Wombat319 ?
There are 2 tricky parts to this question:
? the assumption is that the firm is profitable or that it can get a
tax credit for this project when it turns unprofitable in years 3 and
4 when depreciation outstrips the earnings
? Working capital initially required is $8,000 upfront (often referred
to as ?year 0? in capital budgeting problems like this one).
However, each year $2,000 less is required so it?s important to add it
back into your cash flow as a ?WC recoup?.
A. INITIAL INVESTMENT
$50,000 + $8,000 in WC = $58,000
B. CASH FLOWS EACH YEAR
I?ll outline how to get cash flows for each year that there are
revenues, using year 1 as an example:
Operating income: 24,000 (60% of Revenues)
Depreciation: 12,500 (each year)
EBIT: 12,500 (in years 3 and 4 it?s negative)
Taxes: 4,600 (40% of the EBIT)
Net income: 6,900 (in years 3 and 4 it?s higher than EBIT because
taxes come back as a credit)
WC recoup: 2,000 (each year, as explained above)
CASH FLOW: 21,400 (Net income + WC recoup ? depreciation*)
* note that the sign for Depreciation is negative because it?s a
negative number. In other words, it gets added back to cash flow.
Each year?s cash flows are:
Year 0: 58,000
Year 1: 21,400
Year 2: 17,800
Year 3: 14,200
Year 4: 10,600
C. PROJECT NPV
Project NPVs use the 10% capital cost factor and are:
Year 0: 1
Year 1: .909 = 1/1.10
Year 2: .826 = 1/(1.10)^2
Year 3: .751 = 1/(1.10)^3
Year 4: .683 = 1/(1.10)^4
You use these factors to multiply times each year?s cash flows and
calculate the NPV.
Project NPV here is 5,926. That?s not surprising, given cash flows
of only $64,000 on a $58,000 investment. If there were no tax credits
for depreciation (if the firm were not profitable overall or couldn?t
get a tax credit), the picture would be even worse.
D. IRR
Project IRR is the discount rate at which NPV is zero. Because this
project brings in more cash than it expends, there is a positive NPV ?
we just have to find a number that gives an NPV of zero.
Using each year?s cash flow and adjusting the cost of capital
downwards we can adjust to a lower NPV that works. You?ll find that
4.59% is the number, if you try different discount factors.
If any part of this is unclear, please let us know before rating this
Google Answer.
Best regards,
OmnivorousGA 
Clarification of Answer by
omnivorousga
on
26 May 2005 06:30 PDT
Wombat319 
Once you have the discount rate and cash flows you can see the IRR (a
spreadsheet also has IRR calculations). But it's done the same way as
your NPV calculations, seeking a capital cost that yields an NPV = 0.
In this cash our NPV is negative, so we need a LOWER cost of capital
to get there:
CASH FLOWS
Year 0: 58,000
Year 1: 21,400
Year 2: 17,800
Year 3: 14,200
Year 4: 10,600
If 10% was too high, what about 6% 
Year 0: 1
Year 1: .943 = 1/1.06
Year 2: .890 = 1/(1.06)^2
Year 3: .834 = 1/(1.06)^3
Year 4: .792 = 1/(1.06)^4
That's still too high  NPV is still negative with your cash flows.
5%? NPV is still negative  but small.
4.5%? NPV is positive.
4.91% yields an NPV of about $2  as close to zero as you'll get
(4.92% is negative and 4.90% is positive and larger.)
Best regards,
OmnivorousGA
