1. 1 Determining How Costs Behave

2. 2 Knowing how costs vary by identifying the drivers of costs and by distinguishing fixed from variable costs are frequently the keys to making good management decisions

3. 3 General Issues in Estimating Cost Functions l A cost function is a mathematical function describing cost behavior patterns - how costs change with changes in the cost driver. l Two assumptions are frequently made when estimating cost functions.  Variations in the total costs of a cost-object are explained by variations in a single cost driver.  Cost behavior is adequately approximated by a linear cost function of the cost driver within a relevant range. y = a + bX

4. S U R V E Y S OF C O M P A N Y P R A C T I C E International Comparison of Cost Classification by Companies 86%6048343226 1 1 Production labor Setup labor Materials- handling labor handling laborQuality-control labor laborToolingEnergyBuilding occupancy occupancyDepreciation 6% 6%2534363545 6 7 8% 8%15183033299392 52%4423133142 0 0 5% 5% 616122631 0 0 43%5061754327100100 70%45402125 - - - 20%33302728 - - -10%22305247 - - - Cost Category V M F

5. 5 è The most important issue in estimating a cost function is to determine whether a cause-and-effect relationship exists between the cost driver and the resulting costs. è The cause-and-effect relationship might arise in several ways. 1. It may be due to a physical relationship between costs and cost drivers. 1. It may be due to a physical relationship between costs and cost drivers. 2. Cause and effect can arise from a contractual arrangement. 2. Cause and effect can arise from a contractual arrangement. 3. Cause and effect can be implicitly established by logic and knowledge of operations. 3. Cause and effect can be implicitly established by logic and knowledge of operations. The Cause-and-Effect Criterion in Choosing Cost Drivers

6. 6 è Be careful not to interpret a high correlation, or connection, between two variables to mean that either variable causes the other. è Only a true cause-and-effect relationship, not merely correlation, establishes an economically plausible relationship between costs and their cost drivers. è Establishing economically plausibility is a vital aspect of cost estimation. The Cause-and-Effect Criterion in Choosing Cost Drivers

7. 7 Cost Estimation Approaches  Industrial Engineering Method  Conference Method  Account Analysis Method  Quantitative Analysis of Current or Past Cost Relationships These approaches differ in the costs of conducting the analysis, the assumptions they make, and the evidence they provide about accuracy of the estimated cost function.

8. 8 Industrial Engineering Method u The industrial engineering method (or work- measurement method ) estimates cost functions by analyzing the relationship between inputs and outputs in physical terms. u Time-and-motion study u It can be very time-consuming u Organizations use this approach for direct- cost categories such as materials and labor but not for indirect-cost categories.

9. 9 Conference Method r The conference method estimates cost functions on the basis of analysis and opinions about costs and their drivers gathered from various departments of an organization. r This method allows cost functions and cost estimates to be developed quickly. r The accuracy of the cost estimates largely depends on the care and detail taken by the people providing the inputs.

10. 10 Account Analysis Method W The account analysis method estimates cost functions by classifying cost accounts in the ledger as variable, fixed, or mixed with respect to identified cost driver. W Typically, managers use qualitative rather than quantitative analysis when making these cost-classification decisions. W The account analysis approach is widely used.

11. 11 Quantitative Analysis of Cost Relationships Quantitative analysis of cost relationships are formal methods to fit linear cost functions to past data observations

12. 12 Steps in Estimating A Cost Function Step 1 : Choose the Dependent Variable Step 2 : Identify the Cost Driver(s) Step 3 : Collect Data on the Dependent Variable and Cost Driver(s) Cost Driver(s) Step 4 : Plot the Data Step 5 : Estimate the Cost Function Step 6 : Evaluate the Estimated Cost Function

13. 13 High-Low Method MH IMLC MH IMLC Highest Observation 96 $1,456 Lowest Observation 46 $710 Difference 50 $746 b = $746/50 = $14.92 ^ a = $1,456-($14.92*96) = $23.68 = $23.68 ^ IMLC = $23.68+($14.92*MH)

14. 14 Regression Analysis Method IMLC = $300.98+($10.31*MH) IMLC = $744.67+($7.72*DMLC)

15. 15 Quality Implement Corporation (QIC) produces farm implements for large vehicles used for farming. QIC is refining its cost system and is currently studying the costs of the maintenance activity. Activity analysis indicates that maintenance activity consists primarily of labor setting up machines using certain supplies. Costs include labor, supplies, and energy. QIC employs two full-time mechanics to perform maintenance. The annual salary of a maintenance mechanic is $25,000 (fixed cost). Two plausible cost drivers have been suggested: units produced and number of setups. QIC has performed the first four steps in the cost estimation process. You are asked to estimate and evaluate the prospective cost functions.

16. 16 Plant closed three weeks in March due to storm damage

17. 17 Plant closed three weeks in March due to storm damage

18. 18 Using the visual fit method, determine the monthly fixed maintenance cost and the variable maintenance cost per driver unit based on each potential cost driver. How should the March data be treated?

19. 19 How should the March data be treated? As indicated on page 355 of the text, extreme values of observations occur from nonrepresentative time periods. Such data should be eliminated before estimating cost relationships.

20. 20 Which cost driver best meets the criteria for choosing cost functions: economic plausibility, goodness-of-fit, and slope of the regression line? REGRESSION ANALYSIS RESULTS

21. 21 Both cost drivers appear to be. However, if maintenance activity is primarily associated with a batch-level activity such as setups, the setup driver is preferred. Of the costs associated with maintenance activity, supplies and energy are primarily variable and salaries are fixed at a monthly amount of $4,167 [2*25,000/12]. The regression results indicate a fixed cost of $5,162 using setups, compared to $13,108 using units. Thus, number of setups is the preferred cost driver based on economic plausibility. Both cost drivers appear to be economically plausible. However, if maintenance activity is primarily associated with a batch-level activity such as setups, the setup driver is preferred. Of the costs associated with maintenance activity, supplies and energy are primarily variable and salaries are fixed at a monthly amount of $4,167 [2*25,000/12]. The regression results indicate a fixed cost of $5,162 using setups, compared to $13,108 using units. Thus, number of setups is the preferred cost driver based on economic plausibility.

22. 22 The, measures the percentage of variation in maintenance cost explained by number of setups or units produced. Generally, an R 2 of 0.30 or higher passes the. The coefficient of determination, R 2, measures the percentage of variation in maintenance cost explained by number of setups or units produced. Generally, an R 2 of 0.30 or higher passes the goodness-of-fit test. Units produced has an R 2 of only 0.2052 so it does not pass the goodness-of-fit test. Number of setups has an R 2 of 0.8519, passing the goodness-of-fit test.

23. 23 Do changes in the economically plausible cost driver result in significant changes in maintenance cost?

24. 24 Do changes in the economically plausible cost driver result in significant changes in maintenance cost?

25. 25 Do changes in the economically plausible cost driver result in significant changes in maintenance cost? The slope of the regression line is 0.75, meaning that each additional setup performed results in an average increase in maintenance costs of $750. The importance of setups in driving maintenance costs is measured by the t statistic. Both t statistics are greater than 2.23 implying a significant relationship exists.

26. 26 Learning Curve and Nonlinear Cost Functions a A learning curve is a function that shows how labor-hours per unit decline as units of production increases and workers learn and become better at what they do. a Managers use learning curves to predict how labor-hours(or labor costs) will change as more units are produced. a Managers are now extending the learning-curve notion to include other cost areas in the value chain such as marketing, distribution, and customer service. a The term experience curve describes this broader application of the learning curve. a An experience curve is a function that shows how full product costs per unit(including manufacturing, marketing, distribution, and so on) declines as units of output increase.

27. 27 Cumulative Average-Time Learning Model In the cumulative average-time learning model, the cumulative average time per unit declines by a constant percentage each time the cumulative quantity of units doubles. 16 32 48 64 80 96 112 128 Cumulative units 16 32 48 64 80 96 112 128 Cumulative units Time per Unit Time

28. 28 Incremental Unit-Time Learning Model In the incremental unit- time learning model, the incremental unit time (the time needed to produce the last unit) declines by a constant percentage each time the cumulative quantity of units doubles. 16 32 48 64 80 96 112 128 Cumulative units 16 32 48 64 80 96 112 128 Cumulative units Time per Unit Time

29. 29 Data Collection and Adjustment Issues 1. It contains numerous reliably measured observations of the cost driver(s) and the dependent variable. 1. It contains numerous reliably measured observations of the cost driver(s) and the dependent variable. 2. It contains many values for the cost driver over a wide range. 2. It contains many values for the cost driver over a wide range. The ideal data base for estimating cost functions quantitatively has two characteristics

30. 30 1. The time period for measuring the dependent variable does not properly match the period for measuring cost driver(s). 1. The time period for measuring the dependent variable does not properly match the period for measuring cost driver(s). 2. Fixed costs are allocated as if they are variable. 2. Fixed costs are allocated as if they are variable. 3. Data are either not available for all observations or are not uniformly reliable. 3. Data are either not available for all observations or are not uniformly reliable. 4. Extreme values of observations occur from errors in recording costs; from nonrepresentative time periods; or from observations being outside the relevant range. 4. Extreme values of observations occur from errors in recording costs; from nonrepresentative time periods; or from observations being outside the relevant range. 5. There is no homogeneous relationship between the individual cost items in the dependent variable pool and the cost driver. 5. There is no homogeneous relationship between the individual cost items in the dependent variable pool and the cost driver. 6. The relationship between cost and the cost driver is not stationary; that is, the underlying process that generated the observations has not remained stable over time. 6. The relationship between cost and the cost driver is not stationary; that is, the underlying process that generated the observations has not remained stable over time. 7. Inflation has affected the dependent variable, the cost driver, or both. 7. Inflation has affected the dependent variable, the cost driver, or both. Some Frequently Encountered Data Problems