On January $2,$ Year $4,$ Poplar Ltd$.$ purchased $80\%$ of the outstanding shares of Spruce Ltd$.$ for $$2,030,000.$ At that date, Spruce had common shares of $$500,000$ and retained earnings of $$1,280,000$ and accumulated depreciation of $$630,000.$ 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 $$757,500,$ 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 $7,$ the trial balances of the two companies were as follows: