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Chapter 3
Variations of Cost Behavior
1
Understanding
cost
behavior
is
fundamental to management accounting.
There are numerous real-world cases in which
managers have made seriously wrong
decisions because they had erroneous cost
behavior information. This chapter deserves
careful study.
2
Objective 1
Explain step-and mixed-cost
behavior
3
Chapter 2 described two patterns of cost behavior:
variable and fixed costs. In addition to these pure
versions of cost two additional types of costs combine
characteristics of both fixed and variable cost behavior.
These are step costs and mixed costs.
Step costs (semi-fixed) : are fixed for a given level of
activity but they eventually increase by a constant
amount at some critical points. We can distinguish fixed
costs from semi-fixed costs by the range between the
activity levels before the steps in total fixed costs occur.
If the ranges between the steps are relatively wide and
apply to a specific, broad range of activity, the cost is
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considered a fixed cost over that range of activity.
In fig. 3.1 we assume that the firm is committed to
the fixed cost between activity level X and Y and cannot
increase its activity beyond Y within the current
accounting period. Hence this cost is regarded as a fixed
cost.
Fig. 3.1
Step fixed costs regarded as a fixed cost
Total
fixed cost
(L.E.)
Relevant
range
A
X
Y
Level of activity
5
It is assumed that the firm plans to operate at a
level of activity between point X and Y resulting in fixed
costs of o A.
An example of a semi-fixed cost is the salaries of
supervisors; assume that the supervisory staff can
supervise direct labor up to 500 hours of activity per
week. For each increase in 500 hours of activity per
week the supervision cost of an additional supervisor.
The treatment of semi-fixed costs depend
on the frequency of the steps and the amount of
the increase at each point. If the steps are close
together as in Fig. 3.2 the semi fixed costs may
be approximated by a variable cost as
represented by the straight line in fig. 3.2
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Fig. 3-2 Semi-fixed costs
approximated as a variable cost .
Activity level
7
On the other hand, if the increases in semi-fixed
costs are large and the steps are not too frequent (see fig.
3.3 ) , the increase in the costs should be incorporated in
the analysis as a step cost. The analysis will therefore
include L.E. SF1 for activity level between O and Q1, L.E.
Sf2 for activity level between OQ1 and OQ2, and so on
Fig. 3-3 semi- fixed costs
regarded as a step fixed cost
Activity level
8
Mixed costs
Mixed costs contain elements of both fixed and
variable-cost behavior. Like step costs, the fixed
element is determined by the planned range of
activity level. Unlike step costs, however, usually in a
mixed cost there is only one relevant range of activity
and one level of fixed costs. The variable-cost
element of the mixed cost is a purely variable cost
that varies proportionately with activity within the
single relevant range. In a mixed cost the variable
cost is incurred in addition to the fixed cost : the total
mixed cost is the sum of the fixed cost plus the
variable cost.
9
Mixed cost is a purely variable cost that
varies proportionately with activity within the
single relevant range. In a mixed cost, the
variable cost is incurred in addition to the fixed
cost : The total mixed cost is the sum of the fixed
cost plus the variable cost.
Note: A mixed cost does not fluctuate in direct
proportion with activity, nor does it remain constant
with changes in activity.
10
An example of a mixed cost is rent that is computed as a flat
charge (the fixed component) plus a stated percentage of sales
pounds (the variable component). Fig. 3.4 shows a graph of a rent
charge. The store pays rent to the owners of the shopping center at
a flat rate of L.E. 1000 per month plus 10% of sales. If the shop has
sales of L.E. 300,000 in a month, its total rent is L.E. 4,000. If sales
are L.E. 600,000, the rent is L.E. 7,000.
11
Another example of a mixed cost is maintenance. The
XYZ company maintenance cost has a monthly fixed component
of L.E. 4,800 for maintenance worker salaries. In addition,
maintenance charges for items such as lubricants and
replacement parts average L.E. 1,200 for every unit produced.
Total monthly maintenance cost can be predicted by multiplying
the L.E. 1,200 per-unit variable cost times the number of units
produced and adding the L.E. 4,800 fixed cost as follows:
Expected production
2,000 units 3,000 units
Variable cost (units × L.E. 1.2 )
L.E. 2,400 L.E.3,600
Fixed cost
4,800
Total predicted maintenance cost L.E 7,200
4,800
8,400
12
Cost accountants often separate mixed costs into
their variable and fixed components so that changes in
these costs are more readily apparent. This separation
allows managers to focus on two basic types of costs:
variable and fixed.
An administrator at XYZ company could use
knowledge of the maintenance department cost
behavior to :
1)Plan costs: Suppose the company expected to
produce 4,000 units next month. The month’s
predicated maintenance costs are L.E. 4,800
fixed plus the variable cost of L.E. 4,800 ( 4,000
units times L.E. 1.2 ) , for a total of L.E. 9,600
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2) Provide feedback to managers: suppose
actual maintenance costs were L.E. 11,000 in a
month when production were 4,000 units as
planned. Managers would want to know why
the maintenance department overspent by L.E.
1,400 ( L.E. 11,000 less the planned L.E. 9,600 )
so that they could take corrective action.
3) Make decisions: for example, manager could
evaluate an alternative to acquire a new highly
automated
equipment
against
doing
maintenance work manually.
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Objective 2
Explain management influences
on cost behavior
15
Management can influence cost behavior
through decisions about such factors as:




Product or service attributes
Capacity
Technology
Policies to create incentives to control
costs.
16
1. Product and Service Decisions
Manager’s choice of product mix, design,
quality, features, distribution, and so on,
influence product and service costs. These
decisions should be made in a cost/benefit
framework.
17
2. Capacity Decisions
Strategic decisions about the scale and scope of
an organization’s activities generally result in fixed
level of capacity costs.
Capacity costs are the fixed costs of being able to
achieve a desired level of production or to provide a
desired level of service while maintaining product or
service attribute, such as quality.
All fixed costs fall into two basic categories:
committed and discretionary. The difference
between the two categories is primarily the time
horizon for which management binds itself to the
cost.
18
Committed fixed costs are costs related to the
possession of basic plant assets or personnel
structure that an organization must have to operate.
The level of committed costs is normally dictated by
long-term management decisions involving the
desired level of operations. Committed costs include
depreciation, lease rental interest payments on longterm debts, and executive (key personnel) salaries.
Such costs can not easily be reduced, even during
temporary slowdowns in activity.
Note: A committed cost is an item of cost that
can not be changed in the short run. It results from a
commitment made in the past.
19
Discretionary fixed costs are costs determined by
management as part of the periodic planning
process in order to meet organization’s goals.
Discretionary costs relate to activities that are
important to the organization but viewed as
optional. Discretionary cost activities are usually
service oriented and include advertising,
research and development , and employee
training and development. There is no “ correct”
amount at which to set funding for discretionary
costs, and in case of cash flow shortages or
forecasted operating losses, managers may
reduce these expenditures.
20
Note: The discretionary fixed costs have no obvious
relationship to levels of output activity. The amount
spent can be changed at the discretion of management.
The planned amounts of discretionary costs are
negotiated between the manager and his superior
during the budget process.
Distinguishing committed and discretionary fixed
costs would be the first step to identify where costs
could be reduced .
21
Example:
XYZ company is experiencing financial difficulties. Sales for
its major product are depressed, and XYZ management is
considering cutting back on costs temporarily. XYZ management
must determine which of the following fixed costs to reduce or
eliminate and how much money each would save:
Fixed costs
Advertising and promotion
Depreciation
Employee training
Management salaries
Mortgage payment
Property taxes
Research and development
Total
Planned Amounts
30,000
400,000
100,000
800,000
250,000
600,000
1,500,000
3,680,000
Should XYZ reduce or eliminate any of these fixed costs?
22
The answer
The answer depends on the company long-run outlook.
XYZ could reduce costs but also greatly reduce its ability to
compete in the future if it cuts carelessly. Rearranging these costs
by categories of committed and discretionary costs yields the
following analysis:
Fixed costs
Planned Amounts
Committed :
Depreciation
400,000
Mortgage payment
250,000
Property taxes
600,000
1,250,000
Total Committed
Discretionary (potential savings):
Advertising and promotion
30,000
Employee training
100,000
Management salaries
800,000
Research and development
1,500,000
2,430,000
Total discretionary
Total
3,680,000
23
XYZ would be unwise to eliminate all of
discretionary costs arbitrarily.
Nevertheless, discretionary fixed costs would
be the company’s first step to identify where
costs could be reduced.
24
3. Technology Decisions
One of the most critical decision that
managers make is the type of technology that
the organization will use to produce its
products or deliver its services. Choice of
technology ( for example, labor intensives
capital intensive ) may have a great impact on
the costs of products and services.
25
4. Cost Control Incentives
Finally future costs may be affected by the
incentives that management creates for
employees to control costs. A strong form of
feedback, and a sound system of
compensations could cause the supervisors to
watch costs carefully and to find ways to
reduce costs without reducing quality of
products or services.
26
Objective 3
Measure cost functions and use
them to predict costs
27
The decision making, planning and control
activities of management accounting require
accurate and useful estimates of future fixed
and variable costs.
The first step in estimating or predicting
costs is cost measurement or measuring cost
behavior as a function of appropriate cost
drivers. The second step is to use these cost
measures to estimate future costs at expected,
future levels of cost driver activity.
28
Cost functions
To describe the relationship between a cost and its
cost driver, managers often use an algebraic equation
called a cost function.
Because of the linearity assumption, the general
formula for a straight line can be used to describe any
type of cost within a relevant range of activity. The
straight-line formula is :
Y=a+bx
Where:
Y = Total cost (dependent variable).
a = Fixed portion of total cost
b = Variable cost per unit. (the rate at which
cost changes in relation to changes in x,
b represent the slope of the line)
x = Cost driver activity (independent variable).
29
We shall use this basic equation, but will use
symbols that stands for the particular relationship we
are studying as follows:
Geometry Cost system
Meaning
Y
TC = Total cost in a period.
A
TFC = Total fixed cost in a period
B
X
UVC = Unit Variable cost.
X = Volume, that is number of
units of activity.
The equation then becomes :
TC = TFC + (UVC × X )
30
An entirely variable cost is represented by the
straight – line formula in the following manner :
TC = L.E.0 + (UVC × X )
Or Y = L.E.0 + b x
A zero is shown as the value of TFC ( or a ) because
there is no fixed cost.
A purely fixed cost is shown in the straight line
formula as :
TC = TFC + L.E.0 X
Y = a + L.E.0 x
31
Fixed cost is the value of a ; zero is
substituted in the formula for b (or UVC ),
since there is no cost component that varies
with an activity base.
A mixed cost has values for both a (TFC)
and b (UVC) values in the formula. Exhibit 3.5
illustrates the use of the straight-line formula
for each type of cost behavior.
32
Exhibit 3.5 uses of the straight-line cost formula
to explain or predict a variable cost such as indirect
materials when the cost per unit is L.E. 2 :
TC = TFC + (UVC × X )
= L.E. 0 + L.E. 2 X
Where :
TC = Total indirect material cost.
X = number of units produced.
L.E.
UVC (or b)= L.E. 2
Number of units produced
33
to explain or predict a fixed cost such as building
rent of L.E. 10,000 per year :
TC = L.E. 10,000 + ox
L.E
10,000
Any measure of
activity
34
To explain or predict a mixed cost such as repairs
and maintenance when the fixed element is L.E. 14,000
per year plus L.E. 600 per machine hour :
TC = L.E. 14,000+L.E. 600x
Where:
TC = Total annual repair and maintenance Cost
X = number of machine hours incurred
UVC (or b)= L.E. 600
L.E
14,000
Number of machine hours
35
Objective 4
Analyze Mixed Costs
36
Since a mixed cost contains amounts for both the
fixed and variable values, some methods must be used
to separate the mixed cost into its two component
elements. The simplest method to use is the high-low
method.
The high-low method
is a separation technique that chooses
actual observations of a total cost at two levels of
activity and calculates the change in both activity and
cost. The observations selected are the highest and
lowest activity levels if these levels are representative of
normal costs within the relevant range.
37
Note that the selections of “high” and “low” are made
on the basis of activity levels rather than costs. The
reason for this selection is that the purpose of the
analysis is to understand how costs change in relation to
activity changes. Activities cause costs to change rather
than the opposite relationship.
The high-low method is illustrated using
machine hours and utility cost information for
XYZ company. The company’s normal operating
range of activity is between 3,000 and 10,000
machine hours. The following machine hours
and utility cost information is available :
38
Month
Utility cost
Jan.
Feb.
March
April
May
Level of activity
in machine
hours
4,000
9,000
15,000
4,600
3,000
June
8,620
640
July
5,280
420
August
5,000
415
L.E. 320
640
840
350
280
39
Step (1)
Select the highest and lowest level of activity
within the relevant range and obtain the costs
associated with those levels. These levels and costs
are 3,000 and 9,000 hours and L.E. 280 and L.E. 640,
respectively.
Note that since march reflects data outside the
relevant range, this observation should be
disregarded in analyzing the utility cost.
40
Step (2)
Calculate the change in cost compared to the
change in activity.
Machine hours
Associated total
cost
High activity
9,000
L.E. 640
Low activity
3,000
280
Change
6,000
360
41
Step (3)
Determine the relationship of cost change to
activity change to find the variable cost element.
UVC ( or b )= Change in total cost
Change in activity level
= L.E. 360
6000 MH
= L.E. 0.06 per machine hour
42
Step (4)
Compute total variable cost (TVC) at earlier level
of activity.
High level of activity : TVC = L.E. 0.06 ×(9000)
= L.E. 540
Low level of activity : TVC = L.E. 0.06 × (3000)
= L.E. 180
43
Step (5)
Subtract total variable cost from total cost at either
level of
activity to determine fixed cost.
(This can be shown as an adaptation of the straight –
line formula :
a=Y+bx
Or TFC = TC – (UVC × X)
High level of activity :
TFC = L.E. 640 – ( 0.06 x 9000)
= L.E. 640 – L.E. 540 = L.E. 100
Low level of activity:
TFC = L.E. 280 – ( L.E. 0.06 x 3000)
= L.E. 280 – L.E. 180 = L.E. 100
44
Step (6)
Substitute the fixed and variable cost values in the
straight-line formula to get an equation that can be used
to estimate total cost at any level of activity within the
relevant range.
Y = L.E. 100 + L.E. 0.06 x
Or
TC = L.E. 100 + L.E. 0.06 x
Where x represent machine hours.
45
Note that total mixed cost increases or decreases
with changes in activity. The change in cost is equal
the change in activity times the unit variable cost; the
fixed cost element does not fluctuate because of
changes in activity. Therefore, any increase or decrease
in total cost is due to the increase or decrease in the
independent variable. The variable cost per unit of
activity reflects the average change in cost for each
additional unit of activity. For XYZ company this
average is L.E. 0.06 per machine hour use.
The values selected for use in the high low method
ignored the 15,000 machine hour activity level, because it
was considered to be outside the relevant range.
46
Visual- Fit method ( the Scatter graph)
A method in which the cost analyst visually
fits a straight line through a plot of all the available data,
not just between the high point and the low point,
making it more reliable than the high-low method. A
straight line is drawn through the plotted point. The line
drawn should be the one that appears to best fit the
data. The point at which the line intercepts the Y-axis
(vertical axis) represent an estimate of the fixed cost
component of the mixed cost.
47
The variable cost per unit can then be determined
as follows :
1) Subtract the estimated fixed cost from total
cost at a level of activity that falls on the line,
and
2) Divide the result of (1) by the activity level chosen.
In equation form, variable cost is calculated as :
b=(Y–a)/x
Or
UVC = (TC – TFC ) / x
Where TC (or Y ) = any value on the Y-axis using a
selected associated value for x
TFC (or a ) = estimated fixed cost from
sighted line.
48
The utility cost data given previously for XYZ
company is graphed in Exhibit 3.6. The cost line in
Exhibit 3.6 is sighted, and y – intercept is estimated as
L.E. 100. If 4,000 machine hours are chosen as the
activity level, L.E. 330 is estimated as the visual y –
intercept of total utility cost. Using the equation above,
solve for UVC ( or b ) as follows:
UVC = ( L.E. 330 – L.E. 100 ) / 4000
= L.E. 230 / 4000
= L.E. 0.0575
The linear-cost function measured by the visual fit
method is :
TC = L.E. 100 per month + ( L.E.
0.575 ×machine hours or x )
49
Although the visual- fit method can use all the data,
The placement of the line and the measurement of the
fixed and variable costs are subjective.
Exhibit 3-6 the XYZ company utility cost
Thousands of machine hours
50
Three things are important to note about the
scatter graph method:
First
It provides a means for easily
identifying abnormal or non-representative points.
These points (called outliers ) fall outside the relevant
range of activity. Exhibit 3.6 reveals an outlier at 15,000
machine hours.
Second
The original information on actual
activity – to- cost relationship is not used in
determining the variable cost amount. Estimates are
made of the activity-to-cost relationships that lie on the
line. The scatter graph line may not pass through any or
all of the actual observation points; this is acceptable as
long as the line is representative of the actual data.
51
Third
The estimate of the visual intercept of the y-
axis (fixed cost) may be difficult to read on a scatter graph. It
is only coincidental that the estimate made for (TFC or a )
using the scatter graph is the same amount as was calculated
using the high-low method. Although both fixed-cost amounts
were estimated as L.E. 100, the cost formula resulting from
the scatter graph method was not the same as that of the
high-low method. This difference was caused by the fact that
only two observations were used by the high-low method
whereas the line drawn using the scatter graph method was
based on all observations except outliers.
52
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