Principles of Cost Analysis and Management Calculate Total Cost and Incremental Costs Given Various Production Volumes Principles of Cost Analysis and Management Show Slide #1: Calculate Total Cost and Incremental Costs Given Various Production Volumes References: FM 1-06 Financial Management Operations, Apr 14 Handouts and Excel Spreadsheets Facilitator Material: Each primary facilitator should possess a lesson plan, slide deck, course handouts, practical exercises with answer key, access to Excel spreadsheets, and a summary sheet containing FM 1-06 Financial Management Operations, Apr 14. All required printed reference material, and technical manuals will be provided by the Schoolhouse. Learner Material: Learners should possess all required printed reference material, course handouts, access to Excel spreadsheets, and a summary sheet containing FM 1-06 Financial Management Operations, Apr 14 and standard classroom supplies.

What if? Relationship between cost and unit of output is neither fixed nor variable? There are multiple elements that affect the cost of an output? A different type of cost relationship is relevant to the decision at hand? Show Slide #2: Concrete Experience ( What If?) Facilitator’s Note: (Concrete Experience 5 minutes) Ask the learners the “What If” questions. Facilitate a discussion on the answers given. Facilitator’s Note: (Publish and Process 5 minutes) The critical portion of this part of the ELM process is to force the learners to reflect. Introduction: What if the relationship between cost and unit of output is neither fixed nor variable? In the last lesson we dealt with costs that fit neatly into these two categories. In real world situations, our cost relationships might not. What if there are multiple elements that affect the cost of an output? What if a different cost relationship is relevant to the decision at hand? This lesson will help us identify and express these more complex cost relationships.

Terminal Learning Objective Action: Calculate Total Cost and Incremental Costs Given Various Production Volumes Condition: FM Leaders in a classroom environment working individually and as a member of a small group, using doctrinal and administrative publications, self-study exercises, personal experiences, practical exercises, handouts, and discussion. Standard: With at least 80% accuracy (70% for International learners): Describe multivariate costs Describe incremental costs Describe other multivariate cost relationships Show Slide #3: Terminal Learning Objective (TLO) Action: Calculate Total Cost and Incremental Costs Given Various Production Volumes Condition: FM Leaders in a classroom environment working individually and as a member of a small group, using doctrinal and administrative publications, self-study exercises, personal experiences, practical exercises, handouts, and discussion. Standard: With at least 80% accuracy (70% for International learners) Describe multivariate costs Describe incremental costs Describe other multivariate cost relationships Facilitator’s Note: Throughout this lesson, solicit from learners the challenges they experienced in the current operational environment (OE) and what they did to resolve them. Encourage learners to apply at least 1 of the 8 critical variables: physical environment, political stability of the state, sociological demographics, infrastructure, military capabilities, information, time, and economics. 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. Risk Assessment Level: Low. Hazard Identification: Electrical Shock, Fire, Slippery Floors, Physical Injure/Strain, Tripping Tight Spaces in Classroom, and Influenza. Hazard controls: Primary Instructor (PI) will ensure: All electrical cords are properly stored under desks, liquid containers have lids on them and all spills are immediately cleaned and mopped and allowed to completely dry before allowing learners/personnel to walk on them. All chairs are ergonomically designed, adjust to individual preference and that all learners are awake and paying attention in class. All cables/cords are properly plugged in, sheathed, and secured along tables, walls, and ceilings. No damaged or frayed cords/cables will be used. PI will brief proper hand washing techniques, the use of hand sanitizer, and evacuation procedures. All trash will be removed daily. Environmental Statement: 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. Evaluation: Learners will take the Principles of cost Analysis and Management 2 Exam at the end of Week Two. Learners must score 80% or higher and International officers must score 70% or higher. Instructional Lead in: Knowing how to Calculate Total Cost and Incremental Costs Given Various Production Volumes introduces to the learners the overall concept of incremental analysis which is used as a part of capital budgeting as well as a number of other management decisions and will help your organization reduce costs during the year.

Cost Definitions Multivariate Cost Expressions Mixed Costs - A combination of fixed and variable costs. Total Cost = Variable Cost + Fixed Cost Also known as multivariate costs Multivariate Cost Expressions Variable component: Variable $Cost per Unit * # Unit -Plus- Fixed component: Sum of relevant costs that remain the same regardless of units of output. Show Slide #4: Describe multivariate costs Learning Step/Activity #1: Describe multivariate costs Method of Instruction: DSL-Discussion (small or large group discussion) Facilitator to Student Ratio: 2:25 Time of Instruction: 30 Minutes Media: PowerPoint, Printed Reference Material Facilitator’s Note: All handouts and learner materials for this lesson are located in Tab 23. Facilitator's Note: Before facilitating this lesson, ask the learners which of the 21st Century Soldier (Learner) Competency do they think pertain to this lesson? Facilitate a discussion on the answers given and at the end of the lesson revisit it and see if the learners still believe their choice are the same. For this lesson these competencies should be talked about. 1. Character and accountability 6. Communication and engagement (oral, written, and negotiation) 7. Critical thinking and problem solving 9. Tactical and technical competence (full spectrum capable) Facilitator’s Note: (Facilitator read and facilitate discussion using the slide) Cost Definitions 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. Also, there is an element of cost that is variable and will increase proportionately with the level of activity: the variable cost. 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 lesson. Facilitator’s Note: (Advance slide) One major class of Multivariate Costs involves a mixture of fixed and variable costs. 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.

Multivariate Cost Example Relevant cost of transporting a unit for on-location training is $350,000. Cost of training operations on-location runs $20,000 per day. What is the unit of output? Days of training Days of training. Show Slide #5: Multivariate Cost Example Facilitator’s Note: (Facilitator read and facilitate discussion using the slide) Relevant cost of transporting a unit for on-location training is $350,000. Cost of training operations on-location runs $20,000 per day. What is the unit of output? Facilitator’s Note: (Advance slide) What is the unit of output? Days of training. The cost of training will increase as the number of days spent on location increases. What is the cost expression for Fixed cost? The cost that is fixed regardless of days spent in training is the $350,000 transportation. Therefore the cost expression is: Fixed cost = $350,000 What is the cost expression for Fixed cost? Fixed cost = $350,000 What is the cost expression for Fixed cost? Fixed cost = $350,000

Multivariate Cost Example (Cont.) Relevant cost of transporting a unit for on-location training is $350,000. Cost of training operations on-location runs $20,000 per day. What is the cost expression for Variable Cost? Variable cost = $20,000/day * # of days Variable cost = $20,000 per day * # of days What is the cost expression for Total Cost of on-location training? Show Slide #6: Multivariate Cost Example (con’t) Facilitator’s Note: (Facilitator read and facilitate discussion using the slide) Relevant cost of transporting a unit for on-location training is $350,000. Cost of training operations on-location runs $20,000 per day. What is the cost expression for Variable Cost? Facilitator’s Note: (Advance slide) The variable cost in this example is the daily cost of training operations of $20,000. Therefore the cost expression for Variable Cost is: Variable cost = $20,000 per day * # of days. What is the cost expression for Total Cost of on-location training? Total Cost consists of Variable cost + Fixed Cost Therefore, Total Cost = $20,000 per day * #days + $350,000 Total Cost = Variable cost + Fixed Cost Total Cost = $20,000 per day * #days + $350,000

Graph of Mixed Cost $K $350K Fixed Cost X Axis = Number of Days Show Slide #7: Graph of Mixed Cost Facilitator’s Note: (Facilitator read and facilitate discussion using the slide) The blue line represents fixed cost. The x axis represents number of days spent at the training location. The cost of transporting the unit remains the same ($350K) whether the unit remains at the training location 1 day or 15 days. X Axis = Number of Days As Number of Days increases, Fixed Cost does not change

Graph of Mixed Cost $K Variable cost for 10 days = $20K per day * 10 days = $200K Show Slide #8: Graph of Mixed Cost (con’t) Facilitator’s Note: (Facilitator read and facilitate discussion using the slide) The red line represents Variable Cost. Again, the x axis represents number of days at the training location. As number of days increases, the variable cost of the training increases. Variable cost for 10 days = $20K per day * 10 days = $200K X Axis = Number of Days As Number of Days increases, Variable Cost increases

Total cost for 10 days = $20K per day * 10 days + $350K Graph of Mixed Cost Total cost for 10 days = $20K per day * 10 days + $350K or $550K $K Total Cost $550K Fixed Cost Variable Cost Show Slide #9: Graph of Mixed Cost (con’t) Facilitator’s Note: (Facilitator read and facilitate discussion using the slide) The green line represents Total Cost. It represents the sum of fixed cost and variable cost. Note: that it begins at $350K. That is, total cost if number of training days is zero is $350K, the cost of transporting the unit. The cost of transportation, by definition of a fixed cost, will be incurred by transporting the unit to the training location, even if they do not complete a day of training. The line slopes upward from there, and is parallel to the variable cost line. Total cost increases by $20K per day, just as variable cost does. X Axis = Number of Days As Number of Days increases, both Variable Cost and Total Cost increase

Questions What is the cost expression for Cost per Day? $20,000 per day * # Days + $350,000 # Days How would the graph of Cost per Day look? It should be a downward sloping curve that will level out above $20K. Show Slide #10: Questions Facilitator’s Note: (Facilitator read and facilitate discussion using the slide) The Cost per Day for one day is ($20K per day *1 day+ $350K)/1 or $370K. The cost for 10 days is ($20K per day*10 days + $350K)/10 or $55K. The graph of cost per day will slope downward as the fixed cost is spread over more days, but it will level out above $20K. Why? The cost per day will never be less than the variable cost of $20 per day.

Cost Definitions Semi-variable Cost - Costs that Increase as Unit of Output increases, but not in Direct Proportion. Examples: Hours worked by an employee Miles driven Learners in a course Show Slide #11: Cost Definitions Facilitator’s Note: (Facilitator read and facilitate discussion using the slide) Semi-variable Cost - Costs that Increase as Unit of Output increases, but not in Direct Proportion. Examples: Hours worked by an employee – the pay rate may differ depending upon the number of hours worked or the type of work performed Miles driven – cost is driven primarily by the miles per gallon, which may differ for different types of driving (mountain, highway, city, etc.) Cost is also affected by the price of gasoline Learners in a course – The cost of the course has identifiable fixed and variable components over a relevant range (one to twenty-five Learners). Once the number of learners exceeds twenty five, the cost increases but not in direct proportion to the number of learners.

Example: Semi-Variable Cost Sometimes the Variable Cost per unit remains the same only for a Relevant Range. Example: Employee Wages Employee’s base wage is $15 per hour If the employee works more than 40 hours in a week we must pay time and a half. Show Slide #12: Semi-Variable Cost (Example) Facilitator’s Note: (Facilitator read and facilitate discussion using the slide) Semi-variable Cost - Costs that Increase as Unit of Output increases, but not in Direct Proportion. Sometimes the Variable Cost per unit remains the same only for a Relevant Range. Example: Employee Wages Employee’s base wage is $15 per hour If the employee works more than 40 hours in a week we must pay time and a half

Cost Expression for Semi Variable If the total number of hours worked is 44 and straight-time rate is $15 per hour then: = $690 If the total number of hours worked is 30 and straight-time rate is $15 per hour then: = $450 The cost expression for Total Wage Cost is: Straight Time Hours * Straight Time $ per Hour + Overtime Hours 1.5 Show Slide #13: Cost Expression for Semi Variable Facilitator’s Note: (Facilitator read and facilitate discussion using the slide) The cost expression for Total Wage Cost is: (Straight time hours * Straight time $ per hour) + (Overtime hours * 1.5 * Straight time $ per hour) This is a multivariate cost expression because there are two different types of hours worked: straight time hours and overtime hours. Facilitator’s Note: (Advance slide) If the total number of hours worked is 30 and straight-time rate is $15 per hour then: Total Wage Cost = $450 If the total number of hours worked is 44 and straight-time rate is $15 per hour then: Total Wage Cost = $690

Cost Expression for Semi Variable If the total number of hours worked is 44 and straight-time rate is $15 per hour then: = $690 If the total number of hours worked is 30 and straight-time rate is $15 per hour then: = $450 The cost expression for Total Wage Cost is: 30 Straight Time Hours * $15 per Hour + 0 Overtime Hours 1.5 Straight Time $ per Hour Show Slide #14: Cost Expression for Semi Variable Facilitator’s Note: (Facilitator read and facilitate discussion using the slide) The cost expression for Total Wage Cost is: (Straight time hours * Straight time $ per hour) + (Overtime hours * 1.5 * Straight time $ per hour) This is a multivariate cost expression because there are two different types of hours worked: straight time hours and overtime hours. Facilitator’s Note: (Advance slide) If the total number of hours worked is 30 and straight-time rate is $15 per hour then: Total Wage Cost = $450 If the total number of hours worked is 44 and straight-time rate is $15 per hour then: Total Wage Cost = $690

Cost Expression for Semi Variable If the total number of hours worked is 44 and straight-time rate is $15 per hour then: = $690 If the total number of hours worked is 30 and straight-time rate is $15 per hour then: = $450 The cost expression for Total Wage Cost is: 40 Straight Time Hours * $15 per Hour + 4 Overtime Hours 1.5 $15 per Hour Show Slide #15: Cost Expression for Semi Variable Facilitator’s Note: (Facilitator read and facilitate discussion using the slide) The cost expression for Total Wage Cost is: (Straight time hours * Straight time $ per hour) + (Overtime hours * 1.5 * Straight time $ per hour) This is a multivariate cost expression because there are two different types of hours worked: straight time hours and overtime hours. Facilitator’s Note: (Advance slide) If the total number of hours worked is 30 and straight-time rate is $15 per hour then: Total Wage Cost = $450 If the total number of hours worked is 44 and straight-time rate is $15 per hour then: Total Wage Cost = $690

Graph for Total Wage Cost Show Slide #16: Graph for Total Wage Cost Facilitator’s Note: (Facilitator read and facilitate discussion using the slide) Here is the graph for total wage cost. The X Axis represents # of Hours Worked and the blue line represents total wage cost. As # Hours Worked increases, total Wage Cost increases, but not uniformly. In other words, the increase in cost for each hour worked is not always $15. Once the number of hours reaches 40, the increase in cost for each hour worked is $22.50 X Axis = # of Hours Worked As # Hours Worked increases, total Wage Cost increases, but not uniformly

Graph for Total Wage Cost This is known as a Step Function. Cost per Hour for Hours 0-40 = $15 Cost per Hour for Hours 41-60 = $22.50 Show Slide #17: Graph for Total Wage Cost (con’t) Facilitator’s Note: (Facilitator read and facilitate discussion using the slide) Remember that the variable cost per unit is represented by a horizontal line, because cost per unit does not change as units of output increase. That is not the case with a semi-variable cost. The cost per unit is not always the same, which is why total cost does not increase by the same amount for every unit of output. In our wage example, the cost per unit is the same for the relevant range of 40 hours. This is represented by a horizontal line at $15 for hours 0-40. Once the number of hours increases above 40, the cost per hour also increases. There is a break in our cost per hour graph, and the cost per hour for hours 41-60 is represented by a horizontal line at time and a half, $22.50 per hour. This is known as a Step Function. X Axis = # of Hours Worked As # Hours Worked increases, Wage Cost per Hour remains the same for the relevant range

Questions for Thought What about a volume discount? Units 1-20 cost $10 per unit Units 21-50 cost $9 per unit Units 51-100 cost $8 per unit How would you express this cost relationship? In total? On a per-unit basis? How would the graph of each look? What is the cost of 16 units? Of 67 units? Show Slide #18: Questions for Thought Facilitator’s Note: (Facilitator read and facilitate discussion using the slide) What about a volume discount? Units 1-20 cost $10 per unit Units 21-50 cost $9 per unit Units 51-100 cost $8 per unit How would you express this cost relationship? In total? Total cost = $10/unit * regular units + $9 per unit * 1st tier discounted units + $8 per unit * 2nd tier discounted units On a per-unit basis? Units 1-20 = $10 per unit; units 21-50 = $9 per unit; units 51-100 = $8 per unit How would the graph of each look? The graph of total cost would show an upward sloping line with two articulations. At 21 units the slope of the line would decrease and again at 51 units. The graph of unit cost would show a step function with the units 1-20 at $10 per unit, units 21-50 at $9 and units 51-100 at $8 What is the cost of 16 units? $10 per unit * 16 units = $160 Of 67 units? $10 per unit * 20 units + $9 per unit * 30 units + $8 per unit * 17 units = $606 Facilitator’s Note: How would the graph of each look? (Have the learners think about this and then show the graphs on the next two slides).

Graph of Total Cost Show Slide #19: Graph of Total Cost Facilitator’s Note: (Facilitator read and facilitate discussion using the slide) The graph of total cost would show an upward sloping line with two articulations. At 21 units the slope of the line would decrease and again at 51 units.

Graph of Total Cost Show Slide #20: Graph of Total Cost (con’t) Facilitator’s Note: (Facilitator read and facilitate discussion using the slide) The graph of unit cost would show a step function with the units 1-20 at $10 per unit, units 21-50 at $9 and units 51-100 at $8.

LSA #1 Check on Learning Q1. What is the generic cost expression for a mixed cost? Q2. A cost that increases as output increases but not in direct proportion is called a _____ - ______ cost. A2. A1. Variable $Cost per Unit * # Units + Fixed Cost. Show Slide #21: LSA #1 Check on Learning Facilitator’s Note: Ask the following Questions; (Facilitate discussion on answers given) Q1. What is the generic cost expression for a mixed cost? A1. Variable $Cost per Unit * # Units + Fixed Cost. Q2. A cost that increases as output increases but not in direct proportion is called a ________ - ______________ cost. A2. Semi - Variable ** Facilitator’s Note: LSA Summary will be given at the end of this lesson. Semi-Variable

LSA #1 Summary During this block, we discussed Multivariate Cost Expressions and defined how mixed cost consist of variable, semi-variable, and fixed cost. We then graphed the different types of cost to identify their characteristics in the expressions. Show Slide #22: LSA #1 Summary Facilitator’s Note: During this block, we discussed Multivariate Cost Expressions and defined how mixed cost consist of variable, semi-variable, and fixed cost. We then graphed the different types of cost to identify their characteristics in the expressions.

(Total Cost of # Units + 1) – (Total Cost of # Units) Cost Definition Incremental Costs - The increase in Total Cost caused by increasing output by ONE unit. Reflects the Difference between the Total Cost for a given level of output and the Total Cost for that level plus one. Cost Expression for Incremental Cost: (Total Cost of # Units + 1) – (Total Cost of # Units) Show Slide #23: Cost Definition Facilitator’s Note: Describe Incremental Costs Learning Step/Activity #2: Describe Incremental Costs Method of Instruction: DSL-Discussion (small or large group discussion) Facilitator to Student Ratio: 2:25 Time of Instruction: 30 Minutes Media: PowerPoint, Printed Reference Material Facilitator’s Note: (Facilitator read and facilitate discussion using the slide) Cost Definition Incremental Costs - The increase in Total Cost caused by increasing output by ONE unit. Reflects the Difference between the Total Cost for a given level of output and the Total Cost for that level plus one. Cost Expression for Incremental Cost: (Total Cost of # Units + 1) – (Total Cost of # Units)

Relevant Range and Fixed Cost Sometimes Fixed Cost remains the same only for a relevant range Example : Airline Flight Fixed Cost of $15K per flight cover fuel and crew regardless of number of passengers. The aircraft holds 150 passengers. Show Slide #24: Relevant Range and Fixed Cost Facilitator’s Note: (Facilitator read and facilitate discussion using the slide) Sometimes Fixed Cost remains the same only for a relevant range. The definition of a fixed cost is one that does not change as units of output change. Many fixed costs remain the same as units of output increase until capacity is reached. Then the costs will increase. Example: Airline Flight Fixed Cost of $15K per flight cover fuel and crew regardless of number of passengers. The aircraft holds 150 passengers.

Graph Airline Flight Cost $K Show Slide #25: Graph Airline Flight Cost Facilitator’s Note: (Facilitator read and facilitate discussion using the slide) The red line on this graph represents the fixed cost portion of an airline flight. The X Axis represents Number of passengers. As number of passengers increases, Fixed cost increases in a step-wise fashion. Since the capacity of the aircraft is 150 passengers, the fixed cost of the flight remains the same for that range. But, if number of passengers increases beyond 150 passengers, another aircraft or flight is necessary and the fixed cost increases. X Axis = Number of passengers As number of passengers increases, Fixed cost increases in a step-wise fashion

Example: Incremental Cost Scenario: Our airline provides a $.50 bag of peanuts and a $.75 can of soda to each passenger. Additional fuel cost per passenger is $8.75. Question: What is the cost expression for Total Cost for a single flight? Variable Cost $10 per passenger * # passengers + Fixed Cost $15,000 Show Slide #26: Incremental Cost (Example) Facilitator’s Note: (Facilitator read and facilitate discussion using the slide) Assuming our airline provides a $.50 bag of peanuts and a $.75 can of soda to each passenger. Additional fuel cost per passenger is $8.75. Q. What is the cost expression for Total Cost for a single flight? Facilitator’s Note: (Advance slide) A. Variable Cost $10 per passenger * # passengers + Fixed Cost $15,000 The variable costs are the peanuts, the soda, and the additional fuel costs. $.50 + $.75 + $8.75 = $10 The fixed cost (given on previous slide) is $15,000 for fuel and flight crew. Answer: Variable Cost $10 per passenger * # passengers + Fixed Cost $15,000

Example: Incremental Cost (Cont.) Scenario: Our airline provides a $.50 bag of peanuts and a $.75 can of soda to each passenger. Additional fuel cost per passenger is $8.75. Question: What is Total Cost for 125 passengers? $10 per passenger * 125 passengers + $15,000 = $27,500 Show Slide #27: Incremental Cost (Example) (con’t) Facilitator’s Note: (Facilitator read and facilitate discussion using the slide) Assuming our airline provides a $.50 bag of peanuts and a $.75 can of soda to each passenger. Additional fuel cost per passenger is $8.75. Q. What is Total Cost for 125 passengers? Facilitator’s Note: (Advance slide) A. $10 per passenger * 125 passengers + $15,000 = $16,250 By plugging the quantity of 125 into our cost expression, we get a total cost of $16,250. Answer: $10 per passenger * 125 passengers + $15,000 = $16,250

Example: Incremental Cost (Cont.) Scenario: Our airline provides a $.50 bag of peanuts and a $.75 can of soda to each passenger. Additional fuel cost per passenger is $8.75. Question: What is the Incremental cost of increasing from 125 to 126 passengers? Answer: Incremental cost = Cost of 126 psgrs – Cost of 125 psgrs ($10 * 126 + $15,000) - ($10 * 125 + $15,000) = $10 Show Slide #28: Incremental Cost (Example) (con’t) Facilitator’s Note: (Facilitator read and facilitate discussion using the slide) Assuming our airline provides a $.50 bag of peanuts and a $.75 can of soda to each passenger. Additional fuel cost per passenger is $8.75. Q. What is the Incremental cost of increasing from 125 to 126 passengers? Facilitator’s Note: (Advance slide) Q1. What is the Incremental cost of increasing from 125 to 126 passengers? Remember, incremental cost is the increase in cost from increasing output by one unit. A1. So, the incremental cost will be the difference between cost at 126 passengers and the cost at 125 passengers. Cost of 126 psgrs – Cost of 125 psgrs ($10 * 126 + $15,000) - ($10 * 125 + $15,000) = $10

Graph Airline Flight Cost Incremental cost = $16,260 – $16,250 = 10 $K Total Cost at 125 passengers = 125 * $10 per passenger + $15,000 = $16,250 Total Cost at 126 passengers = 126 * $10 per passenger + $15,000 = $16,260 Show Slide #29: Graph Airline Flight Cost Facilitator’s Note: (Facilitator read and facilitate discussion using the slide) The green line on this graph shows total flight cost. The two highlighted points show the incremental cost of increasing from 125 to 126 passengers. Total Cost at 125 passengers = 125 * $10 per passenger + $15,000 = $16,250 Total Cost at 126 passengers = 126 * $10 per passenger + $15,000 = $16,260 Incremental cost = 16,260 – 16,250 = 10 X Axis = Number of passengers As number of passengers increases, Total Cost increases

Cost of 151 psgrs – Cost of 150 psgrs Example: Incremental Cost (Cont.) Our airline provides a $.50 bag of peanuts and a $.75 can of soda to each passenger Additional fuel cost per passenger is $8.75 What is the Incremental cost of increasing from 150 to 151 passengers? Incremental cost = Show Slide #30: Incremental Cost (Example) Facilitator’s Note: (Facilitator read and facilitate discussion using the slide) Assuming our airline provides a $.50 bag of peanuts and a $.75 can of soda to each passenger. Additional fuel cost per passenger is $8.75. Q. What is the Incremental cost of increasing from 150 to 151 passengers? Facilitator’s Note: (Advance slide) Remember that the capacity of the aircraft is 150 passengers. If we increase from 150 to 151 passengers we need an additional aircraft and flight crew, increasing the fixed cost to $30,000. A. The incremental cost of the 151st passenger is $15,000 for the additional aircraft plus the variable cost of $10 per passenger. Incremental cost = Cost of 151 psgrs – Cost of 150 psgrs ($10 * 151 + $30,000) - ($10 * 150 + $15,000) = $15,010

Graph Airline Flight Cost Incremental cost = $16,500 – $31,510 = $15,010 $K Total Cost at 151 psgrs = 151 * $10 per psgr + $30,000 Or $31,510 Total Cost at 150 psgrs = 150 * $10 per psgr+ $15,000 Or $16,500 Show Slide #31: Graph Airline Flight Cost Facilitator’s Note: (Facilitator read and facilitate discussion using the slide) Incremental cost = 16500 – 31510 = 15,010 The fixed cost increases because at 151 passengers we have exceeded the capacity of the first aircraft and must then get another plane and another crew. This explains why airlines are willing to give away vouchers for overbooked flights. The cost of the voucher (which, for a flight that is not full, is only equal to the incremental cost of one more passenger!) is far less than the cost of putting another flight into the air. The cost of an additional passenger on a flight that is not full is very small, equal only to variable cost. X Axis = Number of passengers As number of passengers increases, Total Cost increases

LSA #2 Check on Learning Q1. What is the generic cost expression for incremental cost? Q2. If the relevant range for fixed cost is not exceeded, incremental cost is equal to ___ . A1. (Total Cost of # Units + 1) – (Total Cost of # Units) Show Slide #32 LSA #2: Check on Learning Facilitator’s Note: Ask the following Questions; (Facilitate discussion on answers given) Q1. What is the generic cost expression for incremental cost? A1. (Total Cost of # Units + 1) – (Total Cost of # Units) Q2. If the relevant range for fixed cost is not exceeded, incremental cost is equal to __________________. A2. Variable Cost ** Facilitator’s Note: LSA Summary will be given at the end of this lesson. A2. Variable Cost

LSA #2 Summary During this block, we defined incremental cost and solved activities by graphing to identify how the expression changes with increases to it’s variable cost. Show Slide #33: LSA #2: Summary Facilitator’s Note: During this block, we defined incremental cost and solved activities by graphing to identify how the expression changes with increases to it’s variable cost.

Describe Other Multivariate Cost Expressions Some cost expressions consist of multiple components Example: Cell phone plan Base plan: $35 for 500 minutes Additional minutes: $.25 per minute Data plan: $10 for 200 MB Additional MB of data: $.50 per MB Show Slide #34: Describe other multivariate cost relationships Learning Step/Activity #3: Describe other multivariate cost relationships Method of Instruction: DSL-Discussion (small or large group discussion) Facilitator to Student Ratio: 2:25 Time of Instruction: 30 Minutes Media: PowerPoint, Printed Reference Material Facilitator’s Note: (Facilitator read and facilitate discussion using the slide) Some Cost Expressions consist of multiple components Example: Cell phone plan Base plan: $35 for 500 minutes Additional minutes: $.25 per minute Data plan: $10 for 200 MB Additional MB of data: $.50 per MB These various costs are stacked together to equal the total cost of cell phone usage.

Example: Cell Phone Plan Base plan: $35 for 500 minutes Additional minutes: $.25 per minute Data plan: $10 for 200 MB Additional MB of data: $.50 per MB What is the cost expression? Show Slide #35: Cell Phone Plan (Example) Base plan: $35 for 500 minutes Additional minutes: $.25 per minute Data plan: $10 for 200 MB Additional MB of data: $.50 per MB What is the cost expression? Facilitator’s Note: (Advance slide) Base plan $35 + ($.25 per min * additional minutes) + data plan $10 + ($.50 per MB * additional MB) The cost expression consists of the sum of each of the four components: base plan + additional minutes + data plan + additional MB $35 + ($.25/min * 0 additional minutes) $10 + ($.50 per MB * 50 additional MB) =$70 The included minutes in the base plan were not exceeded, so there is no charge for additional minutes. The data plan, however, was exceeded so there is a charge for the additional usage. $35 + ($.25 per min * 0 additional minutes) + $10 + ($.50 per MB * 50 additional MB) = $70 Base plan $35 + ($.25 per min * add’l mins) + data plan $10 + ($.50 per MB * add’l MB)

Graph of Cell Phone Cost Show Slide #36: Cell Phone Plan (Example) (con’t) Here we show a graph for total cell phone cost at various levels of usage. The cost of 400 min/250 MB = $35 + ($.25 per min * 0 additional minutes) + $10 + ($.50 per MB * 50 additional MB) = $70 The cost of 600 min/100 MB = $35 + ($.25 per min * 100 additional minutes) + $10 + ($.50 per MB * 0 additional MB) = $70 The cost of 500 min/200 MB = $35 + ($.25 per min * 0 additional minutes) + $10 + ($.50 per MB * 0 additional MB) = $45

LSA #3 Check on Learning Q1. You are planning a one-week vacation for you and your significant other. How would you define the cost expression for the trip? A1. There is not necessarily a right or wrong answer to this, as vacation preferences vary. However, the following variables would likely be common to most vacations: 2 persons * airline tickets/person + hotel/night * 7 nights + entertainment cost + food cost Show Slide #37: LSA #3 Check on Learning Facilitator’s Note: Ask the following Questions; (Facilitate discussion on answers given) Q. You are planning a one-week vacation for you and your significant other. How would you define the cost expression for the trip? A. There is not necessarily a right or wrong answer to this, as vacation preferences vary. However, the following variables would likely be common to most vacations: 2 persons * airline tickets/person + hotel/night * 7 nights + entertainment cost + food cost ** Facilitator’s Note: LSA Summary will be given at the end of this lesson.

LSA #1-3 Check on Learning and Summary The Check on learning and Summary for LSA #1-3 will be conducted after the Practical Exercise (PE). Show Slide #38: LSA #3: Describe other multivariate cost relationships Facilitator's Note: The Check on learning and Summary for LSA #1-3 will be conducted after the Practical Exercise (PE).

TLO Summary Show Slide #39: TLO Summary Action: Calculate Total Cost and Incremental Costs Given Various Production Volumes Condition: FM Leaders in a classroom environment working individually and as a member of a small group, using doctrinal and administrative publications, self-study exercises, personal experiences, practical exercises, handouts, and discussion. Standard: With at least 80% accuracy (70% for International learners): Describe multivariate costs Describe incremental costs Describe other multivariate cost relationships Show Slide #39: TLO Summary Facilitator’s Note: Restate the TLO Action: Calculate Total Cost and Incremental Costs Given Various Production Volumes Condition: FM Leaders in a classroom environment working individually and as a member of a small group, using doctrinal and administrative publications, self-study exercises, personal experiences, practical exercises, handouts, and discussion. Standard: With at least 80% accuracy (70% for International learners) Describe multivariate costs Describe incremental costs Describe other multivariate cost relationships “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. Facilitator’s Note: Some cost expressions involve more than one variable. One such cost is a mixed cost. Mixed costs include a fixed component and a variable component. The graph of a mixed cost is an upward sloping line that reflects the variable cost. The cost expression for total mixed cost is fixed cost + variable cost/unit * # units.   Some costs are semi-variable, meaning that they increase in total as number of units increases, but not in direct proportion. An example would be payroll cost that includes overtime pay, or volume discounts. The cost per unit for these types of costs may be represented by a step function. Incremental cost reflects the change in cost from an increase of one additional unit. The incremental cost is calculated by subtracting the total cost at x units from the total cost at x+1 units. Many costs are “stacked” meaning they are the sum of multiple variables or multiple cost expressions. The ability to identify cost relationships and develop cost expressions is a critical skill in cost management. What are your questions?

Practical Exercises Show Slide #40: Deploy the Practical Exercise (PE) Facilitator’s Note: Conduct the Run-phase Method of Instructions. This is your opportunity to apply what you have learned about Calculate Total Cost and Incremental Costs Given Various Production Volumes. You will have 15 minutes to complete the practical exercise (PE). Do your best to complete the PE in the allotted time. We will conduct an review of the PE as a group.