Calculate Total Cost and Per-Unit Cost for a Given Production Volume Intermediate Cost Analysis and Management Show Slide #1: Calculate Total Cost and Per-Unit Cost for a Given Production Volume Title: Calculate Total Cost and Per-Unit Cost for a Given Production Volume References: Handouts, Excel Spreadsheets Facilitator’s Material and Student Material: Dry erase markers, white boards, access to Excel spreadsheets, case-studies Facilitator’s Material: Each primary Facilitator’s should possess a lesson plan, slide deck, course handouts, practical exercises, access to Excel spreadsheets, case-studies All required references and technical manuals will be provided by the local Command. Student Material: Students should possess course handouts, practical exercises, access to Excel spreadsheets, case-studies and standard classroom supplies. The 21st Century Soldier Competencies are essential to ensure Soldiers and leaders are fully prepared to prevail in complex, uncertain environments. This lesson reinforces the following 21st Century Soldier Competencies:   Communication and Engagement (Oral, written, and negotiation) Critical thinking, intergovernmental, and multinational competence Tactical and Technical Competence Throughout the lesson discussion seek opportunities to link the competencies with the lesson content through the student’s experiences. 2.1

How does total cost change as level of activity changes? Show Slide #2: Concrete Experience: We assume that the more activity or the more output we produce, the higher total cost will be. But the question is, how much higher? Can we define how cost will change as the level of activity changes? Facilitator’s Note: (Concrete Experience 10 minutes) Present students the slide statements Ask students what their thoughts are on “cost vs level of activity” Facilitator’s Note: (Publish and Process 10 minutes) The critical portion of this part of the ELM process is to force the students to reflect. Ask a series of thought influencing questions. Motivator: How does total cost change as activity changes?

Terminal Learning Objective Action: 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 Show Slide #3: TLO Action: Calculate Total Cost and Per-Unit Cost for a Given Production Volume Conditions: 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, and Graph the total and per-unit fixed costs Safety Requirements: In a training environment, leaders must perform a risk assessment in accordance with DA PAM 385-30, Risk Management. Leaders will complete a DD Form 2977 DELIBERATE RISK ASSESSMENT WORKSHEET during the planning and completion of each task and sub-task by assessing mission, enemy, terrain and weather, troops and support available-time available and civil considerations (METT-TC). Local policies and procedures must be followed during times of increased heat category in order to avoid heat related injury. Consider the work/rest cycles and water replacement guidelines IAW TRADOC Regulation 350-29. Environmental Considerations: Environmental protection is not just the law but the right thing to do. It is a continual process and starts with deliberate planning. Always be alert to ways to protect our environment during training and missions. In doing so, you will contribute to the sustainment of our training resources while protecting people and the environment from harmful effects. Refer to FM 3-34.5 Environmental Considerations and GTA 05-08-002 ENVIRONMENTAL-RELATED RISK ASSESSMENT. INSTRUCTIONAL LEAD-IN. Good morning, again, we assume that the more activity or the more output we produce, the higher total cost will be. But the question is, how much higher? Can we define how cost will change as the level of activity changes?

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 Show Slide #4: Why study cost relationships? Facilitator’s Note: Introduction, understanding what drives cost helps to understand how to reduce cost. Knowing how activities affect cost helps managers target activities to manage cost. Recognizing cost relationships helps to define what views of cost are useful. As we have said before, there are many views of cost. Wise cost managers will want to understand which key activities and key elements of cost are useful to their decision making processes.

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 Show Slide #5: Explain Cost Terminology 1. Learning Step/Activity #1 Explain Cost Terminology Method of Instruction: DSL (large or small group discussion) Facilitator’s to Student Ratio: Time of Instruction: 2.0 (Total) Media: Power Point Presentation, Printed Reference Materials Facilitator’s’s Note: Introduction 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

Cost Terminology Direct Costs Indirect 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 Materials Labor Lumber & Hardware for furniture Production Related Show Slide #6: Explain Cost Terminology (Cont.) Facilitator’s Note: in illustrating these concepts it is helpful to have a product to show to the students, to identify the actual direct materials. Example: a piece of furniture. It is easy for the students to identify the direct materials in the finished product, and envision the direct labor that went into producing it.) Direct Costs Materials and Labor that can be Identified with a particular product or process The key with direct costs is that it is possible to identify their use with a particular unit of production. The materials actually become part of the finished product. The labor was directly involved with a particular unit of production. The worker actually had his or her hands on the product at some point during the production process. Facilitator’s Note: (Indirect Costs) Lumber and hardware for furniture Indirect Costs Production-Related costs that cannot be Identified with a particular product or process Indirect costs are costs incurred as part of production, but they aren’t directly identified with a particular product. These costs are perhaps incurred to benefit multiple products. The machinery used in a factory, for example, benefits all of the products that are produced on it. The utilities to run the machinery, light and heat (or cool) the factory also benefit many products, not just one. They also can’t be identified to any particular unit of output because they don’t become part of it. Maintenance on Power Tools

Cost Terminology Manufacturing Overhead of machinery, labor, utilities 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 Aggregation Assigned Show Slide #7: Explain Cost Terminology (Cont.) Facilitator’s Note: Manufacturing Overhead; An aggregation of indirect production-related costs Indirect costs are aggregated into an account called Manufacturing overhead. For external reporting purposes, overhead consists of production related costs only. (costs incurred for storing or selling the product are not considered overhead Overhead will be assigned to products or processes, and become part of the cost of products. Overhead must be assigned in some way since it cannot be directly identified with a particular product. Non-production-related costs will NOT be assigned to products.

LSA #1 Check on Learning Q1. Costs that can be identified with a particular product or process are called what? A1. Direct Costs Q2. An aggregation of indirect costs are called these. A2. Manufacturing and Overhead Show Slide #8: LSA #1 Check on Learning Facilitator’s Note: Ask the following Questions. Facilitate the answers given. Q1. Costs that can be identified with a particular product or process are called what? A1. Direct Costs Q2. An aggregation of indirect costs are called these. A2. Manufacturing and Overhead

LSA #1 Summary During this block, we discussed the definition of a Cost relationship and accompanied terminology Show Slide #9: LSA #1 Summary Facilitator’s Note: Re-state the Summary; During this block, we discussed the definition of a Cost relationship and accompanied terminology

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 Show Slide #10: Express total and per-unit variable cost in an equation Learning Step/Activity #2 Express total and per-unit variable cost in an equation Method of Instruction: DSL (large or small group discussion) Facilitator’s to Student Ratio: Time of Instruction: 2.0 (Total) Media: Power Point Presentation, Printed Reference Materials Facilitator’s Note: Communicates a cost relationship using verbal, numerical and mathematical symbols Use plain language rather than variables x, y, z, etc. This eliminates the need to define the variable as in “let x stand for number of days”. This also prevents students from losing sight of what cost they are calculating, and what variable they are solving for. 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 Show Slide #11: Express total and per-unit variable cost in an equation (Cont.) Facilitator’s Note: Which cost expression is useful? As we said, understanding cost relationships can help us to define the view of cost that is useful in a given situation. 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 Show Slide #12: Express total and per-unit variable cost in an equation (Cont.) Facilitator’s Note: 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 is represented by an upward sloping line. That is, as number of units increases, total cost increases Unit variable cost is represented by a horizontal line. Regardless of the number of units produced, the cost for each individual unit remains the same. We will look at this graphic representation a little later. 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 per Unit * # Units Sum of all Variable inputs Show Slide #13: Express total and per-unit variable cost in an equation (Cont.) Facilitator’s Note: Total variable Cost = Variable $Cost per Unit * # Units Variable $Cost per Unit = Sum of all Variable inputs. That is, we will add up all of the costs that are variable in nature and that will be our total variable cost.

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? Show Slide #14: Express total and per-unit variable cost in an equation (Cont.) Facilitator’s Note: 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 Facilitator’s Note: Questions to ponder; 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?

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? “person per night” Which costs will change as output changes? What is the cost expression for variable cost per unit? For Total Variable Cost? Show Slide #15: Express total and per-unit variable cost in an equation (Cont.) Facilitator’s Note: What is the unit of output? The unit of output is person per night.

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? “person per night” Which costs will change as output changes? What is the cost expression for variable cost per unit? For Total Variable Cost? Show Slide #16: Express total and per-unit variable cost in an equation (Cont.) Facilitator’s Note: The costs that will change as output changes (more people stay for more nights) are laundry service and food. All of the other costs will remain the same regardless of the number of person-nights.

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 Show Slide #17: Express total and per-unit variable cost in an equation (Cont.) Facilitator’s Note: Students will have the blank slide

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-night Show Slide #18: Express total and per-unit variable cost in an equation (Cont.) Facilitator’s Note: The cost expression for variable cost per unit is: $4 laundry + $6 food = $10 per person-night. The cost expression for Total Variable cost is $10 per person per night * # person-nights.

LSA #2 Check on Learning Q1. What is the definition of a variable cost? A1. A cost that increases in direct proportion with the volume produced or consumed. Q2. What is the generic cost expression for total variable cost? A2. Variable $Cost per Unit * # Units. Show Slide #19: LSA #2 Check on Learning Facilitator’s Note: Ask the following Questions. Facilitate the answers given. Q1. What is the definition of a variable cost? A1. A cost that increases in direct proportion with the volume produced or consumed. Q2. What is the generic cost expression for total variable cost? A2. Variable $Cost per Unit * # Units.

LSA #2 Summary During this lesson, we discussed the definitions and the usefulness of both Cost Expression and Variable Cost. Show Slide #20: LSA #2 Summary Facilitator’s Note: Re-state the Summary; During this lesson, we discussed the definitions and the usefulness of both Cost Expression and Variable Cost.

Graph of Total Variable Cost $ Show Slide #21: Graph total and per-unit variable cost 3. Learning Step/Activity #3 Graph total and per-unit variable cost Method of Instruction: DSL (large or small group discussion) Facilitator’s to Student Ratio: Time of Instruction: 2.0 (Total) Media: Power Point Presentation, Printed Reference Materials Facilitator’s’s Note: The x-axis represents number of units and the Y axis represents cost. The blue line represents Total Variable Cost. It is an upward sloping line because as number of units increases, total variable cost increases. X Axis = Number of units As # units increases, total variable cost increases

Graph of Total Variable Cost $ At 10 units, Cost is $100 Show Slide #22: Graph total and per-unit variable cost (Cont.) Facilitator’s Note: At 10 units, Cost is $100 In our example, cost per unit or person-night is $10. So, if 10 units are produced, total variable cost is $100. $10 per unit * 10 units = $100 X Axis = Number of units As # units increases, total variable cost increases

Graph of Total Variable Cost $ At 40 units, Cost is $400 Show Slide #23: Graph total and per-unit variable cost (Cont.) Facilitator’s Note: At 40 units, Cost is $400. That is, $10 per unit * 40 units = $400 X Axis = Number of units As # units increases, total variable cost increases

Graph of Total Variable Cost $ 750 At 75 units, Cost is $750 Show Slide #24: Graph total and per-unit variable cost (Cont.) Facilitator’s Note: At 75 units, Cost is $750. Note: have the students describe the cost expression for this cost: $10 per unit * 75 units = $750. X Axis = Number of units As # units increases, total variable cost increases

Graph of Unit Variable Cost Unit Cost = Total Variable Cost/# Units $ Unit cost at 10 units = $100/10 units or $10 per unit Show Slide #25: Graph total and per-unit variable cost (Cont.) Facilitator’s Note: Here we have a graph of Unit variable cost. The red line represents unit variable cost. The x axis represents number of units produced, the y axis represents cost. As number of units increases, unit variable cost remains the same. Unit Cost = Total Variable Cost/# Units 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 Unit Cost = Total Variable Cost/# Units $ Unit cost at 40 units = $400/40 units or $10 per unit Show Slide #26: Graph total and per-unit variable cost (Cont.) Facilitator’s Note: Unit Cost = Total Variable Cost/# Units 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

Graph of Unit Variable Cost Unit Cost = Total Variable Cost/# Units $ Unit cost at 75 units = $750/75 units or $10 per unit Show Slide #27: Graph total and per-unit variable cost (Cont.) Facilitator’s Note: Unit Cost = Total Variable Cost/# Units 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

LSA #3 Check on Learning Q1. How is Total variable cost represented on the graph? A1. It is represented by an upward sloping line. Q2. What is the generic cost expression for Variable cost per unit? A2. Total variable cost / # units. Show Slide #28: LSA #3 Check on Learning Facilitator’s Note: Ask the following Questions. Facilitate the answers given. Q1. How is Total variable cost represented on the graph? A1. It is represented by an upward sloping line. Q2. What is the generic cost expression for Variable cost per unit? A2. Total variable cost / # units.

LSA #3 Summary During this block, we viewed the cost expression as it was graphed, as well as the total and per-unit variable cost. Show Slide #29: LSA #3 Summary Facilitator’s Note: Re-state the Summary; During this block, we viewed the cost expression as it was graphed, as well as the total and per-unit variable cost.

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 Show Slide #30: Express total and per-unit fixed costs in an equation 4. Learning Step/Activity #4 Express total and per-unit fixed costs in an equation Method of Instruction: DSL (large or small group discussion) Facilitator’s to Student Ratio: Time of Instruction: 2.0 (Total) Media: Power Point Presentation, Printed Reference Materials Facilitator’s’s Note: Fixed Costs - Costs that do not change with the volume produced or consumed. Fixed Costs Total Cost = Horizontal Line. No matter how many units are produced the total fixed cost, by definition, will not change. Therefore it will be represented by a horizontal line. Unit Fixed Cost is non-linear. We will look at this a little later. Example: The cost of the instructor remains the same regardless of the number of students in the class

Total Fixed $Cost / # Units Fixed Cost Expression Total Fixed $Cost = Fixed $Cost per Unit = Sum of all Fixed Inputs Total Fixed $Cost / # Units Show Slide #31: Express total and per-unit fixed costs in an equation (Cont.) Facilitator’s Note: Total Fixed $Cost = Sum of all Fixed Inputs. That is, we will add up all of the costs that are fixed in nature and that will be our total fixed cost. Fixed $Cost per Unit = Total Fixed $Cost / # Units

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? Show Slide #32: Express total and per-unit fixed costs in an equation (Cont.) Facilitator’s Note: We have the same 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?

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? “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? Show Slide #33: Express total and per-unit fixed costs in an equation (Cont.) Facilitator’s Note: Ask the following questions; What is the unit of output? The unit of output is (still) person-night. The costs that will NOT change as output changes (more people stay for more nights) are Depreciation on the building, the maintenance and cleaning staff salaries, and the real estate taxes. These costs will remain the same regardless of the number of person-nights. The cost expression for Total Fixed Cost is: $60,000 depreciation + $30,000 maintenance salary + $24,000 cleaning salary + $10,000 taxes The cost expression for Fixed Cost per Unit is $124,000 / # person-nights

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? “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? Show Slide #34: Express total and per-unit fixed costs in an equation (Cont.) Facilitator’s Note: Which costs will NOT change as output changes? The costs that will NOT change as output changes (more people stay for more nights) are Depreciation on the building, the maintenance and cleaning staff salaries, and the real estate taxes. These costs will remain the same regardless of the number of 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 $60,000 depreciation + $30,000 maintenance salary + $24,000 cleaning salary + $10,000 taxes = $124,000 Show Slide #35: Express total and per-unit fixed costs in an equation (Cont.) Facilitator’s Note: What is the cost expression for Total Fixed Cost? The cost expression for Total Fixed Cost is: $60,000 depreciation + $30,000 maintenance salary + $24,000 cleaning salary + $10,000 taxes The cost expression for Fixed Cost per Unit is $124,000 / # person-nights $124,000 / # person-nights

LSA #4 Check on Learning Q1. What is the definition of a fixed cost? A1. Cost that does not change with the volume produced or consumed. Q2. What is the generic cost expression for fixed cost per unit? A2. Total Fixed $Cost / # Units Show Slide #36: LSA #4 Check on Learning Facilitator’s Note: Ask the following Questions. Facilitate the answers given. Q1. What is the definition of a fixed cost? A1. Cost that does not change with the volume produced or consumed. Q2. What is the generic cost expression for fixed cost per unit? A2. Total Fixed $Cost / # Units

LSA #4 Summary During this Block, we discussed linear cost relationships as it pertains to a Fixed Cost Expression. Show Slide #37: LSA #4 Summary Facilitator’s Note: Re-state the Summary; During this Block, we discussed linear cost relationships as it pertains to a Fixed Cost Expression.

Graph of Total Fixed Cost At 10 units, Total Fixed Cost is $124,000 Show Slide #38: Graph total and per-unit fixed costs in an equation 5. Learning Step/Activity #5 Graph total and per-unit fixed costs in an equation Method of Instruction: DSL (large or small group discussion) Facilitator’s to Student Ratio: Time of Instruction: 2.0 (Total) Media: Power Point Presentation, Printed Reference Materials Facilitator’s’s Note: The green line represents total fixed cost. Again, the x-axis represents number of units produced and the y axis represents cost. 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 At 40 units, Total Fixed Cost is $124,000 Show Slide #39: Graph total and per-unit fixed costs in an equation (Cont.) Facilitator’s Note: 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 At 75 units, Total Fixed Cost is $124,000 Show Slide #40: Graph total and per-unit fixed costs in an equation (Cont.) Facilitator’s Note: 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 Unit Cost = Total Fixed Cost/# Units At 10 units, Unit Fixed Cost = $124,000/10 units or $12,400 per unit $12,400 Show Slide #41: Graph total and per-unit fixed costs in an equation (Cont.) Facilitator’s Note: As we stated earlier, fixed cost per unit is NOT linear. The purple concave downward curve on the graph represents fixed cost per unit. Unit Fixed Cost = Total Fixed Cost/# Units What is Unit Fixed cost if only one unit (person-night) is sold? $124000/1 or $124,000 At 10 units, Unit Fixed Cost = $124,000/10 units or $12,400 per unit X Axis = Number of units As # units increases, Unit Fixed cost decreases

Graph of Unit Fixed Cost Unit Cost = Total Fixed Cost/# Units At 40 units, Unit Fixed Cost = $124,000/40 units or $3,100 per unit Show Slide #42: Graph total and per-unit fixed costs in an equation (Cont.) Facilitator’s Note: At 40 units, Unit Fixed Cost = $124,000/40 units or $3,100 per unit $3,100 X Axis = Number of units As # units increases, Unit Fixed cost decreases

Graph of Unit Fixed Cost Unit Cost = Total Fixed Cost/# Units At 75 units, Unit Fixed Cost = $124,000/75 units or $1,653 per unit Show Slide #43: Graph total and per-unit fixed costs in an equation (Cont.) Facilitator’s Note: The more units are sold, the lower fixed cost per unit. This is called “spreading the fixed cost”. At 75 units, Unit Fixed Cost = $124,000/75 units or $1,653 per unit $1,653 X Axis = Number of units As # units increases, Unit Fixed cost decreases

LSA #5 Check on Learning Q1. How is Total fixed cost represented on the graph? A1. As a horizontal line. As the number of units increases, total fixed cost remains the same. Q2. How is Unit fixed cost represented on the graph? A2. As a concave downward sloping curve. As the number of units increase, unit fixed cost decrease. Show Slide #44: LSA #5 Check on Learning Facilitator’s Note: Ask the following Questions. Facilitate the answers given. Q1. How is Total fixed cost represented on the graph? A1. As a horizontal line. As the number of units increases, total fixed cost remains the same. Q2. How is Unit fixed cost represented on the graph? A2. As a concave downward sloping curve. As the number of units increase, unit fixed cost decrease.

LSA #5 Summary During this block, we graphed total and per-unit fixed costs in an equation. Show Slide #45: LSA #5 Summary Facilitator’s Note: Re-state the summary; During this block, we graphed total and per-unit fixed costs in an equation.

Cost Definitions Mixed Costs - A combination of fixed and variable costs Total Cost = Variable Cost + Fixed Cost Also known as multivariate costs Show Slide #46: Calculate total cost and per-unit cost for a given production volume 6. Learning Step/Activity #6 Calculate total cost and per-unit cost for a given production volume Method of Instruction: DSL (large or small group discussion) Facilitator’s to Student Ratio: Time of Instruction: 2.0 (Total) Media: Power Point Presentation, Printed Reference Materials Facilitator’s’s Note: Mixed Costs - A combination of fixed and variable costs Total Cost = Fixed Cost + Variable Cost Mixed costs have an element of cost that is fixed and will not change as units of output change AND they have an element of cost that is variable and will increase in direct proportion to the increase in the units of output. These costs are also known as multivariate costs. That means that the total cost is comprised of multiple elements of cost. We will look at various types of multivariate costs in this module.

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 Show Slide #47: Calculate total cost and per-unit cost for a given production volume (Cont.) Facilitator’s Note: The cost expression for a mixed cost consists of: A variable component: Variable $Cost per Unit * # Units -Plus- A fixed component: The sum of relevant costs that remain the same regardless of units of output

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? Show Slide #48: Calculate total cost and per-unit cost for a given production volume (Cont.) Facilitator’s Note: 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?

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 Show Slide #49: Calculate total cost and per-unit cost for a given production volume (Cont.) Facilitator’s Note: 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

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 Show Slide #50: Calculate total cost and per-unit cost for a given production volume (Cont.) Facilitator’s Note: 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

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 Show Slide #51: Calculate total cost and per-unit cost for a given production volume (Cont.) Facilitator’s Note: 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? First, let’s think about the cost expression for total cost. It is: cost per repair * # repairs + fixed cost Total cost= $420 per repair * # repairs + $10,000

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 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 Show Slide #52: Calculate total cost and per-unit cost for a given production volume (Cont.) Facilitator’s Note: Total cost at 100 repairs is $420 per repair*100 repairs+$10,000 = $52,000

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 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 Show Slide #53: Calculate total cost and per-unit cost for a given production volume (Cont.) Facilitator’s Note: Total cost at 100 repairs is $420 per repair*200 repairs+$10,000 = $94,000

Graph of Mixed Cost $K X Axis = Number of Repairs Show Slide #54: Describe multivariate costs Facilitator’s Note: The blue line represents fixed cost. The x axis represents number of repairs completed. The cost of rent and other fixed costs remains the same ($10K) whether the shop completes 10 repairs or 300. X Axis = Number of Repairs As Number of Repairs increases, Fixed Cost does not change

Graph of Mixed Cost $K Variable cost for 200 repairs= $420 per repair * 200 repairs = $84,000 $84K Show Slide #55: Describe multivariate costs (Cont.) Facilitator’s Note: The red line represents Variable Cost. Again, the x axis represents number of repairs. As number of repairs increases, the variable cost increases. Variable cost for 200 repairs= $420 per repair * 200 repairs = $84,000 X Axis = Number of Repairs As Number of Repairs increases, Variable Cost increases

Total cost for 200 repairs = $420 per repair * 200 repairs + $10,000 Graph of Mixed Cost $K $94K Total cost for 200 repairs = $420 per repair * 200 repairs + $10,000 or $94,000 Show Slide #56: Describe multivariate costs (Cont.) Facilitator’s Note: The green line represents Total Cost. It represents the sum of fixed cost and variable cost. Note that it begins at $10K. That is, total cost if number of repairs is zero is $10K, the fixed cost. The cost of rent and other fixed costs will be incurred even if no repairs are completed. The line slopes upward from there, and is parallel to the variable cost line. Total cost increases by $420 per repair, just as variable cost does. Total cost for 200 repairs = $420 per repair * 200 repairs + $10,000 or $94,000 X Axis = Number of Repairs 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 Show Slide #57: Calculate total cost and per-unit cost for a given production volume Facilitator’s Note: 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? Again, let’s think about the cost expression for unit cost. It is: Unit cost = Total cost / # repairs

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 Show Slide # 58: Calculate total cost and per-unit cost for a given production volume (Cont.) Facilitator’s Note: Unit cost for 100 repairs = Total cost at 100 repairs $52,000 / 100 repairs = $520 per repair

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 Show Slide #59: Calculate total cost and per-unit cost for a given production volume (Cont.) Facilitator’s Note: Mention to the class Total cost at 200 repairs $94,000 / 200 repairs = $470 per repair Notice that cost per repair decreases as number of repairs increases. That is another example of spreading the fixed cost.

LSA #6 Check on Learning Q1. How would the graph of Cost per Repair appear? A1. It should be a downward sloping curve that will level out above $420. Cost per repair will never drop below $420 (variable cost) Show Slide #60: LSA #6 Check on Learning Facilitator’s Note: Ask the following Questions. Facilitate the answers given. Q1. How would the graph of Cost per Repair appear? A1. It should be a downward sloping curve that will level out above $420. Cost per repair will never drop below $420 (variable cost)

LSA #6 Summary During this block, we discussed multivariate cost expressions, graphed these expressions and then concluded with a demonstration problem. Show Slide #61: LSA #6 Summary Facilitator’s Note: Re-state the Summary; During this block, we discussed multivariate cost expressions, graphed these expressions and then concluded with a demonstration problem.

Conduct Practical Exercises Show Slide #62: Practical Exercise Facilitator’s Note: Have students complete PE AJBIC100.1 and conduct Check on Learning. When satisfied, have students move on AJBIC100.2. Address any questions or areas of concern until students can successfully complete the exercise.

TLO Summary Action: 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 Show Slide #3: TLO Summary Facilitator’s Note: Restate the TLO Action: Calculate Total Cost and Per-Unit Cost for a Given Production Volume Conditions: 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, and Graph the total and per-unit fixed costs “Or” Facilitator's at this time, have one learner from each group to explain the most important take away to them from this lesson. Facilitate a discussion on each answer.