$11-9.($Calculating free cash flows$)$ You are the product manager of Lexcon Fitness and are considering the production of new elliptical trainers. You feel you can sell $5,500$ of these per year for $6$ years $($after which time this project is terminated due to product obsolescence$).$ The elliptical trainers would sell for $$1,200$ each and have a variable cost of $$600.$ The annual fixed costs associated with production would be $$1\mathrm{.}2$ million. In addition, there would be a $$4\mathrm{.}5$ million initial expenditure associated with the purchase of new production equipment. It is assumed that this initial expenditure will be depreciated using the straight$-$line method down to zero in $6$ years. This project will also require a one$-$time initial investment of $$800,000$ in net working capital associated with inventory and working capital investment will be recovered when the project is terminated. Finally, assume that the firm's marginal tax rate is $22$ percent.

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

b$.$ What are the annual free cash flows associated with this project for years $1$ through $5?$

c$.$ What is the terminal cash flow in year $6($that is$,$ what is the free cash flow in year $6$ plus any additional cash flows associated with the termination of the project$)?$

d$.$ What is the project's NPV given a $12$ percent required rate of return?