Session 11

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

2. 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 W. F. Bentz

3. 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. W. F. Bentz

4. Cost Drivers • The issue is: How should we expect totalcosts 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?” W. F. Bentz

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

6. 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. W. F. Bentz

7. 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. W. F. Bentz

8. 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. W. F. Bentz

9. Total fixed cost Total cost Total fixed cost Activity Volume W. F. Bentz

10. 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. W. F. Bentz

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

12. 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. W. F. Bentz

13. 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. W. F. Bentz

14. Discretionary Fixed Costs • Advertising programs • Research programs • Management development programs • Employee recruiting • Training programs • Public relations W. F. Bentz

15. Total mixed cost Total cost Total cost curve Activity Volume W. F. Bentz

16. Total mixed cost Total cost Total cost curve Variable component Fixed component Activity Volume W. F. Bentz

17. 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. W. F. Bentz

18. Total semi-fixed cost Total cost Total cost curve Activity Volume W. F. Bentz

19. 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 = F1[1+X/q], where the brackets represent the greatest integer function, and qrepresents the number of units associated with each increment in cost. W. F. Bentz

20. Functional forms of costs: • TC = F1 + vX + F2[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 vis the total per unit variable cost. W. F. Bentz

21. 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 W. F. Bentz

22. Greatest Integer Function Values EmploymentGI FunctionFctn. Value Case 1 1 [0.9+ 1/10] 1 Case 2 10 [0.9+10/10] 1 Case 3 15 [0.9+15/10] 2 Case 4 20 [0.9+20/10] 2 Case 5 35 [0.9+35/10] 4 W. F. Bentz

23. Semi-fixed cost example EmploymentSupervisorsTotal Cost Case 1 1 1 $ 50,000 Case 2 10 1 $ 50,000 Case 3 15 2 $100,000 Case 4 20 2 $100,000 Case 5 35 4 $200,000 For TC = $50,000[0.9+X/10] W. F. Bentz

24. 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. W. F. Bentz

25. Total cost (micro) Total cost Total cost curve Relevant range Activity Volume W. F. Bentz

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

27. 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. Further Observations W. F. Bentz

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

29. W. F. Bentz