On March $1,2025,$ Walk Company paid $$8,500,000$ to acquire all of the common stock of Jog Corporation, which became a division of Walk. Jog reported the following balance sheet at the time of the acquisition:

Current assets $$700,000$

Noncurrent assets $$6,300,000$

Total assets $$7,000,000$

Current liabilities $$400,000$

Long$-$term liabilities $$700,000$

Stockholders equity $$5,900,000$

Total liabilities and stockholders equity $$7,000,000$

It was determined at the date of the purchase that the fair value of the identifiable net assets of Jog was $$7,900,000.$ At December $31,2025,$ Walk reports the following balance sheet information:

Current assets $$500,000$

Noncurrent assets $($including goodwill recognized in purchase$)$ $$5,400,000$

Current liabilities $$(700,000)$

Long$-$term liabilities $$(800,000)$

Net Assets $$4,400,000$

It is determined that the fair value of the Jog division is $$4,700,000.$

$1.$ Compute the amount of goodwill recognized, if any, on March $1,2025.$

$2.$ Determine the impairment loss, if any, to be recorded on December $31,2025.$ If an impairment loss is not to be recorded, explain why.

$3.$ Assume that the fair value of the Jog division is $$4,100,000$ instead of $4,700,000.$ Prepare the journal entry to record the impairment loss, if any, on December $31,2025.$ If an impairment loss is not to be recorded, explain why.