Question

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.

1. The government is considering imposing three different kinds of taxes:
   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.
What are the present discounted values of government revenues and after-tax profits for the company under each tax regime?

Answer 1

Answer...
Total reserves = 100 million barrels, initial production rate = 8 million barrels during the first year, capital costs are $400 million, the wellhead price of oil is expected to be $50 per barrel, and operating costs are $30 per barrel. The company uses a 10 percent annual discount rate. Production declines at a rate equal to the ratio of initial production to reserves. This rate is therefore 8/100 = 8%.
a. What is the estimated expected present discounted value of gross revenues?
This is 8 million barrel* price per barrel = 8m*50 = $400 milion in first year. On one side the discounting factor is 10% and the production declines by 8%. So stream of revenue will decline by 10% + 8% = 18%.
Expected time = infinite. So use the formula PDV = Gross revenue/rate of discount = 400 million/0.18 = $2.222 billion
b. What is the estimated expected present discounted value of economic rent?
Economic rent is the difference in PDV of revenue and PDV of costs
PDV of revenue = $2.222 billion
PDV of costs = first year costs + discount sum of cost over infinite period
= $400 million + 8 million*30 (or $240 million) + $240 million/0.18
= $400m + $240m + $1333m = $1.973 billion
Economic rent = 2.222 - 1.973 = $249 million. This is the discounted economic rent.