A financial$-$wealth$-$maximizing mining company considers buying a phosphate deposit in the ground. Construction of a mine to enable extraction of the phosphate would cost $$1$ million per year for four years. In the fifth year, extraction would start and last for $12$ years. Each year that the mine would extract, it would generate net operating revenue, that is$,$ total revenue minus total operating costs, of $$60,000.$ Assume that financial flows occur at the end of each year; that is$,$ assume that bills are paid and revenues are earned at the end of each year. How much, if any, would the mining company pay for the deposit if theinterest rate were $10\%,$ annual net operating revenues would be $$1\mathrm{.}6$ million or $$400,000$ with even odds$(50\%$ chance of each$)$ during $12$ years of possible extraction, the company would learn how much the net operating revenues would be at the start of each year of possible extraction, and the company can exercise the option to close the mine in any year when annual net operating revenues would be negative? Please write or type the discounted cash flows as the difference between two annuities, represented with correct formula, and subsequent calculations. Also, does the net present value of the phosphate deposit increase, even though the interest rate stays constant, if the mining company has the option to shut down?