Calculate Total Cost And Per-Unit Cost © Dale R. Geiger 20111.

© Dale R. Geiger 2011 1

Calculate Total Cost And Per-Unit Cost

Principles of Cost Analysis and Management


How does total cost change as level of activity changes?


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


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


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


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


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


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


Variable Cost Expression

• Total Variable Cost = Variable $Cost per Unit * # Units

• Variable $Cost per Unit = Sum of all Variable inputs


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?




• 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?



• 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



• 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


Check on Learning

• What is the definition of a variable cost?• What is the generic cost expression for total

variable cost?

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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

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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$


At 10 units, Cost is $100


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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$




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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$



750


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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


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0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 800

2

4

6

8

10

12$


$10 per unit


Unit Cost = Total Variable Cost/# Units


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0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 800

2

4

6

8

10

12$


$10 per unit


Unit Cost = Total Variable Cost/# Units



Check on Learning

• How is Total variable cost represented on the graph?

• What is the generic cost expression for Variable cost per unit?


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


Fixed Cost Expression

• Total Fixed $Cost = Sum of all Fixed Inputs

• Fixed $Cost per Unit = Total Fixed $Cost / # Units


Fixed Cost Example


• 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?


Fixed Cost Example


• 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?


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


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


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


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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


$124,000



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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


$124,000



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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


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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




$124,000/40 units or $3,100 per unit

$3,100


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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




$124,000/75 units or $1,653 per unit

$1,653



Check on Learning

• How is Total fixed cost represented on the graph?

• How is Unit fixed cost represented on the graph?


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?




• Which costs are fixed? Shop Rent $5,000Staff Salaries 5,000Total Fixed $10,000




• Which costs are variable?Parts per repair $220Commission per repair 200Total $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$420 per repair*200 repairs+$10,000 = $85,000




• 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


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?


Practical Exercises

Calculate Total Cost And Per-Unit Cost © Dale R. Geiger 20111.

Documents

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