Lecture no41 decision tree analysis

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Contemporary Engineering Economics, 6th edition

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Decision Tree Analysis

o The actions available to the decision-maker

o The events that can occur

o The relationship between the actions and events

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Constructing a Decision Tree

A company is considering marketing a new product Once the product is introduced, there is a 70% chance of encountering a competitive product.

Two options are available for each situation.

o Option 1 (with competitive product): Raise your price and see how your competitor responds If the competitor raises price, your profit will be $60 If they lower the price, you will lose $20

o Option 2 (without competitive product): You still have two options: raise your price or lower your price

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Conditional Profits and Probabilities

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Rollback Procedure

• To analyze a decision tree, we begin at the end of the tree and work backward.

• For each chance node, we calculate the expected monetary value (EMV), and place it in the node

to indicate that it is the expected value calculated over all branches emanating from that node.

• For each decision node, we select the one with the highest EMV (or minimum cost) Then those decision alternatives not selected are eliminated from further consideration.

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Making Sequential Investment Decisions

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Decision Rules

o Market the new product.

o Whether or not you encounter a competitive product, raise your price.

o The expected monetary value associated with marketing the new product is $44.

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Bill’s Decision Problem: $50,000 to Invest

 Decision Problem

o Buying a highly speculative stock (d1) with

three potential levels of return: High (50%),

Medium (9%), and Low (−30%)

o Buying a risk-free U.S Treasury bond (d2) with a

guaranteed 7.5% return

 Seek advice from an expert?

o Seek professional advice before making the

decision

o Do not seek professional advice; do on his own

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Financial Data

o Total amount available for investment: $50,000

o Investment horizon: one year

o Commission fee for stock trade: $100

o Commission fee for bond trade: $150

o Tax rate for long-term capital gains on stock: 20%

o Tax rate for long-term capital gains on T Bond: 0%

o Bill’s discount rate (MARR) = 5%

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Decision Tree for Bill’s Investment Problem: Select Option 2

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-Contemporary Engineering Economics, 6th edition

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Expected Value of Perfect Information (EVPI)

o What is EVPI? This is equivalent to asking yourself how much you can improve your decision if you had perfect information.

o Mathematical relationship

EVPI = EPPI − EMV = EOL where EPPI (Expected profit with perfect information) is the expected profit you could obtain if you had perfect information, and EMV (Expected monetary value) is the expected profit you could obtain based

on your own judgment This is equivalent to expected opportunity loss ( EOL ).

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Expected Value of Perfect Information

Potential Return Level

in Bonds

Option1: Invest

in Stock

(Prior Optimal) Option 2: Invest in Bonds

EOL = (0.25)($15,612) + (0.40)(0) + (0.35)(0) = $3,903

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Bill’s Investment Problem with an Option of Getting Professional Advice

Updating Conditional Profit (or Loss) after Paying a Fee to the Expert (Fee =

$200) Revised Decision Tree

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Conditional Probabilities of the Expert’s Prediction, Given a Potential Return on the

Stock

Given Level of Stock Performance

What the Report

Will Say

High (A)

Medium (B)

Low (C)

0.2

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Nature’s Tree: Conditional Probabilities and Joint Probabilities

P(A,F) = P(F|A)P(A) = (0.80)(0.25) = 0.20 P(A,UF|A)P(A) = (0.20)(0.25) = 0.05 P(B,F) = P(F|B)P(B) = (0.65)(0.40) = 0.26

P(B,UF) = P(UF|B)P(B) = (0.35)(0.40) = 0.14 P(F) = 0.20 + 0.26 + 0.07

= 0.53

P(UF) = 1 − P(F) = 1 − 0.53

= 0.47

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Joint and Marginal Probabilities

What the Report Will Say Joint Probabilities

When Potential Level of Return Is Given

Favorable (F) Unfavorable (UF)

Marginal Probabilities of Return Level

High (A) 0.20 0.05 0.25

Medium (B) 0.26 0.14 0.40

Marginal Probabilities of what the

report will say 0.53 0.47 1.00

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Determining Revised Probabilities

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Decision Making After Seeing the Report

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EVPI After Taking the Sample

• EVPI before taking the sample

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Decision Tree Analysis

Trees can grow very quickly as we add more decision options and event nodes.

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