Calculate Total Cost and PerUnit Cost for a

Calculate Total Cost and Per-Unit Cost for a Given Production Volume Intermediate Cost Analysis and Management © 1

How does total cost change as level of activity changes? © 2

Terminal Learning Objective • Task: Calculate Total Cost and Per-Unit Cost for a Given Production Volume • Condition: You are training to become an ACE with access to ICAM course handouts, readings, and spreadsheet tools 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 © 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

Cost Terminology • Direct Costs • MATERIALS and LABOR that can be Identified with a particular product or process • Example: Lumber and hardware for furniture • Indirect Costs • PRODUCTION-RELATED costs that cannot be Identified with a particular product or process • Example: Maintenance on power tools © 6

Cost Terminology • Manufacturing Overhead • An AGGREGATION of indirect productionrelated costs • Will be ASSIGNED to products or processes and become part of the cost of the product • of machinery, labor, utilities © 7

Check on Learning • Costs that can be identified with a particular product or process are called • An aggregation of indirect costs is called © 8

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 © 9

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 © 10

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 © 11

Variable Cost Expression • Total variable Cost = Variable $Cost per Unit * # Units • Variable $Cost per Unit = Sum of all Variable inputs © 12

Variable Cost Expression • Total variable cost = Variable $Cost per Unit * # Units • Variable $Cost per Unit = Sum of all Variable inputs © 13

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? © 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/nights © 15

Check on Learning • What is the definition of a variable cost? • What is the generic cost expression for total variable cost? © 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 © 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 © 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 © 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 © 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 © 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 © 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 © 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? © 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 © 25

Fixed Cost Expression • Total Fixed $Cost = Sum of all Fixed Inputs • Fixed $Cost per Unit = Total Fixed $Cost / # Units © 26

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? © 27

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 © 28

Check on Learning • What is the definition of a fixed cost? • What is the generic cost expression for fixed cost per unit? © 29

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 © 30

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 © 31

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 © 32

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 © 33

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 © 34

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 © 35

Check on Learning • How is Total fixed cost represented on the graph? • How is Unit fixed cost represented on the graph? © 36

Cost Definitions • Mixed Costs - A combination of fixed and variable costs Total Cost = Variable Cost + Fixed Cost • Also known as multivariate costs © 37

Multivariate Cost Expressions • Variable component: • Variable $Cost per Unit * # Units -Plus • Fixed component: • Sum of relevant costs that remain the same regardless of units of output © 38

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? © 39

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 © 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 variable? Parts per repair Commission per repair Total $220 200 $420 © 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. • 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 © 42

Graph of Mixed Cost $K 100 90 80 70 60 50 Fixed Cost 40 30 20 10 300 280 260 240 220 200 180 160 140 120 100 80 60 40 20 0 0 X Axis = Number of Repairs As Number of Repairs increases, Fixed Cost does not change © 43

Graph of Mixed Cost $K 100 Variable cost for 200 repairs= $420 per repair * 200 repairs = $84, 000 90 $84 K 80 70 60 50 Fixed Cost 40 Variable Cost 30 20 10 300 280 260 240 220 200 180 160 140 120 100 80 60 40 20 0 0 X Axis = Number of Repairs As Number of Repairs increases, Variable Cost increases © 44

Graph of Mixed Cost $K 100 $94 K 90 Total cost for 200 repairs = $420 per repair * 200 repairs + $10, 000 or $94, 000 80 70 60 Fixed Cost 50 Variable Cost 40 Total Cost 30 20 10 300 280 260 240 220 200 180 160 140 120 100 80 60 40 20 0 0 X Axis = Number of Repairs 45 As Number of Repairs increases, both Variable Cost and Total Cost increase ©

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 © 46

Question • How would the graph of Cost per Repair appear? • It should be a downward sloping curve that will level out above $420 • Cost per repair will never drop below $420 (variable cost) © 47

Practical Exercises © 48