Slides 3 1 calculate expected values of alternative courses
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Calculate Expected Values of
Alternative Courses of Action
1
Ever had a vacation disaster?
Car trouble?
Lost luggage?
Missed flight?
Something worse?
How did that affect
your vacation
cash flows?
2
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
3
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
4
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
5
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%
6
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
7
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
2
-$100
12
100
3 and 11
-50
All else
-25
8
Expected Value Example
• What are the probabilities of each outcome?
Outcome
Probability
2
1/36
12
1/36
3 and 11
4/36
All else
30/36
Total
36/36
9
Expected Value Example
• Calculate Expected Value:
Outcome Probability * Cash Flow = Expected Value
2
1/36 *
-$100 =
12
1/36 *
100 =
3 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 Example
• Calculate Expected Value:
Outcome Probability * Cash Flow = Expected Value
2
1/36 *
-$100 =
12
1/36 *
100 =
3 and 11
4/36 *
-50 =
All else
30/36 *
-25 =
Total
-$2.78
36/36
• Given this expected value, will you roll the
dice?
11
Expected Value Example
• Calculate Expected Value:
Outcome Probability * Cash Flow = Expected Value
2
1/36 *
-$100 =
-$2.78
12
1/36 *
100 =
2.78
3 and 11
4/36 *
-50 =
All else
30/36 *
-25 =
Total
36/36
• Given this expected value, will you roll the
dice?
12
Expected Value Example
• Calculate Expected Value:
Outcome Probability * Cash Flow = Expected Value
2
1/36 *
-$100 =
-$2.78
12
1/36 *
100 =
2.78
3 and 11
4/36 *
-50 =
-5.55
All else
30/36 *
-25 =
Total
36/36
• Given this expected value, will you roll the
dice?
13
Expected Value Example
• Calculate Expected Value:
Outcome Probability * Cash Flow = Expected Value
2
1/36 *
-$100 =
-$2.78
12
1/36 *
100 =
2.78
3 and 11
4/36 *
-50 =
-5.55
All else
30/36 *
-25 =
-20.83
Total
36/36
• Given this expected value, will you roll the
dice?
14
Expected Value Example
• Calculate Expected Value:
Outcome Probability * Cash Flow = Expected Value
2
1/36 *
-$100 =
-$2.78
12
1/36 *
100 =
2.78
3 and 11
4/36 *
-50 =
-5.55
All else
30/36 *
-25 =
-20.83
Total
36/36
-$26.38
• Given this expected value, will you roll the
dice?
15
Expected Value Example
• Calculate Expected Value:
Outcome Probability * Cash Flow = Expected Value
2
1/36 *
-$100 =
-$2.78
12
1/36 *
100 =
2.78
3 and 11
4/36 *
-50 =
-5.55
All else
30/36 *
-25 =
-20.83
Total
36/36
-$26.38
• Given this expected value, will you roll the
dice?
16
Learning Check
• What variables must be defined before
calculating Expected Value?
• What does Expected Value represent?
17
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
• 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 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
19
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
20
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:
Outcome
Probability
Car
$100
Total
21
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:
Outcome
Probability
Car
1/3 or 33.3%
$100
2/3 or 66.7%
Total
3/3 or 100%
22
Define the Cash Flows
Keep the $1,000
• Cash flow is $1,000
Trade $1,000 for Curtain
Outcome Cash Flow
Car
$100
23
Define the Cash Flows
Keep the $1,000
• Cash flow is $1,000
Trade $1,000 for Curtain
Outcome Cash Flow
Car
$100
24
Define the Cash Flows
Keep the $1,000
• Cash flow is $1,000
Trade $1,000 for Curtain
25
