Calculate Expected Values of Alternative Courses of Action 1.
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Calculate Expected Values of Calculate Expected Values of Alternative Courses of ActionAlternative Courses of Action
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Ever had a vacation disaster?Ever had a vacation disaster?
Car trouble? Lost luggage?
Missed flight? Something worse?
How did that affect your vacation
cash flows?
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Terminal Learning ObjectiveTerminal 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
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What is Expected Value?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
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Applications for Expected ValueApplications 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
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Expected Value CalculationExpected 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%6
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Expected Value ExampleExpected 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
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Expected Value ExampleExpected 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 Flow2 -$100
12 1003 and 11 -50All else -25
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Expected Value ExampleExpected Value Example
• What are the probabilities of each outcome?
Outcome Probability2 1/36
12 1/363 and 11 4/36All else 30/36Total 36/36
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Expected Value ExampleExpected Value Example
• Calculate Expected Value:
• Given this expected value, will you roll the dice?
Outcome Probability * Cash Flow = Expected Value2 1/36 * -$100 =
12 1/36 * 100 =3 and 11 4/36 * -50 =All else 30/36 * -25 =Total 36/36
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Expected Value ExampleExpected Value Example
• Calculate Expected Value:
• Given this expected value, will you roll the dice?
Outcome Probability * Cash Flow = Expected Value2 1/36 * -$100 = -$2.78
12 1/36 * 100 =3 and 11 4/36 * -50 =All else 30/36 * -25 =Total 36/36
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Expected Value ExampleExpected Value Example
• Calculate Expected Value:
• Given this expected value, will you roll the dice?
Outcome Probability * Cash Flow = Expected Value2 1/36 * -$100 = -$2.78
12 1/36 * 100 = 2.783 and 11 4/36 * -50 =All else 30/36 * -25 =Total 36/36
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Expected Value ExampleExpected Value Example
• Calculate Expected Value:
• Given this expected value, will you roll the dice?
Outcome Probability * Cash Flow = Expected Value2 1/36 * -$100 = -$2.78
12 1/36 * 100 = 2.783 and 11 4/36 * -50 = -5.55All else 30/36 * -25 =Total 36/36
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Expected Value ExampleExpected Value Example
• Calculate Expected Value:
• Given this expected value, will you roll the dice?
Outcome Probability * Cash Flow = Expected Value2 1/36 * -$100 = -$2.78
12 1/36 * 100 = 2.783 and 11 4/36 * -50 = -5.55All else 30/36 * -25 = -20.83Total 36/36
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Expected Value ExampleExpected Value Example
• Calculate Expected Value:
• Given this expected value, will you roll the dice?
Outcome Probability * Cash Flow = Expected Value2 1/36 * -$100 = -$2.78
12 1/36 * 100 = 2.783 and 11 4/36 * -50 = -5.55All else 30/36 * -25 = -20.83Total 36/36 -$26.38
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Expected Value ExampleExpected Value Example
• Calculate Expected Value:
• Given this expected value, will you roll the dice?
Outcome Probability * Cash Flow = Expected Value2 1/36 * -$100 = -$2.78
12 1/36 * 100 = 2.783 and 11 4/36 * -50 = -5.55All else 30/36 * -25 = -20.83Total 36/36 -$26.38
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Learning CheckLearning Check
• What variables must be defined before calculating Expected Value?
• What does Expected Value represent?
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Demonstration ProblemDemonstration 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• Behind each of the other two curtains there is a $100 bill
• Task: Calculate the Expected Value of Sheila’s alternative courses of action
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Demonstration ProblemDemonstration 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
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Define the OutcomesDefine 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
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Define the ProbabilitiesDefine 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:
Outcome Probability
Car
$100
Total
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Define the ProbabilitiesDefine 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:
Outcome Probability
Car 1/3 or 33.3%
$100 2/3 or 66.7%
Total 3/3 or 100%
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Define the Cash FlowsDefine the Cash Flows
Keep the $1,000• Cash flow is $1,000
Trade $1,000 for Curtain
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Outcome Cash Flow
Car
$100
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Define the Cash FlowsDefine the Cash Flows
Keep the $1,000• Cash flow is $1,000
Trade $1,000 for Curtain
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Outcome Cash Flow
Car
$100
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Define the Cash FlowsDefine the Cash Flows
Keep the $1,000• Cash flow is $1,000
Trade $1,000 for Curtain
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Define the Cash FlowsDefine the Cash Flows
Keep the $1,000• Cash flow is $1,000
Trade $1,000 for Curtain
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Outcome Cash Flow
Car $40,000 - $1,000 - $9000 = +$30,000
$100 $100 - $1,000 = -$900
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Calculate Expected ValueCalculate Expected Value
Keep the $1,000
Outcome % * CF = EV
Keep $1000 100% $1,000 $1,000
Trade $1,000 for Curtain
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Outcome % * CF = EV
Car 33.3% $30,000 $10,000
$100 66.7% -$900 -$600
Total 100% $9,400
Which would you choose?
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Learning CheckLearning Check
• How can Expected Value be used in comparing alternative Courses of Action?
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Expected Value ApplicationExpected 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
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Expected Value ApplicationExpected Value Application
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Expected Value ApplicationExpected Value Application
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Expected Value ApplicationExpected Value Application
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Expected Value ApplicationExpected Value Application
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Expected Value and PlanningExpected 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?
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Expected Value and PlanningExpected Value and Planning
• Expected Value of outsourcing:
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Outcome % * Cash Flow = EV100 repairs 25% * 100 * $750 = $75,000 = $18,750300 repairs 60% * 300 * $750 = $225,000 = $135,000500 repairs 15% * 500 * $750 = $375,000 = $56,250
Total 100% $210,000
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Expected Value and PlanningExpected 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?
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Expected Value and PlanningExpected 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 insourcing37
Outcome % * Cash Flow = EV100 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% $150,500
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Expected Value and NPVExpected 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
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Expected Value and NPVExpected 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?39
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Practical ExercisesPractical Exercises
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Expected Value SpreadsheetExpected Value Spreadsheet
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Use to calculate single scenario expected values
Assures that sum of all
probabilities equals 100%
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Expected Value SpreadsheetExpected Value Spreadsheet
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Spreadsheet tool permits comparison of up to four
courses of actionUses color coding to rank
options
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Practical ExercisePractical Exercise
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