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# Decision tree analysis of Steeley Associates' and LP model

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Case Problem #2

Steeley Associates, Inc. a property development firm, property development firm purchased an old house near the town square in Concord Falls, where State University is located. The old house was built in the mid-1800s, and Steeley Associates restored it. For almost a decade, Steeley has leased it to the university for academic office space. The house is located on a wide lawn and has become a town landmark.

However, in 2003, the lease with the university expired, and Steeley Associates decided to build high-density student apartments on the site, using all the open space. The community was outraged and objected to the town council. The legal counsel for the town spoke with a representative from Steeley and hinted that if Steeley requested a permit, the town would probably reject it. Steeley had reviewed the town 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 town to force the town to grant a permit.

The principals of Steeley Associates held a series of meetings to review their alternatives. They decided that they had three options: they would request the permit, they could sell the property, or they could request a permit 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. If they build a new office building, their return will depend on town business growth in the future. They feel that there is a 70% chance of future growth, in which case they will see a return of \$1.3 million (over a 10-year planning horizon); if no growth (or erosion) occurs, they will make only 200,000.

If Steeley requests a permit for the apartments, a host of good and bad outcomes is possible. The immediate good outcome is approval of its permit, which it estimates will result in return of \$3 million. However, Steeley gives that result only a 10% chance of occurring. Alternatively, Steeley thinks there is a 90% chance that the town will reject its application, which will result in another set of decisions.

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 it would get only \$700,000. Alternatively, it could construct the office building and face the same potential outcomes it did earlier, namely, a 30% chance of no town growth 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 town building code is vague and a sympathetic judge could throw out its suit. Whether or not it wins, Steeley estimates its possible legal fees to be \$300,000, and it feels it has only a 40% chance of winning. However, if Steeley does win, it estimates the reward 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 and it would incur an additional \$200,000 in legal fees.

If Steeley loses the suit, it would then be faced with the same options of selling the property or constructing an office building. However, if the suit is carried this far into the future, it feels that the selling price it can ask will be somewhat dependent on the town's growth prospects at that time, which it feels it can estimate at only 50-50. If the town is in a growth mode that far in the future, Steeley thinks that \$900,000 is a conservative estimate of the potential sale price, whereas if the town is not growing, it thinks \$500,000 is a more likely estimate. Finally, if Steeley constructs the office building, it feels that the chance of town growth is 50%, in which case the return would be only \$1.2 million. If not growth occurs, it conservatively estimates only a \$100,000 return.

A. Perform a decision tree analysis of Steeley Associates' decision situation using expected value, and indicate the appropriate decision with these criteria.
B. Indicate the decision you would make, and explain your reasons.

https://brainmass.com/statistics/regression-analysis/decision-tree-analysis-of-steeley-associates-and-lp-model-174563

#### Solution Preview

See the attached file for complete solution. The text here may not be copied exactly as some of the symbols / tables may not print. Thanks

Let the dimensions of the optimal patrol area are x in horizontal direction and y in vertical direction

Objective function: Minimize ...

#### Solution Summary

Illustrates how we can do the decision tree analysis, using the expected value, to arrive at the best business decision. Also presents how to solve a decision situation using the linear programming model.

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