At the beginning of $2022,$ Metatec Incorporated acquired Ellison Technology Corporation for $$600$ million. In addition to cash, receivables, and inventory, the following assets and their fair values were also acquired:

$\backslash$table$[[$Plant and equipment $($depreciable assets$),$$$150$ million$],[$Patent$,40$ million$],[$Goodwill$,100$ million$]]$

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 five$-$year useful life, no residual value, and is amortized using the straight$-$line method.

At the end of $2024,$ a change in business climate indicated to management that the assets of Ellison might be impaired. The following amounts have been determined:$*$After first recording any impairment losses on plant and equipment and the patent.Required:

Compute the book value of the plant and equipment and patent at the end of $2024.$

When should the plant and equipment and the patent be tested for impairment?

When should qoodwill be tested for impairment?