Maria's decision making grid answers

Chapter 3

Fundamentals of Decision Making

Using EMVs, EOLs, and EVPIs to Make Choices in Business

I. Decision theory – An analytic and systematic approach to solving problems. Just like

quantitative analysis, decision theory has its own set of steps:

A. Define the problem.

B. List the possible alternatives.

C. Identify the possible outcomes.

D. List the payoff of each combination of alternatives and outcomes.

E. Select one of the mathematical decision theory models.

F. Apply the model and make a decision.

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II. Let’s look at one of these decisions in action: THIS IS NOT HOMEWORK: It is only an example.

A. Define the problem. Maria wants to set up a dress shop in a vacant space at the local mall.

B. List the possible alternatives. She can set up a small shop, a medium shop, or no shop.

C. Identify the possible outcomes. Maria believes that there are three possible outcomes: a

good economy, a fair economy, and a poor economy.

1. Remember: It is important to consider all possible outcomes. Ignoring outcomes—bad

or good—can do considerable damage to the decision making process.

D. List the payoff of each combination of alternatives and outcomes. Maria maps out all

outcomes in terms of profits, but other outcomes can be used. This is what she finds:

Good Market Fair Market Poor Market

Small Shop $75,000 $25,000 -$40,000

Medium Shop $100,000 $35,000 -$60,000

No Shop $0 $0 $0

 If Maria chooses to build a small shop and the market is good, she makes $75,000.

 If Maria chooses to build a medium shop and the market is poor, she loses $60,000.

 If Maria chooses to do nothing, she neither gains nor loses money.

 Etc.

E. Select one of the mathematical decision theory models, and make a decision. This is where

Maria has choices to make, some of which are dependent upon what she wants and what she

knows.

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Decision-Making Tool 1: The Expected Monetary Value (EMV) One tool that Maria can use to help her make a decision is the Expected Monetary Value, or EMV.

 Simply put, the EMV helps weigh the risks and rewards of each choice to make the best

possible decision.

 To do this, the EMV weighs the possible benefits of each decision with the chance of each

event happening.

Let me show you how the EMV works with Maria’s situation.

A. In order to do an EMV, Maria needs two things:

1. The grid we built on page 2, and

2. The odds of how good the economy is going to be over the next year.

B. Let’s suppose Maria knows the odds of the economy going different directions over the next

year (for information on how decision-makers get this information, ask your instructor):

a. First, the chance of a good economy is 20%.

b. Second, the chance of a fair economy is 50%.

c. Third, the chance of a poor economy is 30%.

C. She can use this knowledge to make a decision about what kind of shop to build. Here’s how,

step by step:

How to construct an EMV: Step 1: Build your grid (like Maria’s, below) and include amounts that could be gained or lost (numbers in blue), as well as the probabilities of each economy happening (numbers in red).

Good Economy Fair Economy Poor Economy

Small Shop $75,000 $25,000 -$40,000

Medium Shop $100,000 $35,000 -$60,000

No Shop $0 $0 $0

Probabilities 20% 50% 30%

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Step 2: Multiply the number in each cell (the blue numbers) by the percentage below it (in red).

See the table below to see how this looks:

Good Economy Fair Economy Poor Economy

Small Shop $75,000 x 20% = $15,000

$25,000 x 50% = $12,500

-$40,000 x 30% = -$12,000

Medium Shop $100,000 x 20% =$20,000

$35,000 x 50% = $17,500

-$60,000 x 30% = -$18,000

No Shop $0 x 20% = $0 $0 x 50% = $0 $0 x 30% = $0

Probabilities 20% 50% 30%

Step 3: Add the numbers you just calculated (the ones in green) left to right.

 Small Shop: $15,000 + $12,500 - $12,000 = $15,000

 Medium Shop: $20,000 + $17,500 - $18,000 = $19,500

 No Shop: $0 + $0 + $0 = $0

Step 4: Identify which of these numbers (in orange) has the best payoff. In other words, which of

these numbers is the largest?

 Small Shop: $15,000 + $12,500 - $12,000 = $15,500

 Medium Shop: $20,000 + $17,500 - $18,000 = $19,500 ←largest number

 No Shop: $0 + $0 + $0 = $0

This number ($19,500) is called the EMV amount.

Step 5: Identify the decision associated with the EMV amount. In this example, $19,500 is

associated with “Build a Medium Shop,” which is Maria’s EMV decision.

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TOOL 2: The Expected Opportunity Loss (EOL) Another, slightly more complicated tool that Maria can use to help her make a decision is the

Expected Opportunity Loss, or EOL.

 The EOL is kind of the opposite of the EMV: instead of picking the best choice in case things

go well, the EOL asks “what decision should I make to minimize the chances of me getting

hurt in case things go poorly?”

 The EOL and the EMV are similar, though, in one way: Whatever decision the EMV tells

you to do (for example, build large, build small, or not at all), the EOL will give you the

same decision.

How to construct an EOL: Step 1: Build your grid just like you would with an EMV.

Good Economy Fair Economy Poor Economy

Small Shop $75,000 $25,000 -$40,000

Medium Shop $100,000 $35,000 -$60,000

No Shop $0 $0 $0

Probabilities 20% 50% 30%

Step 2: Identify the best payoff in each column. In other words, what is the most amount of

money that could be made (or the least amount lost) in each column?

Good Economy Fair Economy Poor Economy

Small Shop $75,000 $25,000 -$40,000

Medium Shop $100,000 $35,000 -$60,000

No Shop $0 $0 $0

Probabilities 20% 50% 30%

 For the Good Economy, the best payoff would be $100,000.

 For the Fair Economy, the best payoff would be $35,000.

 For the Poor Economy, the best payoff would be $0.

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Step 3: Subtract the payoff in each box from the best payoff in each column.

Good Economy Fair Economy Poor Economy

Small Shop $100,000 - $75,000

= $25,000 $35,000 - $25,000

= $10,000 $0 - -$40,000

= $40,000

Medium Shop $100,000 - $100,000

= $0 $35,000 - $35,000

= $0 $0 - -$60,000

= $60,000

No Shop $100,000 - $0

= $100,000 $35,000 - $0

= $35,000 $0 - $0

= $0

Probabilities 20% 50% 30%

Note the following:

 The math for every cell is always (best payoff) minus (the number in the cell).

o So, for the first column, for example, the amount in every cell is subtracted from $100,000.

 For the math in the “Poor Economy” column, note that the top two have two minus signs.

o Whenever you subtract from a minus, the result is a positive number.

 After you’ve done the math for Step 3, note that every remainder (the number in purple) is

zero or higher.

o If your math creates a negative number, you’ve made a mistake.

Step 4: Multiply the remainders in each cell (the purple numbers) by the percentage below it (in

red). (Hint: At this point, many students draw another grid because the first one is getting pretty

full.)

See the table below to see how this looks:

Good Economy Fair Economy Poor Economy

Small Shop $25,000 x 20% = $5,000 $10,000 x 50% = $5,000 $40,000 x 30% = $12,000

Medium Shop $0 x 20% =$0 $0 x 50% = $0 $60,000 x 30% = $18,000

No Shop $100,000 x 20% = $20,000 $35,000 x 50% = $17,500 $0 x 30% = $0

Probabilities 20% 50% 30%

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Step 5: Add the numbers you just calculated (the ones in green) left to right.

 Small Shop: $5,000 + $5,000 + $12,000 = $22,000

 Medium Shop: $0 + $0 + $18,000 = $18,000

 No Shop: $20,000 + $17,500 + $0 = $37,500

Step 6: Because we are trying to minimize our losses in case we make a bad choice we choose the

outcome with the smallest amount.

 Small Shop: $5,000 + $5,000 + $12,000 = $22,000

 Medium Shop: $0 + $0 + $18,000 = $18,000 ←smallest number

 No Shop: $20,000 + $17,500 + $0 = $37,500

This number ($18,000) is called the EOL amount.

Step 7: Identify the decision associated with the EOL amount. In this example, $18,000 is

associated with “Build a Medium Shop,” which is Maria’s EOL decision.

NOTE: The EMV and EOL may have different amounts, but if they are done correctly, they will

always have the same decision.

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TOOL 3: The Expected Value of Perfect Information (EVPI) In some cases, you might not have enough information to make a decision with certainty, but you

might be able to hire someone else to get this information for you. The EVPI answers the

question, “How much should I pay for accurate, certain information?”

Step 1: Build your grid just like you would with an EMV and an EOL.

Good Economy Fair Economy Poor Economy

Small Shop $75,000 $25,000 -$40,000

Medium Shop $100,000 $35,000 -$60,000

No Shop $0 $0 $0

Probabilities 20% 50% 30%

Step 2: Just like the EOL, identify the best payoff in each column.

Good Economy Fair Economy Poor Economy

Small Shop $75,000 $25,000 -$40,000

Medium Shop $100,000 $35,000 -$60,000

No Shop $0 $0 $0

Probabilities 20% 50% 30%

 For the Good Economy, the best payoff would be $100,000.

 For the Fair Economy, the best payoff would be $35,000.

 For the Poor Economy, the best payoff would be $0.

Step 3: Multiply only the best payoffs in each column (the numbers in yellow) by the percentage

for that column.

Good Economy Fair Economy Poor Economy

Small Shop - - -

Medium Shop $100,000 x 20% = $20,000 $35,000 x 50% = $17,500 -

No Shop - - $0 x 30% = $0

Probabilities 20% 50% 30%

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Step 4: Add the numbers you just calculated (the ones in green). The sum of these numbers

($37,500) is called the Expected Value with Perfect Information, or EVwPI.

$20,000 + $17,500 + $0 = $37,500

Step 5: To get the Expected Value of Perfect Information (EVPI), subtract the EMV from the

EVwPI.

 (If you haven’t already done an EMV at this point, you will need to do it to solve for the EVPI.)

EVwPI – EMV = EVPI

$37,500 - $19,500 = $18,000

The Expected Value of Perfect Information is $18,000.

This means that, should Maria go to an expert to help her make her decision, she should pay no

more than $18,000 for their advice.

 Any help that costs less than $18,000 would be a bargain.

 Any help that costs more than $18,000 would cost more than the risk Maria is already taking.

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Decision Making under Uncertainty

When you know the chances of certain things happening, you can use the EMV or EOL to make a

decision. In cases where the probability is not known, however, different methods have to be

used. Here are four examples:

1. Maximax – (Maximizes the maximum outcome.) Choose the alternative with the highest

possible gain. Also known as the optimistic decision criterion. (Maria: $100,000 = build large

shop)

2. Maximin – (Maximizes the minimum outcome.) Choose the alternative with the highest

minimum number (zero or higher; don’t consider negative numbers because they are less than

zero). Also known as the pessimistic decision criterion. (Maria: $0 = do nothing)

3. Equally Likely (Laplace) – Finds the alternative with the highest average outcome and choose it.

 Step 1: Add the amounts for each choice left to right:

Small Shop: $75,000 + $25,000 -$40,000 = $60,000

Medium Shop: $100,000 + $35,000 - $60,000 = $75,000

No Shop: $0 + $0 + $0 = $0

 Step 2: Divide the sum of each row by the number of columns (in our example, 3):

Small Shop: $60,000  3 = $20,000

Medium Shop: $75,000  3 = $25,000

No Shop: $0  3 = $0

 Step 3: Identify the largest amount and go with that decision.

Small Shop: $60,000  3 = $20,000

Medium Shop: $75,000  3 = $25,000 ←largest number

No Shop: $0  3 = $0

The Equally Likely amount is $25,000.

The Equally Likely decision is “Build a Medium Shop.”

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4. Criterion of Realism – Is a compromise between maximax and maximin decisions.

a. Decide on a coefficient of realism, a (between 0 and 1; closer to 1, the more optimistic).

b. Coefficient of realism ( a ) works as follows:

Coefficient of realism = a (maximum in row) + (1- a )(minimum in row)

c. Maria: Assume a =0.7.

Small shop = (.7)($75,000) + (.3)(-$40,000) = $40,500

Large shop = (.7)($100,000) + (.3)(-$60,000) = $52,000

Nothing = (.7)($0) + (.3)($0) = $0

Choice: Large shop has highest realistic average.