A wealthy investor spends \(\$ 1\) million to drill and develop an oil well that has estimated reserves of 200,000 barrels. The well is to be operated over 5 years, producing the estimated quantities shown in the second column of Table 2.6. It is estimated that the oil will be sold for \(\$ 20\) per barrel. The net income is also shown.

A depletion allowance, for tax purposes, can be computed in either of two ways each year: \(22 \%\) of gross revenue up to \(50 \%\) of net income before such deduction (option 1), or the investment cost of the product, equal in this case to the unit cost of the reserves, \(\$ 5\) per barrel (option 2). The allowance is deducted from the net income to determine the taxable income. The investor is in the \(45 \%\) tax bracket.

(a) Complete Table 2.6 and show that the total depletion allowance exceeds the original investment.

(b) Calculate the PV and the IRR for this investment. Assume an interest rate of \(20 \%\).

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TABLE 2.6 OIL INVESTMENT DETAILS Barrels Year produced revenue income Gross Net 12345 Option 1 80,000 1,600,000 1,200,000 352,000 70,000 1,400,000 1,000,000 50,000 1,000,000 500,000 30,000 600,000 200,000 10,000 200,000 50,000 Depletion Taxable Option 2 allowance income Tax After-tax income 400,000 400,000 800,000 360,000 840,000