Calculate Expected Values Principles of Cost Analysis and
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Calculate Expected Values Principles of Cost Analysis and Management © Dale R. Geiger 2011 1
Ever had a vacation disaster? Car trouble? Lost luggage? Missed flight? Something worse? How did that affect your vacation cash flows? © Dale R. Geiger 2011 2
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 2011 3
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 2011 4
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 2011 5
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 2011 6
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 2011 7
Expected Value Example • What are the possible outcomes? • 2, 12, 3, 11 and everything else • What are the cash flows associated with each outcome? Outcome 2 12 3 and 11 Cash Flow -$100 -50 All else © Dale R. Geiger 2011 -25 8
Expected Value Example • What are the probabilities of each outcome? Outcome 2 12 3 and 11 Probability 1/36 4/36 All else Total © Dale R. Geiger 2011 30/36 36/36 9
Expected Value Example • Calculate Expected Value: Outcome Probability 2 1/36 12 1/36 3 and 11 4/36 All else Total * Cash Flow = Expected Value * -$100 = * -50 = 30/36 * 36/36 -25 = • Given this expected value, will you roll the dice? © Dale R. Geiger 2011 10
Expected Value Example • Calculate Expected Value: Outcome Probability 2 1/36 12 1/36 3 and 11 4/36 All else Total * Cash Flow = Expected Value * -$100 = -$2. 78 * 100 = * -50 = 30/36 * 36/36 -25 = • Given this expected value, will you roll the dice? © Dale R. Geiger 2011 11
Expected Value Example • Calculate Expected Value: Outcome Probability 2 1/36 12 1/36 3 and 11 4/36 All else Total * Cash Flow = Expected Value * -$100 = -$2. 78 * 100 = 2. 78 * -50 = 30/36 * 36/36 -25 = • Given this expected value, will you roll the dice? © Dale R. Geiger 2011 12
Expected Value Example • Calculate Expected Value: Outcome Probability 2 1/36 12 1/36 3 and 11 4/36 All else Total * Cash Flow = Expected Value * -$100 = -$2. 78 * 100 = 2. 78 * -50 = -5. 55 30/36 * 36/36 -25 = • Given this expected value, will you roll the dice? © Dale R. Geiger 2011 13
Expected Value Example • Calculate Expected Value: Outcome Probability 2 1/36 12 1/36 3 and 11 4/36 All else Total * Cash Flow = Expected Value * -$100 = -$2. 78 * 100 = 2. 78 * -50 = -5. 55 30/36 * 36/36 -25 = -20. 83 • Given this expected value, will you roll the dice? © Dale R. Geiger 2011 14
Expected Value Example • Calculate Expected Value: Outcome Probability 2 1/36 12 1/36 3 and 11 4/36 All else Total * Cash Flow = Expected Value * -$100 = -$2. 78 * 100 = 2. 78 * -50 = -5. 55 30/36 * 36/36 -25 = -20. 83 -$26. 38 • Given this expected value, will you roll the dice? © Dale R. Geiger 2011 15
Expected Value Example • Calculate Expected Value: Outcome Probability 2 1/36 12 1/36 3 and 11 4/36 All else Total * Cash Flow = Expected Value * -$100 = -$2. 78 * 100 = 2. 78 * -50 = -5. 55 30/36 * 36/36 -25 = -20. 83 -$26. 38 • Given this expected value, will you roll the dice? © Dale R. Geiger 2011 16
Check on Learning • What variables must be defined before calculating Expected Value? • What does Expected Value represent? © Dale R. Geiger 2011 17
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 2011 18
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 2011 19
Define the Outcomes Course of Action 1: Course of Action 2: • Keep the $1, 000 • Trade $1, 000 for one of the curtains • Two possible outcomes: • New car • $100 bill © Dale R. Geiger 2011 20
Define the Probabilities Keep the $1, 000 Trade $1, 000 for Curtain: • Sheila already has the $1, 000 in hand • This is a certain event • The probability of a certain event is 100% Outcome Probability Car $100 Total © Dale R. Geiger 2011 21
Define the Probabilities Keep the $1, 000 Trade $1, 000 for Curtain: • Sheila already has the $1, 000 in hand • This is a certain event • The probability of a certain event is 100% Outcome Probability Car 1/3 or 33. 3% $100 2/3 or 66. 7% Total 3/3 or 100% © Dale R. Geiger 2011 22
Define the Cash Flows Keep the $1, 000 • Cash flow is $1, 000 Trade $1, 000 for Curtain Outcome Cash Flow Car $100 © Dale R. Geiger 2011 23
Define the Cash Flows Keep the $1, 000 • Cash flow is $1, 000 Trade $1, 000 for Curtain Outcome Cash Flow Car $100 © Dale R. Geiger 2011 24
Define the Cash Flows Keep the $1, 000 • Cash flow is $1, 000 Trade $1, 000 for Curtain Outcome Cash Flow Car $40, 000 - $1, 000 - $9000 = +$30, 000 $100 Value of the car Gives up $1, 000 Tax 22. 5% on $40, 000 © Dale R. Geiger 2011 = $40, 000 = -$1, 000 = -$9, 000 25
Define the Cash Flows Keep the $1, 000 • Cash flow is $1, 000 Trade $1, 000 for Curtain Outcome Cash Flow Car $100 © Dale R. Geiger 2011 $40, 000 - $1, 000 - $9000 = +$30, 000 $100 - $1, 000 = -$900 26
Calculate Expected Value Keep the $1, 000 Trade $1, 000 for Curtain Outcome % * CF Keep $1000 100% $1, 000 = EV $1, 000 Outcome % * CF = EV Car 33. 3% $30, 000 $100 66. 7% -$900 -$600 Total 100% $9, 400 Which would you choose? © Dale R. Geiger 2011 27
Check on Learning • How can Expected Value be used in comparing alternative Courses of Action? © Dale R. Geiger 2011 28
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 2011 29
Expected Value Application Scenario A +$75, 000 Accepted Scenario B +10, 000 Proposal Rejected © Dale R. Geiger 2011 No change 30
Expected Value Application 50% Scenario A +$75, 000 Accepted 50% Scenario B +10, 000 Proposal Rejected © Dale R. Geiger 2011 100% No change $0 31
Expected Value Application Accepted $42, 500 Proposal $25, 500 Rejected $0 © Dale R. Geiger 2011 50% Scenario A +$75, 000 50% Scenario B +10, 000 100% No change $0 32
Expected Value Application 60% Accepted $42, 500 Proposal $25, 500 40% Rejected $0 © Dale R. Geiger 2011 50% Scenario A +$75, 000 50% Scenario B +10, 000 100% No change $0 33
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 2011 34
Expected Value and Planning • Expected Value of outsourcing: Outcome 100 repairs 300 repairs 500 repairs % 25% 60% 15% Total 100% * * Cash Flow 100 * $750 = $75, 000 300 * $750 = $225, 000 500 * $750 = $375, 000 = = EV $18, 750 $135, 000 $56, 250 $210, 000 © Dale R. Geiger 2011 35
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 2011 36
Expected Value and Planning • Expected Value of insourcing: Outcome % 100 repairs 25% * (100 * $300) + $65, 000 = $95, 000 = $23, 750 300 repairs 60% * (300 * $300) + $65, 000 = $155, 000 = $93, 000 500 repairs 15% * (500 * $300) + $65, 000 = $225, 000 = $33, 750 Total * Cash Flow 100% = EV $150, 500 • 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 2011 37
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 2011 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 = • 70% probability of $200, 000 = • 20% Probability of $100, 000 = $30, 000 $140, 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 2011 39
Check on Learning • How can expected value be used to plan for costs when level of activity is uncertain? © Dale R. Geiger 2011 40
Practical Exercises © Dale R. Geiger 2011 41
Expected Value Spreadsheet Use to calculate single scenario expected values Assures that sum of all probabilities equals 100% © Dale R. Geiger 2011 42
Expected Value Spreadsheet tool permits comparison of up to four courses of action Uses color coding to rank options © Dale R. Geiger 2011 43
Practical Exercise © Dale R. Geiger 2011 44
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