Rory Company has an old machine with a book value of $$85,000$ and a remaining five$-$year useful life. Rory is considering purchasing a

new machine at a price of $$113,000.$ Rory can sell its old machine now for $$61,000.$ The old machine has variable manufacturing costs

of $$42,000$ per year. The new machine will reduce variable manufacturing costs by $$16,800$ per year over its five$-$year useful life.

$($a$)$ Prepare a keep or replace analysis of income effects for the machines.

$($b$)$ Should the old machine be replaced?

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Prepare a keep or replace analysis of income effects for the machines.