Calculate Expected Values Principles of Cost Analysis and Management © Dale R Geiger 2011 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 Terminal Learning Objective • • Task: Calculate Expected Values Of Alternative Courses Of Action • Standard: With at least 80% accuracy: 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 • • • Define possible outcomes Determine cash flow value of each possible outcome Assign probabilities to outcomes © Dale R Geiger 2011 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 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 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% © Dale R Geiger 2011 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 © Dale R Geiger 2011 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 © Dale R Geiger 2011 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 © Dale R Geiger 2011 Expected Value Example • Calculate Expected Value: Outcome • Probability * Cash Flow = 1/36 * -$100 = 12 1/36 * 100 = and 11 4/36 * -50 = Given will you All this else expected value,30/36 * roll the dice?-25 = Total Expected Value 36/36 © Dale R Geiger 2011 10 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 Proposal +10,000 100% Rejected No change $0 © Dale R Geiger 2011 31 Expected Value Application 50% Scenario A Accepted $42,500 +$75,000 50% Scenario B Proposal +10,000 $25,500 Rejected $0 © Dale R Geiger 2011 100% No change $0 32 Expected Value Application 50% Scenario A 60% +$75,000 Accepted $42,500 50% Scenario B Proposal +10,000 $25,500 40% 100% Rejected No change $0 $0 © Dale R Geiger 2011 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 % * 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 © 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 • % * Cash Flow = EV 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 100% attractive: Insourcing is more • • $150,500 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 = $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 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 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 ... cost of medical insurance â Dale R Geiger 2011 Expected Value Calculation • Expected Value = Probability of Outcome1 * Dollar Value of Outcome1 + Probability of Outcome2 * Dollar Value of Outcome2... cash flows? © Dale R Geiger 2011 Terminal Learning Objective • • Task: Calculate Expected Values Of Alternative Courses Of Action • Standard: With at least 80% accuracy: Condition: You are a... roll the dice?-25 = Total Expected Value -$2.78 36/36 © Dale R Geiger 2011 11 Expected Value Example • Calculate Expected Value: Outcome • Probability * Cash Flow = Expected Value 1/36 * -$100