The Drilling Exercise

Decision Tree Analysis using Excel TreePlan & Bayes' Rule

1. Assignment Expectations & Problems to be Answered:

The goal of this assignment is for you create and apply Decision Trees (using TreePlan Excel add-in) to help answer "Drilling Exercise" questions. You will display mastery of understanding the value of information by using Expected Value of Perfect Information (EVPI) and Expected Value of Imperfect Information (EVII) by finding the probabilities by using Bayes' Rule and applying to your Decision Tree models.

You work for a large international oil company searching for oil off the coast of Australia, not too far from Melbourne, 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 classified as "wet"). If there is oil, your geologists believe that the expected present value of a well in this location is $\$ 180$ million. If there is no oil (the site is classified as "dry"), assume that the value of the drilled site is \(\mathbf{\\)} 0$.

1. i. Should you drill at site \(A\) ?
   (Show Excel Decision Tree and explain why/why not you would drill in comprehensive detail.)
   ii. How does the optimal decision change as the "wet" probability changes?
   (Show in Excel using Bayes' rule and describe in comprehensive detail.)
   " See Finding the probabilities by Bayes' rule in Appendix of this document as reference!
   iii. Calculate the break-even probability both algebraically and using Goal Seek in Excel.
   (Show in Excel and describe in comprehensive detail - including what done for Goal Seek.)
2. Suppose you could find out definitively whether or not there was oil at this site, before deciding whether to drill.

1. What is the most you would be willing to pay for this information?
   (Show in Excel and describe in comprehensive detail.)
2. How does the Expected Value with perfect information (EVPI) change as "wet" probability changes?

(Show Excel EVPI Decision Tree and EV without perfect information and describe in comprehensive detail.)

"See EVPI/Bayes' Rule example in Appendix of this document as reference!

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 \((30 \%)\) of the wet sites have structures that can be detected by this seismic test. However many ( \(80 \%)\) of the dry sites also have these structures. The seismic test costs $\$ 2.5$ million.

1. Do you want to do the test?
   - (Show Excel Decision Tree and calculations.)
   - (Explain why/why not you want to do the test in comprehensive detail.)
2. 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,
   What is the maximum you would be willing to pay for the test then?
   - (Show Excel Decision Tree and calculations.)
   - (Explain why is maximum you would pay for test in comprehensive detail.)
3. How does the Expected Value (EV) of doing the seismic test change as "wet" probability changes?

2. Now consider sites \(\mathrm{A}\) and \(\mathrm{B}\), Like site \(\mathrm{A}\), site \(\mathrm{B}\) 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 $A$ was wet, that information would change your assessment of the probability that B is wet from \(20 \%\) to \(60 \%\).

Similarly, if you knew that A was dry, that information would change your assessment of the probability that \(\mathrm{B}\) is wet from \(20 \%\) to \(10 \%\).

1. i. Should you drill one, both, or neither of these sites?
   (Show Excel Decision Tree and explain why/why not you would drill in comprehensive detail.)
2. i. Ignoring the possibility of doing the seismic test, what is the optimal drilling strategy? (Show Excel Decision Tree and explain optimal drilling strategy in comprehensive detail.)

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Solution: The downloadable solution consists of 11 pages, 1339 words and 7 charts.
Deliverable: Word Document