COST MANAGEMENT
Accounting & Control
Hansen▪Mowen▪Guan
Chapter 3
Cost Behavior
COPYRIGHT © 2009 South-Western Publishing, a division of Cengage Learning.
Cengage Learning and South-Western are trademarks used herein under license.
1
Study Objectives
1. Define and describe fixed, variable, and mixed costs.
2. Explain the use of 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.
2
Cost Behavior: Fixed Costs
Fixed costs are costs that in total are
constant within the relevant range as
the level of the activity driver varies.
Two production lines can process 10,000
computers per year each. The workers on each
line are supervised by a production-line manager
who is paid $24,000 per year. For production up
to 10,000 units, only one supervisor is needed.
When production is between 10,001 and 20,000
units, two supervisors are required.
3
Cost Behavior: Fixed Costs
Days Computers, Inc.
Supervision
$54,000
54,000
54,000
108,000
108,000
108,000
Computers
Processed
4,000
8,000
10,000
12,000
16,000
20,000
4
Cost Behavior: Fixed Costs
Days Computers, Inc.
Supervision
$54,000
54,000
54,000
108,000
108,000
108,000
Computers
Processed
4,000
8,000
10,000
12,000
16,000
20,000
5
Cost Behavior: Fixed Costs
Days Computers, Inc.
Supervision
$54,000
54,000
54,000
108,000
108,000
108,000
Computers
Processed
4,000
8,000
10,000
12,000
16,000
20,000
Unit Cost
$13.50
6.75
5.40
9.00
6.75
5.40
6
Cost Behavior: Fixed Costs
7
Cost Behavior: Variable Costs
Variable costs are costs that in total
vary in direct proportion to changes in
an activity driver.
A CD-ROM disk drive is added to each
computer at a cost of $30 per computer.
The total cost of disk drives for each level of
production varies.
8
Cost Behavior: Variable Costs
Days Computers, Inc.
Total Cost of
CD-ROMs
$120,000
240,000
360,000
480,000
600,000
Number of
Computers
Processed
4,000
8,000
12,000
16,000
20,000
9
Cost Behavior: Variable Costs
Days Computers, Inc.
Total Cost of
CD-ROMs
$120,000
240,000
360,000
480,000
600,000
Number of
Computers
Processed
4,000
8,000
12,000
16,000
20,000
Unit Cost of
CD-ROMs
$30.00
30.00
30.00
30.00
30.00
10
Cost Behavior: Variable Costs
11
Cost Behavior: Mixed Costs
Mixed costs are costs that have both a
fixed and a variable component.
Ten sales representatives each earn an
annual salary of $30,000 plus a commission
of $50 per computer sold. 10,000 computers
are sold.
12
Cost Behavior: Mixed Costs
Y = Fixed cost + Total variable cost
Y = F + VX
where
Y = Total cost
For Days Computer, the selling cost is:
Y = $300,000 + $50X
13
Cost Behavior: Mixed Costs
Days Computers, Inc.
Variable
Fixed Cost of
Cost of
Selling
Selling
$300,000
300,000
300,000
300,000
300,000
Computers Selling Cost
Total Cost
$200,000 $500,000
400,000
700,000
600,000
900,000
800,000 1,100,000
1,000,000 1,300,000
Sold
4,000
8,000
12,000
16,000
20,000
per Unit
$125.00
87.50
75.00
68.75
65.00
14
Cost Behavior: Mixed Costs
15
Resources, Activities,
and Cost Behavior
• Flexible resources
– Acquired as used and needed
– Usually considered variable costs
• Examples: materials, energy
• Committed resources
– Acquired in advance of usage
– Usually considered fixed costs
• Examples: buying or leasing buildings, contracts
with employees
16
Resources, Activities,
and Cost Behavior
• Step cost behavior displays a constant
level of cost for a range of output and then
jumps to a higher level of cost at some
point
• Step-Variable costs
• Narrow increments
• Approximate as a strictly variable assumption
• Step-Fixed costs
• Wide increments
• Assigned to the fixed cost category
17
Resources, Activities,
and Cost Behavior
18
Methods for Separating Mixed Costs
into Fixed and Variable Components
Variable
Component
Fixed
Component
• The High-Low Method
• The Scatterplot Method
• The Method of Least Squares
19
Methods for Separating Mixed Costs
into Fixed and Variable Components
Straight-line equation:
Y = F + VX
where
Y = Total activity cost
F = Fixed cost component
V = Variable cost per unit
X = Measure of activity output
20
High-Low Method
Month
January
February
March
April
May
June
July
August
September
October
Materials
Number of
Handling Cost
Moves
$2,000
3,090
2,780
1,990
7,500
5,300
4,300
6,300
5,600
6,240
100
125
175
200
500
300
250
400
475
425
Step 1: Solve for variable cost (V)
V = Change in cost ÷ Change in activity
21
High-Low Method
Month
January
February
March
April
May
June
July
August
September
October
Materials
Number of
Handling Cost
Moves
$2,000
3,090
2,780
1,990
7,500
5,300
4,300
6,300
5,600
6,240
100
125
175
200
500
300
250
400
475
425
$7,500 - $2,000
Step1: V 
 $13.75
500 - 100
Low Activity
High Activity
22
High-Low Method
Step 1: Solve for variable cost (V)
V = Change in cost ÷ Change in activity
V
$7,500 - $2,000
 $13.75
500 - 100
Step 2: Using either the high cost or low cost, solve for
the total fixed costs F
Low cost
Y  F V ( X )
$2,000  F  $13.75(100)
$625  F
High cost
Y  F V ( X )
$7,500  F  $13.75(500)
$625  F
23
Scatterplot Method
Step 1: Plot the data points on a scattergraph
24
Scatterplot Method
Step 2: Choose the two data points most representative
of the data to describe the cost behavior line
25
Method of Least Squares
Actual Predicted
Cost
Cost
Deviation
Deviation
2,000
1,742
258
3,090
2,088
1,002
2,780
2,780
1,990
3,126
(1,136)
7,500
7,278
222
5,300
4,510
790
4,300
3,818
482
6,300
5,894
406
5,600
6,932
(1,332)
6,240
6,240
Total measure of closeness
Squared
66,564
1,004,004
1,290,496
49,284
624,100
232,324
164,836
1,774,224
5,205,832
26
Regression Programs
• The best-fitting line is the line with the
smallest sum of squared deviations
• Regression analysis determines the linear
function with the minimum sum of squared
deviations
• Utilize spreadsheet packages such as
Microsoft Excel to perform the
computation
27
Regression Analysis
for the Method of Least Squares
Spreadsheet Data for
Anderson Company
28
Regression Analysis
for the Method of Least Squares
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.92894908
R. Square
0.862946394
Adjusted R
0.845814693
Square
Standard Error
Observations
Regression Output for
Anderson Company
770.4987038
10
ANOVA
Regression
Residual
Total
df
1
8
9
Intercept
X Variable 1
Coefficient
854.4993582
12.3915276
SS
29903853.98
4749346.021
34653200
MS
29903853.98
593668.2526
F
50.37132077
Standard Error
569.7810263
1.745955536
t-Stat
1.49967811
7.097275588
P-value
0.172079925
0.000102268 29
Regression Analysis
for the Method of Least Squares
The regression analysis gives rise to the following
equation for Anderson’s material handling cost:
$854.50 + ($12.39  number of moves)
30
Reliability of Cost Formulas
Hypothesis test of parameters
– The lower the P-value, the more likely that the
true parameter is significantly different from 0
– Traditional benchmarks of significance are
0.10, 0.05 or 0.01
31
Reliability of Cost Formulas
Goodness of fit
– R2 is the coefficient of determination
– Measures the percentage of change in the
dependent variable explained by changes in
the independent variable
– The closer to 1.0, the better; no benchmark
32
Reliability of Cost Formulas
Confidence intervals
– The standard error is used to determine the ±
range of possible values around the
predicted value:

Standard  t-statistic  Confidence
Error
Interval

33
Multiple Regression
• Least-squares method is used to fit an
equation involving two or more
explanatory variables
Y = F + V1X1 + V2X2 etc.
where
X1 = first explanatory variable
X2 = second explanatory variable
34
Multiple Regression
Spreadsheet Data for
Anderson Company
Materials
X1
Handling Number
Month
January
February
March
April
May
June
July
August
September
October
Cost
$2,000
3,090
2,780
1,990
7,500
5,300
4,300
6,300
5,600
6,240
of Moves
100
125
175
200
500
300
250
400
475
425
Pounds
Moved
6,000
15,000
7,800
600
29,000
23,000
17,000
25,000
12,000
22,400
X2
35
Multiple Regression Analysis
for the Method of Least Squares
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.999420
R Square
0.998841
Adjusted R Square
0.998509
Standard Error
75.762721
Observations
10
ANOVA
Regression
Residual
Total
Intercept
X Variable 1
X Variable 2
df
2
7
9
SS
MS
F
34613020.07 17306510.04 3015.076722
40179.92954 5739.989934
34653200
Coefficients Standard Error
507.309711
57.322496
7.835162
0.234048
0.107181
0.003742
t Stat
8.850098
33.476720
28.642864
P-value
0.000048
0.000000
0.000000
36
Multiple Regression
Based on the multiple regression analysis, the
cost formula is written as:
Y = $507 + $7.84X1 + $0.11X2
In November the company expects to make 350
moves with a weight of 17,000 pounds. The
predicted cost of material handling is:
Y = $507 + $7.84(350) + $0.11(17,000)
= $507 + $2,744 + $1,870
= $5,121
37
Cumulative Average Time Learning
Curve with 80% Learning Rate
Cumulative
Number
of Units
(1)
1
2
3
4
5
6
7
8
16
32
Cumulative
Average Time
per Unit in Hours
(2)
Cumulative Individual Units
Total Time:
Time for nth
Labor Hours Unit-Labor Hours
(3) = (1) × (2)
(4)
100
80
(80% × 100)
70.21
64
(80% × 80)
59.57
56.17
53.45
51.20 (80% × 64)
40.96
32.77
100
160
210.63
256
297.85
337.02
374.15
409.60
655.36
1,048.64
100
60
50.63
45.37
41.85
39.17
37.13
35.45
28.06
38
Graph of Cumulative Total Hours Required
and the Cumulative Average Time per Unit
39
Managerial Judgment
• Managerial judgment is critically important
in determining cost behavior and is by far
the most widely used method in practice
• Advantage – simplicity
• Disadvantage – poor judgment leads to errors
40
COST MANAGEMENT
Accounting & Control
Hansen▪Mowen▪Guan
End Chapter 3
41