ProTech Company purchased a machine for $$50,000$ on January $1,2018.$ The company expects the service life of the machine to be $5$ years. During that time, it is expected that the machine's useful life will be $100,000$ hours. The expected salvage value is $$5,000.$ Actual hours used during the five years of the asset's life was:

$2018$: $15,000$ hours used

$2019$: $30,000$ hours used

$2020$: $20,000$ hours used

$2021$: $25,000$ hours used

$2022$: $10,000$ hours used

Instructions:

$($a$)$ Prepare the $5$ years depreciation schedule for the machine. Find the depreciation expense and the book value of the machine for each of the $5$ years using the following depreciation methods: : $(1)$ straight$-$line, $(2)$ units$-$of$-$activity, and $(3)$ declining$-$balance using double the straight$-$line rate.

Note: Prepare a depreciation schedule $($with columns headings: Year, Beginning Book Value, Depreciation Expense, Accumulated Depreciation, and End Book Value$)$

$($b$)$ On October $1$st$,2020,$ the company is trying to determine if it should sell the machine. Under each of the three depreciation methods, how much should the company sell the dumping machine to have a minimum gain of $$5,000?$

$($c$)$ Under Straight$-$line method, assuming the machine is disposed on October $1$st$,2020.$ Prepare the journal entry to record the disposal of the machine under each of the following independent situation:

$(1)$ The machine is sold for $$20,500$

$(2)$ The machine is trade$-$in on a new, similar machine with a cost of $$56,000.$

A trade$-$in allowance of $$21,100$ was given on the old machine.