Management Accounting
| 67
In Figure 5.2A, the relationship between volume and variable cost is shown
in tabular form. In many cases, management prefers to see costs is this fashion.
However, the graphical portrayal is more effective in demonstrating the theoretical
nature of variable costs from a management accounting viewpoint. The increase in
cost resulting from increases in volume can easily be visualized. It is interesting to
note that V, the variable cost rate, from a mathematical viewpoint measures the slope
of the total variable cost line. The greater the value of V the steeper the slope. The
affect on slope of the line for different values of V is illustrated in Figure 5.3. As the
rate increases, the slope also become steeper.
Figure 5.3
Variable Cost: Effect of change in slope of line
200000
150000
100000
50000
0
Cost
Volume (quantity)
0 5000 10000 150000
V = 12
V= 14
V = 16
As explained previously, V may be interpreted as the average variable cost rate.
One method of computing V is to divide the total variable cost by the related level of
activity; that is, AVC = TVC / Q. Graphically, average variable cost may be illustrated
as shown in Figure 5.4.
Figure 5.4 A Figure 5.4 B
Economic Theory: Average Fixed Cost
Accounting Theory:Graph of Average
Variable Cost
7.00
6.00
5.00
4.00
3.00
2.00
1.00
0
6.00
5.00
4.00
3.00
2.00
1.00
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
Cost
Cost
Volume (quantity)
Volume (quantity)
68 |
CHAPTER FIVE
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Management Accounting Theory of Cost Behavior
Graph A visually illustrates an important management accounting assumption
concerning variable cost: changes in volume have no effect on the average variable
cost rate. In contrast, the average variable cost curve in economic theory is presented
as a U-shaped curve as illustrated in Figure 5.4B. The justication of a constant
average variable cost will be explained in a later section of this chapter.
Variable Cost Rate Components - Variable costs can be discussed at two levels:
the aggregate and micro levels. At the aggregate level, V represents the sum of the
individual variable costs rates. Variable costs/expenses are commonly classied as
material, labor, overhead, selling, and administrative. Consequently, from a micro or
analytical viewpoint, V is the aggregate of these individual rates. Mathematically, the
average variable cost rate or V may be dened as:
V = V
m
+ V
l
+ V
o
+ V
s
+ V
a
Where:
V
m
‑ variable material cost rate
V
l
‑ variable labor cost rate
V
o
‑ variable overhead rate
V
s
‑ variable selling expense rate
V
a
‑ variable administrative rate
In theory the variable cost rate, or V, also may be computed from historical data
by dividing the total variable cost by the related level of activity; that is, from a macro
point of view V = TVC / Q. However, in practice the computation of V in this manner
is not always easy. Very seldom is the total variable cost known without considerable
analysis of cost data at a subclassication or micro level. The computation of V is,
therefore, likely to be preceded by an analysis of variable cost in terms of material,
labor, manufacturing overhead, selling, and administrative costs. After measurement
of the individual rates, the aggregate rate is simply the sum of the individual variable
cost rates.
Illustration of Using Cost Behavior
The management of K. L. Widget Company is considering closing out a plant
that has been operating at a loss. Management is tentatively planning to increase
advertising and certain other xed expenses that should increase sales to $300,000
or 15,000 units. The selling price of the Widget is currently $20.00. Fixed expenses
including the proposed increases is $110,000.
Variable costs have been determined to be:
Material (V
m
) - $5
Labor (V
l
) ‑ $3
Variable M/O (V
o
) - $1
Selling (V
s
) ‑ $3
Administrative (V
a
) - $1
If the increased expenditures do not result in a prot, then the plant will be closed.
Should the proposed expenditures be made and the plant kept open?
Management Accounting
| 69
Analysis:
V = V
m
+ V
l
+ V
o
+ V
s
+ V
a
= ($5 + $3 + $1 + $3 + $1) = $13
TVC = V(Q) = $13(Q)
Sales (15,000 units) $300,000
Variable costs ($13 x 15,000) $195,000
Fixed expenses $110,000
Total expenses $305,000
Net loss ($ 5,000)
Decision: Close the plant as the plant would still operate at a loss. The computation
of total cost at the new level of activity is still greater than revenue.
Managerial Decisions and Variable Costs
An important point that needs understanding is that some costs are not inherently
xed or variable but become one or the other by management exercising its
decision-making powers. Management has the discretionary power to make some
costs either variable or xed. For example, sales people compensation can be either
xed or variable. If management decides to reward sales people on the basis of a
commission, then sales people’s compensation is variable. If the basis for rewarding
sales effort is a salary, then sales people’s compensation is a xed expense. If factory
workers are paid a wage rate, then factory workers’ compensation is variable. The
decision to pay workers a salary would make the factory labor compensation a xed
cost in the short- run.
Some expenditures are unavoidably variable. For example, the direct use of
material will always be a variable cost. However, this per unit cost of material is to a
large extent controllable by the decision-making powers of management. The total
material variable cost may be dened by the equation:
TVMC = V
m
(Q) (2)
In this equation V
m,
represents the variable material cost rate. V
m
is the amount
of material cost incurred per unit of product manufactured. The variable material rate,
V
m,
; however, is the result of two factors: units of material per unit of product and the
cost per unit of material. For example, if a product requires 6 units of material and the
material cost per unit is $2, then the material variable cost rate would be $12. V
m
,
then, may be dened by the following equation:
V
m
= U
m
x C
m
Where:
U
m
= number of units of material and C
m
= cost per unit of material.
As this example illustrates, the number of units and the cost per unit are, within
limits, controllable by management. For example, in the manufacture of furniture the
variable cost rate for material could be decreased by the decision to use less material.
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CHAPTER FIVE
•
Management Accounting Theory of Cost Behavior
Management might use 1/2 inch wood rather than 3/4 inch. Also management could
lower the variable cost rate by deciding to purchase from another seller of material
whose price is lower or management might decide to use a lower quality material
such as particle board.
As will be explained later, the average variable cost can be computed from
historical data, however, you should remember that at any given moment management
can change the variable cost rate by making decisions directly affecting the physical
and cost factors that determined the variable cost rate.
Another example of an cost that is unavoidably variable is direct labor when the
method of compensation is a wage rate. The equation for direct labor is:
TVLC = V
L
(Q) (3)
In this equation, V
L
represents the variable labor cost rate. It is the dollar amount
of labor incurred each time one unit of product is manufactured. As in the case of
material, V
L
is the result of two factors–labor hours per product and the wage rate.
For example, if a product requires two hours of labor and the wage rate is $10 per
hour, then the variable direct labor rate would be $20. V
L
then may be dened by the
following equation:
V
L
= H
L
x R
L
Where:
H
L
denotes the standard hours per product and R
L
the wage rate.
The important principle to remember is that for most types of variable costs,
the factors that determine the variable cost rates can be identied. Furthermore,
in all cases these xed factors, within limits, can be changed by explicit decisions
on the part of management. In Figure 5.5, a summary of the xed factors for the
ve classications of variable costs is presented. In addition, management’s ability
to affect the magnitude of the variable cost rates through decision‑making is also
revealed. For example, management may be able to reduce the variable cost rate
for material by nding a supplier willing to sell the same grade of material at a lower
price.
Variable Cost Behavior and Linearity
In management accounting, the relationship between activity and total variable
cost is assumed to be linear. There are several reasons for this assumption.
First, mathematical equations involving curvilinear relationships can be quite
complex. Furthermore, tting cost data to nonlinear equations may be difcult.
Although the use of nonlinear equations may be preferable, the use of linear equations
which are much easier to use has been found to be useful.
Also, in many cases, actual cost behavior for a signicant portion of the activity
range tends to be linear. The use of standard measurements and automated equipment
in many cases results in a uniform rate of output. Within a relevant range of activity,
the cost per unit of output is the same. Consequently, the use of linear relationships
in management accounting is justied only in what is called the “relevant range of
activity.” If the cost per unit of output sharply changes outside of this range of activity,
Management Accounting
| 71
then the use of a constant average cost per unit values should be avoided. The
concept of the relevant cost range is illustrated in Figure 5.6.
Management Accounting Theory of Fixed Costs
In order to be used, many management accounting decision-making models
explicitly require that all costs be classied as either xed or variable. On the surface,
it would appear that the measurement and use of xed costs is fairly simple matter.
After variable costs have been measured, the remaining costs may be treated as
xed. However, the very nature of xed costs presents conceptual problems that far
exceeds those pertaining to variable costs.
While direct material and direct labor are variable in nature, manufacturing
overhead may be both variable and xed. The accounting for xed costs is at the same
time a problem of accounting for manufacturing overhead. An understanding of xed
manufacturing overhead also requires an understanding of the concepts underlying
the setting of xed overhead rates. Because of the complexity of accounting for xed
manufacturing costs, two theories exist, absorption costing and direct costing. These
two approaches treat xed manufacturing overhead quite differently.
Fixed costs provide capacity to manufacture or to sell. When actual activity
is
less than capacity available, a major problem exist. Theoretically, the portion of
unused capacity cost should be measured as idle capacity cost and not treated as
Figure 5.5
Variable Cost Factors
Variable costs Fixed factors per Variable cost Rate
unit of product
(physical and cost)
Material units of material (U
m
) V
m
= U
m
x C
m
cost per unit (C
m
)
Direct labor hours per unit (H
L
) V
L
= H
L
x R
L
wage rate per hour (R
L
)
Overhead * units of service (U
o
) V
o
= U
o
x C
s
cost per unit of service (C
s
)
Selling ** units of service (U
s
) V
s
= U
s
x C
s
cost per unit of service (C
s
)
Administrative units of services (U
a
) V
a
= U
a
x C
s
cost per unit of service (C
s
)
* Examples of units of overhead service include factory supplies, quarts of oil, kilowatt hours,
repair hours, etc.
** Examples of selling service units include supplies, credit checking time, wrapping
or packaging, accounting time, etc.
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CHAPTER FIVE
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Management Accounting Theory of Cost Behavior
a production cost. In practice, many rms do not measure idle capacity cost. The
consequence is that the per unit cost of goods manufactured varies signicantly with
the percentage of capacity utilized. For example, assume that the xed cost of the K.
L. Widget Manufacturing Company is $10,000, and that the rm has the capacity to
manufacture 10,000 units. When the rm manufactures 1,000 units, the cost per unit
is $10. However, when only 500 units are manufactured the cost per unit is $20 and
when volume is 10,000 the cost is $1 per unit
A second serious problem exists concerning the measurement of xed costs.
The term “xed” costs implies that changes in volume have no effect on the costs
classied as such. Certain management accounting models previously identied in
this book are based on the assumption that the costs identied as xed hold constant
over a range of activity. However, the assumption that these costs remain constant
from zero activity to the limit of capacity is not always true.
In reality, costs dened as xed seldom hold constant over the entire range of
activity. Only in very small businesses with limited changes in activity would some
xed costs not vary. In most businesses, and in large businesses in particular, xed
costs classied as xed in management accounting are actually step cost. When
signicant increases in activity occur, additional staff, equipment, and other resources
involving xed costs must be acquired.
A graphical illustration of xed and step cost is shown in Figure 5.6 (A and B).
Figure 5.6
Relevant Range
Relevant Range
$
Q Q
$
A Fixed
B Step
Despite the more realistic portrayal in Figure 5.6B, xed costs are usually
illustrated as shown in Figure 5.6A. To justify the assumption of non variation of xed
costs as illustrated in Figure 5.6A, the concept of the relevant range is used. As long
as activity remains within the relevant range, no harm is done by portraying step
costs as xed over the entire range of activity. The relevant range may be dened as
that range of activity in which actual sales or production are likely to occur. Outside
of this range, xed costs on the lower end of volume are smaller and outside of the
high end of the relevant range xed costs are higher. However, the magnitude of
these costs outside the relevant range is not likely to be known; and even if known,
Management Accounting
| 73
they are irrelevant. Consequently, to draw xed costs as in Figure 5.6A is a matter of
convenience rather than a portrayal of reality. In the following discussion, therefore,
you should remember that the denition and discussion of xed costs actually refers
to the costs incurred within the relevant range of activity.
Another interesting aspect of xed costs is that as soon as xed costs exist, a
business automatically has a break even point. Conceptually, no business can report
net income until all xed costs have been covered. Break even point analysis will be
discussed in detail in the next chapter.
Fixed costs are those cost that do not change with increases or decreases in
volume, that is, sales or production. In the short run, xed costs such as rent and
salaries remain the same regardless of the level of activity. Fixed costs, unlike
variable costs which relate to activity, are time-related costs. For example, rent is
always for a period of time such as a month or year. Likewise salaries also relate to
a period of time such as a month or year. Consequently, xed costs are commonly
called period charges because these costs expire in the same time period in which
they are incurred.
While variable costs are incurred directly as activity takes place, xed costs are
incurred in anticipation of providing services for an estimated level of activity, and,
consequently, the expenditure is contractually made or committed prior to actual
activity. Fixed cost expenditures are determined prior to the period of activity for a
dened quantity of service potential. Building rent, for example, reects the right to
use a dened amount of oor space. The lease of equipment provides the right to
a dened number of operating hours per period. Fixed cost expenditures are then
capacity costs. An understanding of xed costs requires an understanding of the
different facets of capacity. Fixed costs, therefore, make a range of production activity
possible.
The term capacity in the singular is somewhat misleading. Rather than use the
term “capacity”, a more accurate statement would be that xed costs provide the
“capacities” to produce. Each type of xed cost provides a different capacity service
and, unless management has exercised exceptional care in planning, the capacity
related to each cost might not be in balance. Imbalance in capacities created by xed
costs can create bottlenecks or constraints in both production and sales.
Examples of different xed costs and the corresponding capacities provided are
shown in Figure 5.7.
Figure 5.7 • Examples of Fixed Cost and Capacities Provided
Type of Fixed Cost Service Provided
Manufacturing:
Equipment lease/rent Material processing services
Utilities Heat, power, lights
Insurance Financial protection
Indirect labor Supervision of factory workers
continued on next page
74 |
CHAPTER FIVE
•
Management Accounting Theory of Cost Behavior
Building rent Shelter and auxiliary equipment space
Selling:
Salesmen salaries Order taking services
Automobile lease/rent Transportation
Telephone Order taking
Advertising Customer product awareness
Administrative
Management salaries Supervision and planning
Utilities Lighting, heating, air conditioning
Telephone Communication of information
Computer lease Processing of information
As implied in the discussion above, xed costs are those expenditures that are
not caused by activity but rather make activity or production possible. Fixed cost
provide both the ability or capacity to manufacture and also determine the limits to
production. For example, without the services provided by buildings, equipment, and
supervision production could not take place. Expenditures for xed costs represent
the acquisition of the various capacities necessary for actual activity to take place.
The K. L. Widget Company has 15 machines capable of producing a total
of 15,000 units per quarter. One production supervisor is required for every
5 machines. Currently two supervisors are each paid a $10,000 salary. Five
machines are not in use because of a lack of a supervisor. The building which
the company rents has enough space to hold 20 machines. Consequently,
the company has a machine capacity of 15,000 units while it has supervision
capacity of 10,000 units. The building space capacity is adequate to manufacture
20,000 units.
This example illustrates that different types of xed costs provide different types of
production services each of which provides a different capacity level. In this example,
there are three capacities: machine, supervision, and space. A major concern of
management is to have a balance or equality among the different ranges of capacity
services. Also, in this example, each type of xed cost provide different output limits.
Actual production is limited to the lower of the three levels. Furthermore, production
cannot exceed 10,000 units, even though machine and space capacity is larger. A
major responsibility of management is to make those xed cost decisions that create
a balance among the different types of capacity services.
In contrast to variable costs, xed costs expire with the passing of time. Fixed
costs are expenditures that contractually provide services for a dened period of
time. At the end of the contract period, the services are no longer available without a
new contract or time commitment of resources by management.
For example, the decision to rent ten automobiles for a year provides management
with transportation services for a year. If one auto has the potential to be driven 200
miles a day, then ten autos for a year provide a capacity of 730,000 miles (200 x 365
x 10). At the end of the year, the year’s purchase of transportation has fully expired.
Management Accounting
| 75
The unused portion of miles driven cannot be transferred to the next year. The rent
expenditure for autos is the same whether or not the potential services are used.
The passing of each day proportionately reduces the service potential regardless of
whether activity is ongoing.
Inherent in the nature of xed cost is the potential for idle capacity. Consequently,
from a management accounting viewpoint, the measurement of idle capacity is
important. The cost of idle capacity cannot be transferred to another period in the
manner in which unused material can be stored and used in a later period. The
constant relationship between xed costs and capacity or volume can be explained
and illustrated from three points of view: tabular, mathematical, and graphical.
Tabular Presentation - The presentation of xed costs in a table at different levels
of activity is basically unnecessary for the reason that regardless of the level of
activity the cost is the same. However, for illustrative purposes, a simple table of xed
costs will be presented for three types of xed costs common in all manufacturing
businesses:
Table of Fixed Costs
Volume (units of product)
1,000 2,000 3,000 4,000
Manufacturing $ 50,000 $ 50,000 $ 50,000 $ 50,000
Selling expenses $180,000 $180,000 $180,000 $180,000
General and Administrative $ 90,000 $ 90,000 $ 90,000 $ 90,000
Mathematical Presentation - Fixed costs may be dened mathematically in terms
of total costs and in terms of average cost. On a total cost basis, volume or quantity,
Q, is not a determining factor; however, for average cost quantity or Q is the important
factor in the equation. Total xed cost may be mathematically dened:
TFC = F (4)
Where:
TFC represents total xed cost and F is the amount or magnitude of xed costs for a
given period of time such as a quarter or a year.
The interpretation of this equation is that regardless of the level of activity, the
amount of xed cost is totally independent of actual quantity. The importance of
dening xed cost mathematically as presented in the above equation will be appre‑
ciated in a later section when xed and variable cost are combined in a total cost
equation.
For some decisions such as price, a knowledge of cost per unit or average cost is
very important. Mathematically, average xed cost may be dened as follows:
AFC = F/Q (5)
where AFC represent average xed cost and Q is the current level of activity; that is,
units manufactured or units sold. In the following section, the importance of average
xed cost will be discussed and illustrated.
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CHAPTER FIVE
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Management Accounting Theory of Cost Behavior
Graphical Presentation - The behavior of both total xed cost and average xed
cost can be effectively illustrated graphically. In the following illustration, TFC and AFC
are dependent variables while quantity or Q is the independent variable concerning
the computation of average xed cost. Consequently, values assigned to Q for TFC
and AFC can be plotted graphically. To illustrate, assume that xed cost is $10,000
and activity increases in increments of 100. The following graphs may be drawn:
Figure 5.8
Q TFC AFC
100 10,000 100.00
200 10,000 50.00
300 10,000 33.33
400 10,000 25.00
$
QQ
$
Total Fixed Cost
Average Fixed Cost
These graphs effectively display the relationship of volume to total costs.
In the case of total xed costs, there is no effect or change. However, regarding
average xed cost, the opposite is true. As quantity increases, the average xed
costs becomes less. The effect of different levels of quantity on average xed cost
is extremely important and requires an in-depth understanding. Without a complete
understanding of the impact of different capacity levels on average xed costs, poor
decisions e.g., the pricing decision, could have severe protability consequences.
Fixed Cost Components- As the case for variable costs, xed costs can be analyzed
at two levels: the aggregate level and the micro level. At the aggregate level, F
represents the sum of all the individual xed costs. Fixed costs can be divided into
subclassication levels: labor, manufacturing overhead, selling, and administrative.
From a micro or analytical viewpoint, F is the aggregate of these individual rates.
Mathematically, then F may be dened as:
F = F
L
+ F
o
+ F
s
+ F
a
(6)
Where:
F
L
- xed labor cost F
s
- xed selling expenses
F
o
- xed overhead costs F
a
- xed administrative expenses
In practice, the amount of total xed cost, F, will simply be the sum of the individual
xed cost elements. Some of the techniques used to measure the individual xed
rates will be discussed later in this chapter.
Management Control of Fixed Costs - An important point that must be understood
by both management and management accountants is that xed costs are subject
to a high degree of control. The management accountant as well as management
must understand the consequences of making a cost xed or variable. In order to
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