1. Principles of Cost Analysis and Management
Calculate Total Cost and Per-Unit Cost Given Various Production Volumes
Principles of Cost Analysis and Management

2. Terminal Learning Objective
Action: Calculate Total Cost and Per-Unit Cost Given Various Production Volumes
Condition: FM Leaders in a classroom environment working individually and as a member of a small group, using doctrinal and administrative publications, self-study exercises, personal experiences, practical exercises, handouts, and discussion.
Standard: With at least 80% accuracy (70% for international Learners):
Interpret Fixed and Variable Costs
Calculate Total and Per-Unit Variable Cost in an Equation
Calculate Graph Total and Per-Unit Fixed Costs

3. 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

4. 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.

5. 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

6. 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

7. LSA #1 Check on Learning
Q1. True or False: We should study Cost Relationships to understand what drives cost helps to reduce cost. A1. Q2. True or False: Cost Relationship describes the change in cost that occurs with a change in a variable. A2. Q3. True or False: Cost Expression communicates a cost relationship using verbal, numerical and mathematical symbols. A3.
Q1. True or False: We should study Cost Relationships to understand what drives cost helps to reduce cost.
A1. True
A1. False:
Q2. True or False: Cost Relationship describes the change in cost that occurs with a change in a variable.
A2. True
A2. False:
Q3. True or False: Cost Expression communicates a cost relationship using verbal, numerical and mathematical symbols.
A3. True
A3. False:

8. LSA #1 Summary
Introduced the understanding of what drives cost helps and how to reduce cost, discussed the Cost relationship and cost that occurs with a change in a variable, cost expression relationship using verbal, numerical and mathematical symbols, and which are useful.

9. 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

10. Variable Cost Expression
Total Variable Cost =
Variable $Cost per Unit * # Units
Variable $Cost per Unit =
Sum of all Variable inputs
Total Variable Cost =
Variable $Cost per Unit * # Units
Variable $Cost per Unit =
Sum of all Variable inputs

11. Variable 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?

12. Variable Cost Example (Cont.)
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?

13. Variable Cost Example (Cont.)
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?

14. Variable Cost Example (Cont.)
What is the cost expression for variable cost per person per night?
$son/night
What is the cost expression for Total variable cost?
$10 per person per night * # person/nights
$4 laundry + $6 food = $10 per person-night
$10 per person per night * # person-night

15. Graph of Total Variable Cost$
750
At 75 units, Cost is $750
At 40 units, Cost is $400
At 10 units, Cost is $100
X Axis = Number of units
As # units increases, total variable cost increases

16. Unit Variable Cost Graph (Cont.)
Unit Cost = Total Variable Cost/# Units $
Unit cost at 75 units = $750/75 units or
$10 per unit
Unit cost at 10 units = $100/10 units or
$10 per unit
Unit cost at 40 units = $400/40 units or
$10 per unit
X Axis = Number of units
As # units increases, Unit variable cost remains the same

17. LSA #2 Check on Learning
Q1. How is Total variable cost represented on the graph? A1. Q2. What is the generic cost expression for Variable cost per unit? A2. Q3. What is the definition of a variable cost? A3. Q4. What is the generic cost expression for total variable cost? A4.
Q1. How is Total variable cost represented on the graph?
A1. It is represented by an upward sloping line
Q2. What is the generic cost expression for Variable cost per unit?
A2. Total variable cost / # units
Q3. What is the definition of a variable cost?
A3. A cost that increases in direct proportion with the volume produced or consumed
Q4. What is the generic cost expression for total variable cost?
A4. Variable $Cost per Unit * # Units

18. LSA #2 Summary
During this lesson, we discussed variable expression in an equation using examples and graphs.

19. 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

20. Fixed Cost Expression Total Fixed $Cost = Sum of all Fixed Inputs
Fixed $Cost per Unit =
Total Fixed $Cost / # Units
Total Fixed $Cost =
Sum of all Fixed Inputs
Fixed $Cost per Unit =
Total Fixed $Cost / # Units

21. Fixed 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?

22. Fixed Cost Example (Cont.)
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?

23. Fixed Cost Example (Cont.)
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?

24. Fixed Cost Example (Cont.)
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
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

25. Graph of Total Fixed Cost
At 75 units, Total Fixed Cost is $124,000
At 40 units, Total Fixed Cost is $124,000
At 10 units, Total Fixed Cost is $124,000
X Axis = Number of units
As # units increases, Total Fixed cost remains the same

26. Graph of Unit Fixed Cost
Unit Cost = Total Fixed Cost/# Units
At 10 units, Unit Fixed Cost = $124,000/10 units or $12,400 per unit
At 40 units, Unit Fixed Cost = $124,000/40 units or $3,100 per unit
At 75 units, Unit Fixed Cost = $124,000/75 units or $1,653 per unit
$12,400
$3,100
$1,653
X Axis = Number of units
As # units increases, Unit Fixed cost decreases

27. 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?

28. Demonstration Problem (Cont.)
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
What is unit cost for 100 repairs? 200 repairs?
Unit cost = Total cost / # repairs
repairs $52,000 / 100 repairs = $520
repairs $94,000 / 200 repairs = $470
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
What is unit cost for 100 repairs? 200 repairs?
Unit cost = Total cost / # repairs
repairs $52,000 / 100 repairs = $520
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
Which costs are fixed?
Shop Rent $5,000
Staff Salaries ,000
Total Fixed $10,000
Which costs are variable?
Parts per repair $220
Commission per repair 200
Total $420
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

29. Demo Check on Learning
Q1. What happens to total variable cost as number of units produced increases?
A1.
Q2. What happens to unit fixed cost as number of units produced increases?
A2.
Q1. What happens to total variable cost as number of units produced increases?
A1. It increases (linear, upward sloping)
Q2. What happens to unit fixed cost as number of units produced increases?
A2. It decreases (spread over more units)

30. LSA #3 Check on Learning
Q1. How is Total fixed cost represented on the graph?
A1.
Q2. How is Unit fixed cost represented on the graph? As a concave downward curve.
A2.
Q3. What is the definition of a fixed cost?
A3.
Q4. What is the generic cost expression for fixed cost per unit?
A4.
Q1. How is Total fixed cost represented on the graph?
A1. As a horizontal line. As number of units increases, total fixed cost remains the same.
Q2. How is Unit fixed cost represented on the graph? As a concave downward curve.
A2. As number of units increases, unit fixed cost decreases.
Q3. What is the definition of a fixed cost?
A3. A cost that does not change with the volume produced or consumed.
Q4. What is the generic cost expression for fixed cost per unit?
A4. Total Fixed $Cost / # Units.

31. LSA #3 Summary
During this lesson, we went over and discussed the graph of unit fixed cost and total per-unit fixed costs in an equation using examples. We further went into and conducted via a demonstration problem the calculation for total cost and per-unit cost for a given production volume.

32. TLO Summary
Action: Calculate Total Cost and Per-Unit Cost Given Various Production Volumes
Condition: FM Leaders in a classroom environment working individually and as a member of a small group, using doctrinal and administrative publications, self-study exercises, personal experiences, practical exercises, handouts, and discussion.
Standard: With at least 80% accuracy (70% for international Learners):
Interpret Fixed and Variable Costs
Calculate Total and Per-Unit Variable Cost in an Equation
Calculate Graph Total and Per-Unit Fixed Costs