Lecture no41 decision tree analysis

Decision-Tree Analysis Lecture No 41 Chapter 12 Contemporary Engineering Economics Copyright © 2016 th Contemporary Engineering Economics, edition Park Copyright © 2016 by Pearson Education, Inc All Rights Reserved Decision Tree Analysis • A graphical tool for describing: o o o The actions available to the decision-maker The events that can occur The relationship between the actions and events th Contemporary Engineering Economics, 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 Option (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 Option (without competitive product): You still have two options: raise your price or lower your price o o th Contemporary Engineering Economics, edition Park Copyright © 2016 by Pearson Education, Inc All Rights Reserved Conditional Profits and Probabilities th Contemporary Engineering Economics, 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 th Contemporary Engineering Economics, edition Park Copyright © 2016 by Pearson Education, Inc All Rights Reserved Making Sequential Investment Decisions th Contemporary Engineering Economics, edition Park Copyright © 2016 by Pearson Education, Inc All Rights Reserved Decision Rules o o o Market the new product Whether or not you encounter a competitive product, raise your price The expected monetary value associated with marketing the new product is $44 th Contemporary Engineering Economics, 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 (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; on his own th Contemporary Engineering Economics, edition Park Copyright © 2016 by Pearson Education, Inc All Rights Reserved Financial Data o o o o o o o Total amount available for investment: $50,000 Investment horizon: one year Commission fee for stock trade: $100 Commission fee for bond trade: $150 Tax rate for long-term capital gains on stock: 20% Tax rate for long-term capital gains on T Bond: 0% Bill’s discount rate (MARR) = 5% th Contemporary Engineering Economics, edition Park Copyright © 2016 by Pearson Education, Inc All Rights Reserved Decision Tree for Bill’s Investment Problem: Select Option - th Contemporary Engineering Economics, 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) th Contemporary Engineering Economics, edition Park Copyright © 2016 by Pearson Education, Inc All Rights Reserved Expected Value of Perfect Information Decision Option Potential Return Level Opportunity Loss (Prior Optimal) Probability Option1: Invest Option 2: Invest in in Stock Bonds Optimal Choice with Associated with Investing Perfect Information in Bonds High (A) 0.25 $16,510 $898 Stock $15,612 Medium (B) 0.40 890 898 Bond Low(C) 0.35 −13,967 898 Bond EMV −$405 $898 $3,903 EVPI = EPPI − EV EPPI = (0.25)($16,510) + (0.40)($898) + (0.35)($898) = $4,801 th Contemporary Engineering Economics, edition Park = $4,801 − $898 = $3,903 EOL = (0.25)($15,612) + (0.40)(0) + (0.35)(0) = $3,903 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 th Contemporary Engineering Economics, 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 F Given Level of Stock Performance 0.8 0.2 UF What the Report High Medium Low Will Say (A) (B) (C) A F B UF Favorable (F) 0.80 0.65 0.20 Unfavorable (UF) 0.20 0.35 0.80 C U UF th Contemporary Engineering Economics, 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) = 0.20 + 0.26 + 0.07 = 0.53 P(UF) = − P(F) = − 0.53 = 0.47 th Contemporary Engineering Economics, 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 Marginal Probabilities of Return Level Favorable (F) Unfavorable (UF) High (A) 0.20 0.05 0.25 Medium (B) 0.26 0.14 0.40 Low (C) 0.07 0.28 0.35 Marginal Probabilities of what the 0.53 0.47 1.00 report will say th Contemporary Engineering Economics, edition Park Copyright © 2016 by Pearson Education, Inc All Rights Reserved Posterior Probabilities A P(A/F)= ? B F C 0.53 0.47 A UF B C th Contemporary Engineering Economics, 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 th Contemporary Engineering Economics, edition Park Copyright © 2016 by Pearson Education, Inc All Rights Reserved Posterior Probabilities A 0.38 B 0.49 F C 0.13 0.53 0.47 A UF 0.11 B 0.30 C 0.59 th Contemporary Engineering Economics, edition Park Copyright © 2016 by Pearson Education, Inc All Rights Reserved Decision Making After Seeing the Report th Contemporary Engineering Economics, edition Park Copyright © 2016 by Pearson Education, Inc All Rights Reserved EVPI After Taking the Sample • EVPI before taking the sample EVPI = EPPI - EV = $3,903 • EV after spending $200 EVPIe = EPPIe - EVe = $16,348(0.25) + $729(0.40) + 698(0.35) − $2,836 • = $1,786.90 Expected value of sample information (EVSI): EVSI = $3,903 − $1,786.90 = $2,116.10 th Contemporary Engineering Economics, edition Park Copyright © 2016 by Pearson Education, Inc All Rights Reserved Decision Tree Analysis PROS CONS Describes the decision problem graphically so it is EMV rule to select a decision at a decision node; easier to understand ignore the variability of financial outcome (riskneutral environment) Trees can grow very quickly as we add more decision options and event nodes th Contemporary Engineering Economics, edition Park Copyright © 2016 by Pearson Education, Inc All Rights Reserved ... Education, Inc All Rights Reserved Decision Tree Analysis PROS CONS Describes the decision problem graphically so it is EMV rule to select a decision at a decision node; easier to understand.. .Decision Tree Analysis • A graphical tool for describing: o o o The actions available to the decision- maker The events that can occur The relationship... 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