You are a manager at Northern$$ Fibre, which is considering expanding its operations in synthetic fibre manufacturing. Your boss comes into your$$ 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 $ $25$ 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$)$:

$1$

$2$

$...$

$9$

$10$

Sales revenue

$26\mathrm{.}000$

$26\mathrm{.}000$

$26\mathrm{.}000$

$26\mathrm{.}000$

minusCost of goods sold

$15\mathrm{.}600$

$15\mathrm{.}600$

$15\mathrm{.}600$

$15\mathrm{.}600$

equalsGross profit

$10\mathrm{.}400$

$10\mathrm{.}400$

$10\mathrm{.}400$

$10\mathrm{.}400$

minus$$General$,$sales$,$ and administrative expenses

$2\mathrm{.}000$

$2\mathrm{.}000$

$2\mathrm{.}000$

$2\mathrm{.}000$

minusDepreciation

$2\mathrm{.}500$

$2\mathrm{.}500$

$2\mathrm{.}500$

$2\mathrm{.}500$

equalsNet operating income

$5\mathrm{.}900$

$5\mathrm{.}900$

$5\mathrm{.}900$

$5\mathrm{.}900$

minusIncome tax

$2\mathrm{.}065$

$2\mathrm{.}065$

$2\mathrm{.}065$

$2\mathrm{.}065$

equalsNet income

$3\mathrm{.}835$

$3\mathrm{.}835$

$3\mathrm{.}835$

$3\mathrm{.}835$

All of the estimates in the report seem correct. You note that the consultants used$$ straight$-$line depreciation for the new equipment that will be purchased today$($year $0),$ which is what the accounting department recommended for financial reporting purposes. CRA allows a CCA rate of $30\%$ on the equipment for tax purposes. The report concludes that because the project will increase earnings by $ $3\mathrm{.}835$ million per year for $10$ years, the project is worth $ $38\mathrm{.}35$ million. You think back to your glory days in finance class and realize there is more work to be$$ done!$$

First you note that the consultants have not factored in the fact that the project will require $ $7$ million in working capital up front$($year $0),$ which will be fully recovered in year $10.$ Next you see they have attributed $ $2$ million of$$ selling, general and administrative expenses to the$$ project, but you know that $ $1$ 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?