A local energy provider offers a landowner $180,000 for the exploration rights t

Question

A local energy provider offers a landowner $180,000 for the exploration rights to natural gas on a certain site and the option for future development. This option, if exercised, is worth an additional $1,800,000 to the landowner, but this will occur only if natural gas is discovered during the exploration phase. The landowner, believing that the energy company’s interest in the site is a good indication that gas is present, is tempted to develop the field herself. To do so, she must contract with local experts in natural gas exploration and development. The initial cost for such a contract is $300,000, which is lost forever if no gas is found on the site. If gas is discovered, however, the landowner expects to earn a net profit of $6,000,000. The landowner estimates the probability of finding gas on this site to be 60%.

Question:

Suppose the landowner could request a perfectly reliable soundings test on the site where natural gas is believed to be present. What is the most the landowner should be willing to pay for this test?

Comments: I was thinking it would be up to the max amount that would return a positive return before it becomes a loss, but don't know if I'm correct or if there's a way to calculate the amount.

Explanation / Answer

Let C be the cost of the test and p be the probability of existing of gas. Note that if a test exists which can perfectly tell the existence of gas or other wise, the cost of such test should be less than either the expected gain by exploring the gas herself or by the company.

Her estimate of the presence of gas is 60%, and hence the expected gain by ordinary test is -30000*0.4 + 6000000*0.6 = 3588000. If she goes with the company's offer, the expected gain is 180000 + 0.6*1800000 = 1260000. Thus, only if the cost of a perfect test is less than 1260000, she should go with the perfect test.

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