The Guo Chemical Corporation is considering the purchase of a chemical analysis machine. The purchase of this machine will result in an increase in earnings before interest and taxes of $$$$75,000$ per year. The machine has a purchase price of $$$$400,000,$ and it would cost an additional $8,000$ after tax to install this machine correctly. In$$ addition, to operate this machine$$ properly, inventory must be increased by $12,000.$ This machine has an expected life of $10$ years, after which time it will have no salvage value. $$ Also, assume simplified$$ straight$-$line depreciation, that this machine is being depreciated down to$$ zero, a $30$ percent marginal tax$$ rate, and a required rate of return of $12$ percent.

a$.$What is the initial outlay associated with this$$ project?

b$.$What are the annual$$ after$-$tax cash flows associated with this project for years $1$ through $9?$

c$.$What is the terminal cash flow in year $10($that is$,$ the annual$$ after$-$tax cash flow in year $10$ plus any additional cash flow associated with termination of the$$ project$)?$

d$.$Should this machine be$$ purchased?