Contemporary Engineering Economics, 6 th edition Park Copyright © 2016 by Pearson Education, Inc. All Rights Reserved Decision-Tree Analysis Lecture No. 41 Chapter 12 Contemporary Engineering Economics Copyright © 2016

Contemporary Engineering Economics, 6 th edition Park Copyright © 2016 by Pearson Education, Inc. All Rights Reserved Decision Tree Analysis A graphical tool for describing: o The actions available to the decision- maker o The events that can occur o The relationship between the actions and events

Contemporary Engineering Economics, 6 th edition Park Copyright © 2016 by Pearson Education, Inc. All Rights Reserved 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.

Contemporary Engineering Economics, 6 th edition Park Copyright © 2016 by Pearson Education, Inc. All Rights Reserved Conditional Profits and Probabilities

Contemporary Engineering Economics, 6 th edition Park Copyright © 2016 by Pearson Education, Inc. All Rights Reserved 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.

Contemporary Engineering Economics, 6 th edition Park Copyright © 2016 by Pearson Education, Inc. All Rights Reserved Making Sequential Investment Decisions

Contemporary Engineering Economics, 6 th edition Park Copyright © 2016 by Pearson Education, Inc. All Rights Reserved 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.

Contemporary Engineering Economics, 6 th edition Park Copyright © 2016 by Pearson Education, Inc. All Rights Reserved Bill’s Decision Problem: $50,000 to Invest  Decision Problem o Buying a highly speculative stock (d 1 ) with three potential levels of return: High (50%), Medium (9%), and Low (−30%) o Buying a risk-free U.S. Treasury bond (d 2 ) 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

Contemporary Engineering Economics, 6 th edition Park Copyright © 2016 by Pearson Education, Inc. All Rights Reserved 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%

Contemporary Engineering Economics, 6 th edition Park Copyright © 2016 by Pearson Education, Inc. All Rights Reserved Decision Tree for Bill’s Investment Problem: Select Option 2 -

Contemporary Engineering Economics, 6 th edition Park Copyright © 2016 by Pearson Education, Inc. All Rights Reserved 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).

Contemporary Engineering Economics, 6 th edition Park Copyright © 2016 by Pearson Education, Inc. All Rights Reserved Expected Value of Perfect Information Potential Return Level Probability Decision Option Optimal Choice with Perfect Information Opportunity Loss Associated with Investing in Bonds Option1: Invest in Stock (Prior Optimal) Option 2: Invest in Bonds High (A)0.25$16,510$898Stock$15,612 Medium (B) Bond0 Low(C)0.35−13,967898Bond0 EMV −$405 $898 $3,903 EPPI = (0.25)($16,510) + (0.40)($898) + (0.35)($898) = $4,801 EVPI = EPPI − EV = $4,801 − $898 = $3,903 EOL = (0.25)($15,612) + (0.40)(0) + (0.35)(0) = $3,903

Contemporary Engineering Economics, 6 th edition Park Copyright © 2016 by Pearson Education, Inc. All Rights Reserved 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

Contemporary Engineering Economics, 6 th edition Park Copyright © 2016 by Pearson Education, Inc. All Rights Reserved 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) Favorable (F) Unfavorable (UF) A B C F UF F U

Contemporary Engineering Economics, 6 th edition Park Copyright © 2016 by Pearson Education, Inc. All Rights Reserved Nature’s Tree: Conditional Probabilities and Joint Probabilities Nature’s Tree Joint and Marginal 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) = = 0.53 P(UF) = 1 − P(F) = 1 − 0.53 = 0.47

Contemporary Engineering Economics, 6 th edition Park Copyright © 2016 by Pearson Education, Inc. All Rights Reserved 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) Medium (B) Low (C) Marginal Probabilities of what the report will say

Contemporary Engineering Economics, 6 th edition Park Copyright © 2016 by Pearson Education, Inc. All Rights Reserved Posterior Probabilities A B C A B C F UF P(A/F)= ?

Contemporary Engineering Economics, 6 th edition Park Copyright © 2016 by Pearson Education, Inc. All Rights Reserved Determining Revised Probabilities P(A|F) = P(A,F)/P(F) = 0.20/0.53 = 0.38 P(B|F) = P(B,F)/P(F) = 0.26/0.53 = 0.49 P(C|F) = P(C,F)/P(F) = 0.07/0.53 = 0.13 P(A|UF) = P(A,UF)/P(UF) = 0.05/0.47 = 0.30 P(B|UF) + P(B,UF)/P(UF) = 0.14/0.47 = 0.30 P(C|UF) = P(C,UF)/P(UF) = 0.28/0.47 = 0.59

Contemporary Engineering Economics, 6 th edition Park Copyright © 2016 by Pearson Education, Inc. All Rights Reserved Posterior Probabilities A B C A B C F UF

Contemporary Engineering Economics, 6 th edition Park Copyright © 2016 by Pearson Education, Inc. All Rights Reserved Decision Making After Seeing the Report

Contemporary Engineering Economics, 6 th edition Park Copyright © 2016 by Pearson Education, Inc. All Rights Reserved EVPI After Taking the Sample EVPI before taking the sample EV after spending $200 Expected value of sample information (EVSI):

Contemporary Engineering Economics, 6 th edition Park Copyright © 2016 by Pearson Education, Inc. All Rights Reserved Decision Tree Analysis PROS Describes the decision problem graphically so it is easier to understand CONS EMV rule to select a decision at a decision node; ignore the variability of financial outcome (risk- neutral environment) Trees can grow very quickly as we add more decision options and event nodes.