Session 11
William F. Bentz
January 22 , 2002
Fisher College of Business
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Key Issues in Cost Behavior
 Terminology (fixed, variable, semivariable, 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
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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.
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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?”
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Total variable cost
Total
cost
Total cost curve
Slope is the
rate of change
Activity Volume
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Total variable cost
Variable costs are those costs that vary in
direct proportion to changes in activity
volume. Such costs are normally represented 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.
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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.
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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.
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Total fixed cost
Total
cost
Total fixed cost
Activity Volume
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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.
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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
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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.
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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.
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Discretionary Fixed Costs






Advertising programs
Research programs
Management development programs
Employee recruiting
Training programs
Public relations
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Total mixed cost
Total
cost
Total cost curve
Activity Volume
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Total mixed cost
Total
cost
Total cost curve
Variable component
Fixed component
Activity Volume
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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.
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Total semi-fixed cost
Total
cost
Total cost curve
Activity Volume
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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 q represents the number of
units associated with each increment in
cost.
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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.
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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
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Greatest Integer Function Values
Employment
Case 1
Case 2
Case 3
Case 4
Case 5
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10
15
20
35
GI Function Fctn. Value
[0.9 + 1/10]
[0.9 +10/10]
[0.9 +15/10]
[0.9 +20/10]
[0.9 +35/10]
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1
2
2
4
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Semi-fixed cost example
Employment
Supervisors
Case 1
1
1
Case 2
10
1
Case 3
15
2
Case 4
20
2
Case 5
35
4
For TC = $50,000[0.9+X/10]
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Total Cost
$ 50,000
$ 50,000
$100,000
$100,000
$200,000
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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.
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Total cost (micro)
Total
cost
Total cost curve
Relevant
range
Activity Volume
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Average cost (micro)
Average
Unit
Cost
Relevant
range
Total cost curve
Volume
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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.
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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
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