Calculate Expected Values © Dale R. Geiger 20111

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

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

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

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

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

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

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-$ and All else-25 © Dale R. Geiger 20118

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 Outcome%*Cash Flow=EV 100 repairs25%*(100 * $300) + $65,000 = $95,000=$23, repairs60%*(300 * $300) + $65,000 = $155,000=$93, repairs15%*(500 * $300) + $65,000 = $225,000=$33,750 Total100%$150,500

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

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

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

Practical Exercises © Dale R. Geiger

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

Expected Value Spreadsheet © Dale R. Geiger 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

Practical Exercise © Dale R. Geiger