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Q: Calculate project cash flows, NPV, and IRR ( Answered 5 out of 5 stars,   0 Comments )
Subject: Calculate project cash flows, NPV, and IRR
Category: Business and Money > Finance
Asked by: wombat319-ga
List Price: $10.00
Posted: 25 May 2005 15:32 PDT
Expires: 24 Jun 2005 15:32 PDT
Question ID: 525617
Revenues generated by a new fad product in each of the next 5 years
are forecasted as follows:
Year	Revenues
1	$40,000 
2	30,000 
3	20,000 
4	10,000 
Thereafter	0 
Expenses are expected to be 40 percent of revenues, and working
capital required in each year is expected to be 20 percent of revenues
in the following year. The product requires an immediate investment of
$50,000 in plant and equipment.
a. What is the initial investment in the product? Remember working capital.	

b. If the plant and equipment are depreciated over 4 years to a
salvage value of zero using straight-line depreciation, and the firm's
tax rate is 40 percent, what are the project cash flows in each year?
c. If the opportunity cost of capital is 10 percent, what is the project NPV?	
d. What is the project IRR?
Subject: Re: Calculate project cash flows, NPV, and IRR
Answered By: omnivorous-ga on 25 May 2005 16:39 PDT
Rated:5 out of 5 stars
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?.


$50,000 + $8,000 in WC = $58,000


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


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.


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,


Request for Answer Clarification by wombat319-ga on 25 May 2005 17:44 PDT
I don't understand the calculation for IRR? How did you get that?

Clarification of Answer by omnivorous-ga 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:


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,

wombat319-ga rated this answer:5 out of 5 stars

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