The wide-open spaces of Etobicoke have made it a developer's dream.

ETO Development Corporation is a new real estate developer based in the Greater Toronto Area. The name of the company refers to the Etobicoke that is an anglicized adaptation of Aboriginal languages word that means place where the alders grow .

ETO Development Corporation purchased land not far from the intersection of Dundas Street West and Kipling Avenue. The top managers of ETO, however, have different opinions on how this land can be used. Eventually, ETO commissioned preliminary architectural drawings for three different projects: High-Rise Condos; Low-Rise Condos; Townhouse Complex. Also, it is recognized that the financial success of the project depends on the situation on the real estate market, Strong Demand or Weak Demand. The ETO expectations are summarized in the following table (payoffs are in $$millions).

Decision Alternatives	States of Nature
Strong Demand	Weak Demand
High-Rise Condos	26	11
Low-Rise Condos	16	5
Townhouse Complex	11	9

Originally, ETO specialists counted on 0.680.68 probability of strong demand.

Simple Decision Tree Part

(a) Suppose that you need to construct a simple decision tree that shows the logical sequence of the decision problem. Select the correct sketch of the decision tree based on the information above.

Note that P(S)=probability of strong demand, P(W)=probability of weak demand. Also, we use the following notations:

P₁=Payoff 1 , P₂=Payoff 2 , P₃=Payoff 3 , P₄=Payoff 4 , P₅=Payoff 5 , P₆=Payoff 6 .

• P(S)=0.68 , P(W)=0.32, P1=26, P2=11 , P3=16, P4=5 , P5=11, P6=9
• P(S)=0.68 , P(W)=0.32, P1=26, P2=11 , P3=16 , P4=5 , P5=11 , P6=9
• P(S)=0.32, P(W)=0.68, P1=26 , P2=16, P3=11 , P4=11 , P5=5 , P6=9
• P(S)=0.68 , P(W)=0.32, P1=26 , P2=11 , P3=16 , P4=5 , P5=11 , P6=9
• None of the above.

(b) Using the sketch from the previous question and SilverDecisions/TreePlan, construct a simple decision tree. Based on the simple decision tree answer the following questions.

Keep 2 decimal places in the EMV answers.

• Find the expected monetary value for High-Rise Condos decision.

EMV(High-Rise Condos) == (in $$millions)

• Find the expected monetary value for Low-Rise Condos decision.

EMV(Low-Rise Condos) == (in $$millions)

• Find the expected monetary value for Townhouse Complex decision.

EMV(Townhouse Complex) == (in $$millions)

(c) Using the simple decision tree determine the best decision policy.

• Construct High-Rise Condos.
• Support Townhouse Complex project if the demand is strong.
• Go ahead with Low-Rise Condos project if the demand is strong.
• Support Townhouse Complex project.
• Go ahead with Low-Rise Condos project.
• Construct High-Rise Condos if the demand is strong.
• None of the above.

Submit the simple decision tree in PDF format file (if you use the SilverDecisions app) or the original Excel Workbook file (if you use the Excel Add-In TreePlan). The Assignment 1 Instructions/Hints contain detailed info how to attach/submit the file.

Revised Decision Tree Part

The recent dramatic increase of the prime interest rate affected the company's plans. ETO Development Corporation managers are thinking about hiring Mimico Research Group (MRG) to conduct a market research. The name Mimico is derived from the Ojibwe word that means pigeon . Then, MRG would come up with either a favorable report predicting strong demand, or an unfavorable report predicting weak demand on the real estate market. It is known that in 80%80% of cases when strong demand took place, MRG had predicted it correctly. It is also known that in 86%86% of cases when weak demand occurred, MRG had predicted it correctly. MRG specialists need a month to complete their analysis, and they have to use expensive software, supercomputers, and hire additional computer and logistics analysts.

(d) Suppose that you need to construct a revised decision tree. First, fill in the following revised probability tables for the favorable and unfavorable reports.

Round joint probability values, P(Fav) = P(Favorable report), P(Unfav) = P(Unfavorable report), and the posterior probability values to 4 decimals places.

Probability Revisions given a Favorable Report

State of Nature	Prior Probability	Conditional Probability P(Fav/State of Nature)(Fav/State of Nature)	Joint Probability	Posterior Probability P(State of Nature/Fav)(State of Nature/Fav)
Strong	0.680.
Weak	0.320.
		P((Fav)=)=	1.0000

Probability Revisions given an Unfavorable Report

State of Nature	Prior Probability	Conditional ProbabilityP(Unfav/State of Nature)(Unfav/State of Nature)	Joint Probability	Posterior Probability P(State of Nature/Unfav)(State of Nature/Unfav)
Strong	0.680.
Weak	0.320.
		P((Unfav)=)=	1.0000

(e) Now you start constructing the revised decision tree. Select the correct sketch of the leftmost part of the revised decision tree based on the information above.

• P(Fav)=0.9239 , P(Unfav)=0.6693
• P(Fav)=0.608, P(Unfav)=0.3704
• P(Hire)=0.8 , P(Do not hire)=0.86
• P(Fav)=0.5888 , P(Unfav)=0.4112
• None of the above.

(f) You continue to sketch the revised decision tree. Please select the correct sketch of the fragment incorporating the information from MRG.

• None of the above.

where the probabilities are

Select an answer P(Srtong)=0.32 , P(Weak)=0.68 , P(Strong|Fav)=0.544 , P(Weak|Fav)=0.0448 , P(Strong|Unfav)=0.136 , P(Weak|Unfav)=0.2752 P(Fav)=0.4112 , P(Strong|Fav)=0.3307 , P(Weak|Fav)=0.6693 P(Fav)=0.5888 , P(Strong|Fav)=0.9239 , P(Weak|Fav)=0.0761 None of the above.

If the analysts of Mimico Research Group provide an unfavorable report, how then would the ETO specialists estimate the probability of weak demand? Keep 4 decimal places in the following answer.

P(Weak|Unfav) =

Suppose that the unfavorable report is given, how then would the ETO specialists estimate the probability of strong demand? Keep 4 decimal places in the following answer.

P(Strong|Unfav) =

(g) Construct the revised decision tree and answer the following questions.

Round all EMV answers to 2 decimal places.

• In case of favorable report,

EMV(High-Rise Condos) == (in $$millions)

EMV(Low-Rise Condos) == (in $$millions)

EMV(Townhouse Complex) == (in $$millions)

• In case of unfavorable report,

EMV(High-Rise Condos) == (in $$millions)

EMV(Low-Rise Condos) == (in $$millions)

EMV(Townhouse Complex) == (in $$millions)

• In the revised decision tree, there are the expected monetary values

EMV(Hire) == (in $$millions)

EMV(Do not hire) == (in $$millions)

(h) Based on the revised decision tree formulate the optimal decision policy.

Note that in each answer cell below you have to use the scroll-down menu to select the correct option. If you recommend not hiring MRG, please select N/A in case of favorable/unfavorable report.

Select an answer Hire Do not hire Mimico Research Group. If their report is favorable, then choose the Select an answer High-Rise Condos Townhouse Complex N/A Low-Rise Condos project. If the report is unfavorable, then go ahead with the Select an answer High-Rise Condos Townhouse Complex N/A Low-Rise Condos project.

(i) How much would ETO Development Corporation be willing to pay at most for the information about future economic conditions?

If you recommend not hiring MRG, please enter zero in the answer cell.

Keep 2 decimal places in the following answer.

ETO can pay up to (in $$ millions)

(j) How efficient the MRG information would be?

If you recommend not hiring MRG, please enter zero in the answer cell.

Round your answer to 1 decimal place.

Efficiency == %