#2 Decision Analysis Problem 1 (25 points) A local energy provider offers a landowner $180,000 for the exploration rights to natural gas on a certain site and the option for future development. This option, if exercised, is worth an additional $1,800,000 to the landowner, but this will occur only if natural gas is discovered during the exploration phase. The landowner, believing that the energy company's interest in the site is a good indication that gas is present, is tempted to develop the field herself. To do so, she must contract with local experts in natural gas exploration and development. The initial cost for such a contract is $300,000, which is lost forever if no gas is found on the site. If gas is discovered, however, the landowner expects to earn a net profit of $6,000,000. The landowner estimates the probability of finding gas on this site to be 60%. a. Create a payoff table that specifies the landowner's payoff (in dollars) associated with each possible decision and each outcome with respect to finding natural gas on the site. Decision Outcome Gas is discovered Gas is not discovered EMV Sell exploration rights Develop the field herself b. What is the strategy that maximizes the landowner's expected net earnings from this opportunity? What is the expected payoff associated with this decision? c. Draw by hand a decision tree. Make sure to label all decision and chance nodes and include appropriate costs, payoffs and probabilities. d. Suppose the landowner could request a perfectly reliable soundings test on the site where natural gas is believed to be present. What is the most the landowner should be willing to pay for this test? e. Use the file Landowner_Gas_Exploration_39.xlsx and PrecisionTree add-in to create a decision tree with Excel and perform a sensitivity analysis on the optimal decision, letting each of the five inputs vary one at a time plus or minus 25% from its base value. Submit your Excel file on Canvas. f. Summarize your findings in the hard copy of the homework that you are turning in. g. In response to which model inputs is the expected profit value most sensitive? What chart(s) did you use to make your conclusion? -1- Problem 2 (15 points) Consider again the landowner's decision problem. Suppose now that, at a cost of $90,000, the landowner can request that a soundings test be performed on the site where natural gas is believed to be present. The company that conducts the soundings concedes that 30% of the time the test will indicate that no gas is present when it actually is. When natural gas is not present in a particular site, the soundings test is accurate 90% of the time. a. Given that the landowner pays for the soundings test and the test indicates that gas is present, what is the landowner's revised estimate of the probability of finding gas on this site? b. Given that the landowner pays for the soundings test and the test indicates that gas is not present, what is the landowner's revised estimate of the probability of not finding gas on this site? c. Use the file Landowner_Gas_Exploration_49.xlsx and PrecisionTree add-in to create the appropriate decision tree. Submit your Excel file on Canvas. d. Should the landowner request the given soundings test at a cost of $90,000? Explain why or why not. If not, at what price (if any) would the landowner choose to obtain the soundings test? -2