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 $$1$ million for this report, and I am not sure their analysis makes sense. Before we spend the $$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$)$:

Project Year

$12...910$

Sales revenue $30,00030,00030,00030,000$

$$ Cost of good sold $18,00018,00018,00018,000$

$=$ Gross profit $12,00012,00012,00012,000$

$$ General, sales, and

administrative expenses $2,0002,0002,0002,000$

$$ Depreciation $2,5002,5002,5002,500$

$=$ Net operating income $7,5007,5007,5007,500$

$$ Income tax $2,6252,6252,6252,625$

$=$ Net income $4,8754,8754,8754,875$

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 $$4\mathrm{.}875$ million per year for ten years, the project is worth $$48\mathrm{.}75$ 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 $$10$ million in working capital upfront $($year $0),$ which will be fully recovered in year $10.$ Next, you see they have attributed $$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?

b$.$ If the cost of capital for this project is $14\%,$ what is your estimate of the value of the new project?