Calculate Expected Values
Principles of Cost Analysis and
Management
© Dale R. Geiger 2011
1
Ever had a vacation disaster?
Car trouble?
Lost luggage?
Missed flight?
Something worse?
How did that affect
your vacation
cash flows?
© Dale R. Geiger 2011
2
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 2011
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
© Dale R. Geiger 2011
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
© Dale R. Geiger 2011
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%
© Dale R. Geiger 2011
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
© Dale R. Geiger 2011
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
Cash Flow
-$100
100
3 and 11
All else
© Dale R. Geiger 2011
-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
© Dale R. Geiger 2011
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?
© Dale R. Geiger 2011
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?
© Dale R. Geiger 2011
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?
© Dale R. Geiger 2011
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?
© Dale R. Geiger 2011
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?
© Dale R. Geiger 2011
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?
© Dale R. Geiger 2011
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?
© Dale R. Geiger 2011
16
Check on Learning
• What variables must be defined before
calculating Expected Value?
• What does Expected Value represent?
© Dale R. Geiger 2011
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 (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 2011
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
© Dale R. Geiger 2011
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
© Dale R. Geiger 2011
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
© Dale R. Geiger 2011
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%
© Dale R. Geiger 2011
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Define the Cash Flows
Keep the $1,000
• Cash flow is $1,000
Trade $1,000 for Curtain
Outcome Cash Flow
Car
$100
© Dale R. Geiger 2011
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Define the Cash Flows
Keep the $1,000
• Cash flow is $1,000
Trade $1,000 for Curtain
Outcome Cash Flow
Car
$100
© Dale R. Geiger 2011
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
© Dale R. Geiger 2011
= $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
© Dale R. Geiger 2011
$40,000 - $1,000 - $9000 =
+$30,000
$100 - $1,000 = -$900
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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?
© Dale R. Geiger 2011
27
Check on Learning
• How can Expected Value be used in comparing
alternative Courses of Action?
© Dale R. Geiger 2011
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
© Dale R. Geiger 2011
29
Expected Value Application
Scenario A
+$75,000
Accepted
Scenario B
+10,000
Proposal
Rejected
© Dale R. Geiger 2011
No change
30
Expected Value Application
50%
Scenario A
+$75,000
Accepted
50%
Scenario B
Proposal
+10,000
100%
Rejected
No change
$0
© Dale R. Geiger 2011
31
Expected Value Application
50%
Scenario A
Accepted
+$75,000
$42,500
50%
Scenario B
Proposal
+10,000
$25,500
Rejected
$0
© Dale R. Geiger 2011
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
© Dale R. Geiger 2011
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?
© Dale R. Geiger 2011
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
© Dale R. Geiger 2011
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?
© Dale R. Geiger 2011
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
© Dale R. Geiger 2011
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?
© Dale R. Geiger 2011
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?
© Dale R. Geiger 2011
39
Check on Learning
• How can expected value be used to plan for
costs when level of activity is uncertain?
© Dale R. Geiger 2011
40
Practical Exercises
© Dale R. Geiger 2011
41
Expected Value Spreadsheet
Use to calculate single
scenario expected values
Assures that
sum of all
probabilities
equals 100%
© Dale R. Geiger 2011
42
Expected Value Spreadsheet
Spreadsheet tool permits
comparison of up to four
courses of action
Uses color coding to rank
options
© Dale R. Geiger 2011
43
Practical Exercise
© Dale R. Geiger 2011
44