Transcript Activity Cost Behavior Prepared by Douglas Cloud Pepperdine University 3-1 Objectives 1. Define and describe fixed, variable, and After studying this mixed costs.chapter, you should 2.

Activity Cost
Behavior
Prepared by
Douglas Cloud
Pepperdine University
3-1
Objectives
1. Define and describe
fixed, variable,
and
After studying
this
mixed costs.chapter, you should
2. Explain the use of
beresources
able to: 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.
3-2
Objectives
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.
3-3
Fixed Costs
Fixed costs are costs
that in total are constant
within the relevant
range as the level of the
activity driver varies.
3-4
Fixed Costs
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 computers being
produced, two supervisors are required.
3-5
Total Costs
Total Fixed Cost Graph
$60,000
$50,000
$40,000
$30,000 F = $24000
$20,000
$10,000
Fixed Costs
0
4 8 10 12 16
Units Produced (000)
Supervision
$24,000
24,000
24,000
48,000
48,000
48,000
Computers
Processed
4,000
8,000
10,000
12,000
16,000
20,000
Unit Cost
$6.00
3.00
2.40
4.00
3.00
2.40
3-6
Total Costs
Total Fixed Cost Graph
$60,000
$50,000
$40,000
$30,000 F = $24000
$20,000
$10,000
Fixed Costs
0
4 8 10 12 16
Units Produced (000)
Supervision
$24,000
24,000
24,000
48,000
48,000
48,000
Computers
Processed
4,000
8,000
10,000
12,000
16,000
20,000
Unit Cost
$6.00
3.00
2.40
4.00
3.00
2.40
3-7
Total Costs
Total Fixed Cost Graph
$60,000
$50,000
$40,000
$30,000
$20,000
$10,000
F = $48,000
Fixed Costs
0
4 8 10 12 16
Units Produced (000)
Supervision
$24,000
24,000
24,000
48,000
48,000
48,000
Computers
Processed
4,000
8,000
10,000
12,000
16,000
20,000
Unit Cost
$6.00
3.00
2.40
4.00
3.00
2.40
3-8
Total Costs
Total Fixed Cost Graph
$60,000
$50,000
$40,000
$30,000
$20,000
$10,000
F = $48,000
Fixed Costs
0
4 8 10 12 16
Units Produced (000)
Supervision
$24,000
24,000
24,000
48,000
48,000
48,000
Computers
Processed
4,000
8,000
10,000
12,000
16,000
20,000
Unit Cost
$6.00
3.00
2.40
4.00
3.00
2.40
3-9
Variable costs are
costs that in total
vary in direct
proportion to
changes in an
activity driver.
Variable
Cost
3-10
Variable Cost
A 3½-inch disk drive is added to each
computer at a cost of $30 per computer.
The total cost of disk drives for various
levels of production is a follows:
Total Cost of
Disk Driver
$120,000
240,000
360,000
480,000
600,000
Number of
Computers Produced
4,000
8,000
12,000
16,000
20,000
Unit Cost of
Disk Drives
$30
30
30
30
30
3-11
Variable Cost
Y v = VX
Y v = Total variable costs
V = Variable cost per unit
X = Number of units of the
driver
3-12
Variable Cost
Cost
(in thousands)
$600
480
360
Y v = $30X
240
120
4,000
8,000
12,000
16,000
20,000
Number of Computers Processed
3-13
Nonlinearity of Variable Cost
Cost
($)
Relevant Range
0
Units of Activity Driver
3-14
Mixed costs are
costs that has
both a fixed and
a variable
component.
Mixed
Costs
3-15
Y = Fixed cost + Total variable cost
Y = F + VX
where
Y = Total cost
Mixed
Costs
3-16
Mixed Costs
For Days Computer, the
selling cost is represented by
the following equation:
Y = $300,000 + $50X
3-17
Mixed Costs
Fixed Cost
of Selling
Days Computers, Inc.
Variable Cost Total Cost Computers Selling Cost
of Selling
Sold
Per Unit
$300,000
300,000
300,000
300,000
300,000
$ 200,000
400,000
600,000
800,000
1,000,000
$ 500,000
700,000
900,000
1,100,000
1,300,000
4,000
8,000
12,000
16,000
20,000
$125.00
87.50
75.00
68.75
65.00
3-18
Mixed Cost Behavior
Cost
(in thousands)
$1,500
1,300
1,100
900
Variable
Costs
700
500
300
Fixed Cost
4,000
8,000 12,000 16,000 20,000
Number of Computers Sold
3-19
Basic Terms
When a firm acquires the
resources needed to perform
an activity, it is obtaining
The amount of activity
activity capacity.
capacity needed which
corresponds to the level
where the activity is
performed efficiency is
called practical capacity.
3-20
Flexible Resources
Flexible resources are supplied as used and needed.
They are acquired from outside sources, where the
terms of acquisition do not require any long-term
commitment for any given amount of the resource.
Example: Materials and energy
3-21
Committed Resources
Committed resources are supplied in advance of usage.
They are acquired by the use of either an explicit or
implicit contract to obtain a given quantity of
resource, regardless of whether the amount of the
resource available is fully used or not. Committed
resources may have unused capacity.
Example: Buying or leasing a building or equipment
3-22
Committed Resources
Committed fixed expenses are costs incurred for the
acquisition of long-term capacity.
Example: Plant, equipment, warehouses, vehicles, and
salaries of top employees
Discretionary fixed expenses are shorter-term
committed resources.
Example: The hiring of new receiving clerks
3-23
Step-Cost Behavior
A step cost function displays a
constant level of cost for a range of
output and then jumps to a higher
level of cost at some point.
3-24
Step-Cost Behavior
Cost
$500
400
300
200
100
20
40
60
80
100
120
Activity Output (units)
3-25
Step-Fixed Costs
Cost
$150,000
Normal
Operating
Range
(Relevant
Range)
100,000
50,000
2,500
5,000
7,500
Activity Usage
3-26
Step-Fixed Costs
Cost of orders supplied = Cost of orders used +
Cost of unused orders
7,500($20) = 6,000($20) + 1, 500($20)
$150,000 = $120,000 + $30,000
The $30,000 of excess engineering capacity
means that a new product could be
introduced without increasing current
spending on engineering.
3-27
Methods for Separating Mixed Costs
 The High-Low Method
 The Scatterplot Method
 The Method of Least Squares
Variable
Component
Fixed
Component
3-28
Methods for Separating Mixed Costs
Y = F + VX
TotalFixed cost
Variable
Measure
costof
activitycomponent
cost
per activity
unit of
activity
output
3-29
The High-Low Method
Month
January
February
March
April
May
June
July
August
September
October
Material Handling Costs
$2,000
3,090
2,780
1,990
7,500
5,300
4,300
6,300
5,600
6,240
No. of Moves
100
125
175
200
500
300
250
400
475
425
Step 1: Solve for variable cost (V)
3-30
The High-Low Method
Month
January
February
March
April
May
June
July
August
September
October
Material Handling Costs
$2,000
3,090
2,780
1,990
7,500
5,300
4,300
6,300
5,600
6,240
V=
No. of Moves
100
125
175
200
500
300
250
400
475
425
High Cost – Low Cost
High Units – Low Units
3-31
The High-Low Method
Month
January
February
March
April
May
June
July
August
September
October
Material Handling Costs
$2,000
3,090
2,780
1,990
7,500
5,300
4,300
6,300
5,600
6,240
V=
No. of Moves
100
125
175
200
500
300
250
400
475
425
$7,500 – Low Cost
500 – Low Units
3-32
The High-Low Method
Month
January
February
March
April
May
June
July
August
September
October
Material Handling Costs
$2,000
3,090
2,780
1,990
7,500
5,300
4,300
6,300
5,600
6,240
V=
$7,500
No. of Moves
100
125
175
200
500
300
250
400
475
425
– $2,000
500 –
100
3-33
The High-Low Method
V=
$7,500
– $2,000
500 –
100
V = $13.75
Step 2: Using either the high cost or low cost,
solve for the total fixed cost (F).
3-34
The High-Low Method
Y =
$7,500 =
$625 =
F + V(X)
F + $13.75(500)
F
High
End
Y =
$2,000 =
$625 =
F + V(X)
F + $13.75(100)
F
Low
End
The cost formula using the high-low method is:
Total cost = $625 + ($13.75 x # of moves)
3-35
The Scatterplot Method
Material
Handling Cost
Graph A--Anderson Company
$9,000 –
8,000 –
7,000 –
6,000 –
5,000 –
4,000 –
3,000 –
2,000 –
1,000 –
5
8
10
6
9
7
2
3
4
1
|
100
|
|
200
300
Number of Moves
|
|
400
500
3-36
The Scatterplot Method
Material
Handling Cost
$9,000 –
8,000 –
7,000 –
6,000 –
5,000 –
4,000 –
3,000 –
2,000 –
1,000 –
Graph B--High-Low Line
5
8
10
6
9
7
2
3
4
1
|
100
|
|
200
300
Number of Moves
|
|
400
500
3-37
The Scatterplot Method
Graph C—One Possible
Scattergraph LIne
Material
Handling Cost
$9,000 –
8,000 –
7,000 –
6,000 –
5,000 –
4,000 –
3,000 –
2,000 –
1,000 –
5
8
10
6
9
7
2
3
4
1
|
100
|
|
200
300
Number of Moves
|
|
400
500
3-38
The Scatterplot Method
Graph A--Nonlinear Relationship
Activity
Cost
0
Activity Output
3-39
The Scatterplot Method
Graph B--Upward Shift in Cost Relationship
Activity
Cost
0
Activity Output
3-40
The Scatterplot Method
Graph C--Presence of Outliers
Activity
Cost
Outlier
0
Outlier
Activity Output
3-41
The Method of Least Squares
Annual Cost
Predicted Cost
$2,000
$2,000
3,090
2,300
2,780
2,900
1,990
3,200
7,500
6,800
5,300
4,400
4,300
3,800
6,300
5,600
5,600
6,500
6,240
5,900
Total measure of closeness
Deviation
0
790
-120
-1,10
700
$3,090
900
- 2,300
500
700
-900
340
Deviation Squared
0
624,100
14,400
1,464,100
790
x 790
490,000
810,000
250,000
490,000
810,000
115,600
5,068,200
3-42
The Method of Least Squares
Line Deviations
Material
Handling Cost
$9,000 –
8,000 –
7,000 –
6,000 –
5,000 –
4,000 –
3,000 –
2,000 –
1,000 –
0
5
8
10
6
9
7
2
1
3
4
|
100
|
|
200
300
Number of Moves
|
|
400
500
3-43
The Method of Least Squares
Month
January
February
March
April
May
June
July
August
September
October
Costs
$2,000
3,090
2,780
1,990
7,500
5,300
4,300
6,300
5,600
6,240
# Moves
100
125
175
200
500
300
250
400
475
425
Spreadsheet Data for
Anderson Company
3-44
The Method of Least Squares
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.92894908
R. Square
0.862946394
Adjusted R
0.845814693
Regression Output for Anderson Company
Square
Standard Error
Observations
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
3-45
The Method of Least Squares
The results give rise to the following equation:
Material
handling = $854.50 + ($12.39 x number of items)
cost
3-46
Coefficient of Correlation
Positive Correlation
r approaches +1
Machine Utilities
Hours
Costs
Machine Utilities
Hours
Costs
3-47
Coefficient of Correlation
Negative Correlation
r approaches –1
Hours of Industrial
Safety Accidents
Training
Hours of Industrial
Safety Accidents
Training
3-48
Coefficient of Correlation
No Correlation
r~0
Hair Accounting
Length
Grade
Hair Accounting
Length
Grade
3-49
Multiple Regression
Y = F + V1 X1 + V2 X2
X1 = Number of moves
X2 = The total distance
3-50
Multiple Regression
Month
January
February
March
April
May
June
July
August
September
October
Material Handling
Cost
$2,000
3,090
2,780
1,990
7,500
5,300
4,300
6,300
5,600
6,240
Number
of Moves
Pounds
Moved
100
125
175
200
500
300
250
400
475
425
6,000
15,000
7,800
600
29,000
23,000
17,000
25,000
12,000
22,400
3-51
Multiple Regression
Y = $507 + $7.84X 1 + $0.11X 2
= $507 + $7.84(350) + $0.11(17,000)
= $507 + $2.744 + $1,870
= $5,121
3-52
The Learning
Curve and
Nonlinear
Behavior
3-53
Cumulative
Cumulative
Cumulative Individual Units
Number
Average Time Total Time:
Time for nth
of Units
per Unit in Hours Labor Hours Unit-Labor Hours
(1)
(2)
(3) = (1) x (2)
(4)
1
100
100
100
2
80 (0.8 x 100)
160
60
3
70.21
50.63
Data
for Cumulative
Average210.63
Time Learning
Curve
4
64 (0.8 x 80)
256
45.37
with 80 Percent Learning Rate
5
59.57
297.85
41.85
6
56.17
337.02
39.17
7
53.45
374.15
37.13
8
51.20 (0.8 x 64)
409.60
35.45
16
40.96
655.36
28.06
32
32.77
1,048.64
3-54
Graph of Cumulative Total Hours Required and the
Cumulative Average time per Unit
1,200 –
1,000 –
800 –
600 –
400 –
200 –
0–
1
5
10
15
20
Units
25
30
35 36
3-55
Cumulative
Individual Unit
Cumulative
Cumulative
Number
Time for nth Unit Total Time: Average Time per
of Units
in Labor Hours Labor Hours Unit-Labor Hours
(1)
(2)
(3)
(4) = (3)/(1)
1
100
100
100
2
80 (0.8 x 100)
180
90
3
70.21
259.21 Learning
83.40
Data
for an
Incremental Unit-Time
Curve
4
64 (0.8 x 80)
314.21
78.55
with an 80 Percent Learning Rate
5
59.57
373.78
74.76
6
56.17
429.95
71.66
7
53.45
483.40
69.06
8
51.20 (0.8 x 64)
534.60
66.83
16
40.96
892.00
55.75
3-56
Managerial Judgment
Managerial judgment is
critically important in
determining cost behavior and is
by far the most widely used
method in practice.
3-57
End of
Chapter
3-58
3-59