Calculate Total Cost and Per-Unit Cost for a Given Production Volume ©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 production- related 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 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$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? ©14

Variable 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 ©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 © 17 $ X Axis = Number of units As # units increases, total variable cost increases

Graph of Total Variable Cost © 18 $ X Axis = Number of units As # units increases, total variable cost increases At 10 units, Cost is $100

Graph of Total Variable Cost © 19 $ X Axis = Number of units As # units increases, total variable cost increases At 40 units, Cost is $400

Graph of Total Variable Cost © 20 $ X Axis = Number of units As # units increases, total variable cost increases At 75 units, Cost is $

Graph of Unit Variable Cost © 21 $ Unit Cost = Total Variable Cost/# Units Unit cost at 10 units = $100/10 units or $10 per unit Unit cost at 10 units = $100/10 units or $10 per unit X Axis = Number of units As # units increases, Unit variable cost remains the same

Graph of Unit Variable Cost © 22 $ Unit cost at 40 units = $400/40 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 Unit Cost = Total Variable Cost/# Units

Graph of Unit Variable Cost © 23 $ Unit cost at 75 units = $750/75 units or $10 per unit Unit cost at 75 units = $750/75 units or $10 per unit X Axis = Number of units As # units increases, Unit variable cost remains the same 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? ©24

Linear Cost Relationships Fixed Costs 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$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? ©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 © 30 At 10 units, Total Fixed Cost is $124,000 X Axis = Number of units As # units increases, Total Fixed cost remains the same

Graph of Total Fixed Cost © 31 At 40 units, Total Fixed Cost is $124,000 X Axis = Number of units As # units increases, Total Fixed cost remains the same

Graph of Total Fixed Cost © 32 At 75 units, Total Fixed Cost is $124,000 X Axis = Number of units As # units increases, Total Fixed cost remains the same

Graph of Unit Fixed Cost © 33 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 $12,400

Graph of Unit Fixed Cost © 34 Unit Cost = Total Fixed Cost/# Units X Axis = Number of units As # units increases, Unit Fixed cost decreases At 40 units, Unit Fixed Cost = $124,000/40 units or $3,100 per unit $3,100

Graph of Unit Fixed Cost © 35 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 $1,653

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 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 $5,000 Staff Salaries 5,000 Total Fixed$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$220 Commission per repair 200 Total$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 © 43 X Axis = Number of Repairs As Number of Repairs increases, Fixed Cost does not change $K

Graph of Mixed Cost © 44 X Axis = Number of Repairs As Number of Repairs increases, Variable Cost increases $K Variable cost for 200 repairs= $420 per repair * 200 repairs = $84,000 Variable cost for 200 repairs= $420 per repair * 200 repairs = $84,000

Graph of Mixed Cost © 45 X Axis = Number of Repairs As Number of Repairs increases, both Variable Cost and Total Cost increase $K Total cost for 200 repairs = $420 per repair * 200 repairs + $10,000 or $94,000 Total cost for 200 repairs = $420 per repair * 200 repairs + $10,000 or $94,000

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 repairs $52,000 / 100 repairs = $520 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