1. Calculate Expected Values © Dale R. Geiger 20111

2. Ever had a vacation disaster? Car trouble? Lost luggage? Missed flight? Something worse? How did that affect your vacation cash flows? © Dale R. Geiger 20112

3. Terminal Learning Objective Task: Calculate Expected Values Of Alternative Courses Of Action Condition: You are a cost advisor technician with access to all regulations/course handouts, and awareness of Operational Environment (OE)/Contemporary Operational Environment (COE) variables and actors. Standard: With at least 80% accuracy: Define possible outcomes Determine cash flow value of each possible outcome Assign probabilities to outcomes © Dale R. Geiger 20113

4. What is Expected Value? Recognizes that cash flows are frequently tied to uncertain outcomes Example: It is difficult to plan for cost when different performance scenarios are possible and the cost of each is vastly different Expected Value represents a weighted average cash flow of the possible outcomes © Dale R. Geiger 20114

5. Applications for Expected Value Deciding what cash flows to use in a Net Present Value calculation when actual cash flows are uncertain Reducing multiple uncertain cash flow outcomes to a single dollar value for a “reality check” Example: cost of medical insurance © Dale R. Geiger 20115

6. Expected Value Calculation Expected Value = Probability of Outcome 1 * Dollar Value of Outcome 1 + Probability of Outcome 2 * Dollar Value of Outcome 2 + Probability of Outcome 3 * Dollar Value of Outcome 3 etc. Assumes probabilities and dollar value of outcomes are known or can be estimated Probability of all outcomes must equal 100% © Dale R. Geiger 20116

7. Expected Value Example The local youth center is running the following fundraising promotion: Donors will roll a pair of dice, with the following outcomes: A roll of 2 (snake-eyes): The donor pays $100 A roll of 12: The donor wins $100 3 and 11: The donor pays $50 All other rolls: The donor pays $25 Task: You are considering rolling the dice. Calculate the expected value of your donation © Dale R. Geiger 20117

8. Expected Value Example What are the possible outcomes? 2, 12, 3, 11 and everything else What are the cash flows associated with each outcome? OutcomeCash Flow 2-$100 12100 3 and 11-50 All else-25 © Dale R. Geiger 20118

9. Expected Value Example What are the probabilities of each outcome? OutcomeProbability 21/36 121/36 3 and 114/36 All else30/36 Total36/36 © Dale R. Geiger 20119

10. Expected Value Example Calculate Expected Value: Given this expected value, will you roll the dice? OutcomeProbability*Cash Flow=Expected Value 21/36*-$100= 121/36*100= 3 and 114/36*-50= All else30/36*-25= Total36/36 © Dale R. Geiger 201110

11. Expected Value Example Calculate Expected Value: Given this expected value, will you roll the dice? OutcomeProbability*Cash Flow=Expected Value 21/36*-$100=-$2.78 121/36*100= 3 and 114/36*-50= All else30/36*-25= Total36/36 © Dale R. Geiger 201111

12. Expected Value Example Calculate Expected Value: Given this expected value, will you roll the dice? OutcomeProbability*Cash Flow=Expected Value 21/36*-$100=-$2.78 121/36*100=2.78 3 and 114/36*-50= All else30/36*-25= Total36/36 © Dale R. Geiger 201112

13. Expected Value Example Calculate Expected Value: Given this expected value, will you roll the dice? OutcomeProbability*Cash Flow=Expected Value 21/36*-$100=-$2.78 121/36*100=2.78 3 and 114/36*-50=-5.55 All else30/36*-25= Total36/36 © Dale R. Geiger 201113

14. Expected Value Example Calculate Expected Value: Given this expected value, will you roll the dice? OutcomeProbability*Cash Flow=Expected Value 21/36*-$100=-$2.78 121/36*100=2.78 3 and 114/36*-50=-5.55 All else30/36*-25=-20.83 Total36/36 © Dale R. Geiger 201114

15. Expected Value Example Calculate Expected Value: Given this expected value, will you roll the dice? OutcomeProbability*Cash Flow=Expected Value 21/36*-$100=-$2.78 121/36*100=2.78 3 and 114/36*-50=-5.55 All else30/36*-25=-20.83 Total36/36-$26.38 © Dale R. Geiger 201115

16. Expected Value Example Calculate Expected Value: Given this expected value, will you roll the dice? OutcomeProbability*Cash Flow=Expected Value 21/36*-$100=-$2.78 121/36*100=2.78 3 and 114/36*-50=-5.55 All else30/36*-25=-20.83 Total36/36-$26.38 © Dale R. Geiger 201116

17. Check on Learning What variables must be defined before calculating Expected Value? What does Expected Value represent? © Dale R. Geiger 201117

18. Demonstration Problem Sheila is playing Let’s Make a Deal and just won $1000. She now has two alternative courses of action: A)Keep the $1000 B)Trade the $1000 for a chance to choose between three curtains: Behind one of the three curtains is a brand new car worth $40,000 (which will be taxed at 22.5%) Behind each of the other two curtains there is a $100 bill Task: Calculate the Expected Value of Sheila’s alternative courses of action © Dale R. Geiger 201118

19. Demonstration Problem Step 1: Define the outcomes Step 2: Define the probabilities of each outcome Step 3: Define the cash flows associated with each outcome Step 4: Calculate Expected Value © Dale R. Geiger 201119

20. Define the Outcomes Course of Action 1: Keep the $1,000 Course of Action 2: Trade $1,000 for one of the curtains Two possible outcomes: New car $100 bill © Dale R. Geiger 201120

21. Define the Probabilities Keep the $1,000 Sheila already has the $1,000 in hand This is a certain event The probability of a certain event is 100% Trade $1,000 for Curtain: OutcomeProbability Car $100 Total © Dale R. Geiger 201121

22. Define the Probabilities Keep the $1,000 Sheila already has the $1,000 in hand This is a certain event The probability of a certain event is 100% Trade $1,000 for Curtain: OutcomeProbability Car1/3 or 33.3% $1002/3 or 66.7% Total3/3 or 100% © Dale R. Geiger 201122

23. Define the Cash Flows Keep the $1,000 Cash flow is $1,000 Trade $1,000 for Curtain © Dale R. Geiger 201123 OutcomeCash Flow Car $100

24. Define the Cash Flows Keep the $1,000 Cash flow is $1,000 Trade $1,000 for Curtain © Dale R. Geiger 201124 OutcomeCash Flow Car $100

25. Define the Cash Flows Keep the $1,000 Cash flow is $1,000 Trade $1,000 for Curtain © Dale R. Geiger 201125 OutcomeCash Flow Car $100

26. Define the Cash Flows Keep the $1,000 Cash flow is $1,000 Trade $1,000 for Curtain © Dale R. Geiger 201126 OutcomeCash Flow Car$40,000 - $1,000 - $9000 = +$30,000 $100$100 - $1,000 = -$900

27. Calculate Expected Value Keep the $1,000 Outcome%* CF= EV Keep $1000100%$1,000 Trade $1,000 for Curtain © Dale R. Geiger 201127 Outcome%* CF= EV Car33.3%$30,000$10,000 $10066.7%-$900-$600 Total100%$9,400 Which would you choose?

28. Check on Learning How can Expected Value be used in comparing alternative Courses of Action? © Dale R. Geiger 201128

29. Expected Value Application Your organization has submitted a proposal for a project. Probability of acceptance is 60% If proposal is accepted you face two scenarios which are equally likely: Scenario A: net increase in cash flows of $75,000. Scenario B: net increase in cash flows of $10,000. If proposal is not accepted you will experience no change in cash flows. Task: Calculate the Expected Value of the proposal © Dale R. Geiger 201129

30. Expected Value Application © Dale R. Geiger 201130 Proposal Accepted Scenario A +$75,000 Scenario B +10,000 RejectedNo change

31. Expected Value Application © Dale R. Geiger 201131 ProposalAccepted 50% Scenario A +$75,000 50% Scenario B +10,000 Rejected 100% No change $0

32. Expected Value Application © Dale R. Geiger 201132 Proposal $25,500 Accepted $42,500 50% Scenario A +$75,000 50% Scenario B +10,000 Rejected $0 100% No change $0

33. Expected Value Application © Dale R. Geiger 201133 Proposal $25,500 60% Accepted $42,500 50% Scenario A +$75,000 50% Scenario B +10,000 40% Rejected $0 100% No change $0

34. Expected Value and Planning If you outsource the repair function, total cost will equal $750 per repair. Historical data suggests the following scenarios: 25% probability of 100 repairs 60% probability of 300 repairs 15% probability of 500 repairs How much should you plan to spend for repair cost if you outsource? © Dale R. Geiger 201134

35. Expected Value and Planning Expected Value of outsourcing: © Dale R. Geiger 201135 Outcome%*Cash Flow=EV 100 repairs25%*100 * $750 = $75,000=$18,750 300 repairs60%*300 * $750 = $225,000=$135,000 500 repairs15%*500 * $750 = $375,000=$56,250 Total100%$210,000

36. Expected Value and Planning If you insource the repair function, total cost will equal $65,000 fixed costs plus variable cost of $300 per repair How much should you plan to spend for repair cost if you insource? Given these assumptions, which option is more attractive? © Dale R. Geiger 201136

37. Expected Value and Planning Expected Value of insourcing: Insourcing is more attractive: Total cash flow is higher when repairs are few, but Probabilities of more repairs and the savings when repairs are many justify insourcing © Dale R. Geiger 201137 Outcome%*Cash Flow=EV 100 repairs25%*(100 * $300) + $65,000 = $95,000=$23,750 300 repairs60%*(300 * $300) + $65,000 = $155,000=$93,000 500 repairs15%*(500 * $300) + $65,000 = $225,000=$33,750 Total100%$150,500

38. Expected Value and NPV Proposed project requires a $600,000 up-front investment Project has a five year life with the following potential annual cash flows: 10% probability of $300,000 = $30,000 70% probability of $200,000 = $140,000 20% Probability of $100,000 = $20,000 What is the EV of the annual cash flow? $190,000 How would this information be used to evaluate the project’s NPV? © Dale R. Geiger 201138

39. Expected Value and NPV Proposed project requires a $600,000 up-front investment Project has a five year life with the following potential annual cash flows: 10% probability of $300,000 = $30,000 70% probability of $200,000 = $140,000 20% Probability of $100,000 = $20,000 What is the EV of the annual cash flow? $190,000 How would this information be used to evaluate the project’s NPV? © Dale R. Geiger 201139

40. Check on Learning How can expected value be used to plan for costs when level of activity is uncertain? © Dale R. Geiger 201140

41. Practical Exercises © Dale R. Geiger 201141

42. Expected Value Spreadsheet © Dale R. Geiger 201142 Use to calculate single scenario expected values Assures that sum of all probabilities equals 100%

43. Expected Value Spreadsheet © Dale R. Geiger 201143 Spreadsheet tool permits comparison of up to four courses of action Uses color coding to rank options Spreadsheet tool permits comparison of up to four courses of action Uses color coding to rank options

44. Practical Exercise © Dale R. Geiger 201144