EGRMGMT 580 – Decision Models FALL 2021 Drilling Exercise Due by 11:59pm Sep 5th Assignment: Answer the questions on the next page. Each student should submit the following on Sakai before the beginning of class: • For question 1 • Part a: One sentence stating why you should or should not drill at site A, and the breakeven probability that makes you indifferent between the alternatives. • Part b: An answer to the question “how much would you be willing to pay?”, a tree that shows how you arrived at the number, and a graph showing the expected values of the alternatives and the expected value with perfect information (similar to the one we did in Class #2). • Part c: (i) An answer to the question “do you want to do the test?” and a tree that shows how you arrived at your answer. (ii) A graph showing the expected values of the alternatives and the expected value with imperfect information (similar to the one we did in Class #2). (iii) An answer to the question “how much would you be willing to pay?” and a graph showing the expected values of the alternatives and the expected value with imperfect information. (Bonus question:) A graph showing how the expected value of sampling information changes as you change the accuracy of the test. • For question 2 • One sentence describing the optimal drilling strategy, a tree that shows how you arrived at your answer, and a graph showing the expected values of the alternatives. You may work in groups of 2-3 to build a tree for this assignment (i.e., you can share Excel files within this group), but you should work individually when writing up your answers to submit. Please be sure to note the following at the top of the page: • Your name • Who, if anyone, you worked with on this assignment Retain a copy of these materials for yourself, as you may find it useful for the class discussion. You work for a large international oil company searching for oil off the coast of Norway. Your firm has acquired drilling rights at two locations, sites A and B, and you are contemplating your firm's options. 1. First consider site A alone. The estimated drilling cost is $40 million. For simplicity, assume that if you drill at this site, there are two possible outcomes: either there is oil at the site or there is no oil. Based on the available data, your geologists assign a 20% chance that there is oil at the site (the site is “wet”). If there is oil, your geologists believe that the expected present value of a well in this location is $160 million. If there is no oil (the site is “dry”), assume that the value of the drilled site is $0. a) Should you drill at site A? How does the optimal decision change as the “wet” probability changes? Calculate the break-even probability both algebraically and using Goal Seek in Excel. b) Suppose you could find out definitively whether or not there was oil at this site, before deciding whether to drill. What is the most you would be willing to pay for this information? How does the EV with perfect information change as the “wet” probability changes? c) Although you cannot resolve all the uncertainty about whether the site contains oil, you can gather some information. In particular, you can do seismic testing. In this procedure, one sets off explosives on the ocean floor and measures the seismic waves at other points on the ocean floor. From the seismic data, one can construct a 3D image of the subsurface geology and see if there are structures that may form an oil reservoir. Your geologists estimate that most (90%) of the wet sites have structures that can be detected by this seismic test. However many (60%) of the dry sites also have these structures. The seismic test costs $2.5 million. (i) Do you want to do the test? (ii) How does the EV of doing the seismic test first change as “wet” probability changes? (iii) Suppose instead that your geologists estimate that half of the wet sites have structures that can be detected by the seismic test. However, half of the dry sites also have these structures. How much would you be willing to pay for the test then? How does the EV of doing the seismic test change as “wet” probability changes? (Bonus question:) How sensitive is the EV of sampling information to the accuracy of the test? (Hint: Do a sensitivity analysis changing P(structure | wet) and P(no structure | dry) at the same time.) 2. Now consider sites A and B. Like site A, site B would cost $40 million to drill, with the same assessment of the outcomes: a 20% chance of a value of $160 million (wet) and an 80% chance of $0 (dry). Because of the similarities between the two locations, the outcomes at the two sites are not probabilistically independent. In particular, if you knew that site A were wet, that information would change your assessment of the probability that B is wet from 20% to 60%. Similarly, if you knew that A were dry, that information would change your assessment of the probability that B is wet from 20% to 10%. Should you drill one, both, or neither of these sites? Ignoring the possibility of doing the seismic test, what is the optimal drilling strategy? How does the optimal decision change as the “wet” probability at site A changes?
