17.6. Tax Shelter Ten years from now, having made your first $10 million in the engineering specialty of your choice, you must decide how to dispose of a tract of land originally purchased to avoid taxes. Your options are Spend $3M to develop resort (option R) Spend $1M to open a strip mine for coal (option M) Sell the property for $0.1M (option S) . . The outcomes from options R and M depend on whether a coal seam runs through your property. A geologist friend estimates a 75% probability that there is a coal deposit. He believes that if coal is present it will be on your neighbor's land as well. If there is no coal, the resort would return $12M in revenue, the mine would make nothing. If there is coal, your neighbor will eventually find out about it and start mining, spoiling the view and forcing you to convert the resort to a school worth just $1M in revenue, but the mine would have made $1M profit. (a) Structure the decision tree. Select your best strategy. One of your friends recommends a geological testing service whose test results with indicate either HIGH probability of finding coal, or LOW. Coal- bearing deposits will result in a HIGH test report 76% of the time; noncoal-bearing strata yield HIGH results in only 12% of the cases. (6) What is the most you would pay to test for coal? (c) Construct the decision tree for the test, and find the expected value of the test. Is it worth $1M? 17.6. Tax Shelter Ten years from now, having made your first $10 million in the engineering specialty of your choice, you must decide how to dispose of a tract of land originally purchased to avoid taxes. Your options are Spend $3M to develop resort (option R) Spend $1M to open a strip mine for coal (option M) Sell the property for $0.1M (option S) . . The outcomes from options R and M depend on whether a coal seam runs through your property. A geologist friend estimates a 75% probability that there is a coal deposit. He believes that if coal is present it will be on your neighbor's land as well. If there is no coal, the resort would return $12M in revenue, the mine would make nothing. If there is coal, your neighbor will eventually find out about it and start mining, spoiling the view and forcing you to convert the resort to a school worth just $1M in revenue, but the mine would have made $1M profit. (a) Structure the decision tree. Select your best strategy. One of your friends recommends a geological testing service whose test results with indicate either HIGH probability of finding coal, or LOW. Coal- bearing deposits will result in a HIGH test report 76% of the time; noncoal-bearing strata yield HIGH results in only 12% of the cases. (6) What is the most you would pay to test for coal? (c) Construct the decision tree for the test, and find the expected value of the test. Is it worth $1M
