You are considering buying an oil field. If you buy the field, you can extract the oil in one year. There are 100 barrels of oil that can be extracted from the field; the cost of doing so is $4,000. You expect the price of oil in one year to be $50/barrel. However, there are four equally likely prices of oil in one year: $20/barrel, $35/barrel, $40/barrel, and $105/barrel.
a. Of the below prices, what is the minimum price at which you would drill in year 1, if you buy the field today? Assume the price of oil never changes after one year.
b. If your discount rate is 15%, what is the value of the option to not drill when the price of oil is too low.