Petroleum Incorporated $($PI$)$ controls off$-$shore oil leases. It is considering the construction of a deep$-$sea oil rig at a cost of $$522$ million. The price of oil is $$122$ per bbl$.$ and extraction costs are $$72$ per bbl$.$ Pl expects costs to remain constant. The rig will produce an estimated $1,200,000bbl.$ per year forever. The risk$-$free rate is $10$ percent per year, which is also the cost of capital. $($Ignore taxes$).$ Suppose that oil prices are uncertain and are equally likely to be $$142$ per bbl$.$ or $$102$ per bbl$.$ next year. Suppose that PI has the option to postpone the project by one year. Calculate the value of the real option to postpone the project for one year. $($There is some rounding in the answer.$)$

Multiple Choice

$$82$ million

$$67$ million

$$42$ million