COST MANAGEMENT Accounting & Control Hansen▪Mowen▪Guan COPYRIGHT © 2009 South-Western Publishing, a division of Cengage Learning. Cengage Learning and South-Western are trademarks used herein under license. 1 Chapter 3 Cost Behavior

2 Study Objectives 1.Define and describe fixed, variable, and mixed costs. 2.Explain the use of resources and activities and their relationship to cost behavior. 3.Separate mixed costs into their fixed and variable components using the high-low method, the scatterplot method, and the method of least squares. 4.Evaluate the reliability of the cost formula. 5.Explain how multiple regression can be used to assess cost behavior. 6.Define the learning curve, and discuss its impact on cost behavior. 7.Discuss the use of managerial judgment in determining cost behavior.

3 Two production lines can process 10,000 computers per year each. The workers on each line are supervised by a production-line manager who is paid $24,000 per year. For production up to 10,000 units, only one supervisor is needed. When production is between 10,001 and 20,000 units, two supervisors are required. Cost Behavior: Fixed Costs Fixed costs are costs that in total are constant within the relevant range as the level of the activity driver varies.

4 Cost Behavior: Fixed Costs

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8 Variable costs are costs that in total vary in direct proportion to changes in an activity driver. A CD-ROM disk drive is added to each computer at a cost of $30 per computer. The total cost of disk drives for each level of production varies. Cost Behavior: Variable Costs

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10 Cost Behavior: Variable Costs

11 Cost Behavior: Variable Costs

12 Mixed costs are costs that have both a fixed and a variable component. Ten sales representatives each earn an annual salary of $30,000 plus a commission of $50 per computer sold. 10,000 computers are sold. Cost Behavior: Mixed Costs

13 Y = Fixed cost + Total variable cost Y = F + VX where Y = Total cost For Days Computer, the selling cost is: Y = $300,000 + $50X Cost Behavior: Mixed Costs

14 Cost Behavior: Mixed Costs

15 Cost Behavior: Mixed Costs

16 Flexible resources –Acquired as used and needed –Usually considered variable costs Examples: materials, energy Committed resources –Acquired in advance of usage –Usually considered fixed costs Examples: buying or leasing buildings, contracts with employees Resources, Activities, and Cost Behavior

17 Resources, Activities, and Cost Behavior Step cost behavior displays a constant level of cost for a range of output and then jumps to a higher level of cost at some point Step-Variable costs Narrow increments Approximate as a strictly variable assumption Step-Fixed costs Wide increments Assigned to the fixed cost category

18 Resources, Activities, and Cost Behavior

19 Methods for Separating Mixed Costs into Fixed and Variable Components The High-Low Method The Scatterplot Method The Method of Least Squares Variable Component Fixed Component

20 Y = F + VX Methods for Separating Mixed Costs into Fixed and Variable Components where Y = Total activity cost F = Fixed cost component V = Variable cost per unit X = Measure of activity output Straight-line equation:

21 Step 1: Solve for variable cost (V) V = Change in cost ÷ Change in activity High-Low Method

22 High-Low Method Low Activity High Activity

23 High-Low Method Step 2: Using either the high cost or low cost, solve for the total fixed costs F Step 1: Solve for variable cost (V) V = Change in cost ÷ Change in activity Low cost High cost

24 Scatterplot Method Step 1: Plot the data points on a scattergraph

25 Scatterplot Method Step 2: Choose the two data points most representative of the data to describe the cost behavior line

26 Method of Least Squares

27 Regression Programs The best-fitting line is the line with the smallest sum of squared deviations Regression analysis determines the linear function with the minimum sum of squared deviations Utilize spreadsheet packages such as Microsoft Excel to perform the computation

28 Spreadsheet Data for Anderson Company Regression Analysis for the Method of Least Squares

29 Regression Output for Anderson Company Regression Analysis for the Method of Least Squares

30 The regression analysis gives rise to the following equation for Anderson’s material handling cost: Regression Analysis for the Method of Least Squares

31 Reliability of Cost Formulas Hypothesis test of parameters –The lower the P-value, the more likely that the true parameter is significantly different from 0 –Traditional benchmarks of significance are 0.10, 0.05 or 0.01

32 Reliability of Cost Formulas Goodness of fit –R 2 is the coefficient of determination –Measures the percentage of change in the dependent variable explained by changes in the independent variable –The closer to 1.0, the better; no benchmark

33 Reliability of Cost Formulas Confidence intervals –The standard error is used to determine the ± range of possible values around the predicted value:

34 X 1 = first explanatory variable X 2 = second explanatory variable Multiple Regression Least-squares method is used to fit an equation involving two or more explanatory variables Y = F + V 1 X 1 + V 2 X 2 etc. where

35 Multiple Regression Spreadsheet Data for Anderson Company X2X2 X1X1

36 Multiple Regression Analysis for the Method of Least Squares

37 Y = $507 + $7.84X 1 + $0.11X 2 Y= $507 + $7.84(350) + $0.11(17,000) = $507 + $2,744 + $1,870 = $5,121 Multiple Regression Based on the multiple regression analysis, the cost formula is written as: In November the company expects to make 350 moves with a weight of 17,000 pounds. The predicted cost of material handling is:

(80% × 100) (80% × 80) (80% × 64) , Cumulative Cumulative Cumulative Individual Units Number Average Time Total Time: Time for nth of Units per Unit in Hours Labor Hours Unit-Labor Hours (1) (2) (3) = (1) × (2) (4) Cumulative Average Time Learning Curve with 80% Learning Rate

39 Graph of Cumulative Total Hours Required and the Cumulative Average Time per Unit

40 Managerial Judgment Managerial judgment is critically important in determining cost behavior and is by far the most widely used method in practice Advantage – simplicity Disadvantage – poor judgment leads to errors

COST MANAGEMENT Accounting & Control Hansen▪Mowen▪Guan 41 End Chapter 3