$($Calculating free cash flows$)$ You are considering new elliptical trainers and you feel you can sell $3,000$ of these per year for $5$ years after which time this project is expected to shut down when it is learned that being fit is unhealthy$).$ The elliptical trainers would sell for $$1,800$ each and have a variable cost of $$900$ each. The annual fixed costs associated with production would be $$1,100,000.$ In addition, there would be a $$4,000,000$ initial expenditure associated with the purchase of new production equipment. It is assumed that this initial expenditure will be depreciated using the bonus depreciation method in year $1.$ This project will also require a one$-$time initial investment of $$1,500,000$ in net working capital associated with inventory, and working$-$capital investment will be recovered when the project is shut down. 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 $1,$ and $2$ through $4?$

c$.$ What is the terminal cash flow in year $5($that is$,$ what is the free cash flow in year $5$ plus any additional cash flows associated with the termination of the project$)?$

d$.$ What is the project's NPV given a required rate of return of $9$ percent?