A company is considering buying a machine for $$11,000.$ If purchased, the machine will produce annual cost savings of $$3,000$ for the next $5$ years. The machine will be depreciated over $5$ years using the $5-$year MACRS schedule. At the end of the $5$th year, the machine will be sold for $$4,000.$ However, there is uncertainty about the future market value. The firm's tax rate is $35\%$ and its discount rate is $12\%.$

a$)$ Based on the NPV rule, should the company accept the project?

b$)$ Based on the IRR rule, should the company accept the project?

c$)$ Build a one$-$way data table to examine how sensitive is the NPV to

changes in the market value at the end of year $5.$ The data table should

range from $$1,000$ to $$6,000$ in increments of $$1,000.$