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

A&MIS 212 1W. F. Bentz

Session 11

William F. BentzJanuary 22 , 2002

Fisher College of Business


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


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.


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?”


Total variable cost

Activity Volume

Total cost

Slope is the rate of change

Total cost curve


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.


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.


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.


Total fixed cost

Activity Volume

Total cost Total fixed

cost


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.


Committed Fixed Costs

Committed fixed costs are costs incurred as a result to past decision to acquire and maintain productive capacity.

٠Depreciation on Plant & Equipment

٠Real estate taxes

٠Insurance

٠Compensation of executives


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.


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.


Discretionary Fixed Costs

Advertising programs Research programs Management development programs Employee recruiting Training programs Public relations


Total mixed cost

Activity Volume

Total cost Total cost curve


Total mixed cost

Activity Volume

Total cost

Total cost curve

Fixed component

Variable component


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.


Total semi-fixed cost

Activity Volume

Total cost

Total cost curve


Functional forms of total costs:

Fixed: TC = FVariable: TC = vX, where X is the

measure of the driver activitySemi-variable (mixed): TC = F + vXSemi-fixed: TC = F1[1+X/q], where the

brackets represent the greatest integer function, and q represents the number of units associated with each increment in cost.


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 v is the total per unit variable cost.


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


Greatest Integer Function Values

Employment GI Function Fctn. 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


Semi-fixed cost example

Employment Supervisors Total 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]


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.


Total cost (micro)

Activity Volume

Total cost

Total cost curveRelevant range


Average cost (micro)

Volume

Average Unit Cost Total cost curve

Relevant range


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.


Assumption

In the absence of evidence to the contrary, assume costs may be semi-variable.٠Cost of goods sold (manufacturing

firm)٠Selling expenses٠Distribution expenses٠Administrative expenses


Documents

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