1. Calculate Expected Values of Alternative Courses of Action
Intermediate Cost Analysis
and Management
3.1

2. Ever had a vacation disaster?
Car trouble? Lost luggage? Missed flight? Something worse? How did that affect your vacation cash flows?

3. 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

4. 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

5. 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

6. Expected Value Calculation
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%

7. Expected Value Example (Cont.)
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

8. Expected Value Example (Cont.)
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

9. Expected Value Example (Cont.)
What are the probabilities of each outcome?
Outcome
Probability 2
1/36 12
3 and 11
4/36
All else
30/36
Total
36/36

10. Expected Value Example (Cont.)
Calculate Expected Value:
Given this expected value, will you roll the dice?
Outcome
Probability *
Cash Flow =
Expected Value 2
1/36
-$100 12
100
3 and 11
4/36
-50
All else
30/36
-25
Total
36/36

11. Expected Value Example (Cont.)
Calculate Expected Value:
Given this expected value, will you roll the dice?
Outcome
Probability *
Cash Flow =
Expected Value 2
1/36
-$100
-$2.78 12
100
3 and 11
4/36
-50
All else
30/36
-25
Total
36/36

12. Expected Value Example (Cont.)
Calculate Expected Value:
Given this expected value, will you roll the dice?
Outcome
Probability *
Cash Flow =
Expected Value 2
1/36
-$100
-$2.78 12
100
2.78
3 and 11
4/36
-50
All else
30/36
-25
Total
36/36

13. Expected Value Example (Cont.)
Calculate Expected Value:
Given this expected value, will you roll the dice?
Outcome
Probability *
Cash Flow =
Expected Value 2
1/36
-$100
-$2.78 12
100
2.78
3 and 11
4/36
-50
-5.55
All else
30/36
-25
Total
36/36

14. Expected Value Example (Cont.)
Calculate Expected Value:
Given this expected value, will you roll the dice?
Outcome
Probability *
Cash Flow =
Expected Value 2
1/36
-$100
-$2.78 12
100
2.78
3 and 11
4/36
-50
-5.55
All else
30/36
-25
-20.83
Total
36/36

15. Expected Value Example (Cont.)
Calculate Expected Value:
Given this expected value, will you roll the dice?
Outcome
Probability *
Cash Flow =
Expected Value 2
1/36
-$100
-$2.78 12
100
2.78
3 and 11
4/36
-50
-5.55
All else
30/36
-25
-20.83
Total
36/36
-$26.38

16. Expected Value Example (Cont.)
Calculate Expected Value:
Given this expected value, will you roll the dice?
Outcome
Probability *
Cash Flow =
Expected Value 2
1/36
-$100
-$2.78 12
100
2.78
3 and 11
4/36
-50
-5.55
All else
30/36
-25
-20.83
Total
36/36
-$26.38

17. LSA #1 Check on Learning
Q1. What variables must be defined before calculating Expected Value? A1. Q2. What does Expected Value represent? A2.
Q1. What variables must be defined before calculating Expected Value?
A1. Possible outcomes, cash flows associated with each outcome, and probabilities for each outcome.
Q2. What does Expected Value represent?
A2. A weighted average of the possible cash flows. It gives a reality check by reducing all of the possible cash flow outcomes to a single figure.

18. LSA #1 Summary
During this lesson, we discussed the definition and applications of ‘Expected Value’ and provided a calculated example for learning reinforcement

19. Demonstration Problem
Sheila is playing Let’s Make a Deal and just won $1000.
She now has two alternative courses of action:
Keep the $1000
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

20. Demonstration Problem (Cont.)
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

21. Define the Outcomes Course of Action 1: Course of Action 2:
Keep the $1,000
Trade $1,000 for one of the curtains
Two possible outcomes:
New car
$100 bill

22. Define the Probabilities
Keep the $1,000
Trade $1,000 for Curtain:
Sheila already has the $1,000 in hand
This is a certain event
The probability of a certain event is 100%
Outcome
Probability
Car
$100
Total

23. Define the Probabilities
Keep the $1,000
Trade $1,000 for Curtain:
Sheila already has the $1,000 in hand
This is a certain event
The probability of a certain event is 100%
Outcome
Probability
Car
1/3 or 33.3%
$100
2/3 or 66.7%
Total
3/3 or 100%

24. Define the Cash Flows Keep the $1,000 Trade $1,000 for Curtain
Cash flow is $1,000
Outcome
Cash Flow
Car
$100

25. Define the Cash Flows (Cont.)
Keep the $1,000
Trade $1,000 for Curtain
Cash flow is $1,000
Outcome
Cash Flow
Car
$100

26. Define the Cash Flows (Cont.)
Keep the $1,000
Trade $1,000 for Curtain
Cash flow is $1,000
Outcome
Cash Flow
Car
$40,000 - $1,000 - $9000 = +$30,000
$100
Value of the car = $40,000
Gives up $1,000 = -$1,000
Tax 22.5% on $40,000 = -$9,000

27. Define the Cash Flows (Cont.)
Keep the $1,000
Trade $1,000 for Curtain
Cash flow is $1,000
Outcome
Cash Flow
Car
$40,000 - $1,000 - $9000 = +$30,000
$100
$100 - $1,000 = -$900

28. Calculate Expected Value
Keep the $1,000
Trade $1,000 for Curtain
Outcome %
* CF
= EV
Keep $1000
100%
$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?

29. LSA #2 Check on Learning
Q1. How can Expected Value be used in comparing alternative Courses of Action? A1.
Q1. How can Expected Value be used in comparing alternative Courses of Action?
A1. Generally the higher Expected Value means the more favorable the option. It gives a means of comparing uncertain cash flows to certain outcomes.

30. LSA #2 Summary
During this lesson, we conducted a demonstration problem consisting of an outcome, based on two separate Courses of Action (COA) Resulting in an expected value.

31. 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

32. Expected Value Application (Cont.)
Proposal
Accepted
Scenario A
+$75,000
Scenario B
+10,000
Rejected
No change

33. Expected Value Application (Cont.)
Proposal
Accepted
50%
Scenario A
+$75,000
Scenario B
+10,000
Rejected
100%
No change $0

34. Expected Value Application (Cont.)
Proposal
$25,500
Accepted
$42,500
50%
Scenario A
+$75,000
Scenario B
+10,000
Rejected $0
100%
No change

35. Expected Value Application (Cont.)
Proposal
$25,500
60%
Accepted
$42,500
50%
Scenario A
+$75,000
Scenario B
+10,000
40%
Rejected $0
100%
No change

36. 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?

37. Expected Value and Planning (Cont.)
Expected Value of outsourcing:
Outcome % *
Cash Flow = EV
100 repairs
25%
100 * $750 = $75,000
$18,750
300 repairs
60%
300 * $750 = $225,000
$135,000
500 repairs
15%
500 * $750 = $375,000
$56,250
Total
100%
$210,000

38. Expected Value and Planning (Cont.)
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?

39. Expected Value and Planning (Cont.)
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 insourcing
Outcome % *
Cash Flow = EV
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 = $215,000
$32,250
Total
100%
$149,000

40. Expected Value and NPV
Proposed project requires a $600,000 up-front investment
Discount rate is 12%
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?

41. Expected Value and NPV (Cont.)
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?

42. Practical Exercises

43. Expected Value Spreadsheet
Use to calculate single scenario expected values
Assures that sum of all probabilities equals 100%

44. Expected Value Spreadsheet
Spreadsheet tool permits comparison of up to four courses of action
Uses color coding to rank options
© Dale R. Geiger 2011

45. Conduct Practical Exercise

46. TLO Summary
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