# Statistics Case Study

Statistical & Quantitative Methods Semester 2 of 2009/2010 Problem Context: This case problem is related to a property purchase strategy - **Statistics Case Study** introduction. The president of Oceanview is deciding whether to bid for a property to build and sell condominiums. However, this depends on whether the state can change the zoning of the property to permit construction of condominiums. Here, the decision is whether to bid for the property, and chance events are firstly, whether the bid can be successful, and secondly, whether the state will approve the zoning change.

To assess the likelihood that the state will approve the zoning change, the president can hire a market research service. Hence, the president is facing another decision as to whether he wants to hire the market research service. As a result, if he chooses to hire the service, besides the two chance events mentioned above, there is another chance event concerning whether the market research predicts that the zoning change will be approved. The consequence is that the company will have different profits or losses. Data analysis:

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Below is a timeline showing the sequence of events taking place from now to November where the results of whether the zoning change is approved will be released. Now 1 Jun 1 Aug 15 Aug 1 Sep Nov Market research results available Deadline to submit bid Announcement of winning bid Announcement of zoning referendum results Based on the sequence of events in the timeline, we can draw a decision tree showing all the decisions and chance events. A more detailed decision tree with probabilities for each state of nature will be illustrated in the appendix.

Recommendations 1. If no market research information is available, the expected value of submitting the bid would be a profit of $0. 05 million, whereas the payoff of not submitting the bid would be 0. Therefore, to maximize profit, Oceanview should submit the bid. 2. If the market research is conducted and it predicts the approval of zoning change, the expected value of submitting the bid would be a profit of $0. 23 million, whereas the payoff of not submitting the bid would be 0. Hence, Oceanview should submit the bid. 3.

If market research is conducted and it predicts that the zoning change will be rejected, the expected value of submitting the bid would be a loss of $-0. 075 million, whereas the payoff of not submitting the bid would be 0. Hence, to minimize losses, Oceanview should not submit the bid. The expected value of conducting the market research is $0. 093 million, and the expected value of not conducting the research is $0. 05 million. Hence, the value of information provided by the research is $0. 043 million. This is much larger than the cost of hiring the service ($0. 15 million), hence Oceanview should employ the market research firm. Insights The above analysis is using the expected value approach for decision making. However, to gain a complete picture of the situation, we should also look at the risk associated with each of the decision. For recommendation (1), although it shows an expected profit of $0. 05 million, the risk associated with such a profit is also high as reflected in the standard deviation of $0. 1 million. The risk per unit return is 2, and this shows that the decision of bidding when no research is available is quite risky.

For recommendation (2), the standard deviation is $0. 46 million, and the risk per unit return is still 2. This proves that even when there is market research to improve the expected value of the payoff, there is still a constant level of risk involved, and this is partly due to the fact that there is a very high probability of unsuccessful bid. The above analysis is based on the assumption that Oceanview will only decide to submit a $5 million bid. The probability of winning the bid will improve if Oceanview can submit a higher bid, but the trade-off is that Oceanview will incur a higher cost of purchasing the property.

Our team suggests that Oceanview conducts a more thorough analysis concerning how much to bid in order to get an optimal level of expected payoff with minimized risk. In addition, we also make the assumption that Oceanview will settle the full amount of the property after it wins the bid. In reality, Oceanview might experience financial difficulties of not being able to fulfill the obligation. In such a case, the probability of forfeiting payment has to be considered to present a more comprehensive analysis.