1. A&MIS 2121W. F. Bentz Session 11 William F. Bentz January 22, 2002 Fisher College of Business

2. A&MIS 2122W. F. Bentz Key Issues in Cost Behavior  Terminology (fixed, variable, semi- variable, semi-fixed, capacity, discretionary)  Unit of analysis (total vs. unit costs)  Interpretation of cost drivers  Implications of cost behavior for risk & return  Points of potential confusion

3. A&MIS 2123W. F. Bentz Cost Drivers  There are seven primary cost drivers at the macro level. The one considered most often in accounting is the time-rate of activity. Think of this as the volume of activity experienced during a time period. The driver volume is considered next.

4. A&MIS 2124W. F. Bentz Cost Drivers  The issue is: How should we expect total costs to behave (vary) with respect to changes in the time-rate of activity all else being equal. In traditional accounting terms: “How do total costs behave with respect to changes in volume?”

5. A&MIS 2125W. F. Bentz Total variable cost Activity Volume Total cost Slope is the rate of change Total cost curve

6. A&MIS 2126W. F. Bentz Total variable cost Variable costs are those costs that vary in direct proportion to changes in activity volume. Such costs are normally rep- resented by a simple affine linear equation, Y = vX, where Y represents the total variable cost, v represents the variable cost per unit of activity and X represents the volume of activity during a period.

7. A&MIS 2127W. F. Bentz Total step-variable cost Step-variable costs are those costs that vary in small increments with respect to changes in activity volume. Such costs are also normally represented by a simple affine linear equation, Y = vX, where Y represents the total variable cost, v represents the step-variable cost per unit of activity and X represents the volume of activity during a period.

8. A&MIS 2128W. F. Bentz Total step-variable cost However, at a micro level, the increments may be relatively large and a local manager might treat the cost like a semi-fixed cost. It is a matter of perspective and required level of precision. Manager’s salaries effectively are variable from McDonald’s corporate perspective, but not from the perspective of a local franchisee with two restaurants.

9. A&MIS 2129W. F. Bentz Total fixed cost Activity Volume Total cost Total fixed cost

10. A&MIS 21210W. F. Bentz Total fixed cost Fixed costs are those costs that do not vary in total with respect to modest changes in activity volume. Such costs are represented by Y = F, where Y represents total cost, and F represents total fixed cost. Fixed costs do change over time, due to price changes and as a result of decisions, but they are relatively constant with respect to changes in activity volume, all else being equal.

11. A&MIS 21211W. F. Bentz Committed Fixed Costs  Committed fixed costs are costs incurred as a result to past decision to acquire and maintain productive capacity. ٠ Depreciation on Plant & Equipment ٠ Real estate taxes ٠ Insurance ٠ Compensation of executives

12. A&MIS 21212W. F. Bentz Committed Fixed Costs  Committed costs are also called capacity costs.  These fixed costs are difficult to eliminate, even temporarily. Thus, committed fixed cost are the most difficult to eliminate.  Managers are very careful when increasing capacity due to the fixed nature and duration of the resulting fixed costs.

13. A&MIS 21213W. F. Bentz Discretionary Fixed Costs  Discretionary fixed costs (also called managed fixed costs) are associated with decisions made by management at least annually. These cost are more controllable in that there is little immediate impact, even though there may be a longer-term consequence.

14. A&MIS 21214W. F. Bentz Discretionary Fixed Costs  Advertising programs  Research programs  Management development programs  Employee recruiting  Training programs  Public relations

15. A&MIS 21215W. F. Bentz Total mixed cost Activity Volume Total cost Total cost curve

16. A&MIS 21216W. F. Bentz Total mixed cost Activity Volume Total cost Total cost curve Fixed component Variable component

17. A&MIS 21217W. F. Bentz Total mixed cost Semivariable or mixed costs are those costs that contain both a fixed and a variable component. Such costs are normally represented by a simple linear equation of the form Y = F + vX, where Y represents total cost, F represents total fixed cost, and v represents the variable cost per unit of activity, and X is the volume of activity during a period.

18. A&MIS 21218W. F. Bentz Total semi-fixed cost Activity Volume Total cost Total cost curve

19. A&MIS 21219W. F. Bentz Functional forms of total costs:  Fixed: TC = F  Variable: TC = vX, where X is the measure of the driver activity  Semi-variable (mixed): TC = F + vX  Semi-fixed: TC = F 1 [1+X/q], where the brackets represent the greatest integer function, and q represents the number of units associated with each increment in cost.

20. A&MIS 21220W. F. Bentz Functional forms of costs:  TC = F 1 + vX + F 2 [1+X/q]  For test purposes, focus on cost functions of the form TC = F + vX, where F represent the total of all fixed costs for the activity under consideration, and v is the total per unit variable cost.

21. A&MIS 21221W. F. Bentz Interpreting the greatest integer  Suppose we employ an additional supervisor for every 10 employees. If we at least 1 supervisor, and they earn $50,000 per year, then the cost of supervision varies with employment as follows TC = $50,000[.9+X/10] for X >=1

22. A&MIS 21222W. F. Bentz Greatest Integer Function Values Employment GI FunctionFctn. Value Case 1 1 [0.9 + 1/10]1 Case 210 [0.9 +10/10] 1 Case 315 [0.9 +15/10] 2 Case 420 [0.9 +20/10] 2 Case 535 [0.9 +35/10] 4

23. A&MIS 21223W. F. Bentz Semi-fixed cost example EmploymentSupervisorsTotal Cost Case 1 11$ 50,000 Case 2101$ 50,000 Case 3152$100,000 Case 4202$100,000 Case 5354$200,000 For TC = $50,000[0.9+X/10]

24. A&MIS 21224W. F. Bentz In Practice  In practice, we can develop complicated cost formulas to fit more complicated situations. The business situation will dictate the appropriate level of sophistication.

25. A&MIS 21225W. F. Bentz Total cost (micro) Activity Volume Total cost Total cost curve Relevant range

26. A&MIS 21226W. F. Bentz Average cost (micro) Volume Average Unit Cost Total cost curve Relevant range

27. A&MIS 21227W. F. Bentz Further Observations  The level of analysis will influence how a cost is modeled.  For strategic analyses, most costs will be considered variable. For tactical purposes, the same costs might be modeled as part fixed and part variable.

28. A&MIS 21228W. F. Bentz Assumption  In the absence of evidence to the contrary, assume costs may be semi-variable. ٠ Cost of goods sold (manufacturing firm) ٠ Selling expenses ٠ Distribution expenses ٠ Administrative expenses

29. A&MIS 21229W. F. Bentz