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

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

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

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 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%

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

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

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

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

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

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

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

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

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

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

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.

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

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

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

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

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

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%

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

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

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

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

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?

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.

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.

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

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

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

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

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

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?

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

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?

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

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?

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?

Practical Exercises

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

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

Conduct Practical Exercise

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