Slides calculate expected values of alternative COA

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 possibl

Calculate Expected Values

Principles of Cost Analysis and Management

Ever had a vacation disaster?

Car trouble? Lost luggage?Missed flight? Something worse?How did that affect your vacation

cash flows?

Terminal Learning Objective

regulations/course handouts, and awareness of Operational Environment

(OE)/Contemporary Operational Environment (COE) variables and actors

• Define possible outcomes

• Determine cash flow value of each possible outcome

• Assign probabilities to outcomes

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

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

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

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

Expected Value Example

• What are the possible outcomes?

• 2, 12, 3, 11 and everything else

• What are the cash flows associated with each outcome?

Expected Value Example

• What are the probabilities of each outcome?

Expected Value Example

• Calculate Expected Value:

• Given this expected value, will you roll the dice?

Expected Value Example

• Calculate Expected Value:

• Given this expected value, will you roll the dice?

Expected Value Example

• Calculate Expected Value:

• Given this expected value, will you roll the dice?

Expected Value Example

• Calculate Expected Value:

• Given this expected value, will you roll the dice?

Expected Value Example

• Calculate Expected Value:

• Given this expected value, will you roll the dice?

Expected Value Example

• Calculate Expected Value:

• Given this expected value, will you roll the dice?

Expected Value Example

• Calculate Expected Value:

• Given this expected value, will you roll the dice?

Check on Learning

• What variables must be defined before calculating Expected Value?

• What does Expected Value represent?

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

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

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

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:

Car

$100 Total

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:

Define the Cash Flows

Keep the $1,000

• Cash flow is $1,000

Trade $1,000 for Curtain

Car

$100

Define the Cash Flows

Keep the $1,000

• Cash flow is $1,000

Trade $1,000 for Curtain

Car

$100

Define the Cash Flows

Keep the $1,000

• Cash flow is $1,000

Trade $1,000 for Curtain

Car $40,000 - $1,000 - $9000 = +$30,000

$100

Value of the car = $40,000 Gives up $1,000 = -$1,000

Define the Cash Flows

Keep the $1,000

• Cash flow is $1,000

Trade $1,000 for Curtain

Car $40,000 - $1,000 - $9000 = +$30,000

$100 $100 - $1,000 = -$900

Calculate Expected Value

Check on Learning

• How can Expected Value be used in comparing alternative Courses of Action?

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

Accepted

Scenario A +$75,000

Scenario A +$75,000

Scenario B +10,000

Scenario B +10,000

Expected Value Application

Accepted

50%

Scenario A +$75,000

50%

Scenario A +$75,000

50%

Scenario B +10,000

50%

Scenario B +10,000

100%

100%

Expected Value Application

Scenario A +$75,000

50%

Scenario B +10,000

50%

Scenario B +10,000

100%

100%

Expected Value Application

Scenario A +$75,000

50%

Scenario B +10,000

50%

Scenario B +10,000

40%

Expected Value Application

Expected Value and Planning

• If you outsource the repair function, total cost will equal $750 per repair

• Historical data suggests the following scenarios:

Expected Value and Planning

• Expected Value of outsourcing:

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?

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

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

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?

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?

Check on Learning

• How can expected value be used to plan for costs when level of activity is

uncertain?

Practical Exercises

Expected Value Spreadsheet

Use to calculate single scenario expected values

Use to calculate single scenario expected values

Expected Value Spreadsheet

Spreadsheet tool permits comparison of up to

four courses of action Uses color coding to rank options

Spreadsheet tool permits comparison of up to

four courses of action Uses color coding to rank options

Practical Exercise