1. Cost Behavior: Analysis and Use
Chapter 5
Cost Behavior: Analysis and Use

2. Types of Cost Behavior Patterns
Recall the summary of our cost behavior discussion from Chapter 2.

3. The Activity Base Units produced Miles driven Labor hours
Machine hours
A measure of the event that causes the incurrence of a variable cost – a cost driver

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

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

6. Total cost remains constant within a narrow range of activity.
Step-Variable Costs
Total cost remains constant within a narrow range of activity.
Cost
Activity

7. Step-Variable Costs
Total cost increases to a new higher cost for the next higher range of activity.
Cost
Activity

8. The Linearity Assumption and the Relevant Range
Exh.
5-4
The Linearity Assumption and the Relevant Range
Relevant Range
A straight line closely approximates a curvilinear variable cost line within the relevant range.
Economist’s Curvilinear Cost Function
Total Cost
Accountant’s Straight-Line Approximation (constant unit variable cost)
Activity

9. Total Fixed Cost Example
Exh.
5-5
Total Fixed Cost Example
Your monthly basic telephone bill is probably fixed and does not change when you make more local calls.
Monthly Basic Telephone Bill
Number of Local Calls

10. Fixed Cost Per Unit Example
Exh.
5-5
Fixed Cost Per Unit Example
The fixed cost per local call decreases as more local calls are made.
Monthly Basic Telephone Bill per Local Call
Number of Local Calls

11. Cost Behavior Examples of normally variable costs
Merchandisers
Cost of Goods Sold
Service Organizations
Supplies and travel
Manufacturers
Direct Material, Direct Labor, and Variable Manufacturing Overhead
Merchandisers and Manufacturers
Sales commissions and shipping costs
Examples of normally fixed costs
Merchandisers, manufacturers, and service organizations
Real estate taxes, Insurance, Sales salaries Depreciation, Advertising

12. Types of Fixed Costs Committed Discretionary Examples Examples
Long-term, cannot be reduced in the short term.
Discretionary
May be altered in the short-term by current managerial decisions
Examples
Depreciation on Buildings and Equipment
Examples
Advertising and Research and Development

13. 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.
Continue

14. Fixed Costs and Relevant Range
Exh.
5-6
Fixed Costs and Relevant Range 90
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.
Relevant Range 60
Rent Cost in Thousands of Dollars 30
, , , Rented Area (Square Feet)

15. Fixed Costs and Relevant Range
Step-variable 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-variable cost?

16. Which of the following statements about cost behavior are true?
Quick Check 
Which of the following statements about cost behavior are true?
Fixed costs per unit vary with the level of activity.
Variable costs per unit are constant within the relevant range.
Total fixed costs are constant within the relevant range.
Total variable costs are constant within the relevant range.

17. Fixed Monthly Utility Charge
Mixed Costs
A mixed cost has both fixed and variable components. Consider the example of utility cost. X Y
Total mixed cost
Total Utility Cost
Variable Cost per KW
Fixed Monthly Utility Charge
Activity (Kilowatt Hours)

18. Fixed Monthly Utility Charge
Mixed Costs X Y
Total mixed cost Y = a + bX
Total Utility Cost
Variable Cost per KW
Fixed Monthly Utility Charge
Activity (Kilowatt Hours)

19. The Analysis of Mixed Costs
Account Analysis
Engineering Approach
Scattergraph Plot
High-Low Method
Least-Square Regression Method

20. Account Analysis & Engineering Estimates
Each account is classified as either variable or fixed based on the analyst’s knowledge of how the account behaves.
Cost estimates are based on an evaluation of production methods, and material, labor and overhead requirements.

21. The Scattergraph Method
Plot the data points on a graph (total cost vs. activity). *
Total Cost in 1,000’s of Dollars 10 20
Activity, 1,000’s of Units Produced X Y

22. Quick-and-Dirty Method
Draw a line through the data points with about an equal numbers of points above and below the line. Y 20 * * * * * * * *
Total Cost in 1,000’s of Dollars * * 10
Intercept is the estimated fixed cost = $10,000 X
Activity, 1,000’s of Units Produced

23. Quick-and-Dirty Method
The slope is the estimated variable cost per unit.
Slope = Change in cost ÷ Change in units Y 20 * * * * * * * *
Total Cost in 1,000’s of Dollars * * 10
Horizontal distance is the change in activity.
Vertical distance is the change in cost. X
Activity, 1,000’s of Units Produced

24. 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 fixed cost; and then
express the costs in equation form Y = a + bX.

25. Changein cost Change in units
The High-Low Method
Variable cost per unit = Change in cost ÷ change in units
Changein cost Change in units

26. The High-Low Method Variable cost per unit = $2,400 ÷ 3,000 units

27. The High-Low Method
Variable cost = $2,400 ÷ 3,000 units = $0.80 per unit
Fixed cost = Total cost – Total variable cost
Fixed cost = $9,800 – ($0.80 per unit × 8,000 units)
Fixed cost = $9,800 – $6,400 = $3,400

28. The High-Low Method
Variable cost = $2,400 ÷ 3,000 units = $0.80 per unit
Fixed cost = Total cost – Total variable cost
Fixed cost = $9,800 – ($0.80 per unit × 8,000 units)
Fixed cost = $9,800 – $6,400 = $3,400
Total cost = Fixed cost + Variable cost (Y = a + bX) Y = $3,400 + $0.80X

29. Quick Check 
Sales salaries and commissions are $10,000 when 80,000 units are sold, and $14,000 when 120,000 units are sold. Using the high-low method, what is the variable portion of sales salaries and commission?
a. $0.08 per unit
b. $0.10 per unit
c. $0.12 per unit
d. $0.125 per unit
$4,000 ÷ 40,000 units = $0.10 per unit

30. Quick Check 
Sales salaries and commissions are $10,000 when 80,000 units are sold, and $14,000 when 120,000 units are sold. Using the high-low method, what is the fixed portion of sales salaries and commissions?
a. $ 2,000
b. $ 4,000
c. $10,000
d. $12,000

31. Least-Squares Regression Method
Software can be used to fit a regression line through the data points.
The cost analysis objective is the same: Y = a + bx
Least-squares regression also provides a statistic, called the R2, that is a measure of the goodness of fit of the regression line to the data points.

32. Least-Squares Regression Method
R2 is the percentage of the variation in total cost explained by the activity. Y 20 * * * * * * * * * *
Total Cost 10
R2 for this relationship is near 100% since the data points are very close to the regression line. X
Activity

33. Cost Estimation Methods Regression Analysis
A statistical method used to create an equation relating independent (or X) variables to dependent (or Y) variables.
Past data is used to estimate relationships between costs and activities.
Dependent variables are caused by the independent variables.
Independent variables are the cost drivers that are correlated with the dependent variables.

34. Cost Estimation Methods Regression Analysis
The simple cost model is actually a regression model:
TC = F + VX
Caution: Before doing the analysis, take time to determine if a logical relationship between the variables exists.
This model will only be useful within a relevant range of activity.

35. Cost Estimation Methods Regression Analysis
A set of data can be regressed using several techniques:
Manual computations
SPSS or SAS Statistical Software
Excel or other spreadsheet
The result of the regression process is a regression model:
TC = F + VX
Each regression model has an R-square (R2) measure of how good the model is.
Range of R2 = 0 to 1.0

36. Simple Regression Analysis Example
Fasco wants to know it’s average fixed cost and variable cost per unit.
Using the data to the right, let’s see how to do a regression using Excel.

37. Simple Regression Analysis Example
You will need three pieces of information from your regression analysis:
Estimated Variable Cost per Unit (line slope)
Estimated Fixed Costs (line intercept)
Goodness of fit, or R2
To get these three pieces of information we will need to use THREE different excel functions.
LINEST, INTERCEPT, & RSQ

38. Simple Regression Using Excel 2000
First, open the excel file with your data and click on “Insert” and “Function”

39. Simple Regression Using Excel 2000
When the function box opens, click on “Statistical”, then on “LINEST”

40. Simple Regression Using Excel 2000
By clicking on the buttons to the left, you can highlight the desired cells directly from the spreadsheet.
1. Enter the cell range for the cost amounts in the “Known_y’s” box.
2. Enter the cell range for the quantity amounts in the “Known_x’s” box.

41. Simple Regression Using Excel 2000
The Slope, or estimated variable cost per unit, is identified here. Click OK to put this value on your spreadsheet.

42. Simple Regression Using Excel 2000
Repeat the procedure using “Intercept”, to estimate fixed cost.

43. Simple Regression Using Excel 2000
As previously, enter the appropriate cell ranges in their appropriate places.
The estimated fixed cost is identified here.

44. Simple Regression Using Excel 2000
Finally, determine the “goodness of fit”, or R2, by using the RSQ function.

45. Simple Regression Using Excel 2000
As previously, enter the appropriate cell ranges in their appropriate places.
The estimated R2 for your estimated cost function is identified here.

46. Let’s put our knowledge of cost behavior to work by preparing a contribution format income statement.

47. The Contribution Format
The contribution margin format emphasizes cost behavior. Contribution margin covers fixed costs and provides for income.

48. The Contribution Format
Used primarily for external reporting.
Used primarily by management.

49. End of Chapter 5