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© Dale R. Geiger 2011 1
Calculate Total Cost And Per-Unit Cost
Principles of Cost Analysis and Management
© Dale R. Geiger 2011 3
Terminal Learning Objective
• Task: Calculate Total Cost And Per-Unit Cost For A Given Production Volume
• Condition: You are a cost advisor technician with access to all regulations/course handouts, and awareness of Operational Environment (OE)/Contemporary Operational Environment (COE) variables and actors.
• Standard: With at least 80% accuracy:• Differentiate between fixed and variable costs• Express total and per-unit variable cost in an equation• Graph total and per-unit variable cost• Express total and per-unit fixed costs in an equation• Graph total and per-unit fixed costs
© Dale R. Geiger 2011 4
Why Study Cost Relationships?
• Understanding what drives cost helps to understand how to reduce cost
• Recognizing cost relationships helps to define what views of cost are useful
© Dale R. Geiger 2011 5
What is Cost Relationship?
• Describes the change in cost that occurs with a change in a variable
• Examples: • As number of students in class increases, total cost
of class increases• As snowfall increases, cost of snow removal
increases• As number of miles driven increases, total cost of
trip increases
© Dale R. Geiger 2011 6
What is Cost Expression?
• Communicates a cost relationship using verbal, numerical and mathematical symbols
• Use plain language rather than variables x, y, z, etc. • Use math symbols • Add (+)• Subtract (–)• Multiply (*)• Divide (/)
• Example:Cost of hotel stay = Cost per day * # of days
© Dale R. Geiger 2011 7
Which Cost Expression is Useful?
• Sometimes it is useful to know Total Cost• Relevant cost of all inputs required to achieve
desired output• Example: Cost of PCAM = instructor pay + course
materials + classroom facilities + students’ pay• Sometimes it is useful to know Unit Cost• Unit cost = Total cost / # units• Example: Cost to train one student
© Dale R. Geiger 2011 8
Linear Cost Relationships
• The simplest cost relationships can be represented by a straight line
• Variable Costs - Costs that increase in direct proportion with the volume produced or consumed• Total variable cost = Upward sloping line• Unit variable cost = Horizontal line
• Example: Cost of materials used increases in direct proportion to number of units produced
© Dale R. Geiger 2011 9
Variable Cost Expression
• Total Variable Cost = Variable $Cost per Unit * # Units
• Variable $Cost per Unit = Sum of all Variable inputs
© Dale R. Geiger 2011 10
Variable Cost Expression
• Total Variable Cost = Variable $Cost per Unit * # Units
• Variable $Cost per Unit = Sum of all Variable inputs
© Dale R. Geiger 2011 11
Variable Cost Example
• The Smoky Mountain Inn Bed and Breakfast reports the following cost information:Depreciation on building $60,000 per yearMaintenance person’s salary $30,000 per yearCleaning person’s salary $24,000 per yearReal estate taxes $10,000 per yearLaundry service $4.00 per person per nightFood $6.00 per person per night
• What is the unit of output?• Which costs will change as output changes?• What is the cost expression for variable cost per unit?• For Total Variable Cost?
© Dale R. Geiger 2011 12
Variable Cost Example
• The Smoky Mountain Inn Bed and Breakfast reports the following cost information:Depreciation on building $60,000 per yearMaintenance person’s salary $30,000 per yearCleaning person’s salary $24,000 per yearReal estate taxes $10,000 per yearLaundry service $4.00 per person per nightFood $6.00 per person per night
• What is the unit of output? “person per night”• Which costs will change as output changes?• What is the cost expression for variable cost per unit?• For Total Variable Cost?
© Dale R. Geiger 2011 13
Variable Cost Example
• The Smoky Mountain Inn Bed and Breakfast reports the following cost information:Depreciation on building $60,000 per yearMaintenance person’s salary $30,000 per yearCleaning person’s salary $24,000 per yearReal estate taxes $10,000 per yearLaundry service $4.00 per person per nightFood $6.00 per person per night
• What is the unit of output? “person per night”• Which costs will change as output changes?• What is the cost expression for variable cost per unit?• For Total Variable Cost?
© Dale R. Geiger 2011 14
Variable Cost Example
• What is the cost expression for variable cost per person per night?$4 laundry + $6 food = $10 per person/night
• What is the cost expression for Total variable cost?$10 per person per night * # person/nights
© Dale R. Geiger 2011 15
Variable Cost Example
• What is the cost expression for variable cost per person per night?$4 laundry + $6 food = $10 per person-night
• What is the cost expression for Total variable cost?
$10 per person per night * # person-night
© Dale R. Geiger 2011 16
Check on Learning
• What is the definition of a variable cost?• What is the generic cost expression for total
variable cost?
17
Graph of Total Variable Cost
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 800
100
200
300
400
500
600
700
800$
X Axis = Number of unitsAs # units increases, total variable cost increases
© Dale R. Geiger 2011
18
Graph of Total Variable Cost
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 800
100
200
300
400
500
600
700
800$
X Axis = Number of unitsAs # units increases, total variable cost increases
At 10 units, Cost is $100
© Dale R. Geiger 2011
19
Graph of Total Variable Cost
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 800
100
200
300
400
500
600
700
800$
X Axis = Number of unitsAs # units increases, total variable cost increases
At 40 units, Cost is $400
© Dale R. Geiger 2011
20
Graph of Total Variable Cost
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 800
100
200
300
400
500
600
700
800$
X Axis = Number of unitsAs # units increases, total variable cost increases
At 75 units, Cost is $750
750
© Dale R. Geiger 2011
21
Graph of Unit Variable Cost
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 800
2
4
6
8
10
12$Unit Cost = Total Variable Cost/# Units
Unit cost at 10 units = $100/10 units or
$10 per unit
X Axis = Number of unitsAs # units increases, Unit variable cost remains the same
© Dale R. Geiger 2011
22
Graph of Unit Variable Cost
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 800
2
4
6
8
10
12$
Unit cost at 40 units = $400/40 units or
$10 per unit
X Axis = Number of unitsAs # units increases, Unit variable cost remains the same
Unit Cost = Total Variable Cost/# Units
© Dale R. Geiger 2011
23
Graph of Unit Variable Cost
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 800
2
4
6
8
10
12$
Unit cost at 75 units = $750/75 units or
$10 per unit
X Axis = Number of unitsAs # units increases, Unit variable cost remains the same
Unit Cost = Total Variable Cost/# Units
© Dale R. Geiger 2011
© Dale R. Geiger 2011 24
Check on Learning
• How is Total variable cost represented on the graph?
• What is the generic cost expression for Variable cost per unit?
© Dale R. Geiger 2011 25
Linear Cost Relationships
• Fixed Costs - Costs that do not change with the volume produced or consumed• Total fixed cost = Horizontal line
• Unit Fixed Cost is non-linear
• Example: The cost of the instructor remains the same regardless of the number of students in the class
© Dale R. Geiger 2011 26
Fixed Cost Expression
• Total Fixed $Cost = Sum of all Fixed Inputs
• Fixed $Cost per Unit = Total Fixed $Cost / # Units
© Dale R. Geiger 2011 27
Fixed Cost Expression
• Total Fixed $Cost = Sum of all Fixed Inputs
• Fixed $Cost per Unit = Total Fixed $Cost / # Units
© Dale R. Geiger 2011 28
Fixed Cost Example
• The Smoky Mountain Inn Bed and Breakfast reports the following cost information:Depreciation on building $60,000 per yearMaintenance person’s salary $30,000 per yearCleaning person’s salary $24,000 per yearReal estate taxes $10,000 per yearLaundry service $4.00 per person per nightFood $6.00 per person per night
• What is the unit of output?• Which costs will NOT change as output changes?• What is the cost expression for Total Fixed Cost?• For Fixed Cost per Unit?
© Dale R. Geiger 2011 29
Fixed Cost Example
• The Smoky Mountain Inn Bed and Breakfast reports the following cost information:Depreciation on building $60,000 per yearMaintenance person’s salary $30,000 per yearCleaning person’s salary $24,000 per yearReal estate taxes $10,000 per yearLaundry service $4.00 per person per nightFood $6.00 per person per night
• What is the unit of output? “per person per night”• Which costs will NOT change as output changes?• What is the cost expression for Total Fixed Cost?• For Fixed Cost per Unit?
© Dale R. Geiger 2011 30
Fixed Cost Example
• The Smoky Mountain Inn Bed and Breakfast reports the following cost information:Depreciation on building $60,000 per yearMaintenance person’s salary $30,000 per yearCleaning person’s salary $24,000 per yearReal estate taxes $10,000 per yearLaundry service $4.00 per person per nightFood $6.00 per person per night
• What is the unit of output? “per person per night”• Which costs will NOT change as output changes?• What is the cost expression for Total Fixed Cost?• For Fixed Cost per Unit?
© Dale R. Geiger 2011 31
Fixed Cost Example
• What is the cost expression for Total Fixed Cost?$60,000 depreciation + $30,000 maintenance
salary + $24,000 cleaning salary + $10,000 taxes = $124,000
• What is the cost expression for Fixed Cost per Unit?
$124,000 / # person/nights
© Dale R. Geiger 2011 32
Fixed Cost Example
• What is the cost expression for Total Fixed Cost?$60,000 depreciation + $30,000 maintenance
salary + $24,000 cleaning salary + $10,000 taxes = $124,000
• What is the cost expression for Fixed Cost per Unit?
$124,000 / # person-nights
© Dale R. Geiger 2011 33
Check on Learning
• What is the definition of a fixed cost?• What is the generic cost expression for fixed
cost per unit?
34
Graph of Total Fixed Cost
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80$0
$20,000
$40,000
$60,000
$80,000
$100,000
$120,000
$140,000
At 10 units, Total Fixed Cost is
$124,000
X Axis = Number of unitsAs # units increases, Total Fixed cost remains the same
© Dale R. Geiger 2011
35
Graph of Total Fixed Cost
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80$0
$20,000
$40,000
$60,000
$80,000
$100,000
$120,000
$140,000
At 40 units, Total Fixed Cost is
$124,000
X Axis = Number of unitsAs # units increases, Total Fixed cost remains the same
© Dale R. Geiger 2011
36
Graph of Total Fixed Cost
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80$0
$20,000
$40,000
$60,000
$80,000
$100,000
$120,000
$140,000
At 75 units, Total Fixed Cost is
$124,000
X Axis = Number of unitsAs # units increases, Total Fixed cost remains the same
© Dale R. Geiger 2011
37
Graph of Unit Fixed Cost
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80$0
$5,000
$10,000
$15,000
$20,000
$25,000Unit Cost = Total Fixed Cost/# Units
X Axis = Number of unitsAs # units increases, Unit Fixed cost decreases
At 10 units, Unit Fixed Cost =
$124,000/10 units or $12,400 per unit
$12,400
© Dale R. Geiger 2011
38
Graph of Unit Fixed Cost
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80$0
$5,000
$10,000
$15,000
$20,000
$25,000Unit Cost = Total Fixed Cost/# Units
X Axis = Number of unitsAs # units increases, Unit Fixed cost decreases
At 40 units, Unit Fixed Cost =
$124,000/40 units or $3,100 per unit
$3,100
© Dale R. Geiger 2011
39
Graph of Unit Fixed Cost
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80$0
$5,000
$10,000
$15,000
$20,000
$25,000Unit Cost = Total Fixed Cost/# Units
X Axis = Number of unitsAs # units increases, Unit Fixed cost decreases
At 75 units, Unit Fixed Cost =
$124,000/75 units or $1,653 per unit
$1,653
© Dale R. Geiger 2011
© Dale R. Geiger 2011 40
Check on Learning
• How is Total fixed cost represented on the graph?
• How is Unit fixed cost represented on the graph?
© Dale R. Geiger 2011 41
Demonstration Problem
• A vehicle repair shop incurs an average parts cost per repair of $220. Shop rent is $5,000 per month. Staff salaries are $5,000 per month and technicians earn a commission on repairs that averages $200 per repair.
• Which costs are fixed? • Which are variable?• What is total cost of 100 repairs? 200 repairs? • What is unit cost for 100 repairs? 200 repairs?
© Dale R. Geiger 2011 42
Demonstration Problem
• A vehicle repair shop incurs an average parts cost per repair of $220. Shop rent is $5,000 per month. Staff salaries are $5,000 per month and technicians earn a commission on repairs that averages $200 per repair.
• Which costs are fixed? Shop Rent $5,000Staff Salaries 5,000Total Fixed $10,000
© Dale R. Geiger 2011 43
Demonstration Problem
• A vehicle repair shop incurs an average parts cost per repair of $220. Shop rent is $5,000 per month. Staff salaries are $5,000 per month and technicians earn a commission on repairs that averages $200 per repair.
• Which costs are variable?Parts per repair $220Commission per repair 200Total $420
© Dale R. Geiger 2011 44
Demonstration Problem
• A vehicle repair shop incurs an average parts cost per repair of $220. Shop rent is $5,000 per month. Staff salaries are $5,000 per month and technicians earn a commission on repairs that averages $200 per repair.
• What is total cost of 100 repairs? 200 repairs? Total cost= $420 per repair * # repairs + $10,000$420 per repair*100 repairs+$10,000 = $52,000$420 per repair*200 repairs+$10,000 = $85,000
© Dale R. Geiger 2011 45
Demonstration Problem
• A vehicle repair shop incurs an average parts cost per repair of $220. Shop rent is $5,000 per month. Staff salaries are $5,000 per month and technicians earn a commission on repairs that averages $200 per repair.
• What is total cost of 100 repairs? 200 repairs? Total cost= $420 per repair * # repairs + $10,000$420 per repair*100 repairs+$10,000 = $52,000$420 per repair*200 repairs+$10,000 = $85,000
© Dale R. Geiger 2011 46
Demonstration Problem
• A vehicle repair shop incurs an average parts cost per repair of $220. Shop rent is $5,000 per month. Staff salaries are $5,000 per month and technicians earn a commission on repairs that averages $200 per repair.
• What is total cost of 100 repairs? 200 repairs? Total cost= $420 per repair * # repairs + $10,000$420 per repair*100 repairs+$10,000 = $52,000$420 per repair*200 repairs+$10,000 = $94,000
© Dale R. Geiger 2011 47
Demonstration Problem
• A vehicle repair shop incurs an average parts cost per repair of $220. Shop rent is $5,000 per month. Staff salaries are $5,000 per month and technicians earn a commission on repairs that averages $200 per repair.
• What is unit cost for 100 repairs? 200 repairs?Unit cost = Total cost / # repairs
Total @100 repairs $52,000 / 100 repairs = $520Total @200 repairs $94,000 / 200 repairs = $470
© Dale R. Geiger 2011 48
Demonstration Problem
• A vehicle repair shop incurs an average parts cost per repair of $220. Shop rent is $5,000 per month. Staff salaries are $5,000 per month and technicians earn a commission on repairs that averages $200 per repair.
• What is unit cost for 100 repairs? 200 repairs?Unit cost = Total cost / # repairs
Total @100 repairs $52,000 / 100 repairs = $520Total @200 repairs $94,000 / 200 repairs = $470
© Dale R. Geiger 2011 49
Demonstration Problem
• A vehicle repair shop incurs an average parts cost per repair of $220. Shop rent is $5,000 per month. Staff salaries are $5,000 per month and technicians earn a commission on repairs that averages $200 per repair.
• What is unit cost for 100 repairs? 200 repairs?Unit cost = Total cost / # repairs
Total @100 repairs $52,000 / 100 repairs = $520Total @200 repairs $94,000 / 200 repairs = $470
© Dale R. Geiger 2011 50
Check on Learning
• What happens to total variable cost as number of units produced increases?
• What happens to unit fixed cost as number of units produced increases?