An oil company has acquired the right to drill for and extract oil in a geologically promising area. While the area is promising, history has shown that only 10% of areas with similar geological promise have resulted in productive, profitable oil fields. If this particular area has a productive oil field the firm estimates that the discounted net present value (i.e. net profit) of the oil will be $100 M. However, drilling a well and finding that there is no oil will cost the firm $12 M. So before investing in drilling a well to extract oil and potentially coming up with a dry well, the firm decides to conduct a test for oil. The test costs $1 M. The test is not perfectly accurate; it is correct 80% of time, whether there is oil or not. That is, if the area has a profitable oilfield, there is an 80% chance that the test will indicate that there is a profitable oil field and a 20% that it will indicate that there is not a profitable oil field. Conversely, if in fact there is not a profitable oil field, there is an 80% chance that the test will indicate that there is not a profitable oil field (and a 20% that it will (falsely) indicate that there is a profitable oil field).
a) Suppose the firm conducts the test and the test indicates that there is a profitable oil field. What is the actual (revised) probability that there is a profitable oil field?
b) A priori (before conducting the test) what is the expected net profit of each of
i) drilling for oil without conducting a test,
ii) just walking away without drilling for oil
iii) conducting the test and drilling for oil if the test indicates a profitable oil field? (Ignore the cost of acquiring the right to the oil field – that’s a sunk cost at tis point). (10 marks)