Question

1. Perform a complete decision tree analysis of this problem for Steeley Associates and indicate the recommended solution. (40 points).
   1. Use Excel QM Decision Analysis - Decision Tree to build the Tree.
   2. Make sure that you label every branch and state probability if/when needed

2. Using the “best” decision you arrived at in question #1, is this the decision you believe the firm should make.

Steeley Associates, Inc., a 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 2008, 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 at Steeley Associates held a series of meetings to review their alternatives. They decided that they had three options: They could 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 Steeley sells the house and property, it thinks it can get $900,000. If it builds a new office building, its return will depend on town business growth in the future. It feels that there is a 70% chance of future growth, in which case Steeley will see a return of $1.3 million (over a 10-year planning horizon); if no growth (or erosion) occurs, it will make only $200,000. If Steeley requests a permit for the apartments, a host of good and bad outcomes are possible. The immediate good outcome is approval of its permit, which it estimates will result in a return of $3 million. However, Steeley gives that result only a 10% chance that it will occur. 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 will undoubtedly decrease the value to potential buyers, and Steeley estimates that it will get only $700,000. Alternatively, it can 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 that the award will be approximately $1 million, and it will 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 will 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 will be only $1.2 million. If no growth occurs, it conservatively estimates only a $100,000 return

Answer 1

Overview: SA Inc. is a property development firm who purchased an old house near the town square in CC Falls area near to the State University. The problem aroused when the SA Inc. wanted to build a new high-density student apartment demolishing this house after the lease with state university expired. This was opposed by the town council. The SA Inc. had developed three options to gain permit in building apartment in the proposed area. SA Inc. has estimated all the probabilities of problems that could occur if they chose any of the three options. An optimal appropriate decision is to be recommended.

The decisions at the respective nodes are given below: NODES DESCRIPTION 1-2 Request permit for apartment 1-3 Sell property 1-4 Request permit for office 2-5 Pemit not granted 2-6 Permit granted 4-7 Town growth 4-8 No growth 5-9 Pursue case 5-10 Sell 5-11 Build office building 9-12 Case lingers 9-13 Win the case 9-14 Lose the case 11-15 Town growth 11-16 No growth 14-17 Sell 14-18 Build office building 17-19 Growth 17-20 No growth 18-21 Growth 18-22 No growth

The decision tree analysis can be explained with the below tables: Table 1: Analysis before the event occurred NODES DESCRIPTION PROBABILITY PAY-OFF (in S) Request permit for ZERO Sell property Request permit for office Permit not ZERO ZERO 900,000 0.90 nted 2-6 4-7 4-8 5-9 5-10 5-11 Permit granted Town growth No growth Pursue case Sell Build office buildin Case lingers Win the case Lose the case 0.10 0.70 0.30 ZERO ZERO ZERO 3,000,000 1,300,000 200,000 3,00,000 7,00,000 9-12 9-13 9-14 11-15 11-16 14-17 14-18 200,000 400,000 0.10 0.40 0.50 0.70 0.30 ZERO ZERO Town growth No growth Sell 1,300,000 200,000 Build office buildin Growth 17-19 17-20 18-21 18-22 0.50 0.50 0.50 0.50 900,000 500,000 1,200,000 1,00,000 No growth Growth No growth

Calculate the payoff at each node by calculating the expected value thereby considering the respective probability Calculate Pay-off for Node 1-4 as follows: Pay-off for Node 1-4 -(Pay-off for node 4-8 Pay-off for node 4-8)] -(0.30x 200,000) (0.70x1,300,000)] 970,000 Similarly, calculate expected values for Nodes 1-3 and 1-2 and proceed. Table 2: Analvsis after the decision made NODES 1-2 1-3 1-4 2-5 2-6 4-7 4-8 5-9 5-10 5-11 9-12 9-13 9-14 11-15 11-16 14-17 14-18 17-19 17-20 18-21 18-22 PROBABILITY ZERO ZERO ZERO 0.9 PAY-OFF 2,266,500 9,00,000 9,70,000 1,966,500 3,00,000 9,10,000 60,000 515,000 7,00,000 9,70,000 20,000 160,000 675,000 9,10,000 60,000 7,00,000 6,50,000 4,50,000 2,50,000 6,00,000 50,000 0.7 0.3 ZERO ZERO ZERO 0.5 0.7 0.3 ZERO ZERO 0.5 0.5 0.5 0.5

The pay-off of Request a permit for the apartment is valued to $2,266,500. Since this pay-off expected value is highest, thus decision of going with request permit for the constructing the building should be considered.