1. Calculate Expected Values of Alternative COA
Principles of Cost Analysis and Management
Show Slide #1: Calculate Expected Values of Alternative Courses of Action (COA)
References:
FM Financial Management Operations, Apr 14
Handouts and Excel Spreadsheets
Facilitator Material: Each primary facilitator should possess a lesson plan, slide deck, course handouts, and practical exercises, with Answer Key, and a summary sheet containing FM 1-06 Financial Management Operations, Apr 14. All required printed reference material, and technical manuals will be provided by the Schoolhouse.
Learner Material: Learners should possess all required printed reference material, course handouts, and a summary sheet containing FM 1-06 Financial Management Operations, Apr 14 and standard classroom supplies.

2. Ever had a vacation disaster?
Car trouble? Lost luggage? Missed flight? Something worse? How did that affect your vacation cash flows?
Show Slide #2: Concrete Experience: Ever had a vacation disaster?
Facilitator’s Note: (Concrete Experience 5 minutes) Ask the learners the following Questions. Facilitate a discussion on the answers given by the learners.
Facilitator’s Note: (Publish and Process 5 minutes) The critical portion of this part of the ELM process is to force the learners to reflect.
Introduction:
Most of us have had some sort of travel or vacation “adventure” where things didn’t go as planned. Most of us can laugh at them now. But those unplanned adventures can wreak havoc on our vacation cash flows.
Lost luggage might mean replacing clothing and other essential items. A missed flight might mean additional meals, hotel stays, or cost of alternative transportation. Should you factor these kinds of things into your vacation spending plan? How much should you plan for these contingencies? It really depends upon the probability that they might occur.
Expected value is one way of taking into consideration the probability and cost of various scenarios.

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
Show Slide #3: Terminal Learning Objective (TLO)
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)
1. Define expected value calculation
2. Determine cash flow value of each possible outcome
3. Analyze probabilities to outcomes
Facilitator’s Note: Throughout this lesson, solicit from learners the challenges they experienced in the current operational environment (OE) and what they did to resolve them. Encourage learners to apply at least 1 of the 8 critical variables: physical environment, political stability of the state, sociological demographics, infrastructure, military capabilities, information, time, and economics.
Safety Requirements: In a training environment, leaders must perform a risk assessment in accordance with DA PAM , Risk Management. Leaders will complete a DD Form 2977 DELIBERATE RISK ASSESSMENT WORKSHEET during the planning and completion of each task and sub-task by assessing mission, enemy, terrain and weather, troops and support available-time available and civil considerations (METT-TC). Local policies and procedures must be followed during times of increased heat category in order to avoid heat related injury. Consider the work/rest cycles and water replacement guidelines IAW TRADOC Regulation
Risk Assessment Level: Low. Hazard Identification: Electrical Shock, Fire, Slippery Floors, Physical Injure/Strain, Tripping Tight Spaces in Classroom, and Influenza. Hazard controls: Primary Instructor (PI) will ensure: All electrical cords are properly stored under desks, liquid containers have lids on them and all spills are immediately cleaned and mopped and allowed to completely dry before allowing learners/personnel to walk on them. All chairs are ergonomically designed, adjust to individual preference and that all learners are awake and paying attention in class. All cables/cords are properly plugged in, sheathed, and secured along tables, walls, and ceilings. No damaged or frayed cords/cables will be used. PI will brief proper hand washing techniques, the use of hand sanitizer, and evacuation procedures. All trash will be removed daily.
Environmental Statement: Environmental protection is not just the law but the right thing to do. It is a continual process and starts with deliberate planning. Always be alert to ways to protect our environment during training and missions. In doing so, you will contribute to the sustainment of our training resources while protecting people and the environment from harmful effects. Refer to FM Environmental Considerations and GTA ENVIRONMENTAL-RELATED RISK ASSESSMENT.
Evaluation: No formal written examination will be administered; the learners understanding of the material will be evaluated through check on learning questions and practical exercise.
Instructional Lead In: Calculate Expected Values of Alternative Courses is a lesson designed to help Financial Managers recognize that cash flows are frequently tied to uncertain outcomes and will require good decision making. Good Decision making is important and is a central aspect of your role. Note, an organization’s long-term survival depends on it’s manager’s decision making skills.

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.
Show Slide #4: Define expected value calculation
Learning Step/Activity #1: Define expected value calculation
Method of Instruction: DSL-Discussion (small or large group discussion)
Facilitator to Student Ratio: 2:25
Time of Instruction: 25 Minutes
Media: PowerPoint, Printed Reference Material
Facilitator’s Note: All handouts and learner materials for this lesson are located in Tab 23.
Facilitator's Note: Before facilitating this lesson, ask the learners which of the 21st Century Soldier (Learner) Competency do they think pertain to this lesson? Facilitate a discussion on the answers given and at the end of the lesson revisit it and see if the learners still believe their choice are the same. For this lesson these competencies should be talked about.
1. Character and accountability
6. Communication and engagement (oral, written, and negotiation)
7. Critical thinking and problem solving
9. Tactical and technical competence (full spectrum capable)
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
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. You can and should plan for routine maintenance on your car. But what if a situation arises (work or family emergency) that requires you to drive many more miles than you planned. Not only will your car require more maintenance, but the probability of needing a major repair also increases.
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
Show Slide #5: Applications for Expected Value
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
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”.
For example: we can weigh the cost of medical insurance against the expected value of NOT carrying medical insurance. The cost of a hospital stay is significant enough to justify the cost of medical insurance even if the probability of an illness requiring a hospital stay is low.

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%
Show Slide #6: Expected Value Calculation
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
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. In most cases, estimates of probabilities will be close enough to give us the “reality check” we need. We will look at testing those estimates and assumptions in Day 10. It is more important to be thorough in our cash flow estimations, since that is easier to quantify.
Of course, 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.
Show Slide #7: Expected Value Example
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
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.

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
-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
-5.55
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 *
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
2.78
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
Show Slide #8: Expected Value Example
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
Calculate Expected Value:
What are the possible outcomes? The first thing we need to do is define the possible outcomes. In this case, they are: 2, 12, 3, 11 and everything else.
What are the cash flows associated with each outcome? The second step is to define the cash flows for each outcome. The table lays these out. If we roll a 2 our cash flow is -$100, if we roll a 12 our cash flow is +$100. If we roll 3 or 11 the cash flow is -$50 and for every other roll the cash flow is -$25.
Facilitator’s Note: (Advance slide).
What are the probabilities of each outcome? The third step is to define the probabilities of each outcome.
We know there are 36 possible outcomes from rolling two dice. Only one of them yields a 2, so the probability of a 2 or snake-eyes is 1/36 (2.8%).
There is also only one way to roll a 12 (two sixes) so the probability of rolling 12 is the same: 1/36 or 2.8%.
The probability of 3 and 11 is equal to probability of 3 + probability of 11. There are two ways to roll 3 (1-2, 2-1) and two ways to roll 11 (5-6, 6-5) so the probability is (2+2)/36 or 4/36 which is equal to 11.1%.
Finally, everything else. This is the probability of NOT rolling 2, 12, 3 or 11. Or, 1 – ( )/36 = 30/36 (83.3%) . Notice that the sum of the probabilities of all possible outcomes is equal to 36/36 or 100%
Now that we have defined the cash flows and probabilities, the final step is to multiply each cash flow by its respective probability to achieve a weighted cash flow. Then sum up all weighted cash flows to achieve the expected value.
The weighted cash flow from rolling snake-eyes (2) is probability of 1/36 * cash flow of -$100 = -$2.78
The weighted cash flow from rolling 12 is probability of 1/36 * cash flow of +$100 = +$2.78
The weighted cash flow from rolling 3 or 11 is 4/36 * -$50 = -$5.55
The weighted cash flow from any other outcome is 30/36 * -$25 = -$20.38
The expected value is the sum: -$2.78 +$2.78 -$5.55-$20.38 = -$26.38
Notice that the weighted cash flow of winning $100 is only +$ The probability of winning $100 is small enough that this seems relatively insignificant. In fact, it is completely offset by the equally small probability of having to pay out $100, which results in a weighted cash flow of -$ Not surprisingly, the expected value is very close to the outcome with the highest probability, the cash outflow of $25.
Given this expected value, will you roll the dice?
Bear in mind that the expected value of -$26.38 is not equal to ANY of the possible outcomes. It is just a way of factoring in the probabilities of the possible outcomes to get an idea of the probable impact on cash flows. Most likely you will end up donating $25. But if you can’t afford to make the $50 or $100 donation, you should probably avoid rolling the dice.
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. Possible outcomes, cash flows associated with each outcome, and probabilities for each outcome.
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. 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.

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.
Show Slide #10: Determine cash flow value of each possible outcome
Learning Step/Activity #2: Determine cash flow value of each possible outcome
Method of Instruction: DSL-Discussion (small or large group discussion)
Facilitator to Student Ratio: 2:25
Time of Instruction: 25 Minutes
Media: PowerPoint, Printed Reference Material
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
Demonstration Problem
Sheila is playing Let’s Make a Deal and just won $1000.
She now has two options:
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
Behind each of the other two curtains 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
Show Slide #11: Demonstration Problem
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
First let’s review the steps to follow in calculating expected value. They are:
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
Show Slide #12: Define the Outcomes
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
Step 1: Define the outcomes
There are two courses of action: Keep the $1000 or Trade the $1000 for one of the three curtains.
There is only one outcome for COA 1: Sheila keeps $1000.
There are two possible outcomes for COA 2: She either gets the new car, or a $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
Show Slide #13: Define the Probabilities
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
Step 2: Define the probabilities.
COA 1: Keep the $1000.
Sheila already has the $1,000 in hand.
This is a certain event.
The probability of a certain event is?
Facilitator’s Note: (Advance slide).
The probability of a certain event is 100%.
COA 2: Trade $1000 for Curtain:
The probability of getting the car is 1 in 3 or 33.3%. There are three curtains, and only one has a car behind it.
The probability of getting the $100 bill is 2 in 3 or 66.7%. There are three curtains, and two of the three have a $100 bill behind them. The sum of all probabilities is 100%.

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
$100
Outcome
Cash Flow
Car
$40,000 - $1,000 - $9000 = +$30,000
$100
$100 - $1,000 = -$900
Show Slide #14: Calculate Expected Value
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
Step 3: Define the cash flows.
COA 1: Keep the $1,000. The cash flow associated with this COA is?
Facilitator’s Note: (Advance slide).
The cash flow associated with this COA is clearly $1000.
COA 2: Trade $1000 for one of the three curtains.
The cash flow associated with the car is $40,000 - $1000 -$9000= $30,000. The car is worth $40,000 but Sheila must give up the $1000 in order to choose one of the curtains. She will also have to pay tax on the car (assume total 22.5% tax rate * $40,000 = $9,000) if she wins.
The cash flow associated with the $100 bill is $100 - $1000 = -$900. This option has a negative cash flow because she must give up the $1000.
The cash flow associated with the $100 bill is $100 - $1,000 = -$900. Since Sheila must give up the $1000 to choose the curtain, this option represents a negative cash flow.
The expected value of COA 1 is 100% * $1000 = $1000
The expected value of COA2 is:
33.3% * $ = $10,000
66.7% * -$900 = -$600
Total = $9,400
Again, note that NONE of the outcomes will yield exactly $9,400. This just gives us a basis for comparing to the certain outcome of keeping the $1000.
Based on this expected value, which would you choose? The cash flow from winning the car is large enough and the probability is sufficiently high that the expected value of trading the $1000 for the curtain is significantly higher than $ It makes sense to take the chance and choose the curtain. Sheila made exactly this choice…and walked away with $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. Generally the higher Expected Value means the more favorable the option. It gives a means of comparing uncertain cash flows to certain outcomes.
Show Slide #15 LSA #2: Determine cash flow value of each possible outcome
Check on Learning
Facilitator’s Note: Ask the following Questions: (Facilitate discussion on answers given).
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.
** Facilitator’s Note: LSA Summary will be given at the end of this lesson.

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.
Show Slide #16: Analyze probabilities to outcomes
Learning Step/Activity #3: Assign probabilities to outcomes
Method of Instruction: DSL-Discussion (small or large group discussion)
Facilitator to Student Ratio: 2:25
Time of Instruction: 25 Minutes
Media: PowerPoint, Printed Reference Material
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
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
Show Slide #17: Calculate Expected Value
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
This diagram shows the possible outcomes. After we make our proposal, the possible outcomes are that the proposal is either accepted or rejected. These are conditions (remember conditional probabilities?)
If the condition “Accepted” is met, then there are two possible outcomes: Scenario A, an increase of $75,000, and Scenario B, an increase of $10,000.
If the condition “Rejected” is met, then there is only one outcome: No change.
Facilitator’s Note: (Advance slide).
Starting on the right side of the chart:
We will first consider the outcomes if the proposal is accepted. Scenarios A and B are equally likely. That means there is a chance of either. So, we will assign them each a probability of 50%.
The probabilities of the possible outcomes must add up to 100%.
If the proposal is rejected the outcome is certain, so it has a probability of 100%
Moving from right to left:
The expected value of the proposal being accepted is Probability of Scenario A * cash flow from A + Probability of Scenario B * cash flow from B.
50% * $75, % * $10,000 = $42,500
The expected value of the proposal being rejected is 100% * $0
Again, moving from right to left:
The overall expected value of the proposal is equal to: Probability of Acceptance * EV of Acceptance + Probability of Rejection * EV of Rejection
Therefore: 60% * $42, % * $0 = $25,500
Note that none of the actual outcomes will be exactly $25,500, but this gives an idea of the potential value of this proposal to the organization.

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?
Show Slide #18: Expected Value and Planning
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
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
Show Slide #19: Expected Value and Planning
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
The higher probabilities of the outcomes with fewer repairs brings the expected value down.

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?
Show Slide #20: Expected Value and Planning
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
If you insource the repair function, total cost will equal $65,000 fixed costs plus variable cost of $100 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
Show Slide #21: Expected Value and Planning
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
The higher probabilities of the outcomes with fewer repairs brings the expected value down.

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?
Show Slide #22: Expected Value and NPV
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
You are considering a project that requires a $600,000 up-front investment.
The project has a five year life and the potential annual cash flows are as follows:
10% probability of $300,000
70% probability of $200,000
20% Probability of $100,000
What is the expected value of the annual cash flow?

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?
Show Slide #23: Expected Value and NPV
Facilitator’s Note: (Facilitator read and facilitate discussion using the slide).
The EV is as follows:
10% probability of $300,000 = $30,000
70% probability of $200,000 = $140,000
20% Probability of $100,000 = $20,000
What is the expected value of the annual cash flow? =
How would this information be used to evaluate the project’s NPV? This would be the cash flow in the 5 year annuity calculation. The discount rate is 12% The PV annuity factor for 12%, 5 years is What is the project’s NPV? (190000*3.605) = 84,950
Given these assumptions, what is your recommendation on the project? Since it has a positive NPV, the project should be accepted.

24. LSA #3 Check on Learning
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).
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? 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?
Show Slide #25 LSA #1-3 Summary:
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.
Show Slide #26: TLO Check on Learning
Facilitator’s Note: 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
Show Slide #27: TLO Summary
Facilitator’s Note: Restate the TLO
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)
1. Define expected value calculation
2. Determine cash flow value of each possible outcome
3. Analyze probabilities to outcomes
Facilitator’s Note: Throughout this lesson, solicit from learners the challenges they experienced in the current operational environment (OE) and what they did to resolve them. Encourage learners to apply at least 1 of the 8 critical variables: physical environment, political stability of the state, sociological demographics, infrastructure, military capabilities, information, time, and economics.
Safety Requirements: In a training environment, leaders must perform a risk assessment in accordance with DA PAM , Risk Management. Leaders will complete a DD Form 2977 DELIBERATE RISK ASSESSMENT WORKSHEET during the planning and completion of each task and sub-task by assessing mission, enemy, terrain and weather, troops and support available-time available and civil considerations (METT-TC). Local policies and procedures must be followed during times of increased heat category in order to avoid heat related injury. Consider the work/rest cycles and water replacement guidelines IAW TRADOC Regulation
Risk Assessment Level: Low. Hazard Identification: Electrical Shock, Fire, Slippery Floors, Physical Injure/Strain, Tripping Tight Spaces in Classroom, and Influenza. Hazard controls: Primary Instructor (PI) will ensure: All electrical cords are properly stored under desks, liquid containers have lids on them and all spills are immediately cleaned and mopped and allowed to completely dry before allowing learners/personnel to walk on them. All chairs are ergonomically designed, adjust to individual preference and that all learners are awake and paying attention in class. All cables/cords are properly plugged in, sheathed, and secured along tables, walls, and ceilings. No damaged or frayed cords/cables will be used. PI will brief proper hand washing techniques, the use of hand sanitizer, and evacuation procedures. All trash will be removed daily.
Environmental Statement: Environmental protection is not just the law but the right thing to do. It is a continual process and starts with deliberate planning. Always be alert to ways to protect our environment during training and missions. In doing so, you will contribute to the sustainment of our training resources while protecting people and the environment from harmful effects. Refer to FM Environmental Considerations and GTA ENVIRONMENTAL-RELATED RISK ASSESSMENT.
Evaluation: No formal written examination will be administered; the learners understanding of the material will be evaluated through check on learning questions and practical exercise.
Instructional Lead In: Calculate Expected Values of Alternative Courses is a lesson designed to help Financial Managers recognize that cash flows are frequently tied to uncertain outcomes and will require good decision making. Good Decision making is important and is a central aspect of your role. Note, an organization’s long-term survival depends on it’s manager’s decision making skills.

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.
Show Slide #27: TLO Summary
Facilitator’s Note: (Facilitator read).
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?
What are your questions?

29. Practical Exercises Show Slide #28: Deploy the Practical Exercise (PE)
Facilitator’s Note: Direct learners to the Handout and have them review the material. Ask them to complete the first PE. This is your opportunity to demonstrate what you have learned. You will have 15 minutes to complete the practical exercise (PE). Do your best to complete the PE in the allotted time.
When satisfied that learners are demonstrating sufficient awareness of the concepts, have them continue exercises. We will conduct an review of the PE as a group.

30. Expected Value Spreadsheet
Use to calculate single scenario expected values
Show Slide #29: Expected Value Spreadsheet
Facilitator’s Note: Use to calculate single scenario expected values. The spreadsheet assures that sum of all probabilities equals 100%.
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
Show Slide #30: Expected Value Spreadsheet
Facilitator’s Note: Spreadsheet tool permits comparison of up to four courses of action. Uses color coding to rank options.
© Dale R. Geiger 2011

32. Practical Exercises Show Slide #31: Expected Value Spreadsheet
Facilitator’s Note: When satisfied that learners are demonstrating sufficient awareness of the concepts, have them continue exercises. We will conduct an review of the PE as a group.