t$$ present, Solartech Skateboards is considering expanding its product line to include$$ gas$-$powered skateboards;$$ however, it is questionable how well they will be received by skateboarders. Although you feel there is a $50$ percent chance you will sell $9$ comma $000$ of these per year for $10$ years$($after which time this project is expected to shut down because$$ solar$-$powered skateboards will become more$$ popular$),$ you also recognize that there is a $25$ percent chance that you will only sell $2$ comma $000$ and also a $25$ percent chance you will sell $15$ comma $000.$ The gas skateboards would sell for $ $120$ each and have a variable cost of $$$$50$ each. Regardless of how many you$$ sell, the annual fixed costs associated with production would be $$$$130$ comma $000.$ In$$ addition, there would be an initial expenditure of $$$$1$ comma $000$ comma $000$ associated with the purchase of new production equipment which will be depreciated using the bonus depreciation method in year $1.$ Because of the number of stores that will need$$ inventory, the working capital requirements are the same regardless of the level of sales. This project will require a$$ one$-$time initial investment of $ $70$ comma $000$ in net working$$ 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 $11$percent$?$ What would the$$ project's NPV be if $9$ comma $000$ skateboards were$$ sold?