You are a manager at Percolated$$ Fiber, which is considering expanding its operations in synthetic fiber manufacturing. Your boss comes into your$$ office, drops a$$ consultant's report on your$$ desk, and$$ complains, $"$We owe these consultants $$$$1\mathrm{.}4$ million for this$$ report, and I am not sure their analysis makes sense. Before we spend the $$$$21$ million on new equipment needed for this$$ project, look it over and give me your$$ opinion." You open the report and find the following estimates$($in millions of$$ dollars$)$:TABLE

All of the estimates in the report seem correct. You note that the consultants used$$ straight$-$line depreciation for the new equipment that will be purchased today$($year $0),$ which is what the accounting department recommended. The report concludes that because the project will increase earnings by $$$$7\mathrm{.}856$ million per year for $10$ years, the project is worth $$78\mathrm{.}56$ million. You think back to your halcyon days in finance class and realize there is more work to be$$ done!$$

$$First$,$ you note that the consultants have not factored in the fact that the project will require $$$$12$ million in working capital upfront$($year $0),$ which will be fully recovered in year $10.$ Next, you see they have attributed $$$$1\mathrm{.}68$ million of$$ selling, general and administrative expenses to the$$ project, but you know that $$$$0\mathrm{.}84$ million of this amount is overhead that will be incurred even if the project is not accepted.$$ Finally, you know that accounting earnings are not the right thing to focus$$ on$!$

a$.$ Given the available$$ information, what are the free cash flows in years $0$ through $10$ that should be used to evaluate the proposed$$ project?

b$.$ If the cost of capital for this project is $16\%,$ what is your estimate of the value of the new$$ project?

a$.$ Given the available$$ information, what are the free cash flows in years $0$ through $10$ that should be used to evaluate the proposed$$ project?

$($answered$)$ The free cash flow for year $0$ is $$$ $-33\mathrm{.}00$ million. $($Round to three decimal places and enter a decrease as a negative$$ number.$)$

The free cash flows for years $1$ to $9$ is $$$$\_\_\_$ million. $($Round to three decimal places and enter a decrease as a negative$$ number.$)$

The free cash flow for year $10$ is $$$ $\_\_\_$ million. $($Round to three decimal places and enter a decrease as a negative$$ number.$)$

b$.$ If the cost of capital for this project is $10\%,$ what is your estimate of the value of the new$$ project?

The value of the new project is $$$$\_\_\_$ million. $($Round to three decimal$$ places.$)$