$18$ million pounds of coal still in mine, and that the cost of opening up the mines will be $$2\mathrm{.}5$ million $($in present value dollars$).$ The capacity output rate is $600,000$ pounds a year, and the price of coal is expected to increase $5\%$ a year. The local government is willing to grant a $25-$year lease on the mine. The average production cost is expected to be $40$ cents a pound, and the current price per pound of coal is $85$ cents. $($The production cost is expected to grow $4\%$ a year, once initiated.$)$ The annualized standard deviation in coal prices is $25\%,$ and the $25-$year bond rate is $7\%$

a$.$ Estimate the value of the mine using traditional capital budgeting techniques $($NPV$)$