Calculate Total Cost And PerUnit Cost Principles of

How does total cost change as level of activity changes? © Dale R. Geiger

Terminal Learning Objective • Task: Calculate Total Cost And Per-Unit Cost For A Given

Why Study Cost Relationships? • Understanding what drives cost helps to understand how to

What is Cost Relationship? • Describes the change in cost that occurs with a

What is Cost Expression? • Communicates a cost relationship using verbal, numerical and mathematical

Which Cost Expression is Useful? • Sometimes it is useful to know Total Cost

Linear Cost Relationships • The simplest cost relationships can be represented by a straight

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

Variable Cost Example • The Smoky Mountain Inn Bed and Breakfast reports the following

Variable Cost Example • What is the cost expression for variable cost person per

Check on Learning • What is the definition of a variable cost? • What

Graph of Total Variable Cost $ 800 700 600 500 400 300 200 100

Graph of Total Variable Cost $ 800 700 600 500 400 At 10 units,

Graph of Total Variable Cost $ 800 700 600 500 400 At 40 units,

Graph of Total Variable Cost $ 800 750 700 600 500 At 75 units,

Graph of Unit Variable Cost Unit Cost = Total Variable Cost/# Units $ 12

Check on Learning • How is Total variable cost represented on the graph? •

Linear Cost Relationships • Fixed Costs - Costs that do not change with the

Fixed Cost Expression • Total Fixed $Cost = Sum of all Fixed Inputs •

Fixed Cost Example • The Smoky Mountain Inn Bed and Breakfast reports the following

Fixed Cost Example • What is the cost expression for Total Fixed Cost? $60,

Check on Learning • What is the definition of a fixed cost? • What

Graph of Total Fixed Cost $140 000 $120 000 $100 000 At 10 units,

Graph of Total Fixed Cost $140 000 $120 000 $100 000 At 40 units,

Graph of Total Fixed Cost $140 000 $120 000 $100 000 At 75 units,

Graph of Unit Fixed Cost Unit Cost = Total Fixed Cost/# Units $25 000

Check on Learning • How is Total fixed cost represented on the graph? •

Demonstration Problem • A vehicle repair shop incurs an average parts cost per repair

Check on Learning • What happens to total variable cost as number of units

Practical Exercises © Dale R. Geiger 2011 51

Slides: 51

Download presentation

Calculate Total Cost And Per-Unit Cost Principles of Cost Analysis and Management © Dale R. Geiger 2011 1

How does total cost change as level of activity changes? © Dale R. Geiger 2011 2

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 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 © Dale R. Geiger 2011 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 © Dale R. Geiger 2011 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 © Dale R. Geiger 2011 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 © Dale R. Geiger 2011 7

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 8

Variable Cost Expression • Total Variable Cost = Variable $Cost per Unit * # Units • Variable $Cost per Unit = Sum of all Variable inputs © 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 Example • The Smoky Mountain Inn Bed and Breakfast reports the following cost information: Depreciation on building Maintenance person’s salary Cleaning person’s salary Real estate taxes Laundry service Food • • $60, 000 per year $30, 000 per year $24, 000 per year $10, 000 per year $4. 00 person per night $6. 00 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 11

Variable Cost Example • The Smoky Mountain Inn Bed and Breakfast reports the following cost information: Depreciation on building Maintenance person’s salary Cleaning person’s salary Real estate taxes Laundry service Food • • $60, 000 per year $30, 000 per year $24, 000 per year $10, 000 per year $4. 00 person per night $6. 00 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 12

Variable Cost Example • The Smoky Mountain Inn Bed and Breakfast reports the following cost information: Depreciation on building Maintenance person’s salary Cleaning person’s salary Real estate taxes Laundry service Food • • $60, 000 per year $30, 000 per year $24, 000 per year $10, 000 per year $4. 00 person per night $6. 00 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 • What is the cost expression for variable cost person per night? $4 laundry + $6 food = $10 person/night • What is the cost expression for Total variable cost? $10 person per night * # person/nights © Dale R. Geiger 2011 14

Variable Cost Example • What is the cost expression for variable cost person per night? $4 laundry + $6 food = $10 person-night • What is the cost expression for Total variable cost? $10 person per night * # person-night © Dale R. Geiger 2011 15

Check on Learning • What is the definition of a variable cost? • What is the generic cost expression for total variable cost? © Dale R. Geiger 2011 16

Graph of Total Variable Cost $ 800 700 600 500 400 300 200 100 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 X Axis = Number of units As # units increases, total variable cost increases © Dale R. Geiger 2011 17

Graph of Total Variable Cost $ 800 700 600 500 400 At 10 units, Cost is $100 300 200 100 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 X Axis = Number of units As # units increases, total variable cost increases © Dale R. Geiger 2011 18

Graph of Total Variable Cost $ 800 700 600 500 400 At 40 units, Cost is $400 300 200 100 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 X Axis = Number of units As # units increases, total variable cost increases © Dale R. Geiger 2011 19

Graph of Total Variable Cost $ 800 750 700 600 500 At 75 units, Cost is $750 400 300 200 100 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 X Axis = Number of units As # units increases, total variable cost increases © Dale R. Geiger 2011 20

Graph of Unit Variable Cost Unit Cost = Total Variable Cost/# Units $ 12 10 Unit cost at 10 units = $100/10 units or $10 per unit 8 6 4 2 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 X Axis = Number of units As # units increases, Unit variable cost remains the same © Dale R. Geiger 2011 70 75 80 21

Graph of Unit Variable Cost Unit Cost = Total Variable Cost/# Units $ 12 10 Unit cost at 40 units = $400/40 units or $10 per unit 8 6 4 2 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 X Axis = Number of units As # units increases, Unit variable cost remains the same © Dale R. Geiger 2011 70 75 80 22

Graph of Unit Variable Cost Unit Cost = Total Variable Cost/# Units $ 12 10 Unit cost at 75 units = $750/75 units or $10 per unit 8 6 4 2 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 X Axis = Number of units As # units increases, Unit variable cost remains the same © Dale R. Geiger 2011 70 75 80 23

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 24

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 25

Fixed Cost Expression • Total Fixed $Cost = Sum of all Fixed Inputs • Fixed $Cost per Unit = Total Fixed $Cost / # Units © 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 Example • The Smoky Mountain Inn Bed and Breakfast reports the following cost information: Depreciation on building Maintenance person’s salary Cleaning person’s salary Real estate taxes Laundry service Food • • $60, 000 per year $30, 000 per year $24, 000 per year $10, 000 per year $4. 00 person per night $6. 00 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 28

Fixed Cost Example • The Smoky Mountain Inn Bed and Breakfast reports the following cost information: Depreciation on building Maintenance person’s salary Cleaning person’s salary Real estate taxes Laundry service Food • • $60, 000 per year $30, 000 per year $24, 000 per year $10, 000 per year $4. 00 person per night $6. 00 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 29

Fixed Cost Example • The Smoky Mountain Inn Bed and Breakfast reports the following cost information: Depreciation on building Maintenance person’s salary Cleaning person’s salary Real estate taxes Laundry service Food • • $60, 000 per year $30, 000 per year $24, 000 per year $10, 000 per year $4. 00 person per night $6. 00 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 • 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 31

Check on Learning • What is the definition of a fixed cost? • What is the generic cost expression for fixed cost per unit? © Dale R. Geiger 2011 33

Graph of Total Fixed Cost $140 000 $120 000 $100 000 At 10 units, Total Fixed Cost is $124, 000 $80 000 $60 000 $40 000 $20 000 $0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 X Axis = Number of units As # units increases, Total Fixed cost remains the same © Dale R. Geiger 2011 34

Graph of Total Fixed Cost $140 000 $120 000 $100 000 At 40 units, Total Fixed Cost is $124, 000 $80 000 $60 000 $40 000 $20 000 $0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 X Axis = Number of units As # units increases, Total Fixed cost remains the same © Dale R. Geiger 2011 35

Graph of Total Fixed Cost $140 000 $120 000 $100 000 At 75 units, Total Fixed Cost is $124, 000 $80 000 $60 000 $40 000 $20 000 $0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 X Axis = Number of units As # units increases, Total Fixed cost remains the same © Dale R. Geiger 2011 36

Graph of Unit Fixed Cost Unit Cost = Total Fixed Cost/# Units $25 000 At 10 units, Unit Fixed Cost = $124, 000/10 units or $12, 400 per unit $20 000 $15 000 $12, 400 $10 000 $5 000 $0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 X Axis = Number of units As # units increases, Unit Fixed cost decreases © Dale R. Geiger 2011 37

Graph of Unit Fixed Cost Unit Cost = Total Fixed Cost/# Units $25 000 $20 000 $15 000 At 40 units, Unit Fixed Cost = $124, 000/40 units or $3, 100 per unit $10 000 $5 000 $3, 100 $0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 X Axis = Number of units As # units increases, Unit Fixed cost decreases © Dale R. Geiger 2011 38

Graph of Unit Fixed Cost Unit Cost = Total Fixed Cost/# Units $25 000 $20 000 $15 000 At 75 units, Unit Fixed Cost = $124, 000/75 units or $1, 653 per unit $10 000 $5 000 $1, 653 $0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 X Axis = Number of units As # units increases, Unit Fixed cost decreases © Dale R. Geiger 2011 39

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 40

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 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? Shop Rent Staff Salaries Total Fixed $5, 000 $10, 000 © 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 variable? Parts per repair Commission per repair Total $220 200 $420 © 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. • 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 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 = $94, 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 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 © 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 = $520 Total @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 = $520 Total @200 repairs $94, 000 / 200 repairs = $470 © Dale R. Geiger 2011 49

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? © Dale R. Geiger 2011 50