calculate expected values of alternative courses of action 1

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

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

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

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

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?

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

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

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

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

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%

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

Practical ExercisePractical Exercise

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