TABLE $2\mathrm{.}6$ OIL INVESTMENT DETAILS

$\backslash$table$[[$Year$,\backslash$table$[[$Barrels$],[$produced$]],\backslash$table$[[$Gross$],[$revenue$]],\backslash$table$[[$Net$],[$income$]],$Option $1,$Option $2,\backslash$table$[[$Depletion$],[$allowance$]],\backslash$table$[[$Taxable$],[$income$]],$Tax,$\backslash$table$[[$After$-$tax$],[$Income$]]],[1,80,000,1,600,000,1,200,000,352,000,400,000,400,000,800,000,360,000,840,000],[2,70\mathrm{.}000,1,40,1,000,000,308,350,350,650,292,500,10.907],[3,50,000,1,000,000,500,000,220,250,250,250,113500,0],[4,30,000,600,000,200,000,132,150,150,50,22,50,],[5,10,000,200,000,50,000,44,50,50,0,,]]$

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 $2\mathrm{.}6$ 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 $20\%.$