2. CHAPTER 4
Cost-Volume-Profit Analysis

3. Purpose of Budgeting Planning Control Decision making
How many units of input do I need to support a budgeted output?
Control
Are operations effective and efficient?
Decision making
How do we decide on a price, and choose quantity given constraints?
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
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
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 10%, cost increases by 10%
Learning objective 1: Identify common cost behavior patterns

7. Variable Costs
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
Learning objective 1: Identify common cost behavior patterns

8. Variable Costs Total Variable Cost = $91 × Units produced
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
Activity increases by 10%, costs remain unchanged
Learning objective 1: Identify common cost behavior patterns

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

11. Fixed Costs Discretionary Fixed Costs Committed Fixed Costs
Management can easily change
Advertising, research and development
Many companies cut back on these costs when sales drop. This can be shortsighted. Why?
Committed Fixed Costs
Cannot be easily changed
Rent, insurance
Learning objective 1: Identify common cost behavior patterns

12. Using Less Water but Paying Higher Rates!
Fixed Costs
LINK TO PRACTICE
Using Less Water but Paying Higher Rates!
What happens to cost per unit when fixed costs remain the same but volume or activity declines?
Can you think of another way to set rates to make ratepayers less angry?
Learning objective 1: Identify common cost behavior patterns

13. 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
Learning objective 1: Identify common cost behavior patterns

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

15. Step Costs Fixed cost for a specific range
Increases to higher level when upper bound of range is exceeded
Use correct cost when budgeting for a particular relevant range
Company adds third production shift, cost increase includes supervisory salary
Learning objective 1: Identify common cost behavior patterns

16. Step Costs Total step costs =
$94,000 for relevant range 0 – 3,000 units produced
$144,000 for relevant range 3,001 – 6,000 units
$194,000 for relevant range 6,001 – 9,000 units
Learning objective 1: Identify common cost behavior patterns

17. Direct Labor Q Is direct labor always a variable cost?
Are you willing to lay off workers when production declines?
What if the decline is temporary?
What if the decline is permanent?
Does the degree of automation make a difference in whether direct labor is fixed or variable?
Learning objective 1: Identify common cost behavior patterns

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
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
Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method

20. Account Analysis
Total cost = ($81.50 Variable cost per unit × Units produced) + $102,000 Fixed costs
Expected cost of 2,500 units = ($81.50 × 2,500) + $102,000 = $305,750
Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method

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

22. Scattergraphs Utilization of cost information from previous periods
Weekly, monthly, or quarterly cost reports
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
Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method

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

24. High-Low Method Utilization of cost information from previous periods
Connect straight line from lowest activity level to highest activity level
Slope of the line (change in cost divided by change in activity) equals variable cost per unit
Total cost at lowest or highest activity level minus variable cost at that level equals fixed cost
Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method

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

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

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

28. 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
Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method

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

30. Regression Analysis
Input Y range are the costs. Input X range is the production.
Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method

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

32. The Relevant Range
Range of activity for which estimates and predictions are expected to be accurate
- Accuracy expected only for production levels within range
Difficult to assess costs outside the relevant range
Learning objective 3: Perform cost-volume profit analysis for single products

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

34. 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
Learning objective 3: Perform cost-volume profit analysis for single products

35. 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
Learning objective 3: Perform cost-volume profit analysis for single products

36. Cost-Volume-Profit Analysis
Break-Even Point
$0 = SP(x) – VC(x) – TFC
$0 = [$ (x)] – [$90.83(x)] – $160,285
$0 = [($ – $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)
Learning objective 3: Perform cost-volume profit analysis for single products

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

38. Exercise 1
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
$6,000 / ($500 - $200) = 20 cakes
2. How many cakes must be sold to earn a profit of $9,000?
($9,000 + $6,000) / ($500 - $200) = 50 cakes
Learning objective 3: Perform cost-volume profit analysis for single products

39. 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.
Learning objective 3: Perform cost-volume profit analysis for single products

40. Review 1
At Winford Corp., the selling price per lawn mower is $120, variable cost per lawn mower is $55. Fixed costs are $130,000. Expected sales are 4,200 units. The Margin of Safety is?
$264,000
$384,000
$143,000
$121,000
Answer a:
Expected sales = 4,200 units X $120 = $504,000
Break even sales = 2,000 units X $120 = $240,000
Margin of safety = $504,000 – $240,000 = $264,000
Learning objective 3: Perform cost-volume profit analysis for single products 40

41. Review 2
At Winford Corp., the selling price per lawn mower is $120, variable cost per lawn mower is $55. Fixed costs are $130,000. Expected sales are 4,200 units. What is profit expected to be?
Answer here: _________________
Margin of safety in units = 4,200 – 2,000 = 2,200
2,200 units × $65 unit CM = $143,000
$143,000
Learning objective 3: Perform cost-volume profit analysis for single products 41

42. Contribution Margin Difference between revenue and variable costs
Total revenue minus total variable costs
Unit contribution margin =
Selling price minus variable cost per unit
- The unit contribution margin measures the amount of incremental profit generated by selling an additional unit
Learning objective 3: Perform cost-volume profit analysis for single products

43. Contribution Margin Ratio
The 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
Learning objective 3: Perform cost-volume profit analysis for single products

44. Exercise 2
Rhetorix, Inc. produces stereo speakers. The selling price per pair of speakers is $800. The variable cost of production is $300 and the fixed cost per month is $50,000.
Calculate the unit contribution margin associated with a pair of speakers
$800 – $300 = $500
Calculate the contribution margin ratio for Rhetorix associated with a pair of speakers
($800 – $300) / $800 = 0.625
Learning objective 3: Perform cost-volume profit analysis for single products

45. Contribution Margin
Using the contribution margin and the contribution margin ratio
SP = $200.00, VC = $90.83, CM = 200 – = $109.17, TFC = 160,285, profit = $40,000
Units to produce =
(Profit + TFC) / Unit contribution margin
($40,000 + $160,285) / = 1,835 units
Sales required (in dollars) =
(Profit + TFC) / Contribution margin ratio
CM ratio = $ / $ =
($40,000 + $160,285) / = $366,890
Learning objective 3: Perform cost-volume profit analysis for single products

46. Exercise 3
Rhetorix, Inc. produces stereo speakers. The selling price per pair of speakers is $800. The variable cost of production is $300 and the fixed cost per month is $50,000.
If the company sells five more speakers than planned, what is the expected effect on profit of selling the additional speakers?
5 speakers × $500 unit CM = $2,500 profit
If the company has sales that are $5,000 higher than expected, what is the expected effect on profit?
$5,000 × = $3,125
Learning objective 3: Perform cost-volume profit analysis for single products

47. Review 3
At Winford Corp., the selling price per lawn mower is $120, variable cost per lawn mower is $55. Fixed costs are $130,000. Contribution Margin per unit is?
$65
$75
$175
$30
Answer a: $120 – $55 = $65
Learning objective 3: Perform cost-volume profit analysis for single products 47

48. Review 4
At Winford Corp., the selling price per lawn mower is $120, variable cost per lawn mower is $55. Fixed costs are $130,000. Break-Even Point in units is?
1,000 units
1,083 units
2,000 units
None of these
Answer c: $130,000 / ($120 – $55) = 2,000 units
Learning objective 3: Perform cost-volume profit analysis for single products 48

49. Cost-Volume-Profit Analysis
“What If” Analysis
Utilize profit equation to determine impact of managerial decisions
Change in Fixed and Variable Costs
Change in Selling Price
Taxes in CVP Analysis
After tax profit =
[SP(x) – VC(x) – TFC](1 – t)
Learning objective 3: Perform cost-volume profit analysis for single products

50. Multiproduct Analysis
Contribution Margin Approach
Used if products are similar
Identify number of units needed to be sold to break even
Calculate weighted average contribution margin based on expected units sold and product mix
Assume product mix to calculate break-even point and target profit
Learning objective 3: Perform cost-volume profit analysis for single products

51. Multiproduct Analysis
Rohr Watch Company
Model A
Model B
Total
Selling price
$2,000
$3,000
Variable cost
800
1,200
Contribution margin
$1,200
$1,800
Units produced and sold
4,000
2,000
6,000
Weight ,000 / 6, ,000 / 6,000
Weighted average contribution margin is [(2 × $1,200) + (1 × $1,800)]/3 = $1,400 per unit
Break-even is $3,500,000 / $1,400 = 2,500 units
Break-even is 2,500 × (4,000 / 6,000) = 1,667 Model A units (Whole units.)
Break-even is 2,500 × (2,000 / 6,000) = 834 Model B units (Whole units.)
Learning objective 4: Perform cost-volume profit analysis for multiple products

52. 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
Learning objective 4: Perform cost-volume profit analysis for multiple products

53. 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 $1,260,000
Total common fixed costs $1,120,000
Calculate total company contribution margin
($6,450,000 – $4,706,000) / $6,450,000 = .2704
Calculate total company break-even sales in dollars.
($1,260,000 + $1,120,000) / = $8,801,775
Learning objective 4: Perform cost-volume profit analysis for multiple products

54. 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
Learning objective 4: Perform cost-volume profit analysis for multiple products

55. Operating Leverage Level of fixed versus variable costs in a company
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
Learning objective 5: Discuss the effect of operating leverage

56. Fixed vs. Variable Costs
LINK TO PRACTICE
Fixed Costs Too High—Make Them Variable!
Can you think of any ways other than incentive compensation and outsourcing to turn fixed costs into variable costs?
Would you rather have fixed or variable costs when revenues are increasing? When revenues are decreasing?
Learning objective 5: Discuss the effect of operating leverage

57. Constraints Constraints on how many items can be produced
Shortage of space, equipment, or labor
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
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
Product A has the higher contribution margin, but Product B has the higher contribution margin per machine hour
Learning objective 6: Use the cost per unit of the constraint to analyze situations involving a resource constraint

59. Copyright
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