### Perform a decision tree analysis

Assignment Help Basic Statistics
##### Reference no: EM1378577

Steeley Associates Inc., a property development firm, purchased an old house near the Lakeshore Campus of Humber College. The house was built shortly after World War I and Steeley Associates restored it. For almost a decade, Steeley has leased it to Humber College for academic office space. The house has unique architecture and is located on a large piece of property.

In 2006, the lease with the college expired, and Steeley Associates decided they would like to build high-density student apartments on the site so proceeded to request a zoning change from the city of Toronto. The Lakeshore community objected to the proposed zoning change through their city council representatives. The legal counsel for the city spoke with a representative from Steeley and hinted that if Steeley requested a zoning change and consequent building permit the city would probably reject it. Steeley had reviewed the city building code and felt confident that its plan was within the guidelines, but that did not necessarily mean that it could win a lawsuit against the city to force the city to grant a zoning change and grant the permit.

The principals at Steeley Associates had a series of meetings to review their alterna-tives. They decided that they had three options: They could request the zoning change for high density apartments, they could sell the property, or they could request a zoning change for a low-density office building, which the town had indicated it would not fight. Regarding the last two options, if they sell the house and property, they think they can get \$900,000; while if they build a new office building, their return will depend on growth in the Lakeshore area in the future. They feel that there is a 70% chance of future growth, in which case they will see a return of \$1 300 000 (over a 10-year planning horizon); if no growth (or a decline) occurs, they estimate a return of only \$200 000.

If Steeley requests a zoning change for the apartments, a series of good and bad outcomes are possible. The immediate good outcome would be approval of its zoning change application for high density estimated to generate a return of \$3 million. However, Steeley gives that result only a 10% chance of occurring. There is a 90% chance that the town will reject its application for a zoning change, which will result in another set of decision possibilities.

Steeley can sell the property at that point. However, the rejection of the permit would undoubtedly decrease the value to potential buyers, and Steeley estimates the selling price would decrease to about \$700 000. Alternatively, it could construct the office building and face the same potential outcomes it did earlier, namely, a 30% chance of no growth in the Lakeshore area and a \$200,000 return, or a 70% chance of growth with a return of \$1.3 million.

A third option is to sue the town. On the surface, Steeley's case looks good, but the city's zoning building code is vague and a sympathetic judge could throw out the case. Whether or not it wins, Steeley estimates the possible legal fees to be \$300,000, and believes there is only a 40% chance of winning. However, if Steeley does win, it estimates the award will be approximately \$1 million, and it would also get its \$3 million return for building the apartments. Steeley also estimates that there is a 10% chance that the suit could linger on in the courts for such a long time that any future return would be negated during its planning horizon. It would also incur an additional \$200,000 in legal fees if the case lingered.

If Steeley loses the suit, it would then be faced with the same options of selling the property or constructing an office building. However, after taking time to take the case to court, Steeley believes that a realistic selling price for the property will be somewhat dependent on the Lakeshore community's growth prospects at that time, which are estimated at 50-50. If the community is in a growth mode at that time, Steeley thinks that \$900,000 is a conservative estimate of the potential sale price, whereas if the community is not growing, it thinks \$500,000 is reasonable estimate.

Finally, if Steeley decides to construct the office building after losing the case, it believes that if there is growth in the community (50% chance) the return would be \$1 200 000 and if no growth occurs; (50% chance) estimates a \$100 000 return.

Part 1

a) Give a brief description of the decision problem facing Steeley Associates.
b) Draw the decision tree and perform a decision tree analysis of Steeley Associates decision situation using expected monetary value.
c) State the decision and the expected value of the decision.

Part 2

Because the likelihood of winning the case against the city is such an important factor in the decision process, the planning department suggests that the firm hire Bernard consultants for \$50 000 to conducts a study about the likelihood of winning the zoning change case. The results of the study will either be a prediction that Steeley wins the case or a prediction that Steeley loses the case. Using past records of the consulting firm, the company developed estimates of the consultant's information as follows:

90% chance of predicting winning the case given that the case is won
80% chance of predicting losing the case given that the case is lost
50% chance of predicting winning given that the case lingered
50% chance of predicting losing given that the case lingered.

d) Calculate the posterior probabilities and construct a revised decision tree. Analyse the revised decision and state the expected monetary value of Steeley's decision with Bernard Consultant's information.

e) What is the value of the information provided by Bernard Consultants (EVSI)? Give a recommendation as to whether or not Steeley should hire the consultant.

f) Comment on the use of decision analysis in this case.

Calculate the efficiency of the consultant's information

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