Calculate Expected Values of
Alternative Courses of Action
Intermediate Cost Analysis
and Management
3.1
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
2
12
3 and 11
All else
Cash Flow
-$100
100
-50
-25
8
Expected Value Example
• What are the probabilities of each outcome?
Outcome
2
Probability
1/36
12
3 and 11
All else
Total
1/36
4/36
30/36
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
All else
Total
4/36 *
30/36 *
36/36
-50 =
-25 =
• 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 =
-$2.78
12
1/36 *
100 =
3 and 11
All else
Total
4/36 *
30/36 *
36/36
-50 =
-25 =
• 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
All else
Total
4/36 *
30/36 *
36/36
-50 =
-25 =
• 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
All else
Total
4/36 *
30/36 *
36/36
-50 =
-25 =
-5.55
• 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
All else
Total
4/36 *
30/36 *
36/36
-50 =
-25 =
-5.55
-20.83
• 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
All else
Total
4/36 *
30/36 *
36/36
-50 =
-25 =
-5.55
-20.83
-$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
All else
Total
4/36 *
30/36 *
36/36
-50 =
-25 =
-5.55
-20.83
-$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
Outcome Cash Flow
Car
$40,000 - $1,000 - $9000 =
+$30,000
$100
Value of the car
Gives up $1,000
Tax 22.5% on $40,000
= $40,000
= -$1,000
= -$9,000
25
Define the Cash Flows
Keep the $1,000
• Cash flow is $1,000
Trade $1,000 for Curtain
Outcome Cash Flow
Car
$100
$40,000 - $1,000 - $9000 =
+$30,000
$100 - $1,000 = -$900
26
Calculate Expected Value
Keep the $1,000
Trade $1,000 for Curtain
Outcome
%
* CF
Keep $1000
100%
$1,000
= EV
$1,000
Outcome
%
* CF
= EV
Car
33.3%
$30,000
$10,000
$100
66.7%
-$900
-$600
Total
100%
$9,400
Which would you choose?
27
Learning Check
• How can Expected Value be used in comparing
alternative Courses of Action?
28
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
29
Expected Value Application
Scenario A
+$75,000
Accepted
Scenario B
+10,000
Proposal
Rejected
No change
30
Expected Value Application
50%
Scenario A
+$75,000
Accepted
50%
Scenario B
Proposal
+10,000
100%
Rejected
No change
$0
31
Expected Value Application
50%
Scenario A
Accepted
+$75,000
$42,500
50%
Scenario B
Proposal
+10,000
$25,500
Rejected
$0
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
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?
34
Expected Value and Planning
• Expected Value of outsourcing:
Outcome
100 repairs
300 repairs
%
*
25% *
60% *
Cash Flow
=
100 * $750 = $75,000 =
300 * $750 = $225,000 =
EV
$18,750
$135,000
500 repairs
Total
15% *
100%
500 * $750 = $375,000 =
$56,250
$210,000
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?
36
Expected Value and Planning
• Expected Value of insourcing:
Outcome
%
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
*
Cash Flow
100%
=
EV
$150,500
• 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
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?
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 =
• 70% probability of $200,000 =
• 20% Probability of $100,000 =
$30,000
$140,000
$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 Exercises
40
Expected Value Spreadsheet
Use to calculate single
scenario expected values
Assures that
sum of all
probabilities
equals 100%
41
Expected Value Spreadsheet
Spreadsheet tool permits
comparison of up to four
courses of action
Uses color coding to rank
options
42
Practical Exercise
43