Question

An oil exploration company must decide whether to drill a well on a site before its option expires or to abandon its rights to the site. Drilling costs $1,000,000. If oil is struck, the company will sell its rights for $5,000,000. Before deciding whether to drill or not, the company can take a seismic sounding of the site at a cost of $150,000. Such soundings reveal whether the geophysical substructure of the land is of type A, type B or type C, each type having a different degree of favorability for the existence of oil. The probability that oil is present is 0.8 for substructure type A, 0.4 for type B, and 0.1 for type C. Based on knowledge of adjacent areas, the probabilities for substructure types A, B and C at this site are 0.20, 0.30 and 0.50, respectively. a) Build a decision tree model to help the company decide what to do. b) What is the strategy that maximizes expected value? c) Suppose that the oil exploration company has a risk tolerance of $2,000,000. Based on this risk tolerance, what is the optimal course of action for the company? d) Given their risk tolerance, what is the most the company would be willing to pay for the seismic sounding?

          An oil exploration company must decide whether to drill a well on a site before its option expires or to abandon its rights to the site. Drilling costs $1,000,000. If oil is struck, the company will sell its rights for $5,000,000. Before deciding whether to drill or not, the company can take a seismic sounding of the site at a cost of $150,000. Such soundings reveal whether the geophysical substructure of the land is of type A, type B or type C, each type having a different degree of favorability for the existence of oil. The probability that oil is present is 0.8 for substructure type A, 0.4 for type B, and 0.1 for type C. Based on knowledge of adjacent areas, the probabilities for substructure types A, B and C at this site are 0.20, 0.30 and 0.50, respectively. a) Build a decision tree model to help the company decide what to do. b) What is the strategy that maximizes expected value? c) Suppose that the oil exploration company has a risk tolerance of $2,000,000. Based on this risk tolerance, what is the optimal course of action for the company? d) Given their risk tolerance, what is the most the company would be willing to pay for the seismic sounding?

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Added by Stephen C.

Mathematics for Finance An Introduction to Financial Engineering

Marek Capinski 1st Edition

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Solved by Expert Supreeta N

12/03/2023

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a) The decision tree model would look like this: - Show more…

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An oil exploration company must decide whether to drill a well on a site before its option expires or to abandon its rights to the site. Drilling costs $1,000,000. If oil is struck, the company will sell its rights for $5,000,000. Before deciding whether to drill or not, the company can take a seismic sounding of the site at a cost of $150,000. Such soundings reveal whether the geophysical substructure of the land is of type A, type B or type C, each type having a different degree of favorability for the existence of oil. The probability that oil is present is 0.8 for substructure type A, 0.4 for type B, and 0.1 for type C. Based on knowledge of adjacent areas, the probabilities for substructure types A, B and C at this site are 0.20, 0.30 and 0.50, respectively. a) Build a decision tree model to help the company decide what to do. b) What is the strategy that maximizes expected value? c) Suppose that the oil exploration company has a risk tolerance of $2,000,000. Based on this risk tolerance, what is the optimal course of action for the company? d) Given their risk tolerance, what is the most the company would be willing to pay for the seismic sounding?

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Transcript

00:01 Hi, here for the given question, we know that expected value of drilling can be written as 0 .8 into 5 million.

00:09 So this will be equal to here.

00:12 The next term will be plus 0 .4 into minus 1 million.

00:17 So here in our case, now further expected value of not drilling.

00:22 So we will write it as d dash is equal to 0 .0 multiplied with 0 .20 plus 0 .30, 0 multiplied with 0 .30 plus 0 .0 multiplied with 0 .50.

00:40 So this value will be zero.

00:42 So here in our case, now calculating the cost of drilling, expected cost of the drilling will be equal to 4 million dollars.

00:51 Now further in the next part of the company.

00:53 So here from this, we can conclude the second part also.

00:57 This is the maximum expected value.

01:00 So for this is drilling, not drilling, we have value equals to zero.

01:05 So e of d dash will be equal to zero.

01:08 Now further we need to find the value of the risk tolerance.

01:11 So here in our case, we know that the value of risk tolerance can be calculated as from the drilling.

01:18 So here in our case, we know that the risk is of 1 million.

01:23 So here the risk tolerance will be for the 1 million dollars.

01:28 And since the company has a risk tolerance of, so here this is the value of expected loss and the company's policy for the risk tolerance is, this is for the risk tolerance, this will be equal to 2 million dollars.

01:44 So here in our case, it is within their, it is within their limit, within their limit...

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