution margin ratio measures the amount of incremental profit generated by an additional dollar of sales
Two methods to calculate the contribution margin ratio
Contribution margin divided by sales revenue (Sales – TVC) / Sales
Unit contribution margin divided by selling price (SP – VC) / SP
Slide 4-43
Learning objective 3: Perform cost-volume profit analysis for single products

44. Contribution Margin Ratio
For the Model DX375 bar code reader, the contribution margin ratio is
$𝟐𝟎𝟎.𝟎𝟎 −$𝟗𝟎.𝟖𝟑 $𝟐𝟎𝟎.𝟎𝟎 =
This indicates that the company earns an incremental $ for every dollar of sales
If sales increase $10,000 the incremental profit is * $10,000 = $5,458.50
Slide 4-44
Learning objective 3: Perform cost-volume profit analysis for single products

45. “What If” Analysis
“What if” analysis examines what will happen if an action is taken
The profit equation can show how profit will be affect by various options under consideration
CodeConnect is selling 3,000 units at $200, with variable cost of $90.83 and fixed cost of $160,285
Management is considering a change to $80.00 variable cost and fixed cost of $210,285
Slide 4-45
Learning objective 3: Perform cost-volume profit analysis for single products

46. “What If” Analysis Change in fixed and variable costs
Without the change, the profit is
$200(3,000) - $90.83(3,000) - $160,285 = $167,225
If the price and quantity stay the same, the profit assuming the alternative is selected would be
$200(3,000) - $80(3,000) - $210,285 = $149,715
The alternative would hurt profitability
Slide 4-46
Learning objective 3: Perform cost-volume profit analysis for single products

47. “What If” Analysis Change in selling price
Any one of the variables in the profit equation can be considered
For example, if CodeConnect sells 3,000 units, what selling price is required to earn a profit of $200,000?
$200,000 = SP(3,000) - $90.83(3,000) - $160,285
SP(3,000) = $632,775
SP = $210.93
Slide 4-47
Learning objective 3: Perform cost-volume profit analysis for single products

48. Test Your Knowledge 5
Matthews Consulting expects to work 5,000 hours next month. It has variable costs of $100 per hour and fixed costs of $600,000. What price must the company charge to earn a monthly profit of $900,000?
$500
$350
$400
$200
Answer: c
Slide 4-48
Learning objective 3: Perform cost-volume profit analysis for single products

49. Test Your Knowledge 5
Matthews Consulting expects to work 5,000 hours next month. It has variable costs of $100 per hour and fixed costs of $600,000. What price must the company charge to earn a monthly profit of $900,000?
$900,000 = SP(5,000) - $100(5,000) - $600,000
$900,000 = SP(5,000) - $1,100,000
SP(5,000) = $2,000,000
SP = $2,000,000 / 5,000 = $400
Slide 4-49
Learning objective 3: Perform cost-volume profit analysis for single products

50. Multiproduct Analysis
Contribution margin approach
Used if the items sold are similar
Calculate a weighted average contribution margin per unit
Use the weighted average contribution margin in the profit formula to calculate breakeven point and target sales
The relative product mix is then used to calculate the required sales of individual items
Slide 4-50
Learning objective 3: Perform cost-volume profit analysis for single products

51. Multiproduct Analysis
The company has fixed costs of $3,500,000
Slide 4-51
Learning objective 4: Perform cost-volume profit analysis for multiple products

52. Multiproduct Analysis
Break-even sales in units
𝐏𝐫𝐨𝐟𝐢𝐭+𝐓𝐨𝐭𝐚𝐥 𝐟𝐢𝐱𝐞𝐝 𝐜𝐨𝐬𝐭𝐬 𝐖𝐞𝐢𝐠𝐡𝐭𝐞𝐝 𝐚𝐯𝐞𝐫𝐚𝐠𝐞 𝐜𝐨𝐧𝐭𝐫𝐢𝐛𝐮𝐭𝐢𝐨𝐧 𝐦𝐚𝐫𝐠𝐢𝐧 𝐩𝐞𝐫 𝐮𝐧𝐢𝐭 =
𝟎+$𝟑,𝟓𝟎𝟎,𝟎𝟎𝟎 $𝟏,𝟒𝟎𝟎 = 2,500 units
The 2,500 units is made up of the 2:1 mix, so Rohr must sell 1,667 Model A (2/3 of 2,500) and 833 Model B units (1/3 0f 2,500)
Slide 4-52
Learning objective 4: Perform cost-volume profit analysis for multiple products

53. Multiproduct Analysis
Contribution Margin Ratio Approach
Products are substantially different
Calculate total company contribution margin ratio
Use total company contribution margin ratio to compute required sales in dollars
Total company fixed costs (common costs) are not included for contribution margin approach but used for contribution margin ratio approach
Slide 4-53
Learning objective 4: Perform cost-volume profit analysis for multiple products

54. Multiproduct Analysis
A company with 4 divisions has the following information available:
Total sales $6,450,000
Total variable costs $4,706,000
Total direct fixed costs $484,000
Total common fixed costs $1,120,000
Calculate total contribution margin ratio
($6,450,000 – $4,706,000) / $6,450,000 = .2704
Calculate total company break-even sales in dollars
($484,000 + $1,120,000) / = $5,931,953
Slide 4-54
Learning objective 4: Perform cost-volume profit analysis for multiple products

55. Assumptions in CVP Analysis
Assumptions can affect the validity of the analysis
Costs can be separated into fixed and variable components
Total fixed cost and unit variable cost do not change over the levels of interest
Multiproduct analysis assumes the product mix does not change
Despite assumptions, CVP is useful
Slide 4-55
Learning objective 4: Perform cost-volume profit analysis for multiple products

56. Operating Leverage Level of fixed versus variable costs in a company
A company with a high level of fixed costs has a high operating leverage
Companies with high operating leverage have large fluctuations in profit when sales increase or decrease
These companies are seen as more risky
High operating leverage is better when sales are expected to increase
Slide 4-56
Learning objective 5: Discuss the effect of operating leverage

57. Constraints
Due to shortages of space, equipment or labor there can be constraints on how many items can be produced
Utilize contribution margin per unit to analyze situations
Calculate contribution margin per unit of constraint
Produce product with highest contribution margin per unit of constraint
Linear programming can solve multiple constraints
Slide 4-57
Learning objective 6: Use the cost per unit of the constraint to analyze situations involving a resource constraint

58. Constraints
A company can produce Product A or Product B using the same machinery. Only 1,000 machine hours are available
Slide 4-58
Learning objective 6: Use the cost per unit of the constraint to analyze situations involving a resource constraint

59. Constraints With the 1,000 available machine hours,
Product A generates $20,000 of contribution margin
Product B generates $50,000 of contribution margin
Although Product A has the higher contribution margin per unit, Product B has the higher contribution margin per unit of constraint
Slide 4-59
Learning objective 6: Use the cost per unit of the constraint to analyze situations involving a resource constraint

60. CHAPTER 4
Cost-Volume-Profit Analysis
Appendix
Slide 4-60

61. Regression Analysis Slide 4-61
Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method

62. Regression Analysis Slide 4-62
Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method

63. Regression Analysis Slide 4-63
Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method

64. Copyright
© 2010 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 permission 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.
Slide 4-64