Transcript Libby, Libby and Short - Yogyakarta State University

3 -1
CHAPTER
Activity Cost
Behavior
3 -2
Objectives
1. Define cost behavior for fixed, variable, and
mixed costs.
2. Explain the role of the resource usage model
in understanding 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.
continued
3 -3
Objectives
4. Evaluate the reliability of a cost equation.
5. Discuss the role of multiple regression in
assessing cost behavior.
6. Describe the use of managerial judgment in
determining cost behavior.
3 -4
Fixed Costs
A cost that stays the
same as output changes
is a fixed cost.
3 -5
Fixed Costs
Cutting machines are
leased for $60,000 per
year and have the
capacity to produce up
to 240,000 units a year.
3 -6
Total Costs
Total Fixed Cost Graph
$120,000
$100,000
$80,000
$60,000
$40,000
$20,000
F = $60,000
Fixed Costs
0
60 120 180 240
Units Produced (000)
Lease of
Machines
$60,000
60,000
60,000
60,000
60,000
Number
of Units
0
60,000
120,000
180,000
240,000
Units
Cost
N/A
$1.00
0.50
0.33
0.25
3 -7
Cost per Unit
Unit Fixed Cost Graph
$1.00
Fixed Costs
$0.50
$0.33
$0.25
0
60 120 180 240
Units Produced (000)
Lease of
Machines
$60,000
60,000
60,000
60,000
60,000
Number
of Units
0
60,000
120,000
180,000
240,000
Units
Cost
N/A
$1.00
0.50
0.33
0.25
3 -8
A variable cost is a cost
that, in total, varies in
direct proportion to
changes in output.
Variable
Cost
Variable Cost
As the cutting machines cut each unit,
they use 0.1 kilowatt-hour at $2.00 per
kilowatt hour. Thus, the cost of each
unit is $0.20 ($2 x 0.1).
3 -9
3 -10
Total Costs
Total Variable Cost Graph
$48,000
$36,000
Yv = .20x
Variable Cost
$24,000
$12,000
0 60 120 180 240
Units Produced (000)
Cost of
Power
$
0
12,000
24,000
36,000
48,000
Number
of Units
0
60,000
120,000
180,000
240,000
Units
Cost
$ 0
0.20
0.20
0.20
0.20
3 -11
Cost per Unit
Unit Variable Cost Graph
$0.40
$0.30
Variable Cost
$0.20
$0.10
0
60 120 180 240
Units Produced (000)
Cost of
Power
$
0
12,000
24,000
36,000
48,000
Number
of Units
0
60,000
120,000
180,000
240,000
Units
Cost
$ 0
0.20
0.20
0.20
0.20
3 -12
A mixed cost is a cost
that has both a fixed
and a variable
component.
3 -13
Sales representatives
often are paid a
salary plus a
commission on sales.
Total Costs
Mixed Cost Behavior
3 -14
$130,000
$110,000
$90,000
$70,000
$50,000
$30,000
0
40 80 120 160 180 200
Units Sold (000)
Inserts
Sold
40,000
80,000
120,000
160,000
200,000
Variable
Cost of
Selling
Fixed
Cost of
Selling
Total
Selling
Cost
Selling
Cost per
Unit
$ 20,000
40,000
60,000
80,000
100,000
$30,000
30,000
30,000
30,000
30,000
$ 50,000
70,000
90,000
110,000
130,000
$1.25
0.86
0.75
0.69
0.65
3 -15
Activity Cost Behavior Model
Input:
Materials
Energy
Labor
Activities
Activity
Output
Capital
Changes
in Input
Cost
Changes
in Output
Cost Behavior
3 -16
Flexible resources are
resources acquired as used and
needed. Materials and energy
are examples.
3 -17
Committed resources are supplied in
advance of usage. Buying or leasing a
building is an example of this form of
advance resource acquisition.
3 -18
A step cost displays a constant level
of cost for a range of output and then
jumps to a higher level of cost at
some point.
Step-Cost Behavior
3 -19
Step-Cost Behavior
Cost
$500
400
300
200
100
10
20
30
40
50
Activity Output (units)
3 -20
Step-Fixed Costs
Cost
$150,000
Normal
Operating
Range
(Relevant
Range)
100,000
50,000
2,500
5,000
Activity Usage
7,500
3 -21
Step-Cost Behavior
 Three engineers hired at $50,000 each
 Each engineer is capable of processing 2,500
change orders
 $90,000 was spent on supplies for the
engineering activity
 There were 6,000 orders processed
 The company could process as many as 7,500
orders
3 -22
Step-Cost Behavior
Available orders = Orders used + Orders unused
7,500 orders = 6,000 orders + 1,500 orders
Fixed engineering rate
= $150,000/7,500
= $20 per change order
Variable engineering rate = $90,000/6,000
= $15 per change order
3 -23
Step-Cost Behavior
The relationship between resources supplied and
resources used is expressed by the following
equation:
Resources available = Resources used + Unused
capacity
3 -24
Step-Cost Behavior
Cost of orders supplied = Cost of orders used +
Cost of unused orders
= [($20 + $15) x 6,000] + ($20
x 1,500)
= $240,000
The $30,000 of excess engineering capacity
means that a new product could be
Equal to the $150,000 spent on
introducedengineers
without and
increasing
current
the $90,000
spending
on engineering.
spent
on supplies.
3 -25
Methods for Separating Mixed Costs
The High-Low Method
The Scatterplot Method
The Method of Least Squares
Variable
Component
Fixed
Component
3 -26
The linearity assumption
assumes that variable costs
increase in direct proportion to
the number of units produced
(or activity units used).
3 -27
Methods for Separating Mixed Costs
Y = a + bx
Total Fixed
Cost
Total Cost
Variable
Cost per
Unit
Number of
Units
3 -28
The High-Low Method
Month
Setup Costs
Setup Hours
January
$1,000
100
February
1,250
200
March
2,250
300
April
2,500
400
May
3,750
500
Step 1: Solve for variable cost (b)
3 -29
The High-Low Method
Month
January
February
March
April
May
Setup Costs
$1,000
1,250
2,250
2,500
3,750
b=
Setup Hours
100
200
300
400
500
High Cost – Low Cost
High Units – Low Units
3 -30
The High-Low Method
Month
January
February
March
April
May
Setup Costs
$1,000
1,250
2,250
2,500
3,750
b=
Setup Hours
100
200
300
400
500
High
$3,750
Cost – Low Cost
High500
Units –– Low
Low Units
Units
3 -31
The High-Low Method
Month
January
February
March
April
May
Setup Costs
$1,000
1,250
2,250
2,500
3,750
b=
$3,750
Setup Hours
100
200
300
400
500
– Low
$1,000
Cost
500 – Low
100
Units
3 -32
The High-Low Method
b=
$3,750
– $1,000
500 –
100
b = $6.875
Step 2: Using either the high cost or low cost,
solve for the total fixed cost (a).
3 -33
The High-Low Method
Y =
$3,750 =
$312.50 =
a +
b (x)
a + $6.875(500)
a
High
End
Y =
$1,000 =
$312.50 =
a +
b (x)
a + $6.875(100)
a
Low
End
The cost formula using the high-low method is:
Total cost = $312.50 + ($6.875 x Setup hours)
3 -34
The Scatterplot Method
The Scatterplot Method
Nonlinear Relationship
Activity
Cost
*
*
*
*
*
0
Activity Output
3 -35
The Scatterplot Method
Upward Shift in Cost Relationship
Activity
Cost
*
*
0
*
*
*
*
Activity Output
3 -36
The Scatterplot Method
Presence of Outliers
Activity
Cost
*
*
Estimated
fixed cost
0
*
*
*
*
Estimated
regression
line
Activity Output
3 -37
LEAST SQUARE METHOD
Y = a + bX
∑XY = a ∑X + b ∑X^2 (1)
∑Y = na + b ∑X
(2)
Ekstrapolasi rumus (1) dan (2)
3 -38
The Method of Least Squares
Month
Jan
Feb
Mar
Apr
May
Setup Costs Setup Hours
1,000
100
1,250
200
2,250
300
2,500
400
3,750
500
Spreadsheet Data for
Larson Company
3 -39
The Method of Least Squares
Regression Output:
Constant
Std. Err of Y Est
R Squared
No. of Observation
Degrees of Freedom
X Coefficient(s)
Std. Err of Coef.
125
299.304749934466
0.944300518134715
5
3
6.75
0.9464847243
Regression Output for
Larson Company
3 -40
The Method of Least Squares
The results give rise to the following equation:
Setup costs = $125 + ($6.75 x Setup hours)
R2 = .944, or 94.4 percent of the variation in
setup costs is explained by the number of setup
hours variable.
3 -41
3 -42
Coefficient of Correlation
Positive Correlation
r approaches +1
Machine Utilities
Hours
Costs
Machine Utilities
Hours
Costs
3 -43
Coefficient of Correlation
Negative Correlation
r approaches -1
Hours of Industrial
Safety Accidents
Training
Hours of Industrial
Safety Accidents
Training
3 -44
Coefficient of Correlation
No Correlation
r~0
Hair Accounting
Length
Grade
Hair Accounting
Length
Grade
3 -45
Multiple Regression
TC = b0 + ( b1X1) + (b2X2) + . . .
b0 = the fixed cost or intercept
b1 = the variable rate for the first independent variable
X1 = the first independent variable
b2 = the variable rate for the second independent variable
X2 = the second independent variable
3 -46
Multiple Regression
Month
Jan
Feb
Mar
April
May
June
July
August
Sept
Oct
Nov
Dec
Mhrs
1,340
1,298
1,376
1,405
1,500
1,432
1,322
1,416
1,370
1,580
1,460
1,455
Summer
0
0
0
0
1
1
1
1
1
0
0
0
Utilities Cost
$1,688
1,636
1,734
1,770
2,390
2,304
2,166
2,284
1,730
1,991
1,840
1,833
Data for Phoenix Factory
Utilities Cost Regression
3 -47
Multiple Regression
Constant
Std Err of Y Est
R Squared
No. of Observation
Degrees of Freedom
X Coefficient(s)
Std Err of Coef.
243.1114997159
55.5082829356447
0.96717927255452
12
9
1.0971575051946
0.210226332115593
510.49073361447
32.5489464532519
Multiple Regression for Phoenix
Factory Utilities Cost
3 -48
Multiple Regression
The results gives rise to the following equation:
Utilities cost = $243.11 + $1.097(Machine hours) +
($510.49 x Summer)
R2 = .967, or 96.7 percent of the variation in utilities
cost is explained by the machine hours and summer
variables.
3 -49
Managerial Judgment
Managerial judgment is critically
important in determining cost behavior,
and it is by far the most widely used
method in practice.
3 -50
Chapter Three
The End