Question 2:

Exxon is evaluating an oil well that will produce oil for two years. In year 1, the company plans to produce 100,000 barrels of oil, and the production cost will be $20 per barrel. In year 2, it plans to produce 50,000 barrels of oil, but the production cost will go up to $30 per barrel. The well will be fully depleted in two years, and it has no salvage value afterwards. The forward price of oil to be delivered one year from now is $80, and the forward price oil to be delivered two years from now is $90. The risk-free rate for all maturities is 5%.

(a) (10 points): Find the certainty equivalent cash flows of the oil well in years 1 and 2. Find the current market value of the well using the certainty equivalents.

(b) (10 points): Describe the tracking portfolio of the oil well, i.e., a portfolio of financial assets that synthetically replicates the cash flows from the well.

(c) (10 points): Suppose that the production plans for year 1 are as above, but there is some uncertainty about production in year 2. Specifically, a technical report indicates that, after the first year production of 100,000 barrels, the well will have either 25,000 or 75,000 barrels of oil left. The two possibilities have equal likelihood. Given this information, indicate whether you need to change your analysis of the valuation of the well in part (a), and if so, how.