4. Calculating IRR. A firm evaluates all of its projects by applying
the IRR rule. If the required return is 18 percent, should the firm
accept the following project?

Year    Cash Flow
0       $90,000
1        35,000
2        43,000
3        40,000

Hi!!

Present Value (PV):

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


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

Where I is the initial investment (Year 0 cash flow)

Then IRR is the discount rate r at which:
PV = I

The IRR criterion states that you must accept only projects with IRR
greater than the cost of capital or the required rate of return.

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:
Assuming that the Year 0 cash flow is the initial investment (so it is
a negative value) we have that:

Column A :               Column B
A1: -90,000              B1: =IRR(A1:A4)
A2: 35,000
A3: 43,000
A4: 10,000

IRR = 14.51%

IRR lower than the required rate of return!! --->> reject this project.


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

Best regards.
livioflores-ga

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Request for Answer Clarification by yourtime4mymoney-ga on 12 May 2005 00:26 PDT

I understood the IRR, but the NPV was were I was lost.  When I
calculated it I used the following formula in Excel: (where did I go
wrong?

npv=(12%,d20:D22)+d19 = 

-5428571.42857143000%


years	
0	-90000  (D19)
1	35000   (D20)
2	43000   (D21)
3	40000   (D22)

---

Clarification of Answer by livioflores-ga on 12 May 2005 04:53 PDT

Hi!!

The wrong result that you get comes from a bad cell format, you are
using % format in cells which must be in normal or money format. Try
to format all cells to the correct way.

More:
The correct formula using Excel for the NPV in your spreadsheet is:
=NPV(12%;D20:D22)+D19

Note that, depending on your Excel version, the separator could be a
comma (,) or dot+comma (;) .

Using the above formula I get an NPV of $4,000.55

In the problem the required rate is 18% not 12% so you must use that,
you will get an NPV of -$5,111.82 .

You can also use the formula for NPV = PV - I in Excel using the following entry:
=+D20/(1+18%)+D21/POWER((1+18%);2)+D22/POWER((1+18%);3)+D19

You will get again a NPV of -$5,111.82 .


For references see the following page:
"Excel functions for investment appraisal: Making investment decisions
using Excel Calculating Net Present Value (NPV) and Internal Rate of
Return (IRR)":
http://www.meadinkent.co.uk/excel_npv.htm


Hope that this help you to understand better the NPV calculation.

regards.
livioflores-ga