$($Calculating project cash flows and NPV$)$ 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 $$80,000$ per year. The machine has a purchase price of $$400,000,$ and it would cost an additional $$7,000$ after tax to install this machine correctly. In addition, to operate this machine properly, inventory must be increased by $$14,000.$ 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 $32$ percent marginal tax rate, and a required rate of return of $9$ 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?

a$.$ The initial cash outlay associated with this project is $ $q,($Round to the nearest dollar.$)$X