I do not want the answer to this question. Rather the right formula to use. 

Could you give me formula to draw a NPV profile of the following project

Project A   cash flow     cash flow yr 1       cash flow yr 2   cash flow yr 3
              -20,000       +8,000                +8,000          +8,000


Also, I could use the formula to determine how to determine the IRR of
this project.

Thanks, any help would be great.

Hi!!


NPV = PV of Cash Flows - Investment (or initial cash flow)

The hard part of the above formula is the PV of the cash flows:

         CF1           CF2            CF3      
PV  = ---------  +  ----------  +  ---------- 
      (1 + r)^1     (1 + r)^2	  (1 + r)^3      


Then:

         CF1           CF2            CF3      
NPV  = ---------  +  ----------  +  ---------- - I
       (1 + r)^1     (1 + r)^2	    (1 + r)^3    


In this case we have that:
CF1 = 8,000
CF2 = 8,000
CF3 = 8,000
I = 20,000
r is undefined yet, so you must use the value suggested by the
problem, if you need to make a table of possible NPVs start from
1%(0.01) and increase its value 1% each time (2%, 3%,...,12% 13%,
etc.).

In cases like this, when all the cash flows are equal, the PV formula
can be simplified:

      CF             1
PV = ---- * [1 - ---------] 
       r          (1+r)^3

And we will have that:

       CF             1
NPV = ---- * [1 - ---------] - I
       r           (1+r)^3


To determine IRR recall that IRR is the discount rate r at which the
NPV equals zero, in other
words it is the rate that satisfies:

NPV = PV - I = 0

Then IRR is the discount rate r at which:

PV = I

You can use different ways to calculate the IRR, for example:
-Trial & Error
-Calculator
-Computer (Excel spreadsheet)


I used an Excel spreadsheet for the calculations:

-Project A:

Column A :               Column B
A1: -20,000              B1: =IRR(A1:A4)
A2: 8,000
A3: 8,000
A4: 8,000

IRR(A) = 9.70%


To do it manually just plug an small value for r in the NPV formula
(say 2%) and check the result, if the value is greater than zero,
increase r until you get a zero or a negative value. If you get zero
for NPV you have found the IRR if the value is negative, just decrease
half way from the greater r that results in a positive NPV. Use this
iteration process until you consider that the NPV is enough closer to
zero, the last r used will be a good aproximation for the IRR.
Since we know the result (IRR = 9.7%) you can start with 9% -->
positive NPV, next guess for r 10% --> negative NPV, next guess 9.5%
--> positive NPV, etc.


I hope that this helps you. Feel free to request for a clarification
if you need it.

Regards.
livioflores-ga

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Request for Answer Clarification by baseball2-ga on 24 Jul 2005 11:27 PDT

Can you help me with making sure I am plugging in the exel formula right?

I plugged the numbers in as you indicated than clicked on the arrow
next to auto sum and requested average of A1:A4 and I got 100% not
9.70

HELP!

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Request for Answer Clarification by baseball2-ga on 24 Jul 2005 12:17 PDT

Forget my last clarification. I fugured it out.

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Clarification of Answer by livioflores-ga on 24 Jul 2005 15:36 PDT

OK!!

Thank you for the good rating.