An industrial machine costing $$14,000$ will produce net cash savings of $$5,000$ per year. The machine has a five$-$year useful life but must be returned to the factory for major repairs after three years of operation. These repairs cost $$5,000.$

a$)$ What IRR will be earned on the purchase of this machine?

b$)$ Analyze the sensitivity of IRR to $+-$$$2,000$ changes in the repair cost.

c$)$ If the company's MARR is $10\%$ per year, should the machine be purchased if the repairs cost is $$4,000?$