At the beginning of $2022.$ Metatec Incorporated acquired Ellison Technology Corporation for $$680$ 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$),$$$158$ mililion$],[$Patent$,48$ million$],[$Goodwill$,120$ 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:

Plant and equipment:

Undiscounted sum of future cash flows

Fair value

Patent:

Undiscounted sum of future cash flows

Fair value

$$88$ million

$68$ million

Goodwill:

Fair value of Ellison Technology Corporation

Book value of Bllison's net assets $($excluding goodwill$)$ $$530$ milion

Book value of Ellison's net assets $($including goodwill$)550$ million$*$

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 goodwill be tested for impairment?

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