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 c
Trang 1Calculate Total Cost And
Per-Unit Cost
Principles of Cost Analysis and
Management
Trang 2How does total cost change as level of
activity changes?
Trang 3Terminal 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
Trang 4Why 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
Trang 5What is Cost Relationship?
• Describes the change in cost that occurs with
Trang 6What 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
Trang 7Which 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
Trang 8Linear 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
Trang 9Variable Cost Expression
• Total Variable Cost =
Variable $Cost per Unit * # Units
• Variable $Cost per Unit =
Sum of all Variable inputs
Trang 10Variable Cost Expression
• Total Variable Cost =
Variable $Cost per Unit * # Units
• Variable $Cost per Unit =
Sum of all Variable inputs
Trang 11Variable Cost Example
• The Smoky Mountain Inn Bed and Breakfast reports the following cost information:
Depreciation on building $60,000 per year
Maintenance person’s salary $30,000 per year
Cleaning person’s salary $24,000 per year
Real estate taxes $10,000 per year
Laundry service $4.00 per person per night
Food $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?
Trang 12Variable Cost Example
• The Smoky Mountain Inn Bed and Breakfast reports the following cost information:
Depreciation on building $60,000 per year
Maintenance person’s salary $30,000 per year
Cleaning person’s salary $24,000 per year
Real estate taxes $10,000 per year
Laundry service $4.00 per person per night
Food $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?
Trang 13Variable Cost Example
• The Smoky Mountain Inn Bed and Breakfast reports the following cost information:
Depreciation on building $60,000 per year
Maintenance person’s salary $30,000 per year
Cleaning person’s salary $24,000 per year
Real estate taxes $10,000 per year
Laundry service $4.00 per person per night
Food $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?
Trang 14Variable 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
Trang 15Variable 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
Trang 16Check on Learning
• What is the definition of a variable cost?
• What is the generic cost expression for total variable cost?
Trang 17Graph of Total Variable Cost
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 0
X Axis = Number of units
As # units increases, total variable cost increases 17
Trang 18Graph of Total Variable Cost
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 0
At 10 units, Cost is $100
Trang 19Graph of Total Variable Cost
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 0
X Axis = Number of units
As # units increases, total variable cost increases
At 40 units, Cost is $400
At 40 units, Cost is $400
19
Trang 20Graph of Total Variable Cost
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 0
At 75 units, Cost is $750 750
Trang 21Graph of Unit Variable Cost
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 0
$ Unit Cost = Total Variable Cost/# Units
Unit cost at 10 units =
X Axis = Number of units
As # units increases, Unit variable cost remains the same 21
Trang 22Graph of Unit Variable Cost
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 0
X Axis = Number of units
Unit Cost = Total Variable Cost/# Units
Trang 23Graph of Unit Variable Cost
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 0
X Axis = Number of units
As # units increases, Unit variable cost remains the same
Unit Cost = Total Variable Cost/# Units
23
Trang 24Check on Learning
• How is Total variable cost represented on the graph?
• What is the generic cost expression for
Variable cost per unit?
Trang 25Linear 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
Trang 26Fixed Cost Expression
• Total Fixed $Cost =
Sum of all Fixed Inputs
• Fixed $Cost per Unit =
Total Fixed $Cost / # Units
Trang 27Fixed Cost Expression
• Total Fixed $Cost =
Sum of all Fixed Inputs
• Fixed $Cost per Unit =
Total Fixed $Cost / # Units
Trang 28Fixed Cost Example
• The Smoky Mountain Inn Bed and Breakfast reports the following cost information:
Depreciation on building $60,000 per year
Maintenance person’s salary $30,000 per year
Cleaning person’s salary $24,000 per year
Real estate taxes $10,000 per year
Laundry service $4.00 per person per night
Food $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?
Trang 29Fixed Cost Example
• The Smoky Mountain Inn Bed and Breakfast reports the following cost information:
Depreciation on building $60,000 per year
Maintenance person’s salary $30,000 per year
Cleaning person’s salary $24,000 per year
Real estate taxes $10,000 per year
Laundry service $4.00 per person per night
Food $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?
Trang 30Fixed Cost Example
• The Smoky Mountain Inn Bed and Breakfast reports the following cost information:
Depreciation on building $60,000 per year
Maintenance person’s salary $30,000 per year
Cleaning person’s salary $24,000 per year
Real estate taxes $10,000 per year
Laundry service $4.00 per person per night
Food $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?
Trang 31Fixed 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
Trang 32Fixed 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
Trang 33Check on Learning
• What is the definition of a fixed cost?
• What is the generic cost expression for fixed cost per unit?
Trang 34Graph of Total Fixed Cost
$124,000
At 10 units, Total Fixed Cost is
$124,000
X Axis = Number of units
Trang 35Graph of Total Fixed Cost
$124,000
At 40 units, Total Fixed Cost is
$124,000
X Axis = Number of units
As # units increases, Total Fixed cost remains the same 35
Trang 36Graph of Total Fixed Cost
$124,000
At 75 units, Total Fixed Cost is
$124,000
X Axis = Number of units
Trang 37Graph of Unit Fixed Cost
$25,000 Unit Cost = Total Fixed Cost/# Units
X Axis = Number of units
As # units increases, Unit Fixed cost decreases
At 10 units, Unit Fixed Cost =
$124,000/10 units
or $12,400 per unit
At 10 units, Unit Fixed Cost =
$124,000/10 units
or $12,400 per unit
$12,400
37
Trang 38Graph of Unit Fixed Cost
$25,000 Unit Cost = Total Fixed Cost/# Units
X Axis = Number of units
At 40 units, Unit Fixed Cost =
$124,000/40 units
or $3,100 per unit
At 40 units, Unit Fixed Cost =
$124,000/40 units
or $3,100 per unit
$3,100
Trang 39Graph of Unit Fixed Cost
$25,000 Unit Cost = Total Fixed Cost/# Units
X Axis = Number of units
As # units increases, Unit Fixed cost decreases
At 75 units, Unit Fixed Cost =
$124,000/75 units
or $1,653 per unit
At 75 units, Unit Fixed Cost =
$124,000/75 units
or $1,653 per unit
$1,653
39
Trang 41averages $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?
Trang 42Demonstration 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?
Trang 43Demonstration 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 $220
Total $420
Trang 44averages $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
Trang 45averages $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
Trang 46averages $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
Trang 47averages $200 per repair
• What is unit cost for 100 repairs? 200 repairs?
Unit cost = Total cost / # repairs
Total @100 repairs $52,000 / 100 repairs = $520 Total @200 repairs $94,000 / 200 repairs = $470
Trang 48averages $200 per repair
• What is unit cost for 100 repairs? 200 repairs?
Unit cost = Total cost / # repairs Total @100 repairs $52,000 / 100 repairs = $520
Total @200 repairs $94,000 / 200 repairs = $470
Trang 49averages $200 per repair
• What is unit cost for 100 repairs? 200 repairs?
Unit cost = Total cost / # repairs Total @100 repairs $52,000 / 100 repairs = $520 Total @200 repairs $94,000 / 200 repairs = $470
Trang 50Check 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?
Trang 51Practical Exercises