CHAPTER 3
Activity Cost Behavior
LEARNING OBJECTIVES
After studying this chapter, you should be able to:
1. Define and describe fixed, variable, and mixed costs.
2. Explain the use of the resources and activities and their relationship to cost behavior.
3. Separate mixed costs into their fixed and variable components using the high-low method, the
scatterplot method, and the method of least squares.
4. Evaluate the reliability of the cost formula.
5. Explain how multiple regression can be used to assess cost behavior.
6. Define the learning curve, and discuss its impact on cost behavior.
7. Discuss the use of managerial judgment in determining cost behavior.
CHAPTER SUMMARY
This chapter introduces cost behavior as the way in which a cost changes in relation to changes in
activity output. The resource usage model helps one better understand the cost behavior. It emphasizes that the committed resources may have excess capacity because they are frequently
fixed. There are three methods of separating mixed costs presented in the chapter with their
strengths and weaknesses. The method of least squares produces the line that best fits the data
points and is therefore recommended over the high-low and scatterplot methods. The leastsquares method has the advantage of offering methods to assess the reliability of cost equations.
The learning curve is discussed to better describe a nonlinear relationship between labor hours
and output. The chapter concludes by describing how managers use their judgment alone or in
conjunction with the cost behavior analytical methods.
CHAPTER REVIEW
Knowledge of cost behavior allows you to assess changes in costs that result from changes
in activities. Cost accountants use this knowledge to assess the effects of decisions that
change activities.
I.
Basics of Cost Behavior
Learning Objective #1
A.
Cost behavior is the way a cost changes in relation to changes in the levels of activity
usage.
B.
The types of cost behavior include variable costs, fixed costs, and mixed costs.
39
40
Chapter 3
Summary of Variable and Fixed Cost Behavior
Cost
In Total
Per Unit
Variable
Total variable cost changes as activity
level changes.
Variable cost per unit remains the same
over wide ranges of activity.
Fixed
Total fixed cost remains the same even
when the activity level changes.
Fixed cost per unit goes down as activity
level goes up.
Review textbook Exhibit 3-1, which graphically illustrates fixed cost behavior.
Review textbook Exhibit 3-2, which graphically illustrates variable cost behavior.
 Mixed costs are costs that have both a fixed and a variable component.
Review textbook Exhibit 3-5, which graphically illustrates mixed cost behavior.
C.
Linearity Assumption
A linear cost function is used to approximate the underlying cost function within a relevant range because it is less time consuming and less expensive to estimate. A relevant range is the range of activity for which the assumed cost relationship is valid.
Review textbook Exhibit 3-4, which graphically illustrates
linear cost function approximation within the relevant range.
D.
Time Horizon
1. The longer the time period, the more likely that a cost will be a variable cost. In the
long run, all costs are variable.
2. The short run is a period of time in which at least one cost is fixed.
3. Two factors determine what is long run and what is short run:
 Management judgment
 Types of decisions that management faces (short-term and long-term decisions)
4. Understanding of the nature of long-run and short-run cost behavior provides insights
to activities and the resources needed to enable an activity to be performed.
II.
Resources, Activities, and Cost Behavior
A.
Learning Objective #2
Introduction
1. Resources are the economic elements that are consumed in performing activities.
2. When a firm acquires the resources needed to perform an activity, it is obtaining activity capacity. Activity capacity is the ability to perform activities.
a. Practical capacity is the level at which the activity is performed efficiently.
b. Unused capacity occurs when the activity capacity acquired is not used.
Unused capacity = Activity capacity – Capacity used
Activity Cost Behavior
B.
41
Flexible Resources
Flexible resources are acquired from outside sources with no long-term commitments. They are supplied as used and needed.
1. There is no unused capacity for this category of resources (Resource supplied
= Resource usage).
2. Flexible resources are generally treated as a variable cost.
C.
Committed Resources
Committed resources are acquired by the use of either an explicit or implicit contract
to obtain a given quantity of resource. They are supplied in advance of usage, regardless of whether the resources acquired are fully used or not.
Acquisition of committed resources include:
1. Committed fixed expenses are the costs incurred to provide long-term activity
capacity. They are not subject to change in the short run.
Examples:
 Acquiring multiperiod service capacities by hiring employees.
 Purchasing a long-lived asset or entering a long-term contract (buildings and
equipment, either purchased or leased).
2. Discretionary fixed expenses are the costs incurred for the acquisition of shortterm activity capacity. They are independent of actual activity usage, but the levels
of usage can be changed quickly.
Example:
 Salaries of employees, because workers may not be laid off if there is a shortterm drop in production.
D.
Implications for Control and Decision Making
1. Operational control information systems encourage managers to pay more attention to controlling resource usage and spending and to eliminate excess capacity.
2. Managers need to calculate and evaluate the changes in supply and demand of
resources resulting from different decisions.
E.
Step-Cost Behavior
A step-cost function displays a constant level of cost for a range of activity output
and then jumps to a higher level of cost at some point, where it remains for a similar
range of activity.
1. Step-variable costs are costs that follow a step-cost behavior with narrow steps
(resources must be purchased in small chunks).
 Step-variable costs can be approximated with a strictly variable cost assumption.
2. Step-fixed costs are costs that follow a step-cost behavior with wide steps (resources are acquired at large quantities).
 Many so-called fixed costs are best described by a step-cost function because
they are fixed over the normal operating range of a firm (relevant range).
 Many committed resources, such as engineers’ salaries, follow a step-cost function.
42
Chapter 3
3. A contemporary cost management system informs users of the relationship between
resources supplied and resources used as follows:
Activity availability = Activity output + Unused capacity
Activity rate is the average unit cost obtained by dividing the resource expenditure
by the activity’s practical capacity. The activity rate is used to calculate the cost of
the activity used (resource usage) and the cost of unused activity as follows:
Cost of activity used = Activity rate × Actual activity output
Cost of unused activity = Activity rate × Unused activity
Thus,
Cost of activity supplied = Cost of activity used + Cost of unused activity
Note that a traditional cost management system typically provides information only
about the cost of the resources supplied.
F.
Activities and Mixed Cost Behavior
1. Mixed costs have a fixed and a variable component.
2. The accounting records often reveal the total cost of an activity and a measure of
activity output. Thus, it is necessary to separate the total costs into their fixed and
variable components.
III.
Methods for Separating Mixed Costs
into Fixed and Variable Components
A. Introduction
Learning Objective #3
1. The expression of the mixed cost as a linear equation is:
Y = F + VX
 Total activity cost (Y ) is the dependent variable because its value depends on
the value of another variable.
 Measure of activity output (X ) is the independent variable because it measures
activity output and explains changes in the activity cost. There may be more than
one independent variable. The choice of an independent variable is related to its
economic plausibility.
 The intercept parameter corresponds to fixed activity cost (F ) or total fixed cost.
Graphically, the intercept parameter is the point at which the mixed cost line intercepts the cost (vertical) axis.
 The slope parameter corresponds to the variable cost per unit of activity
(V ). Graphically, this represents the slope of the mixed cost line.
2. There are three widely used methods of separating mixed costs into their fixed and
variable components: the high-low method, the scatterplot method, and the method
of least squares.
B.
The High-Low Method
The high-low method uses two points to determine the equation of the cost line.
1. Two activity points, the highest and the lowest, and their corresponding costs are
used to determine the cost formula.
2. The parameters for the cost formula (F and V ) are computed using the following equations:
43
Activity Cost Behavior
Variable cost per unit of activity = Change in cost / Change in activity
V = (Y2 – Y1) / (X2 – X1)
Fixed activity cost = Total cost – Total variable cost
F = Y2 – VX2 or
F = Y1 – VX1
3. Advantages of the high-low method:
 Objectivity—Any two people using a particular set of data will come up with
the same answer.
 Quick estimation—Only two points of data are needed.
4. Disadvantage of the high-low method:
 The high and low points may not be representative of the cost-activity relationship.
C.
The Scatterplot Method
In the scatterplot method, data points are plotted so that the relationship between the
dependent variable and the independent variable can be seen.
1. A scattergraph is a visual portrait of the relationship between cost and activity.
 Total activity cost (material-handling cost) is the vertical axis.
 The activity driver or output measure (number of moves) is the horizontal axis.
Review textbook Exhibit 3-8, which shows an example of plotting a scattergraph.
2. A scattergraph allows the users to:
 Determine whether a relationship between the dependent variable and the independent variable exists.
 Assess the validity of the assumed linear relationship.
 Identify outliers (i.e., points that do not fit the general pattern of behavior).
3. Comparison of the high-low method and the scatterplot method:
a. The main advantage of the high-low method is that it directs the manager as to
which two points to select to compute the linear cost formula. Thus, the highlow method removes subjectivity from the estimation process.
b. The advantage of the scatterplot method over the high-low method is that it
allows the users to inspect the data visually.
Review textbook Exhibit 3-9, which illustrates cost behavior situations not appropriate for the
high-low method. Using a scattergraph to inspect data visually would be more advantageous.
D.
The Method of Least Squares
The method of least squares produces a best-fitting line that is closer to the data points
than any other line.
44
Chapter 3
1. Mathematically, closer is defined as the line with the smallest sum of the squared
deviations. Deviation is defined as the difference between the predicted and actual
cost.
2. The method of least squares uses the sum of squared deviations to identify the
best-fitting line because:
 Squaring the deviations eliminates the canceling effect of positive and negative
deviations.
 Squaring the deviations also assesses a larger “penalty” to data points that have
a large deviation. Many small deviations are better than a few large deviations.
Since the measure of closeness is the sum of the squared deviation of points from
the line, the smaller the measure, the better the line fits the data points.
E.
Using the Regression Programs
1. Spreadsheet packages such as Microsoft Excel, Lotus 1-2-3, and Quattro Pro1
have regression routines that will perform the least squares computations.
For example, in Excel pull down the “Tools” menu and choose “Add-in” to activate
the “Data Analysis Toolpack.” Reopen the “Tools” menu to choose “Data Analysis”
and then click on “Regression.” Specify the dependent variable data range in the Y
window and the independent variable data range in the X window within the Regression dialog box.
Review textbook Exhibit 3-12, which shows regression output produced by Excel.
2. Use the coefficients of the intercept and the X variable reported at the bottom of
the regression output to construct the cost formula.
IV.
Reliability of Cost Formulas
Learning Objective #4
Regression output is useful to assess the reliability of the estimated cost formula because it
provides the results of hypothesis testing of cost parameters, goodness of fit, and confidence intervals. These tests help the manager determine whether there is a strong association between an activity cost and an activity driver. Strong test results provide
evidence to the manager about the correctness of the driver selection.
A.
Hypothesis Test of Parameters
The hypothesis test of cost parameters indicates whether the parameters are different
from zero.
1. The t statistic is used to test the hypothesis that the cost parameters are statistically different from zero.
2. The reported P-value shows the level of statistical significance achieved by the
t statistic.
 If the reported P-value is less than the specified degree of confidence (for example, 0.05), the independent variable is a significant explanatory variable.
1
Excel is a registered trademark of Microsoft Corporation. Lotus and 1-2-3 are registered trademarks of the Lotus Development
Corporation. Quattro Pro is a registered trademark of Novell, Inc. Any further reference to Excel, Lotus 1-2-3, or Quattro Pro
refers to this footnote.
45
Activity Cost Behavior
 If the reported P-value is greater than the specified degree of confidence (for example, 0.05), the independent variable is not a significant explanatory variable.
B.
Goodness of Fit Measures
Goodness of fit measures the degree of association between cost and activity output.
Measures of goodness of fit include the coefficient of determination and the coefficient
of correlation.
1. The coefficient of determination measures the percentage of variability in the dependent variable that is explained by the independent variable.
 The coefficient of determination is labeled as R Square (R2) in regression output.
 R2 always ranges between 0 and 1.00. The higher the percentage of cost variability explained, the better the fit.
2. The coefficient of correlation is the square root of the coefficient of determination. It provides information on the direction of the relationship between cost and
activity, because the value of the coefficient of correlation can range between –1
and +1.
 When a positive correlation exists, as activity increases, costs also increase.
 When a negative correlation exists, as activity increases, costs decrease.
Review textbook Exhibit 3-13, which illustrates various correlations
and the associated correlation coefficients.
C.
Confidence Intervals
A confidence interval provides a range of values for the actual cost with a prespecified degree of confidence.
1. The confidence interval of the predicted costs is used to measure the discrepancy
between the actual cost and the predicted cost using the least-squares cost equation.
The predicted cost can be expected to be different from the actual cost because:
 The cost equation may have omitted a relevant activity driver.
 A sample was used to estimate the relationship.
2. The standard error (Se) in the regression statistics and a t statistic is required to
construct the confidence interval for the predicted cost.
Confidence interval = Predicted cost ± t × Standard error
where
 Standard error is the measure of dispersion found in the data.
 t statistic is a specified degree of confidence that describes the likelihood that the
prediction interval will contain the actual costs. The value of the t statistic depends on the following:
 Degree of freedom = n – p
where n = Number of data points used to calculate the cost formula
p = Number of parameters in the cost equation
 Confidence level
46
Chapter 3
Review textbook Exhibit 3-14, which provides a table of selected t values.
3. Implications of the confidence interval include the following:
 The wider the confidence interval, the less useful the cost equation.
 The width of the confidence interval can be reduced by using more data points.
With a larger sample, both the standard error and the t statistic will decrease.
V.
Multiple Regression
Learning Objective #5
Multiple regression uses least squares to fit an equation involving two or more explanatory
variables.
 The hypothesis test of the parameters now is a test of whether or not the independent
variable should be included in the equation.
 The “adjusted R Square” is used as the goodness of fit measure.
 The t statistic for each regression coefficient is calculated, and the achieved level of statistical significance (the reported p value) is tested in the same way as those in simple
regression.
 Calculate the confidence interval in the same way as those in simple regression.
Review textbook Exhibit 3-15, which shows a sample multiple regression analysis output.
VI.
The Learning Curve and Nonlinear Cost Behavior
Learning Objective #6
The learning curve describes the mathematical or graphic representation of how the labor
hours worked per unit decrease as the volume produced increases in a nonlinear fashion.
The learning rate, expressed as a percent, gives the percentage of time needed to make
the next unit, based on the time it took to make the previous unit.
The use of the learning curve concept helps management to be more accurate in budgeting
and performance evaluation for processes in which learning occurs. The learning curve can
be applied to the service industry and to the manufacturing industry using the following
models:
A.
Cumulative Average-Time Learning Curve
The cumulative average-time learning curve model states that the cumulative average time per unit decreases by a constant learning rate each time the cumulative
quantity of units produced doubles.
Review textbook Exhibit 3-16, which gives the data for a cumulative average-time learning
curve with an 80 percent learning rate and 100 direct labor hours for the first unit.
Note that the bold rows give the cumulative average time and
cumulative total time according to the doubling formula.
Activity Cost Behavior
47
 Calculate the amounts for units that are not doubles of the original amount using the following formula:
Y = pXq
Where:
Y = Cumulative average time per unit
X = Cumulative number of units produced
p = Time in labor hours required to produce the first unit
q = Rate of learning = ln (percent learning) / ln 2
Review textbook Exhibit 3-17, which shows the graph of both the cumulative
average time per unit and the cumulative total hours required.
B.
Incremental Unit-Time Learning Curve
The incremental unit-time learning curve model describes that the incremental time
per unit decreases by a constant learning rate each time the cumulative quantity of
units produced doubles.
Review textbook Exhibit 3-18, which gives data for an incremental unit-time learning
curve with an 80 percent learning rate and 100 direct labor hours for the first time.
 Calculate the amounts for units that are not doubles of the original amount using the following formula:
m = pXq
Where:
m = Time needed to produce the last unit
X = Cumulative number of units produced
p = Time in labor hours required to produce the first unit
q = Rate of learning = ln (percent learning) / ln 2
C.
The difference between the cumulative average-time learning curve model and the incremental unit-time learning curve model is in the underlying assumptions of the two
models.
1. The cumulative average-time learning curve model assumes that the decrease in
learning applies to all the units in between the original observation and the doubled
observation, not just to the incremental unit.
2. The incremental unit-time learning curve model assumes that the decrease in
learning applies only to the incremental unit, not to all the units in between the original observation and the doubled observation.
3. In general, the incremental unit-time learning curve model does not decrease as
rapidly as the cumulative average-time learning curve model.
48
VII.
Chapter 3
Managerial Judgment
Learning Objective #7
 Managers may use their experience and past observations of cost relationships to determine fixed and variable costs. This is the most widely used method in practice; its appeal is simplicity.
 Managers may use their experience and judgment to refine the statistical estimates. For
example, experienced managers might “eyeball” the data and throw out several points
as outliers, excluding them from the computations.
49
Activity Cost Behavior
KEY TERMS TEST
SET #1
From the list that follows, select the term that best completes each statement and write it in the
space provided.
activity capacity
activity rate
committed fixed expenses
cost behavior
cost of resource usage
cumulative average-time learning curve
model
discretionary fixed expenses
fixed costs
flexible resources
learning curve
long run
mixed costs
practical capacity
relevant range
resources supplied in advance of usage
short run
step-cost function
step-fixed cost
step-variable cost
unused capacity
variable costs
1. If the cost remains constant over wide ranges of activity usage, it is a(n) ________
_____________________; if the ranges are relatively narrow, it is a(n) ________
_____________________.
2. The ability to perform activities is called ______________________________.
3. The __________________________________________ states that the cumulative average
time per unit decreases by a constant learning rate each time the cumulative quantity of units
produced doubles.
4. The efficient level of activity performance is the ______________________________.
5. The period of time in which all costs are variable is the __________________; the period of
time in which at least one cost is fixed is the __________________.
6. The activity rate multiplied by actual activity usage is the formula for _____________
_______________________.
7. The ______________________ is the average unit cost.
8. Costs incurred for the acquisition of short-term
_____________________________________________.
capacity
or
services
are
9. _______________________ is the way in which a cost changes in relation to changes in
activity usage.
10. The difference between the acquired activity capacity and the actual activity usage is the
______________________________.
11. Costs incurred for the acquisition of long-term activity capacity are _____________________
________________________.
50
Chapter 3
12. When the cost function is defined for ranges of activity usage, it is a(n) _______________
______________.
13. ______________________________ are resources acquired from outside sources with no
requirement of any long-term commitment, while ___________________________________
____________________________ are acquired through either an explicit or implicit contract
to obtain a given quantity of resource, whether fully used or not.
14. _________________________ vary in total in direct proportion to changes in an activity
driver.
15. _________________________ have both a fixed and a variable component.
16. _________________________ are in total constant within the relevant range as the level of
the activity driver varies.
17. The assumed cost relationship is valid only for the __________________________.
18. The ____________ describes the mathematical or graphic representation of how the labor
hours worked per unit decrease as the volume produced increases in a nonlinear fashion.
SET #2
From the list that follows, select the term that best completes each statement and write it in the
space provided.
activity output
coefficient of correlation
coefficient of determination
committed resources
confidence interval
dependent variable
deviation
flexible resources
goodness of fit
high-low method
hypothesis test of cost parameters
independent variable
intercept parameter
incremental unit-time learning curve
learning rate
method of least squares
multiple regression
nonunit-level drivers
scattergraph
scatterplot method
slope parameter
unit-level drivers
1. __________________ is the difference between the predicted value and the actual cost.
2. The ________________________________________ is a measure of the relationship between two variables, including the direction of the relationship.
3. The plot of cost versus activity is a(n) _____________________.
4. The __________________________________ is used to predict the _________________
_____________.
5. The ______________________________________________ is the percentage of total variability in the dependent variable that is explained by the independent variable.
Activity Cost Behavior
51
6. The ___________________________ is the degree of association between cost and activity.
7. Two methods that fit a line to data using only two points are the _________________
_____________ and the _______________________________.
8. A(n) ________________________________ provides a range of predicted values rather than
a single point estimate.
9. The fixed cost is estimated by the ________________________________, while the variable
cost per unit of activity usage is estimated by the ________________________________.
10. The statistical method of finding the equation of the line that best fits the set of data is
the _______________________________________. If two or more variables are used, it
is called _______________________________.
11. The _________________________________model states that the incremental time per unit
decreases by a constant learning rate each time the cumulative quantity of units produced
doubles.
12. The percentage of time needed to make the next unit, based on the time it took to make the
previous unit, is called ____________.
MULTIPLE-CHOICE QUIZ
Complete each of the following statements by circling the letter of the best answer.
1. The amount of activity capacity used in producing the organization’s output is:
a. practical capacity.
b. resource spending.
c. resource usage.
d. unused capacity.
e. none of the above.
2. Which of the following costs remain constant in total when the level of the activity driver varies?
a. conversion costs
b. direct costs
c. fixed costs
d. mixed costs
e. variable costs
52
Chapter 3
3. Committed fixed expenses are costs:
a. incurred that provide long-term activity capacity.
b. that can easily be changed.
c. incurred that provide short-term activity capacity.
d. that are allocated from another organizational unit.
4. Discretionary fixed expenses are costs:
a. incurred that provide long-term activity capacity.
b. that are supplied as used and needed.
c. that cannot be changed.
d. incurred that provide short-term activity capacity.
e. that are allocated from another organizational unit.
5. Which of the following is true about resources supplied in advance of usage?
a. There is no unused activity capacity for this category of resources.
b. The organization is free to buy only the quantity of resources needed.
c. These resources may take the form of either committed fixed expenses or discretionary
fixed expenses.
d. Normally a long-term commitment is not required.
e. All of the above are true.
6. Which of the following is the best definition of a step-fixed cost?
a. It is a cost that is constant in total over the relevant range.
b. It is a cost that varies in total in direct proportion to changes in activity.
c. It is a cost that follows a step-cost behavior with narrow steps.
d. It is a cost that follows a step-cost behavior with wide steps.
e. It is a cost that measures activity usage in steps—first, the fixed cost of resources used;
then, the fixed cost of unused capacity.
7. The variable whose value is based on the value of another variable is the:
a. activity variable.
b. dependent variable.
c. independent variable.
d. intercept parameter.
e. slope parameter.
8. The item that corresponds to the variable cost per unit of activity is the:
a. activity variable.
b. dependent variable.
c. independent variable.
d. intercept parameter.
e. slope parameter.
53
Activity Cost Behavior
9. Which of the following best describes the difference between the high-low method and the
scatterplot method?
a. The high-low method uses all of the activity points; the scatterplot method uses only two
points.
b. The high-low method uses the high activity point and the low activity point; the scatterplot
method allows the user to select two points that better represent the relationship between
activity and costs.
c. The high-low method uses the coefficient of correlation; the scatterplot method uses the
coefficient of determination.
d. The high-low method uses costs from the accounting records; the scatterplot method uses
costs from the operating records.
e. None of the above accurately describe the difference between the high-low method and
the scatterplot method.
10. Which of the following is not an advantage of using the least squares method rather than the
high-low method?
a. The equation line is the best-fitting line to the data points.
b. All of the data points, rather than just two points, are used.
c. A measure of the goodness of fit is available.
d. Measures of the reliability of the resulting line are available.
e. All of the above are advantages of the least squares method.
11. Which of the following is true about the coefficient of determination R 2?
a. R 2 is the probability that the actual value will be included in the confidence interval.
b. An R 2 of 95% means that 95% of the data points fall on the equation line.
c. A negative R 2 means that as activity increases, costs will decrease.
d. R 2 measures the percentage of the total variability of the costs that is explained by the
equation line.
e. None of the above are true.
12. Why is managerial judgment so critical in determining cost behavior?
a. All statistical methods are notoriously unreliable.
b. Statistical methods are highly accurate in depicting the past, but they cannot foresee the
future.
c. The fixed and variable cost breakdowns are recorded in the accounting records; management just needs to know the appropriate accounts to search.
d. The managers can use their experience to refine the statistical estimates.
e. Managerial judgment is not critical; statistical methods can capture all of the manager’s
expertise without any bias.
13. XYZ Corporation has reported activity costs. When 10,000 units are produced, the average
cost is $23 per unit. When the activity is only 6,000 units, the average cost is $30 per unit.
What are the fixed and variable costs?
Fixed
a. $105,000.00
b.
12.50
c.
19.50
d.
(8,400.00)
e. 180,000.00
Variable
$
12.50
105,000.00
(1.75)
0.08
7.00
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Chapter 3
14. Almost Company had setup costs totaling $265,000 when 2,750 setups were performed. When
3,500 setups were performed, setup costs totaled $310,000. Determine the fixed and variable cost breakdown for setup costs.
Fixed
Variable
a. $ (1,666.67)
b. 475,000.00
c. 100,000.00
d.
12,000.00
e. (12,000.00)
$ 16.67
(60.00)
60.00
92.00
92.00
15. Colfax, Inc., had packaging costs of $150,000 when 12,500 packages were shipped.
Packaging costs were $190,000 when 17,500 packages were shipped. The variable costs
were:
a. $8.00.
b. $10.86.
c. $11.33.
d. $12.00.
e. none of the above.
16. Acme Company has just completed a least squares regression analysis of its material-handling
costs. The cost analyst has provided you with the following summary, with apologies that the
original computer output was not available:
Parameter
Intercept ...................................
Number of moves .....................
Estimate
Standard Error of Parameter
347.86
3.731
61.758
0.2387
Summary regression statistics are provided as follows:
R Square (R 2) ..........................
0.876
Standard Error (Se)...................
53.51
Observations ............................
22
What is a 95 percent confidence interval for an estimated 150 moves of material (use t =
2.086)?
a. 97.56 ± 46.87
b. 351.59 ± 150.00
c. 794.98 ± 45.89
d. 907.51 ± 111.62
e. 907.51 ± 128.83
Activity Cost Behavior
55
PRACTICE TEST
EXERCISE 1
Fisk Engineering is an independent testing laboratory with contracts to perform standardized quality testing for local manufacturers. Fisk employs four engineers who are responsible for all phases
of the testing. Each engineer is paid an average salary of $40,000 and is capable of conducting
3,200 tests per year. The facility was recently constructed for $450,000 and is being depreciated
on a straight-line basis over 20 years. Testing equipment is leased for $6,000 per year on a fiveyear lease. Consumable supplies are expected to average $175,000 per year at full capacity. During
20XX, there were 11,000 tests performed.
Required:
1. Classify the resources into one of the following: (1) long-term resources supplied in advance,
(2) short-term resources supplied in advance, or (3) resources supplied as needed.
2. Calculate the activity rate, breaking it down into fixed and variable components.
3. Calculate the total activity available, breaking it down into activity usage and unused activity.
56
Chapter 3
EXERCISE 2
Antz Industries has provided you with the following data for its materials storeroom:
Month
January .....................
February....................
March ........................
April ...........................
May ...........................
June ..........................
July............................
August .......................
September ................
October .....................
November .................
December .................
Number of Shipments
Storeroom Costs
175
225
275
175
200
225
300
325
275
200
150
175
$3,000
3,600
4,300
3,800
2,700
3,200
4,250
4,400
4,100
3,150
2,650
2,750
Required:
1. Determine the cost behavior using the high-low method.
2. Prepare a scattergraph of the data points, using cost as the vertical axis and number of shipments as the horizontal axis. Do any of the points seem to be outliers?
57
Activity Cost Behavior
EXERCISE 2 (Continued)
3. Determine the cost behavior using the scatterplot method. How do these results compare with
the high-low method?
EXERCISE 3
The Saints Company wants to develop an estimate of its supplies costs. George Saint, the controller, has collected what he believes to be the relevant data for the past 12 months. It is Mr. Saint’s
professional opinion that the supplies cost should be closely related to the volume of the product
produced; thus, he has provided you with the following information:
Month
Units Produced
January .....................
February ...................
March .......................
April ..........................
May...........................
June..........................
July ...........................
August ......................
September ................
October.....................
November .................
December .................
Cost of Supplies
100
80
70
50
60
80
70
80
100
70
60
50
$3,550
2,980
2,970
2,410
2,530
3,180
2,830
2,820
3,220
2,950
2,560
2,420
REGRESSION SUMMARY OUTPUT
Regression Statistics
Multiple R
0.9324129
R Square
0.8693939
Adjusted R Square
0.8563333
Standard Error
132.26091
Observations
12
ANOVA
Regression
Residual
Total
Intercept
Units Produced
df
1
10
11
SS
1164437.19
174929.4766
1339366.667
MS
1164437
17492.9
F
66.56609354
Coefficients
1445.8953
19.619835
Standard Error
178.4756267
2.404743773
t Stat
8.10136
8.1588
P-value
1.05437E-05
9.9085E-06
Significance F
9.909E-06
Lower 95%
1048.2268
14.261731
Upper 95%
1843.5639
24.977939
58
Chapter 3
EXERCISE 3 (Continued)
Required:
1. Prepare a cost formula for the supplies cost using the regression output.
2. Determine the coefficient of determination.
3. Determine the coefficient of correlation.
4. Prepare a 95 percent confidence interval for supplies cost when 90 units are produced (using
t statistic = 2.228).
59
Activity Cost Behavior
EXERCISE 4
The Yuma Company has accumulated the following information in its quest to determine the cost
behavior of the Receiving Department. Gail Nelson, the manager of Yuma, feels that tons of material received, the dollar value of receipts, the number of purchase orders, and the number of incoming shipments could all reasonably influence the Receiving Department costs.
Receiving
Department Costs
Tons of Material
Received
Dollar Value
of Receipts
$67,100
75,200
92,200
88,600
87,700
80,200
98,000
67,600
68,500
78,500
71,700
80,300
78,000
80,000
93,800
47,300
68,200
93,500
79,200
96,800
49,500
73,700
40,700
46,200
63,800
50,600
48,400
55,000
69,300
53,900
$138,600
157,000
158,400
139,900
144,000
134,100
162,000
117,000
152,100
143,100
117,000
148,500
127,800
136,800
153,000
Number
of POs
90
89
96
105
91
110
128
85
88
90
87
108
103
98
125
Number of
Incoming Shipments
103
117
139
148
120
138
156
114
117
133
130
136
115
126
168
Required:
1. Prepare a cost formula for the Receiving Department costs. How many activity drivers are used?
Are they all different from zero?
60
Chapter 3
EXERCISE 4 (Continued)
Use this space to continue your answer.
2. How well does your model explain the variability in the costs?
3. Prepare an estimate of costs for a month when 75,000 tons valued at $125,000 are received,
90 purchase orders are handled, and 125 shipments are received.
4. Prepare a 95 percent confidence interval for the point estimate you prepared in Requirement 3.
61
Activity Cost Behavior
EXERCISE 5
Titan Corp. manufactures high-tech equipment for space shuttles. It has completed manufacturing
the first unit of the new TN-3 machine design. Management believes that the 100 labor hours required to complete this unit are reasonable and is prepared to go forward with the manufacture of
additional units. An 80 percent cumulative average-time learning curve model for direct labor
hours is assumed to be valid. Data on costs are as follows:
Direct materials
$750 per unit
Direct labor
$15 per direct labor hour
Variable manufacturing overhead
$40 per direct labor hour
Required:
1. Set up a table with columns for cumulative number of units, cumulative average time per unit
in hours, cumulative total time in hours, and individual unit time for the nth unit in hours. Complete the table for 1, 2, 4, and 8 units.
2. What is the total variable cost of producing 1, 2, 4, and 8 units? What is the variable cost per
unit for 1, 2, 4, and 8 units?
62
Chapter 3
“CAN YOU?” CHECKLIST
 Can you explain the relationship among activities, resource usage, and cost behavior? Can
you explain how resource spending, resource usage, and unused capacity are interrelated?
Can you describe how resources supplied affect cost behavior?
 Can you describe the different patterns of step-cost behavior? Can you explain how the concept of the relevant range affects the estimation of these costs?
 Can you determine cost behavior using either the high-low method or the scatterplot method?
Can you explain the difference between these two methods?
 Can you explain how the method of least squares defines closest and best-fitting line?
 Can you use the least squares method to develop a cost formula? Can you determine whether
or not the resulting cost formula is reliable?
 Can you use the cumulative average-time learning curve model and the incremental unit-time
learning curve model to produce more accurate estimates in budgeting and performance evaluation for processes in which learning occurs?
 Can you describe the role that managerial judgment plays in determining cost behavior?
ANSWERS
KEY TERMS TEST
SET #1
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
step-fixed cost, step-variable cost
activity capacity
cumulative average-time learning curve model
practical capacity
long run, short run
cost of resource usage
activity rate
discretionary fixed expenses
Cost behavior
unused capacity
11. committed fixed expenses
12. step-cost function
13. Flexible resources, resources supplied in advance
of usage
14. Variable costs
15. Mixed costs
16. Fixed costs
17. relevant range
18. learning curve
SET #2
1.
2.
3.
4.
5.
6.
Deviation
coefficient of correlation
scattergraph
independent variable, dependent variable
coefficient of determination
goodness of fit
7.
8.
9.
10.
11.
12.
high-low method, scatterplot method
confidence interval
intercept parameter, slope parameter
method of least squares, multiple regression
incremental unit-time learning curve
learning rate
63
Activity Cost Behavior
MULTIPLE-CHOICE QUIZ
1.
2.
3.
4.
5.
6.
7.
8.
9.
c
c
a
d
c
d
b
e
b
10.
11.
12.
13.
e
d
b
a
14. c
15. a
16. d
Variable = ($23 × 10,000 – $30 × 6,000) / (10,000 – 6,000) = $50,000 / 4,000 = $12.50
Fixed = $230,000 – ($12.50 × 10,000) = $105,000
Variable = ($310,000 – $265,000) / (3,500 – 2,750) = $45,000 / 750 = $60.00
Fixed = $310,000 – ($60 × 3,500) = $100,000
Variable = ($190,000 – $150,000) / (17,500 – 12,500) = $40,000 / 5,000 = $8.00
Y = 347.86 + (3.731 × 150) = 907.51
Y = 2.086 × 53.51 = 111.62
PRACTICE TEST
EXERCISE 1 (Resources and Activities)
1. Engineers:
Facility:
Leased Equipment:
Supplies:
short-term resources supplied in advance
long-term resources supplied in advance
long-term resources supplied in advance
resources supplied as needed
2. Activity rate:
Fixed:
[4 × $40,000 + ($450,000 / 20) + $6,000] / (4 × 3,200) = $188,500 / 12,800 = $14.7266 per test
Variable: $175,000 / 12,800 = $13.6719
3. Activity available = Activity usage + Unused Activity
12,800
=
11,000
+
1,800
EXERCISE 2 (High-Low Method and Scatterplot Method)
1. Variable: ($4,400 – $2,650) / (325 – 150) = $1,750 / 175 = $10.00 per shipment
Fixed:
$4,400 – ($10 × 325) = $4,400 – $3,250 = $1,150
Storeroom Cost = $1,150 + $10 × number of shipments
2. In Excel, click on the Chart Wizard button and choose XY (Scatter) to produce a scattergraph as follows:
Storeroom costs
5000
4000
3000
Series1
2000
1000
0
0
100
200
300
400
Number of shipments
An analysis of the scattergraph indicates that further investigation on April data is needed. The storeroom costs
in April do not fit the general pattern of behavior in the data and, thus, can be an outlier.
64
Chapter 3
3. Any two points that appear reasonable could be used to calculate the cost formula. Individual results may be
very similar to the high-low results, or they could be very different.
EXERCISE 3 (Least Squares)
1. The estimated cost formula using the regression output can be expressed as follows:
Supplies cost = $1,445.895 + $19.6198 × Units produced
2. The coefficient of determination (R Square) is 0.869.
3. r  0.869  0.932
Actual
$3,550
2,980
2,970
2,410
2,530
3,180
2,830
2,820
3,220
2,950
2,560
2,420
Predicted
$3,408
3,015
2,819
2,427
2,623
3,015
2,819
3,015
3,408
2,819
2,623
2,427
Deviation
142)
(35)
151)
(17)
(93)
165)
11)
(195)
(188)
131)
(63)
(7)
Sum ................
Deviation2
20,198
1,259
22,715
285
8,665
27,066
115
38,213
35,298
17,087
3,980
47
174,928
4. Confidence interval = Predicted value ± t × Standard error
Confidence interval = 1,445.895 + (19.61983 × 90) ± 2.228 × 132.26
Confidence interval = 3,211.6797 ± 294.6752
Confidence interval = 2,917.0045 < Y < 3,506.3549
EXERCISE 4 (Multiple Regression)
1. The main objective is to decide how many independent variables should be included in the cost formula. To deter mine whether or not an independent variable should be included, perform the hypothesis test of the parameters.
Any variable that is not significantly different from zero should be excluded. Thus, the multiple regression analysis
will be performed in the following step-wise manner.
First Pass: Include all four variables in the regression.
SUMMARY OUTPUT: All FOUR VARIABLES
Regression Statistics
Multiple R
0.9927017
R Square
0.98545666
Adjusted R Square
0.97963933
Standard Error
1397.87556
Observations
15
ANOVA
Regression
Residual
Total
df
4
10
14
SS
MS
1324068773 331017193
19540560.7 1954056.1
1343609333
F
169.4
Significance F
3.85634E-09
65
Activity Cost Behavior
Intercept
Tons of DM received
Dollar value of receipts
No. of purchase orders
No. of incoming shipments
Coefficients Standard Error
5058.15695 4090.100748
0.32367875 0.025601107
-0.00771516 0.033722885
349.727053 50.73502222
164.702734 38.54285933
t Stat
1.2366827
12.643154
-0.228781
6.8932078
4.273236
P-value
0.24446
1.8E-07
0.82365
4.2E-05
0.00163
Lower 95%
-4055.15701
0.266635918
-0.08285444
236.6823593
78.82387702
Upper 95%
14171.4709
0.38072158
0.06742413
462.771747
250.581591
Based on the P-values, the results suggest that the tons of direct material received, number of purchase orders,
and number of incoming shipments are significantly different from zero, because their P-values are less than
the 5% degree of confidence. These variables seem to be good explanatory variables of the cost behavior of the
Receiving Department.
Adjusted R 2 = 0.9796, or 97.96%
Standard Error = 1397.876
Second Pass: Drop the variable and redo the regression, since the P-value for the variable of “dollar value of
receipts” is not significant.
SUMMARY OUTPUT: THREE VARIABLES
Regression Statistics
Multiple R
0.99266336
R Square
0.98538054
Adjusted R Square
0.98139342
Standard Error
1336.30554
Observations
15
ANOVA
Regression
Residual
Total
Intercept
Tons of DM received
No. of purchase orders
No. of incoming shipments
df
3
11
14
SS
MS
1323966496 441322165
19642837.45 1785712.5
1343609333
Coefficients Standard Error
4439.25537 2932.575239
0.3209441 0.021642175
346.374717 46.43353003
164.917318 36.83431142
Adjusted R 2 = 0.9814, or 98.14%
t Stat
1.5137737
14.829568
7.4595818
4.4772744
F
247.141
Significance F
2.26457E-10
P-value
0.15827
1.3E-08
1.3E-05
0.00094
Lower 95%
-2015.30248
0.27330997
244.1751551
83.84550461
Upper 95%
10893.8132
0.36857823
448.57428
245.989132
Standard Error = 1336.306
Since all P-values of explanatory variables are significant at a 5% confidence level, the three-variable model is adequate. The three-variable model also has a higher adjusted R 2 value (98.14%) than the four-variable model
(97.96%). Thus, the estimated cost formula is as follows:
Receiving Department costs = $4,439.255 + ($0.320944 × tons) + ($346.3747 × POs) + ($164.9173 × shipments)
2. The model chosen explains the variability in Receiving Department costs very well, because the adjusted R2 equals
98.14%.
3. Based on the estimated cost formula, an estimate of Receiving Department costs for a month when 75,000 tons are
received, 90 purchase orders are handled, and 125 shipments are received will be as follows:
Receiving Department costs = $4,439.255 + ($0.320944 × 75,000) + ($346.3747 × 90) + ($164.9173 × 125)
Receiving Department costs = $80,298.44
66
Chapter 3
4. Confidence interval of the estimated Receiving Department costs
= $80,298.44 ± t (95%, 11 degrees of freedom) × Se
= $80,298.44 ± 2.201 × 1,336.306
Thus,
$80,298.44 ± $2,941.21
That is,
$77,357.23 < Estimated Receiving Department costs < $83,239.65
EXERCISE 5 (Learning Curve)
1. The table with columns for cumulative number of units, cumulative average time per unit in hours, cumulative total
time in hours, and individual unit time for the nth unit in hours for 1, 2, 4, and 8 units is presented below.
Cumulative
Number
of Units
Cumulative Average Cumulative Total Individual Time for
Time per Unit in
Time: Labor
nth Unit: Labor
Hours
Hours
Hours
(1)
(2)
(3) = (1) x (2)
(4)
1
100
100
100
2
80 (0.8 x 100)
160
60
4
64 (0.8 x 80)
256
45.4
8
51.2 (0.8 x 64)
409.6
35.5
2. The calculation of total variable cost of producing 1, 2, 4, and 8 units and the variable cost per unit for 1, 2, 4, and 8
units is presented below.
1 unit
2 units
4 units
8 units
750
$ 1,500
$ 3,000
$ 6,000
Direct labor
1,500
2,400
3,840
6,144
Variable overhead
4,000
6,400
10,240
16,384
Total variable cost
$ 6,250
$10,300
$ 17,080
$ 28,528




Direct materials
Divided by units
Unit variable cost
$
1
$ 6,250
2
$ 5,150
4
$ 4,270
8
$ 3,566