This is an example to help solve the real question below

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

$2.1

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

$31

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	36.000	36.000		36.000	36.000
Cost of goods sold	21.600	21.600		21.600	21.600
=Gross profit	14.400	14.400		14.400	14.400
General, sales, and administrative expenses	2.480	2.480		2.480	2.480
Depreciation	3.100	3.100		3.100	3.100
=Net operating income	8.8200	8.8200		8.8200	8.8200
Income tax	3.087	3.087		3.087	3.087
=Net income	5.733	5.733		5.733	5.733

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

46%

on the equipment for tax purposes. The report concludes that because the project will increase earnings by

$5.733

million per year for ten years, the project is worth

$57.33

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

$16

million in working capital up front (year 0), which will be fully recovered in year 10. Next you see they have attributed

$2.48

million of selling, general and administrative expenses to the project, but you know that

$1.24

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!

b. If the cost of capital for this project is

17%,

what is your estimate of the value of the new project?

There are two ways to solve for the

NPVby

either indirectly computing the FCF excluding the CCA tax shields and then adding the present value of all the CCA tax savings to it OR by directly computing the present value of the free cash flows from years 1 to 10 and then adding the present value of the remaining CCA tax shields from time 11 in perpetuity. We will use the first method.

Indirectly compute the free cash flow excluding CCA tax shields by using the following equation:

FreeCashFlowexcludingCCATS=(RevenuesCosts)1cCapExNWC

where CCATS is the present value of the CCA tax shields from time 0 to

,

c

is the corporate tax rate, CapEx is the capital expenditure, and

NWC

is the change in net working capital.

The present value of the free cash flows (excluding CCA tax shields) for each of years 0 to 10 are (in millions of dollars):

	Year
Free Cash Flow (FCF) ($000,000s)	0	1	2	3	4	5	6	7	8	9	10
Sales Revenue		36.000	36.000	36.000	36.000	36.000	36.000	36.000	36.000	36.000	36.000
Cost of Goods Sold		21.600	21.600	21.600	21.600	21.600	21.600	21.600	21.600	21.600	21.600
=Gross Profit		14.400	14.400	14.400	14.400	14.400	14.400	14.400	14.400	14.400	14.400
General, Selling and Admin Exp.		2.480	2.480	2.480	2.480	2.480	2.480	2.480	2.480	2.480	2.480
CCA (analyze separately)
=Net operating income		11.920	11.920	11.920	11.920	11.920	11.920	11.920	11.920	11.920	11.920
Income Tax (at35%)		4.17	4.17	4.17	4.17	4.17	4.17	4.17	4.17	4.17	4.17
=Net Income		7.75	7.75	7.75	7.75	7.75	7.75	7.75	7.75	7.75	7.75
+Overhead (after tax at 35%)		0.806	0.806	0.806	0.806	0.806	0.806	0.806	0.806	0.806	0.806
+CCA (analyze separately)
CapEx	31.000
Inc. in NWC	16.000										16.000
Free Cash Flow (excluding CCA tax shields)	47.000	8.556	8.556	8.556	8.556	8.556	8.556	8.556	8.556	8.556	24.556
Discount factor (at 17%)	1.000	0.8547	0.7305	0.6244	0.5337	0.4561	0.3898	0.3332	0.2848	0.2434	0.2080
Free Cash Flow (excluding CCAtax shields) Discount factor	47.000	7.313	6.250	5.342	4.566	3.902	3.335	2.851	2.437	2.083	5.108

The PV of the free cash flows (excluding CCA tax shields) in millions:

$47.000+$7.313+$6.250+$5.342+$4.566+$3.902+$3.335+$2.851+$2.437+$2.083+$5.108=$3.813million

The present value of the CCA tax shields can be found using the equation shown below, where CapEx is the capital expenditure, d is the CCA rate, r is the cost of capital, and

c

is the corporate tax rate.

PVCCAtaxshields=CapExdcr+d1+r2(1+r)

The present value of the CCA tax shields are found as:

$31million0.460.350.17+0.461+0.172(1+0.17)=$7.347million

The NPV equals the sum of the present value of the

free

cash flows (excluding CCA tax shields) and present value of the CCA tax shields:

NPV=$3.813million+$7.347million=$3.534million

b. If the cost of capital for this project is

17%,

what is your estimate of the value of the new project?

Value of project is

$3.534

million.

Since the project's NPV is positive, it should be accepted.

This is the real question needed to be solve below

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

$1.5

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

$23

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	27.000	27.000		27.000	27.000
Cost of goods sold	16.200	16.200		16.200	16.200
=Gross profit	10.800	10.800		10.800	10.800
General, sales, and administrative expenses	1.840	1.840		1.840	1.840
Depreciation	2.300	2.300		2.300	2.300
=Net operating income	6.6600	6.6600		6.6600	6.6600
Income tax	2.331	2.331		2.331	2.331
=Net income	4.329	4.329		4.329	4.329

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

$4.329

million per year for ten years, the project is worth

$43.29

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

$1.84

million of selling, general and administrative expenses to the project, but you know that

$0.92

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!

b. If the cost of capital for this project is

15%,

what is your estimate of the value of the new project?

b. If the cost of capital for this project is

15%,

what is your estimate of the value of the new project?

Value of

project=

million(Round to three decimal places.)