Brief Exercise $10-5($Algo$)$ Asset retirement obligation $[$L$010-1]$

Smithson Mining operates a silver mine in Nevada. Acquisition, exploration, and development costs totaled $$6\mathrm{.}1$ 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: $(1)$

$$550,000,10\%$ probability; $(2)$ $$600,000,50\%$ probability; and $(3)$ $$700,000,40\%$ 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 $$646,000,$ what amount of gain or loss will Smithson recognize

on retirement of the liability?

Note: Use appropriate factor$($s$)$ from the tables provided. Do not round intermediate calculations. Enter your answers in dollars

not in millions of dollars. $($FV of $$1,$ PV of $$1,$ FVA of $$1,$ PVA of $$1,$ FVAD of $$1$ and PVAD of $$1)$