Calculate Expected Values of Alternative Courses of Action

Calculate Expected Values of Alternative Courses of Action Intermediate Cost Analysis and Management 3. 1 1

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

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 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 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 5

Expected Value Calculation • Expected Value = Probability of Outcome 1 * Dollar Value of Outcome 1 + Probability of Outcome 2 * Dollar Value of Outcome 2 + Probability of Outcome 3 * Dollar Value of Outcome 3 etc. • Assumes probabilities and dollar value of outcomes are known or can be estimated • Probability of all outcomes must equal 100% 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 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 3 and 11 All else Cash Flow -$100 -50 -25 8

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

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

Expected Value Example • Calculate Expected Value: Outcome Probability 2 1/36 12 1/36 3 and 11 4/36 All else Total * Cash Flow = Expected Value * -$100 = -$2. 78 * 100 = * -50 = 30/36 * 36/36 -25 = • Given this expected value, will you roll the dice? 11

Expected Value Example • Calculate Expected Value: Outcome Probability 2 1/36 12 1/36 3 and 11 4/36 All else Total * Cash Flow = Expected Value * -$100 = -$2. 78 * 100 = 2. 78 * -50 = 30/36 * 36/36 -25 = • Given this expected value, will you roll the dice? 12

Expected Value Example • Calculate Expected Value: Outcome Probability 2 1/36 12 1/36 3 and 11 4/36 All else Total * Cash Flow = Expected Value * -$100 = -$2. 78 * 100 = 2. 78 * -50 = -5. 55 30/36 * 36/36 -25 = • Given this expected value, will you roll the dice? 13

Expected Value Example • Calculate Expected Value: Outcome Probability 2 1/36 12 1/36 3 and 11 4/36 All else Total * Cash Flow = Expected Value * -$100 = -$2. 78 * 100 = 2. 78 * -50 = -5. 55 30/36 * 36/36 -25 = -20. 83 • Given this expected value, will you roll the dice? 14

Expected Value Example • Calculate Expected Value: Outcome Probability 2 1/36 12 1/36 3 and 11 4/36 All else Total * Cash Flow = Expected Value * -$100 = -$2. 78 * 100 = 2. 78 * -50 = -5. 55 30/36 * 36/36 -25 = -20. 83 -$26. 38 • Given this expected value, will you roll the dice? 15

Expected Value Example • Calculate Expected Value: Outcome Probability 2 1/36 12 1/36 3 and 11 4/36 All else Total * Cash Flow = Expected Value * -$100 = -$2. 78 * 100 = 2. 78 * -50 = -5. 55 30/36 * 36/36 -25 = -20. 83 -$26. 38 • Given this expected value, will you roll the dice? 16

Learning Check • What variables must be defined before calculating Expected Value? • What does Expected Value represent? 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 • Behind each of the other two curtains there is a $100 bill • Task: Calculate the Expected Value of Sheila’s alternative courses of action 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 19

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 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 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% 22

Define the Cash Flows Keep the $1, 000 • Cash flow is $1, 000 Trade $1, 000 for Curtain Outcome Cash Flow Car $100 23

Define the Cash Flows Keep the $1, 000 • Cash flow is $1, 000 Trade $1, 000 for Curtain Outcome Cash Flow Car $100 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 = -$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 $40, 000 - $1, 000 - $9000 = +$30, 000 $100 - $1, 000 = -$900 26

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 $100 66. 7% -$900 -$600 Total 100% $9, 400 Which would you choose? 27

Learning Check • How can Expected Value be used in comparing alternative Courses of Action? 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 29

Expected Value Application Scenario A +$75, 000 Accepted Scenario B +10, 000 Proposal Rejected No change 30

Expected Value Application 50% Scenario A Accepted Proposal +$75, 000 50% Scenario B +10, 000 Rejected 100% No change $0 31

Expected Value Application 50% Scenario A Accepted +$75, 000 $42, 500 50% Scenario B Proposal +10, 000 $25, 500 Rejected $0 100% No change $0 32

Expected Value Application 60% Accepted $42, 500 Proposal 50% Scenario A +$75, 000 50% Scenario B +10, 000 $25, 500 40% Rejected 100% No change $0 $0 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? 34

Expected Value and Planning • Expected Value of outsourcing: Outcome 100 repairs 300 repairs 500 repairs % 25% 60% 15% Total 100% * * Cash Flow 100 * $750 = $75, 000 300 * $750 = $225, 000 500 * $750 = $375, 000 = = EV $18, 750 $135, 000 $56, 250 $210, 000 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? 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 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? 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? 39

Practical Exercises 40

Expected Value Spreadsheet Use to calculate single scenario expected values Assures that sum of all probabilities equals 100% 41

Expected Value Spreadsheet tool permits comparison of up to four courses of action Uses color coding to rank options 42

Practical Exercise 43