A depletion allowance, for tax purposes, can be computed in either of two wayseach. year: $22\%$ of gross revenue up to $50\%$ of net income before such deduction $($option $1),$ at 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 taxablile income. The investor is in the $45\%$ tax bracket.

$($a$)$ Complete Table $2\mathrm{.}6$ and show that the total depletion allowance exceeds the origimal investment.

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