Question

Decision tree (Show formulas)

Senior executives of an oil company are trying to decide whether to drill for oil in a particular field. It costs the company $300,000 to drill in the selected field. Company executives believe that if oil is found in this field its estimated value will be $1,800,000. At present, this oil company believes that there is a 48% chance that the selected field actually contains oil. Before drilling, the company can hire a geologist at a cost of $30,000 to prepare a report that contains a recommendation regarding drilling in the selected field. There is a 55% chance that the geologist will issue a favorable recommendation and a 45% chance that the geologist will issue an unfavorable recommendation. Given a favorable recommendation from the geologist, there is a 75% chance that the field actually contains oil. Given an unfavorable recommendation from the geologist, there is a 15% chance that the field actually contains oil.

This oil company wishes to maximize its expected net earnings, and so wishes to implement a decision tree.

.Using PrecisionTree, construct the decision tree that would enable the company to determine its optimal strategy. Attach the decision tree as Exhibit A (an image would be sufficient).

Describe the optimal strategy in words.

Answer 1

Decision tree is following:

Expected Value of node 2 (Drill) = .48*(1800000-300000)+.52*(0-300000) = $ 564,000

Expected Value of node 6 (Drill | Favorable) = .75*(1800000-300000)+.25*(0-300000) = $ 1,050,000

Expected Value of node 7 (Drill | Unfavorable) = .15*(1800000-300000)+.85*(0-300000) = $ -30,000

Expected Value of node 4 = MAX(1050000, 0) = $ 1,050,000

Expected Value of node 5 = MAX(-30000, 0) = $ 0

Expected Value of node 3 (Hire geologist) = .55*1050000+.45*0-30000 = $ 547,500

Expected Value of node 2 is the highest

Therefore, the company should simply drill the oil field.

Expected Value (net earnings) of this decision = $ 564,000