A. An oil company is developing a discovery with 100 million barrels of reserves located on lands leased from the government. The initial production rate would be 8 million barrels during the first year (about 20,000 barrels per day). Capital costs are $250 million, the wellhead price of oil -- the price after deducting costs of transportation to the market -- is expected to be $50 per barrel, and operating costs are $30 per barrel. The company uses a 10 percent annual discount rate. Assume that production declines at a rate equal to the ratio of initial production to reserves (in this case 8/100 = 8% per year). If production keeps declining at the same rate, and ignoring the last few barrels that stay in the ground after the field shuts down, the discounted annual stream of revenues declines over time at a constant rate, equal to the sum of the discount rate and the decline rate.

a. A 33 percent tax on cash flow (an income tax with capital and operating costs deducted from income in the year they are incurred);

b. a 10 percent production tax (levied as a percentage of gross wellhead revenues);

c. a property tax with a present value equal to 20 percent of capital costs.

d. All three of these taxes imposed at the same time.

B. Now consider that the oil company has not found the oil field described in part A, but has a lease to explore. Exploration costs are $10 million, and the company has a 10 percent chance of finding the discovery described in part A.

2. What are the expected present discounted values of government revenues and expected after-tax profits for the company under each tax regime in part A, considering the exploration risk? Assume that the company can deduct the exploration costs from its taxable income regardless of whether it finds oil or not. The exploration costs are not subject to property taxes or production taxes.