$(50$ points$).$ The Durant corporation is considering the purchase of a chemical analysis machine. Although the machine being considered will result in an increase in earnings before interest and taxes of $$35,000$ per year, it has a purchase price of $$72,000,$ and it would cost an additional $$3,000$ to properly install the machine. In addition, to properly operate the machine, the inventory must be increased by $$4,000.$ The machine has an expected life of $6$ years, after which it will have no salvage value. Also, assume simplified straight$-$line depreciation and that the machine is being depreciated down to zero, a $21$ percent marginal tax rate, and a required rate of return of $10$ percent.

What is the initial investment associated with this project? $(9$ points$).$

What are the annual after$-$tax cash flows associated with this project for years $1$ through $5?(12$ points$).$

What is the net cash flow in year $6($what is the annual after$-$tax cash flow in year $6$ plus any additional cash flows associated with the termination of the project$)?(10$ points$).$

Should the machine be purchased? $(19$ points$).$