1. Managerial Accounting by James Jiambalvo
Chapter 4:
Cost-Volume-Profit Analysis
Slides Prepared by:
Scott Peterson
Northern State University

2. Chapter 4: Cost-Volume-Profit-Analysis
Chapter Themes:
It’s all about how costs change in total with respect to changes in activity.
C-V-P-A is linear.
You must be able to put all costs into either variable or fixed cost categories.
Learning Objectives:
Identify common cost behavior patterns.
Estimate the relation between cost and activity using account analysis, the high-low method, and scattergraphs.
Perform cost-volume-profit-analysis for single products.
Perform cost-volume-profit-analysis for multiple products.
Discuss the effect of operating leverage.
Use the contribution margin per unit of the constraint to analyze situations involving a resource constraint.

3. Common Cost Behavior Patterns
To perform Cost-Volume-Profit-Analysis (C-V-P-A), you need to know how costs behave when business activity (production volume, sales volume…) changes.
Related Learning Objectives:
Identify common cost behavior patterns.
Estimate the relation between cost and activity using account analysis, the high-low method, and scattergraphs.
Perform cost-volume-profit-analysis for single products.
Perform cost-volume-profit-analysis for multiple products.
Discuss the effect of operating leverage.
Use the contribution margin per unit of the constraint to analyze situations involving a resource constraint.

4. Variable Costs
By definition, Variable Costs are costs that change (in total) in response to changes in volume or activity. It is assumed, too, that the relationship between variable costs and activity is proportional. That is, if production volume increases by 10%, then variable costs in total will rise by 10%. Examples include direct labor, raw materials and sales commissions.
Related Learning Objectives:
Identify common cost behavior patterns.
Estimate the relation between cost and activity using account analysis, the high-low method, and scattergraphs.
Perform cost-volume-profit-analysis for single products.
Perform cost-volume-profit-analysis for multiple products.
Discuss the effect of operating leverage.
Use the contribution margin per unit of the constraint to analyze situations involving a resource constraint.

5. Fixed Costs
By definition, Fixed Costs are costs that do not change (in total) in response to changes in volume or activity. Examples include depreciation, supervisory salaries and maintenance expenses.
Related Learning Objectives:
Identify common cost behavior patterns.
Estimate the relation between cost and activity using account analysis, the high-low method, and scattergraphs.
Perform cost-volume-profit-analysis for single products.
Perform cost-volume-profit-analysis for multiple products.
Discuss the effect of operating leverage.
Use the contribution margin per unit of the constraint to analyze situations involving a resource constraint.

6. Mixed Costs
Mixed Costs are costs that contain both a variable cost element and a fixed cost element. These costs are sometimes referred to as semi-variable costs. An example would be a salesperson’s salary where she receives a base salary plus commissions.
Related Learning Objectives:
Identify common cost behavior patterns.
Estimate the relation between cost and activity using account analysis, the high-low method, and scattergraphs.
Perform cost-volume-profit-analysis for single products.
Perform cost-volume-profit-analysis for multiple products.
Discuss the effect of operating leverage.
Use the contribution margin per unit of the constraint to analyze situations involving a resource constraint.

7. Cost Estimation Methods
Managers need to be able to predict (plan) costs at various activity levels. And because cost information is often not broken out in terms of fixed and variable components, managers use cost estimation methods to do just that. Four common methods are:
Account analysis
Scattergraph
High-Low
Regression
Related Learning Objectives:
Identify common cost behavior patterns.
Estimate the relation between cost and activity using account analysis, the high-low method, and scattergraphs.
Perform cost-volume-profit-analysis for single products.
Perform cost-volume-profit-analysis for multiple products.
Discuss the effect of operating leverage.
Use the contribution margin per unit of the constraint to analyze situations involving a resource constraint.

8. Account Analysis
Account Analysis is a common approach to estimating fixed and variable costs. This method requires the manager to exercise professional judgment to classify costs into variable and fixed categories. Once this is done, total variable costs are divided by the activity level to determine variable costs per unit of activity. Costs classified as fixed costs are used to estimate total fixed cost.
Related Learning Objectives:
Identify common cost behavior patterns.
Estimate the relation between cost and activity using account analysis, the high-low method, and scattergraphs.
Perform cost-volume-profit-analysis for single products.
Perform cost-volume-profit-analysis for multiple products.
Discuss the effect of operating leverage.
Use the contribution margin per unit of the constraint to analyze situations involving a resource constraint.

9. Scattergraph Approach
The Scattergraph Approach uses cost information from a number of reporting periods (monthly for example) to determine how costs change with respect to changes in activity. The periodic cost data are then plotted on a graph to get a visual picture of the correlation between costs and activity levels. A sample Scattergraph appears on the next slide.
Related Learning Objectives:
Identify common cost behavior patterns.
Estimate the relation between cost and activity using account analysis, the high-low method, and scattergraphs.
Perform cost-volume-profit-analysis for single products.
Perform cost-volume-profit-analysis for multiple products.
Discuss the effect of operating leverage.
Use the contribution margin per unit of the constraint to analyze situations involving a resource constraint.

10. Sample Scattergraph Related Learning Objectives:
Identify common cost behavior patterns.
Estimate the relation between cost and activity using account analysis, the high-low method, and scattergraphs.
Perform cost-volume-profit-analysis for single products.
Perform cost-volume-profit-analysis for multiple products.
Discuss the effect of operating leverage.
Use the contribution margin per unit of the constraint to analyze situations involving a resource constraint.

11. High-Low Method
Using the same periodic data as the scattergraph method, the High-Low Method may be used to estimate the fixed and variable components at various levels of activity. This method “fits” a line to the data, but uses only the high and low data points. Here, the slope of the line (total cost curve) represents the variable cost. The Y-intercept represents the estimate of the fixed costs.
Related Learning Objectives:
Identify common cost behavior patterns.
Estimate the relation between cost and activity using account analysis, the high-low method, and scattergraphs.
Perform cost-volume-profit-analysis for single products.
Perform cost-volume-profit-analysis for multiple products.
Discuss the effect of operating leverage.
Use the contribution margin per unit of the constraint to analyze situations involving a resource constraint.

12. Regression Analysis
Regression Analysis is a statistical technique that uses all available data points to estimate the slope and intercept. That is, unlike the High-Low method which uses only the high and low data points, regression uses ALL of the data points to find the “best fit.” It should be noted that Regression Analysis is a superior method of cost estimation.
Related Learning Objectives:
Identify common cost behavior patterns.
Estimate the relation between cost and activity using account analysis, the high-low method, and scattergraphs.
Perform cost-volume-profit-analysis for single products.
Perform cost-volume-profit-analysis for multiple products.
Discuss the effect of operating leverage.
Use the contribution margin per unit of the constraint to analyze situations involving a resource constraint.

13. The Relevant Range
The Relevant Range is the activity level within which cost behavior holds true. Most models have limits and this type of linear analysis is not different. Above or below this range, forecasts of cost behavior may not be accurate.
Related Learning Objectives:
Identify common cost behavior patterns.
Estimate the relation between cost and activity using account analysis, the high-low method, and scattergraphs.
Perform cost-volume-profit-analysis for single products.
Perform cost-volume-profit-analysis for multiple products.
Discuss the effect of operating leverage.
Use the contribution margin per unit of the constraint to analyze situations involving a resource constraint.

14. Cost-Volume-Profit Analysis
Cost-Volume-Profit Analysis (C-V-P) explores the relationship between costs (fixed and variable), activity levels and profits. That is, once the variable and fixed elements have been determined using the tools discussed in the preceding slides, we use the following profit equation: Profit = SP(x) - VC(x) – TFC=Net Income.
Related Learning Objectives:
Identify common cost behavior patterns.
Estimate the relation between cost and activity using account analysis, the high-low method, and scattergraphs.
Perform cost-volume-profit-analysis for single products.
Perform cost-volume-profit-analysis for multiple products.
Discuss the effect of operating leverage.
Use the contribution margin per unit of the constraint to analyze situations involving a resource constraint.

15. Break-Even Point Related Learning Objectives:
One of the primary purposes of C-V-P is to calculate the Break-Even Point. It simply represents the number of units the firm must sell to generate exactly zero net income– to earn neither profit nor loss. Graphically, as shown in the next slide, Break-Even is the point where the sales curve and cost curve cross. It should be noted here that managers are seldom interested in merely breaking even. But the Break-Even is an important benchmark!
Related Learning Objectives:
Identify common cost behavior patterns.
Estimate the relation between cost and activity using account analysis, the high-low method, and scattergraphs.
Perform cost-volume-profit-analysis for single products.
Perform cost-volume-profit-analysis for multiple products.
Discuss the effect of operating leverage.
Use the contribution margin per unit of the constraint to analyze situations involving a resource constraint.

16. Break-Even Point (Graphic)
Related Learning Objectives:
Identify common cost behavior patterns.
Estimate the relation between cost and activity using account analysis, the high-low method, and scattergraphs.
Perform cost-volume-profit-analysis for single products.
Perform cost-volume-profit-analysis for multiple products.
Discuss the effect of operating leverage.
Use the contribution margin per unit of the constraint to analyze situations involving a resource constraint.

17. Margin of Safety
The Margin of Safety is the difference between the expected level of sales and break-even sales. It may be expressed in units or dollars of sales.
Related Learning Objectives:
Identify common cost behavior patterns.
Estimate the relation between cost and activity using account analysis, the high-low method, and scattergraphs.
Perform cost-volume-profit-analysis for single products.
Perform cost-volume-profit-analysis for multiple products.
Discuss the effect of operating leverage.
Use the contribution margin per unit of the constraint to analyze situations involving a resource constraint.

18. Contribution Margin
The Contribution Margin is the difference between selling price and variable cost per unit. It measures the amount each unit sold contributes to covering fixed cost (first) and increasing profit (once fixed costs are covered).
The relationship is as follows:
SP-VC
Related Learning Objectives:
Identify common cost behavior patterns.
Estimate the relation between cost and activity using account analysis, the high-low method, and scattergraphs.
Perform cost-volume-profit-analysis for single products.
Perform cost-volume-profit-analysis for multiple products.
Discuss the effect of operating leverage.
Use the contribution margin per unit of the constraint to analyze situations involving a resource constraint.

19. Contribution Margin Ratio
The Contribution Margin Ratio expresses the contribution of every sales dollar to covering fixed cost (first) and operating profit (second). It is calculated as follows: SP – VC SP
In other words, for every dollar of sales, X% of that will contribute to covering the fixed costs, and once fixed costs are covered X% of every dollar of sales will be contribute to net income.
Related Learning Objectives:
Identify common cost behavior patterns.
Estimate the relation between cost and activity using account analysis, the high-low method, and scattergraphs.
Perform cost-volume-profit-analysis for single products.
Perform cost-volume-profit-analysis for multiple products.
Discuss the effect of operating leverage.
Use the contribution margin per unit of the constraint to analyze situations involving a resource constraint.

20. “What If” Analysis
Once the cost structure is modeled (variable and fixed costs are estimated) managers can do sensitivity analyses or “What If” Analyses. This analysis examines what will happen if a particular action is taken. For example, what will happen if fixed costs rise by X dollars and variable costs decrease by Y dollars? Or what will happen if selling price is decrease by Z dollars?
Related Learning Objectives:
Identify common cost behavior patterns.
Estimate the relation between cost and activity using account analysis, the high-low method, and scattergraphs.
Perform cost-volume-profit-analysis for single products.
Perform cost-volume-profit-analysis for multiple products.
Discuss the effect of operating leverage.
Use the contribution margin per unit of the constraint to analyze situations involving a resource constraint.

21. Multiproduct Analysis
Up until now we looked at C-V-P analysis for a single product. The next few slides examine C-V-P as it applies to multiple product scenarios. There are two approaches we will consider in this section:
Contribution Margin Approach (for similar products)
Contribution Margin Ratio Approach (for substantially different products).
Related Learning Objectives:
Identify common cost behavior patterns.
Estimate the relation between cost and activity using account analysis, the high-low method, and scattergraphs.
Perform cost-volume-profit-analysis for single products.
Perform cost-volume-profit-analysis for multiple products.
Discuss the effect of operating leverage.
Use the contribution margin per unit of the constraint to analyze situations involving a resource constraint.

22. Contribution Margin Approach
As indicated, if the products under analysis are similar (e.g., various flavors of ice cream, various models of boats), the Weighted Average Contribution Margin Approach can be used. For example, if the contribution margin of product A is $8 and the contribution margin of product B is $5, and if two units of B are sold for each unit of A, the Weighted Average Contribution Margin is $6.00.
Related Learning Objectives:
Identify common cost behavior patterns.
Estimate the relation between cost and activity using account analysis, the high-low method, and scattergraphs.
Perform cost-volume-profit-analysis for single products.
Perform cost-volume-profit-analysis for multiple products.
Discuss the effect of operating leverage.
Use the contribution margin per unit of the constraint to analyze situations involving a resource constraint.

23. Contribution Margin Ratio Approach
If the products under analysis are substantial different (e.g., products in a department store), the Contribution Margin Ratio Approach should be used. It makes little sense in this case to ask how many units to break even. The question should be “how many dollars of sales to break even.”
Related Learning Objectives:
Identify common cost behavior patterns.
Estimate the relation between cost and activity using account analysis, the high-low method, and scattergraphs.
Perform cost-volume-profit-analysis for single products.
Perform cost-volume-profit-analysis for multiple products.
Discuss the effect of operating leverage.
Use the contribution margin per unit of the constraint to analyze situations involving a resource constraint.

24. Assumptions in C-V-P Analysis
As with most models, there are certain assumptions which are made that affect the validity of the analysis.
Costs can be accurately separated into variable and fixed components.
Fixed costs remain fixed.
Variable costs per unit do not change over the relevant range.
Related Learning Objectives:
Identify common cost behavior patterns.
Estimate the relation between cost and activity using account analysis, the high-low method, and scattergraphs.
Perform cost-volume-profit-analysis for single products.
Perform cost-volume-profit-analysis for multiple products.
Discuss the effect of operating leverage.
Use the contribution margin per unit of the constraint to analyze situations involving a resource constraint.

25. Operating Leverage
Operating Leverage relates to the level of fixed versus variable costs in a firm’s cost structure. The higher the degree of fixed costs, the more operating leverage a firm is considered to have. Firms with lower variable and higher fixed costs have higher contribution margins. This translates into greater profit or loss as sales increase or decrease.
Related Learning Objectives:
Identify common cost behavior patterns.
Estimate the relation between cost and activity using account analysis, the high-low method, and scattergraphs.
Perform cost-volume-profit-analysis for single products.
Perform cost-volume-profit-analysis for multiple products.
Discuss the effect of operating leverage.
Use the contribution margin per unit of the constraint to analyze situations involving a resource constraint.

26. Constraints
In the real world there are constraints on how many items can be manufactured or how much service can be delivered. So the focus shifts from contribution margin per unit to contribution margin per unit of the constraint. Examples of constraints include manufacturing space, labor, parts and materials etc…
Related Learning Objectives:
Identify common cost behavior patterns.
Estimate the relation between cost and activity using account analysis, the high-low method, and scattergraphs.
Perform cost-volume-profit-analysis for single products.
Perform cost-volume-profit-analysis for multiple products.
Discuss the effect of operating leverage.
Use the contribution margin per unit of the constraint to analyze situations involving a resource constraint.

27. Copyright
© 2001 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.