1. Calculate Expected Values of Alternative COA
Principles of Cost Analysis and Management

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
Action: Calculate Expected Values of Alternative Courses of Action.
Condition:   FM Leaders in a classroom environment working individually and as a member of a small group, using doctrinal and administrative publications, self-study exercises, personal experiences, practical exercises, handouts, and discussion.
Standard: With at least 80% accuracy (70% for International learners):
Define expected value calculation
Determine cash flow value of each possible outcome
Analyze 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
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/or 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
What are the probabilities of each outcome?
Calculate Expected Value:
Given this expected value, will you roll the dice?
Calculate Expected Value:
Given this expected value, will you roll the dice?
Calculate Expected Value:
Given this expected value, will you roll the dice?
Calculate Expected Value:
Given this expected value, will you roll the dice?
What are the possible outcomes?
2, 12, 3, 11 and everything else
What are the cash flows associated with each outcome?
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
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
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
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
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
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
Outcome
Probability 2
1/36 12
3 and 11
4/36
All else
30/36
Total
36/36
Outcome
Cash Flow 2
-$100 12
100
3 and 11
-50
All else
-25
Given this expected value, will you roll the dice?

9. LSA #1 Check on Learning
Q1. What variables must be defined before calculating Expected Value? Q2. What does Expected Value represent?
A1.
Show Slide #9 LSA #1: Define expected value calculation
Check on Learning
Facilitator’s Note: Ask the following Questions: (Facilitate discussion on answers given).
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, which can be weighed against other alternative courses of action.
** Facilitator’s Note: LSA Summary will be given at the end of this lesson.
A2.

10. 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.

11. 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

12. 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

13. 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%
Outcome
Probability
Car
$100
Total

14. Calculate Expected Value
Define the Cash Flows
Keep the $1,000
Trade $1,000 for Curtain:
Cash flow is $1,000
Cash flow is $1,000
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
Outcome
Cash Flow
Car
$40,000 - $1,000 - $9000 = +$30,000
$100
Outcome
Cash Flow
Car
$40,000 - $1,000 - $9000 = +$30,000
$100
$100 - $1,000 = -$900
Outcome
Cash Flow
Car
$100
Value of the car = $40,000
Gives up $1,000 = -$1,000
Tax 22.5% on $40,000 = -$9,000
Which would you choose?

15. 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.

16. 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.

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

18. 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?

19. Expected Value and Planning
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

20. 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?

21. Expected 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 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

22. Expected Value and NPV
Proposed project requires a $600,000 up-front investment.
The 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?

23. 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?

24. LSA #3 Check on Learning
Q1. How can expected value be used to plan for costs when level of activity is uncertain?
A1.
Show Slide #24: LSA #3 Check on Learning
Facilitator’s Note: Ask the following Questions: (Facilitate discussion on answers given).
Q1. How can expected value be used to plan for costs when level of activity is uncertain?
A1. Determine the outcomes (levels of activity) and determine the cost or cash flow associated with each. Determine the approximate probability of each outcome (the sum of all probabilities must add up to 1) and then calculate the expected value (costs).

25. LSA # 1-3 Summary What are your questions?
During this lesson, we covered the following Learning Step Activities:
Define expected value calculation
Determine cash flow value of each possible outcome
Analyze probabilities to outcomes
What are your questions?

26. TLO Check on Learning
Divide the learners into two groups, have each group as a group write down one question from this lesson, give about two minutes. Once the groups have their question written, pass it to another group to answer it. Facilitate a discussion on each question.

27. TLO Summary
Action: Calculate Expected Values of Alternative Courses of Action.
Condition:   FM Leaders in a classroom environment working individually and as a member of a small group, using doctrinal and administrative publications, self-study exercises, personal experiences, practical exercises, handouts, and discussion.
Standard: With at least 80% accuracy (70% for International learners):
Define expected value calculation
Determine cash flow value of each possible outcome
Analyze probabilities to outcomes

28. TLO Summary (Cont.) What are your questions?
Expected Value is a useful method for estimating cash flows under uncertain circumstances.
Expected value assumes probabilities and dollar value of outcomes are known or can be estimated.
The probability of all outcomes must equal 100%. Expected value may be used to evaluate alternatives.
The expected value of an uncertain outcome can be weighed against the value of a known (100% probable) outcome.
Expected value is also useful in estimating cash flows when multiple cost scenarios are possible, such as the demand for services.
What are your questions?

29. Practical Exercises

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

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

32. Practical Exercises