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

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Calculate Total Cost and Per-Unit Cost for a Given Production Volume

Intermediate Cost Analysis and Management

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How does total cost change as level of activity changes?

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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

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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

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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

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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

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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

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Check on Learning

• Costs that can be identified with a particular product or process are called

• An aggregation of indirect costs is called

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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

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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

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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

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Variable Cost Expression

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

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

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Variable Cost Expression

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

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

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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?

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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

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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

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X Axis = Number of unitsAs # units increases, total variable cost increases

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At 10 units, Cost is $100

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750

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Graph of Unit Variable Cost

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$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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$10 per unit


Unit Cost = Total Variable Cost/# Units

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$10 per unit


Unit Cost = Total Variable Cost/# Units

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Check on Learning

• How is Total variable cost represented on the graph?

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

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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

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Fixed Cost Expression

• Total Fixed $Cost = Sum of all Fixed Inputs

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

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Fixed 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 NOT change as output changes?• What is the cost expression for Total Fixed Cost?• For Fixed Cost per Unit?

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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

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Check on Learning

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

cost per unit?

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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

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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

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$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

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$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

$25,000

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Unit 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

$25,000

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$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

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$25,000

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

$1,653

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Check on Learning

• How is Total fixed cost represented on the graph?

• How is Unit fixed cost represented on the graph?

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Cost Definitions

• Mixed Costs - A combination of fixed and variable costs

Total Cost = Variable Cost + Fixed Cost

• Also known as multivariate costs

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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

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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?

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

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• Which costs are variable?Parts per repair $220Commission per repair 200Total $420

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• 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

Graph of Mixed Cost0 20 40 60 80 100

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Fixed Cost

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X Axis = Number of Repairs As Number of Repairs increases, Fixed Cost does not change

$K


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Fixed CostVariable Cost

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X Axis = Number of RepairsAs Number of Repairs increases, Variable Cost increases

$KVariable cost

for 200 repairs=$420 per repair *

200 repairs = $84,000

$84K


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Fixed CostVariable CostTotal Cost

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X Axis = Number of RepairsAs 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

$94K

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• 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

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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)

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Practical Exercises

Documents

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