2. 3 -2
Cost Behavior
• describing whether costs change
as output changes
• Costs react to output changes in
many different ways.
3. 3 -3
Fixed Costs
A cost that stays the
same as output changes
is a fixed cost.
4. 3 -4
Cutting machines are
leased for $60,000 per
year and have the
capacity to produce up
to 240,000 units a year.
Fixed Costs
5. 3 -5
Lease of
Machines
Number
of Units
$60,000 0 N/A
60,000 60,000 $1.00
60,000 120,000 0.50
60,000 180,000 0.33
60,000 240,000 0.25
Units
Cost
Fixed Costs
Total Fixed Cost Graph
Total
Costs
$120,000
$100,000
$80,000
$60,000
$40,000
$20,000
60
120
180
240
0
Units Produced (000)
F = $60,000
6. 3 -6
Lease of
Machines
Number
of Units
$60,000 0 N/A
60,000 60,000 $1.00
60,000 120,000 0.50
60,000 180,000 0.33
60,000 240,000 0.25
Units
Cost
Fixed Costs
Unit Fixed Cost Graph
Cost
per
Unit
$1.00
$0.50
$0.33
$0.25
60
120
180
240
0
Units Produced (000)
8. 3 -8
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).
Variable Cost
9. 3 -9
Total Variable Cost Graph
Cost of
Power
Number
of Units
$ 0 0 $ 0
12,000 60,000 0.20
24,000 120,000 0.20
36,000 180,000 0.20
48,000 240,000 0.20
Units
Cost
Total
Costs
0
Units Produced (000)
$48,000
$36,000
$24,000
$12,000
60
120 180
240
Variable Cost
Yv = .20x
10. 3 -10
Cost of
Power
Number
of Units
$ 0 0 $ 0
12,000 60,000 0.20
24,000 120,000 0.20
36,000 180,000 0.20
48,000 240,000 0.20
Units
Cost
Variable Cost
Unit Variable Cost Graph
60
120
180
240
Units Produced (000)
$0.40
$0.30
$0.20
$0.10
0
Cost
per
Unit
11. 3 -11
A mixed cost is a cost
that has both a fixed
and a variable
component.
13. 3 -13
Inserts
Sold
Variable
Cost of
Selling
40,000 $ 20,000 $30,000 $ 50,000
$1.25
80,000 40,000 30,000 70,000 0.86
120,000 60,000 30,000 90,000 0.75
160,000 80,000 30,000 110,000 0.69
Total
Selling
Cost
Fixed
Cost of
Selling
Selling
Cost per
Unit
Mixed Cost Behavior
Total
Costs
0
Units Sold (000)
$130,000
$110,000
$90,000
$70,000
$50,000
$30,000
40 80 120 160 180 200
14. 3 -14
• in the long run, all costs are variable; short run, at least one cost
is fixed.
Time Horizon
• Every activity needs resources (e.g energy/fuel, labor, and capital)
as input, combined to produce output
Resources Needed and Output Activity
• E.g. if the activity: moving materials, the inputs: crates
(materials), fuel (energy), a forklift operator (labor), and a forklift
(capital). The output = moved materials, i.e. the number of moves.
The more moves that are made, the higher the cost of moving
Measure the inputs & outputs and determine the
impact of output changes on the activity cost.
Classifying Costs According to Behavior
15. 3 -15
Activity Cost Behavior Model
Input:
Materials
Energy
Labor
Capital
Activities
Activity
Output
Cost Behavior
Changes
in Output
Changes
in Input
Cost
16. 3 -16
Flexible resources are resources
acquired as used and needed. Materials
and energy are examples.
“the quantity of the resource supplied
(purchased) equals the quantity demanded”
no unused capacity
Activities, Resource Usage, and Cost Behavior
For example,
direct materials are frequently
purchased at the time and in the
amount needed.
17. 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.
18. 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
21. 3 -21
✔ 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
Step-Cost Behavior
22. 3 -22
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
Step-Cost Behavior
23. 3 -23
The relationship between resources supplied and
resources used is expressed by the following
equation:
Resources available = Resources used + Unused
capacity
Step-Cost Behavior
24. 3 -24
Cost of orders supplied = Cost of orders used +
Cost of unused orders
= [($20 + $15) x 6,000] + ($20
x 1,500)
= $240,000
Equal to the $150,000 spent on
engineers and the $90,000
spent on supplies.
The $30,000 of excess engineering capacity
means that a new product could be
introduced without increasing current
spending on engineering.
Step-Cost Behavior
25. 3 -25
• The High-Low Method
• The Scatterplot Method
• The Method of Least Squares
Methods for Separating Mixed Costs
Variable
Component
Fixed
Component
26. 3 -26
The linearity assumption
assumes that variable costs
increase in direct proportion to
the number of units produced
(or activity units used).
27. 3 -27
Methods for Separating Mixed Costs
Y = a + bx
Total Cost
Total Fixed
Cost
Variable
Cost per
Unit
Number of
Units
28. 3 -28
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
The High-Low Method
Step 1: Solve for variable cost (b)
29. 3 -29
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
b =
High Cost – Low Cost
High Units – Low Units
The High-Low Method
30. 3 -30
b =
High Cost – Low Cost
High Units – Low Units
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
The High-Low Method
b =
$3,750 – Low Cost
500 – Low Units
31. 3 -31
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
b =
$3,750 – Low Cost
500 – Low Units
b =
$3,750 – $1,000
500 – 100
The High-Low Method
32. 3 -32
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).
The High-Low Method
33. 3 -33
Y = a + b (x)
$3,750 = a + $6.875(500)
$312.50 = a
High
End
Y = a + b (x)
$1,000 = a + $6.875(100)
$312.50 = a
Low
End
The cost formula using the high-low
method is:
Total cost = $312.50 + ($6.875 x Setup hours)
The High-Low Method
37. 3 -37
Activity
Cost
0 Activity Output
*
*
*
*
*
*
The Scatterplot Method
Presence of Outliers
Estimated
regression
line
Estimated
fixed cost
38. 3 -38
The Method of Least Squares
Spreadsheet Data for
Larson Company
39. 3 -39
The Method of Least Squares
Regression Output for
Larson Company
40. 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.
41. 3 -41
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
Multiple Regression
44. 3 -44
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.
Multiple Regression
45. 3 -45
Managerial Judgment
Managerial judgment is critically
important in determining cost behavior,
and it is by far the most widely used
method in practice.
