Problem:
There's an oil leasing opportunity that looks too good to be true, and it probably is too good to be true: an estimated 1,500,000 barrels of oil sitting underground that can be leased for 3 years for just $1,000,000. It looks like a golden opportunity: pay a million, bring the oil to the surface, sell it at the current spot price of $18.36 per barrel, and retire.
However, upon closer investigation, you come across the facts that explain why nobody else has snapped up this 'opportunity.' Evidently, it is difficult to remove the oil from the ground due to the geology and the remote location. A careful analysis shows that estimated costs of extracting the oil are $30,000,000. You conclude that be developing this oil field, you would actually lose money.
During the next week, although you are busy investigating other capital investment opportunities, your thoughts keep returning to this particular project. In particular, the fact that the lease is so cheap and that it lasts for 3 years inspired you to do a "what if" scenario analysis, recognizing that there is no obligation to extract the oil and that it could be extracted fairly quickly (taking about a month) at any time during the 3-year lease. You are wondering: What if the price of oil rises enough during the 3 years for it to be profitable to develop the oil field? If so, then you would extract the oil. But if the price of oil didn't rise enough, you would let the term of the lease expire in 3 years, leaving the oil still in the ground. You would let the future price of oil determine whether or not to exercise the option to extract the oil.
But such a proposition is risk. How much risk is there? What are the potential rewards? You have identified the following basic probability structure for the source of uncertainty in this situation:
Future Price Probability
$10 0.1
15 0.2
20 0.4
25 0.2
30 0.1
Should you sign the lease? Why or why not?