Calculate Expected Values of Alternative Courses of Action Ever had a vacation disaster? Car trouble? Lost luggage? Missed flight? Something worse? How did that affect your vacation cash flows? Terminal Learning Objective • Task: Calculate Expected Values of Alternative Courses of Action • 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: • Define possible outcomes • Determine cash flow value of each possible outcome • Assign probabilities to outcomes 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 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 Expected Value Calculation • Expected Value = Probability of Outcome1 * Dollar Value of Outcome1 + Probability of Outcome2 * Dollar Value of Outcome2 + Probability of Outcome3 * Dollar Value of Outcome3 etc • Assumes probabilities and dollar value of outcomes are known or can be estimated • Probability of all outcomes must equal 100% 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 (snake-eyes): The donor pays $100 A roll of 12: The donor wins $100 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 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 Cash Flow -$100 12 100 and 11 -50 All else -25 Expected Value Example • What are the probabilities of each outcome? Outcome Probability 1/36 12 1/36 and 11 4/36 All else 30/36 Total 36/36 Expected Value Example • Calculate Expected Value: Outcome Probability * Cash Flow = Expected Value 1/36 * -$100 = 12 1/36 * 100 = and 11 4/36 * -50 = All else 30/36 * -25 = Total 36/36 • Given this expected value, will you roll the dice? 10 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 29 Expected Value Application 30 Expected Value Application 31 Expected Value Application 32 Expected Value Application 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? 34 Expected Value and Planning • Expected Value of outsourcing: Outcome % * Cash Flow = EV 100 repairs 25% * 100 * $750 = $75,000 = $18,750 300 repairs 60% * 300 * $750 = $225,000 = $135,000 500 repairs 15% * 500 * $750 = $375,000 = $56,250 Total 100% $210,000 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? 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 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? 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? 39 Practical Exercises 40 Expected Value Spreadsheet Use to calculate single scenario expected values Assures that sum of all probabilities equals 100% 41 Expected Value Spreadsheet Spreadsheet tool permits comparison of up to four courses of action Uses color coding to rank options 42 Practical Exercise 43 ... Task: Calculate Expected Values of Alternative Courses of Action • Condition: You are training to become an ACE with access to ICAM course handouts, readings, and spreadsheet tools and awareness of. .. cost of medical insurance Expected Value Calculation • Expected Value = Probability of Outcome1 * Dollar Value of Outcome1 + Probability of Outcome2 * Dollar Value of Outcome2 + Probability of. .. brand new car worth $40,000 • Behind each of the other two curtains there is a $100 bill • Task: Calculate the Expected Value of Sheila’s alternative courses of action 18 Demonstration Problem • Step