Smithson Mining operates a silver mine in Nevada. Acquisition, exploration, and development costs totaled $$7\mathrm{.}3$ million. After the silver is extracted in approximately five years, Smithson is obligated to restore the land to its original condition, including constructing a wildlife preserve. The company$$s controller has provided the following three cash flow possibilities for the restoration costs: $(1)$ $$670,000,10\%$ probability; $(2)$ $$720,000,50\%$ probability; and $(3)$ $$820,000,40\%$ probability. The company$$s credit$-$adjusted, risk$-$free rate of interest is $5\%.$

What is the book value of the asset retirement liability at the end of one year?

Assuming that the actual restoration costs incurred after five years are $$766,000,$ what amount of gain or loss will Smithson recognize on retirement of the liability?