On January $2,$ Year $4,$ Poplar Ltd$.$ purchased $\backslash (80\backslash \%\backslash )$ of the outstanding shares of Spruce Ltd$.$ for $\backslash (\backslash$$ $2,100,000\backslash ).$ At that date, Spruce had common shares of $\backslash (\backslash$$ $500,000\backslash )$ and retained earnings of $\backslash (\backslash$$ $1,350,000\backslash )$ and accumulated depreciation of $\backslash (\backslash$$ $700,000\backslash ).$ Poplar acquired the Spruce shares to obtain control of mineral rights owned by Spruce. At the date of acquisition, these mineral rights were valued at $\backslash (\backslash$$ $775,000\backslash ),$ were not recognized on Spruce's separate$-$entity balance sheet, and had an useful life of $10$ years. Except for the mineral rights, the carrying amount of the recorded assets and liabilities of Spruce were equal to their fair values. On December $31,$ Year $7,$