Crain Energy announced that it has discovered oil in an oil exploration well in
ID: 3325575 • Letter: C
Question
Crain Energy announced that it has discovered oil in an oil exploration well in Northwestern India. Initial estimates placed the find between 50 million and 200 million barrels of recoverable oil. To extract the oil, there is a $400M investment in the field and a $50M remediation cost at the end of the project. Regardless of the size of the reserve, the net annual revenue of $66M per year can be expected. However, at the constant extraction rate of 10,000 barrels per day, the smaller reserve will last 14 years, while the larger reserve 56 years. The chance of hitting a large reserve is 60% and the chance of hitting a small reserve is 40%. Assume the interest rate is 15%. Before making the initial investment to extract oil, Crain Energy has the option of digging an appraisal well and performs additional seismic testing to better understand the amount of reserves. Assume that the testing can be characterized as “Favorable---F” or “Unfavorable---UF”. More important we know that the test will predict “Favorable” if it is actually large 90% of the time, and it will predict “Unfavorable” if the well is actually small 80% of the time. The corresponding decision tree is as follows: The following computations provide the necessary conditional, marginal and other probabilities. Fill in the missing entries Testing Result Prior Joint probability Favorable F Unfavorable U Probability Favorable F Unfavorable U Large reserve (L) 0.90 0.10 0.60 0.54 ……. Small reserve (S) 0.20 0.80 0.40 …… 0.32 …….. …… Marginal Pr Pr(F) Pr(U) Large reserve (L) Pr(L|F) …… .….. P(L|U) Small reserve (S) Pr(S|F) …… .….. P(S|U) 9 a) Write down all cash flows and probabilities on the tree. Then perform all the necessary roll-back calculations on the decision tree b) If the test costs $1M, what would be your optimal strategy? c) What is the maximum worth of the test (i.e find EVSI)? And also, what is the value of perfect information (EVPI)?
Explanation / Answer
We have given table as :
Testing results
Favorable Unfavorable Total
Large reserve 0.9 0.1 1
Small reserve 0.2 0.8 1
Total 1.1 0.9 2
Table for Joint probability :
Favorable Unfavorable Marginal probability of reserve
Large reserve 0.9/2 = 0.45 0.1/2 = 0.05 1/2 =0.5
Small reserve 0.2/2 =0.1 0.8/2 =0.4 1/2=0.5
Marginal probability 1.1/2=0.55 0.9/2 =0.45 1
P( L|F) = 0.45/0.55 = 0.8182
P(S|F) = 0.1/0.55 = 0.1818
P(L|U) = 0.05/0.45 = 0.1111
P( S|U) =0.4/0.45=0.8889