Problem $11-12($Algo$)$ Depreciation and amortization; impairment $[$LO$11-2,11-4,11-8]$

At the beginning of $2019,$ Metatec Inc. acquired Ellison Technology Corporation for $$500$ million. In addition to cash, receivables, and inventory, the following assets and their fair values were also acquired:

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$$Plant and equipment $($depreciable assets$)$$$140$millionPatent$30$millionGoodwill$120$million

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The plant and equipment are depreciated over a $10-$year useful life on a straight$-$line basis. There is no estimated residual value. The patent is estimated to have a $5-$year useful life, no residual value, and is amortized using the straight$-$line method.

At the end of $2021,$ a change in business climate indicated to management that the assets of Ellison might be impaired. The following amounts have been determined:

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$$Plant and equipment:$$Undiscounted sum of future cash flows$$70$millionFair value$50$millionPatent:$$Undiscounted sum of future cash flows$$19$millionFair value$12$millionGoodwill:$$Fair value of Ellison Technology Corporation$$340$millionFair value of Ellison's net assets $($excluding goodwill$)290$millionBook value of Ellison's net assets $($including goodwill$)370$million$*$

$*$After first recording any impairment losses on plant and equipment and the patent.

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Required:

$1.$ Compute the book value of the plant and equipment and patent at the end of $2021.$

$4.$ Determine the amount of any impairment loss to be recorded, if any, for the three assets.