Smithson Mining operates a silver mine in Nevada. Acquisition, exploration, and development costs totaled $\backslash (\backslash$$ $5\mathrm{.}6\backslash )$ million. After the silver is extracted in approximately five years, Smithson is obligated to restore the land to its original condition, including constructing a wildlife preserve. The company's controller has provided the following three cash flow possibilities for the restoration costs: $(1)\backslash$$$500,000,20\backslash \%$ probability; $(2)\backslash$$$550,000,45\backslash \%$ probability; and $(3)\backslash$$$650,000,35\backslash \%$ probability. The company's credit$-$adjusted, risk$-$free rate of interest is $\backslash (6\backslash \%\backslash ).$ What is the initial cost of the silver mine?