$($Calculating free cash flows$)$ At present, Solartech Skateboards is considering expanding its product line to include gas$-$powered skateboards; however, it is questionable how well they will be received by skateboarders. Although you feel there is a $50$ percent chance you will sell $8,000$ of these per year for $10$ years $($after which time this project is expected to shut down because solar$-$powered skateboards will become more popular$),$ you also recognize that there is a $25$ percent chance that you will only sell $2,000$ and also a $25$ percent chance you will sell $17,000.$ The gas skateboards would sell for $$120$ each and have a variable cost of $$30$ each. Regardless of how many you sell, the annual fixed costs associated with production would be $$130,000.$ In addition, there would be an initial expenditure of $$800,000$ associated with the purchase of new production equipment which will be depreciated using the bonus depreciation method in year $1.$ Because of the number of stores that will need inventory, the working capital requirements are the same regardless of the level of sales. This project will require a one$-$time initial investment of $$40,000$ in net working capital, 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 the project?

b$.$ What are the annual free cash flows associated with the project for years $1,$ and $2$ through $9$ under each sales forecast? What are the expected annual free cash flows for year $1,$ and years $2$ through $9?$

c$.$ What is the terminal cash flow in year $10($that is$,$ what is the free cash flow in year $10$ plus any additional cash flows associated with the termination of the project$)?$

d$.$ Using the expected free cash flows, what is the project's NPV given a required rate of return of $8$ percent? What would the project's NPV be if $8,000$ skateboards were sold?