A risk-neutral gas company is prospecting for new gas reserves. A candidate gas field is thought...

 

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A risk-neutral gas company is prospecting for new gas reserves. A candidate gas field is thought to have a probability a of holding gas worth £4 million (excluding the cost of drilling), otherwise the site has zero commercial value. It would cost £750,000 to drill the site. (a) Calculate the minimum value of T necessary to incentivise the gas company to drill for gas at the site. (4 marks) (b) Briefly explain how the gas company might estimate the value of 7. (2 marks) Suppose now the gas company considers the probability of there being gas at the site to be 0.45. At a cost of £300,000 the executive board could hire a geologist to conduct a seismographic test which would indicate whether gas (worth £4 million, again excluding the cost of drilling) was present. However, the seismographic test is not perfect and has: • a 20% false positive rate (predicting the presence of gas when there is no gas) a 30% false negative rate (predicting no gas when it is present). (c) Draw a complete decision tree to assist the executive board in making the decision about whether to hire the geologist to conduct the seismographic test. Based on your decision tree, would you recommend that the geologist is hired? Justify your answer. (12 marks) (d) Explain briefly, with reasoning, how the value of the imperfect seismographie test would be sensitive to the false positive rate and the false negative rate. (No calculations are required for this part.) (3 marks) (e) Suppose the seismographic test was perfect, i.e. the false positive rate and false negative rate were both 0%. What would be the gas company's maximum willingness to pay for the geologist to conduct a perfect seismographic test? (4 marks) A risk-neutral gas company is prospecting for new gas reserves. A candidate gas field is thought to have a probability a of holding gas worth £4 million (excluding the cost of drilling), otherwise the site has zero commercial value. It would cost £750,000 to drill the site. (a) Calculate the minimum value of T necessary to incentivise the gas company to drill for gas at the site. (4 marks) (b) Briefly explain how the gas company might estimate the value of 7. (2 marks) Suppose now the gas company considers the probability of there being gas at the site to be 0.45. At a cost of £300,000 the executive board could hire a geologist to conduct a seismographic test which would indicate whether gas (worth £4 million, again excluding the cost of drilling) was present. However, the seismographic test is not perfect and has: • a 20% false positive rate (predicting the presence of gas when there is no gas) a 30% false negative rate (predicting no gas when it is present). (c) Draw a complete decision tree to assist the executive board in making the decision about whether to hire the geologist to conduct the seismographic test. Based on your decision tree, would you recommend that the geologist is hired? Justify your answer. (12 marks) (d) Explain briefly, with reasoning, how the value of the imperfect seismographie test would be sensitive to the false positive rate and the false negative rate. (No calculations are required for this part.) (3 marks) (e) Suppose the seismographic test was perfect, i.e. the false positive rate and false negative rate were both 0%. What would be the gas company's maximum willingness to pay for the geologist to conduct a perfect seismographic test? (4 marks)