Consider an oil-wildcatting problem. You have mineral rights on a piece of land that you believe may have oil underground. There is only a 15% chance that you will strike oil if you drill, and the payoff is $150,000. It costs $10,000 to drill. The alternative is not to drill at all, in which case your profit is zero.
(1) Construct the 1st decision tree that is the “No Any Information” tree to represent the problem.
(2) Based on (1), should you drill? Why or Why not. Please explain in detail.
(3) Construct the 2nd decision tree that includes both “No Any Information” and “Perfect Information” decision alternatives.
(4) Calculate EVPI based on (3).
(5) Based on (4), is it better for us with the perfect information before you drill? Why or Why not. Please explain in detail.
(6) Before you drill, you might consult a geologist who can assess the promise of the piece of land. She can tell you whether your prospects are “good” or “poor.” But she is not a perfect predictor. If there is oil, the conditional probability is 0.90 that she will say prospects are good. If there is no oil, the conditional probability is 0.80 that she will say poor. Construct the 3rd decision tree that includes both “No Any Information” and “Consult Geologist” alternative. Be careful to calculate the appropriate conditional probabilities and to include them in the decision tree. Note that the Geologist charges $4,500 for the consultation.
(7) Calculate EVII based on (6).
(8) Based on (7), as the Geologist charges $4,500, what should you do and why?
Note that all of your trees that you built above should include the following considerations if any:
- Use the negative sign (-) for the cost, the expenses, cash outflow, etc.
- Use the positive sign (+) for the revenue, profit, cash inflow, etc.
- The tree that you build for Part 1, Part 3, and Part 6 must be separated from one another.