1. Calculate Total Cost And Incremental Costs © Dale R. Geiger 20111

2. 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? © Dale R. Geiger 20112

3. Terminal Learning Objective Task: Calculate Total Cost And Incremental Costs Given Various Production Volumes Condition: You are a cost advisor technician with access to all regulations/course handouts, and awareness of Operational Environment (OE)/Contemporary Operational Environment (COE) Standard: With at least 80% accuracy: Describe multivariate (mixed) and incremental costs Express total multivariate cost in an equation Graph total multivariate cost over a relevant range Express incremental cost in an equation © Dale R. Geiger 20113

4. Cost Definitions Mixed Costs Mixed Costs - A combination of fixed and variable costs Total Cost = Variable Cost + Fixed Cost Also known as multivariate costs © Dale R. Geiger 20114

5. 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 © Dale R. Geiger 20115

6. 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 © Dale R. Geiger 20116

7. 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 © Dale R. Geiger 20117

8. 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 cost expression for Fixed cost? Fixed cost = $350,000 © Dale R. Geiger 20118

9. 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 cost expression for Fixed cost? Fixed cost = $350,000 © Dale R. Geiger 20119

10. 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 cost expression for Variable Cost? Variable cost = $20,000/day * # of days © Dale R. Geiger 201110

11. 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 cost expression for Variable Cost? Variable cost = $20,000 per day * # of days © Dale R. Geiger 201111

12. 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 cost expression for Total Cost of on-location training? © Dale R. Geiger 201112

13. 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 cost expression for Total Cost of on-location training? Total Cost = Variable cost + Fixed Cost Total Cost = $20,000 per day * #days + $350,000 © Dale R. Geiger 201113

14. Graph of Mixed Cost X Axis = Number of Days As Number of Days increases, Fixed Cost does not change $K © Dale R. Geiger 2011 14

15. Graph of Mixed Cost X Axis = Number of Days As Number of Days increases, Variable Cost increases $K Variable cost for 10 days = $20K per day * 10 days = $200K Variable cost for 10 days = $20K per day * 10 days = $200K © Dale R. Geiger 2011 15

16. Graph of Mixed Cost X Axis = Number of Days As Number of Days increases, both Variable Cost and Total Cost increase $K Total cost for 10 days = $20K per day * 10 days + $350K or $550K Total cost for 10 days = $20K per day * 10 days + $350K or $550K © Dale R. Geiger 2011 16

17. Questions © Dale R. Geiger 201117

18. Cost Definitions Semi-variable Cost Semi-variable Cost - Costs that Increase as Unit of Output increases, but not in Direct Proportion Examples: Hours worked by an employee Miles driven Students in a course © Dale R. Geiger 201118

19. Semi-Variable Cost Example 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 © Dale R. Geiger 201119

20. Cost Expression for Semi Variable The cost expression for Total Wage Cost is: Straight Time Hours * Straight Time $ per Hour + Overtime Hours * 1.5 * Straight Time $ per Hour © Dale R. Geiger 201120

21. Cost Expression for Semi Variable If the total number of hours worked is 30 and straight-time rate is $15 per hour then: = $450 30 Straight Time Hours *$15 per Hour+ 0 Overtime Hours * 1.5 * Straight Time $ per Hour © Dale R. Geiger 201121

22. Cost Expression for Semi Variable If the total number of hours worked is 44 and straight-time rate is $15 per hour then: = $690 40 Straight Time Hours *$15 per Hour+ 4 Overtime Hours * 1.5 * $15 per Hour © Dale R. Geiger 201122

23. Graph for Total Wage Cost X Axis = # of Hours Worked As # Hours Worked increases, total Wage Cost increases, but not uniformly © Dale R. Geiger 2011 23

24. Graph for Wage Cost per Hour X Axis = # of Hours Worked As # Hours Worked increases, Wage Cost per Hour remains the same for the relevant range This is known as a Step Function. Cost per Hour for Hours 0-40 = $15 Cost per Hour for Hours 41-60 = $22.50 This is known as a Step Function. Cost per Hour for Hours 0-40 = $15 Cost per Hour for Hours 41-60 = $22.50 © Dale R. Geiger 2011 24

25. 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? © Dale R. Geiger 201125

26. Graph of Total Cost © Dale R. Geiger 201126

27. Graph of Unit Cost © Dale R. Geiger 201127

28. Check on Learning What is the generic cost expression for a mixed cost? A cost that increases as output increases but not in direct proportion is called a - cost. © Dale R. Geiger 201128

29. Cost Definition Incremental Costs - 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) © Dale R. Geiger 201129

30. 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 © Dale R. Geiger 201130

31. Graph Airline Flight Cost $K X Axis = Number of passengers As number of passengers increases, Fixed cost increases in a step-wise fashion © Dale R. Geiger 2011 31

32. Incremental Cost Example 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 cost expression for Total Cost for a single flight? Variable Cost $10 per passenger * # passengers + Fixed Cost $15,000 © Dale R. Geiger 201132

33. Incremental Cost Example 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 cost expression for Total Cost for a single flight? Variable Cost $10 per passenger * # passengers + Fixed Cost $15,000 © Dale R. Geiger 201133

34. Incremental Cost Example 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 Total Cost for 125 passengers? $10 per passenger * 125 passengers + $15,000 = $27,500 © Dale R. Geiger 201134

35. Incremental Cost Example 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 Total Cost for 125 passengers? $10 per passenger * 125 passengers + $15,000 = $16,250 © Dale R. Geiger 201135

36. Incremental Cost Example 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 125 to 126 passengers? Incremental cost = Cost of 126 psgrs – Cost of 125 psgrs ($10 * 126 + $15,000) - ($10 * 125 + $15,000) = $10 © Dale R. Geiger 201136

37. Incremental Cost Example 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 125 to 126 passengers? Incremental cost = Cost of 126 psgrs – Cost of 125 psgrs ($10 * 126 + $15,000) - ($10 * 125 + $15,000) = $10 © Dale R. Geiger 2011 37

38. Graph Airline Flight Cost $K X Axis = Number of passengers As number of passengers increases, Total Cost increases Total Cost at 125 passengers = 125 * $10 per passenger + $15,000 = $16,250 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 Total Cost at 126 passengers = 126 * $10 per passenger + $15,000 = $16,260 Incremental cost = $16,260 – $16,250 = 10 © Dale R. Geiger 2011 38

39. Incremental Cost Example 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 = Cost of 151 psgrs – Cost of 150 psgrs ($10 * 151 + $30,000) - ($10 * 150 + $15,000) = $15,010 © Dale R. Geiger 201139

40. Incremental Cost Example 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 = Cost of 151 psgrs – Cost of 150 psgrs ($10 * 151 + $30,000) - ($10 * 150 + $15,000) = $15,010 © Dale R. Geiger 201140

41. Graph Airline Flight Cost $K X Axis = Number of passengers As number of passengers increases, Total Cost increases Total Cost at 150 psgrs = 150 * $10 per psgr+ $15,000 Or $16,500 Total Cost at 150 psgrs = 150 * $10 per psgr+ $15,000 Or $16,500 Total Cost at 151 psgrs = 151 * $10 per psgr + $30,000 Or $31,510 Total Cost at 151 psgrs = 151 * $10 per psgr + $30,000 Or $31,510 Incremental cost = $16,500 – $31,510 = $15,010 © Dale R. Geiger 2011 41

42. Check on Learning What is the generic cost expression for incremental cost? If the relevant range for fixed cost is not exceeded, incremental cost is equal to. © Dale R. Geiger 201142

43. 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 © Dale R. Geiger 201143

44. 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? Base plan $35 + $.25/min * additional minutes + data plan $10 + $.50/MB * additional MB © Dale R. Geiger 201144

45. 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? Base plan $35 + ($.25 per min * add’l mins) + data plan $10 + ($.50 per MB * add’l MB) © Dale R. Geiger 201145

46. 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 if 400 minutes and 250 MB are used? $35 + ($.25/min * 0 additional minutes) + $10 + ($.50/MB * 50 additional MB) © Dale R. Geiger 201146

47. 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 if 400 minutes and 250 MB are used? $35 + ($.25 per min * 0 additional minutes) + $10 + ($.50 per MB * 50 additional MB) = $70 © Dale R. Geiger 201147

48. Graph of Cell Phone Cost © Dale R. Geiger 201148

49. Check on Learning You are planning a one-week vacation for you and your significant other. How would you define the cost expression for the trip? © Dale R. Geiger 201149

50. Practical Exercises © Dale R. Geiger 201150