Question

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 $1.5 million for this​ report, and I am not sure their analysis makes sense. Before we spend the $ $28 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
Earnings Forecast​ ($ million)	1	2	. . .	9	10
Sales revenue	33.000	33.000		33.000	33.000
minus−Cost of goods sold	19.800	19.800		19.800	19.800
equals=Gross profit	13.200	13.200		13.200	13.200
minus−​Selling, general, and administrative expenses	2.240	2.240		2.240	2.240
minus−Depreciation	2.800	2.800		2.800	2.800
equals=Net operating income	8.160	8.160		8.160	8.160
minus−Income tax	1.632	1.632		1.632	1.632
equals=Net unlevered income	6.528	6.528		6.528	6.528

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 $6.528 million per year for ten​ years, the project is worth $65.28 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 $9 million in working capital upfront​ (year 0), which will be fully recovered in year 10.​ Next, you see they have attributed $2.24 million of​ selling, general and administrative expenses to the​ project, but you know that $1.12 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 12 %12%​, what is your estimate of the value of the new​ project?

Answer 1

a)	Earnings Forecast​ ($ million)	0	1	2	3	4	5	6	7	8	9	10
	Sales revenue		33.000	33.000	33.000	33.000	33.000	33.000	33.000	33.000	33.000	33.000
	minus−Cost of goods sold		19.800	19.800	19.800	19.800	19.800	19.800	19.800	19.800	19.800	19.800
	equals=Gross profit		13.200	13.200	13.200	13.200	13.200	13.200	13.200	13.200	13.200	13.200
	minus−​Selling, general, and administrative expenses (incremental)		1.120	1.120	1.120	1.120	1.120	1.120	1.120	1.120	1.120	1.120
	minus−Depreciation		2.800	2.800	2.800	2.800	2.800	2.800	2.800	2.800	2.800	2.800
	equals=Net operating income		9.280	9.280	9.280	9.280	9.280	9.280	9.280	9.280	9.280	9.280
	minus−Income tax at 20%		1.856	1.632	1.632	1.632	1.632	1.632	1.632	1.632	1.632	1.632
	equals=Net unlevered income		7.424	7.648	7.648	7.648	7.648	7.648	7.648	7.648	7.648	7.648
	add-Depreciation		2.800	2.800	2.800	2.800	2.800	2.800	2.800	2.800	2.800	2.800
	OCF		10.224	10.448	10.448	10.448	10.448	10.448	10.448	10.448	10.448	10.448
	Capital expenditure	28.000
	Change in NWC	9.000										-9.000
	FCF	-37.000	10.224	10.448	10.448	10.448	10.448	10.448	10.448	10.448	10.448	19.448
b)	PVIF at 12% [PVIF = 1/1.12^n]	1	0.89286	0.79719	0.71178	0.63552	0.56743	0.50663	0.45235	0.40388	0.36061	0.32197
	PV at 12%	-37.000	9.129	8.329	7.437	6.640	5.928	5.293	4.726	4.220	3.768	6.262
	NPV	24.731
	Estimated value of the project (NPV) =	$      24.73	million