Please calculate the NPV, PI and IRR for the following project:
The initial cash outlay is $50,000.  The required rate of return is 12 percent.
The expected annual free cash flow from the project are as follows:

year   
0      -$50,000
1       12,000
2       12,000
3       12,000
4       12,000
5       12,000
6       12,000

K9Queen –

NPV (net present value) = PV net cash flows – net cash invested
PV net cash flows are calculated:  NCF(year t)/(1+r)^t ; where t is
the number of complete years and r is the cost of capital.  NCF is the
net cash flow.

NPV Calculation:
-----------------------

Year     Net Cash Flow
O . . . .  –$50,000
1  . . . .  $10,714 = $12,000/1.1200
2  . . . .  $  9,566 = $12,000/1.2544 
3  . . . .  $  8,542 = $12,000/1.4049
4  . . . .  $  7,626 = $12,000/1.5735
5  . . . .  $  6,809 = $12,000/1.7623
6  . . . .  $  6,080 = $12,000/1.9738


NPV = -$663

This project wouldn't have a positive net present value until a 7th
year of free cash flow, assuming a 12% cost of capital.  This also
tells us that the internal rate of return will be slightly less than
12%.


IRR Calculation:
-----------------

IRR is the cost of capital r where:
NCF(year t)/(1+r)^t = net cash invested

This calculation is usually done with a financial calculator or Excel
spreadsheet because it's a six-year series depending on choosing the
right value of r, your cost-of-capital.  (If I had to guess, I'd run
back through the calculations above using 11.9% to see how much closer
0.1% gets to a $0 NPV.)

In this case 11.53% is the IRR.


PI Calculation:
--------------------

PI (profitability index) = present value net cash flows / net
investment

Here you're looking for a value higher than 1 to allow you to give a
project the go-ahead.  But our profitability index is:
$49,337/$50,000 = 0.9867


Here's an excellent presentation outlining not just the mathematical
definitions of these financial accounting terms but their advantages
and limitations:
University of Houston, Bauer School of Business
"Capital Budgeting" (2003)
http://www.bauer.uh.edu/~csheh/Lecture%208.ppt


Google search strategy:
NPV + IRR + PI


If any part of this answer is confusing, please let us know via a
clarification request before rating the answer.

Best regards,

Omnivorous-GA

Very clear and thorough!
Thank you for all the explanations!