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From: tmoran@bix.com
Subject: Re: IRR formula - Please help me
Date: 1996/02/26
Message-ID: <4gspnm$4nh@news2.delphi.com>#1/1
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organization: Delphi Internet Services Corporation
newsgroups: 
 comp.lang.ada,comp.lang.basic.misc,comp.lang.c,comp.lang.c++,comp.lang.clipper,comp.lang.pascal.delphi.misc
Date: 1996-02-26T00:00:00+00:00
List-Id: <comp.lang.ada>

In <312EAB76.5463@pixie.co.za> Maurizio Incani asked:
>I don't have a clue on what is (or looks like) the IRR.
  From the Capital Budgeting chapter of a Managerial Finance book:
"The internal rate of return (IRR) is defined as the interest rate
that equates the present value of the expected future cash flows,
or receipts, to the inital cost outlay."  Or to be more general,
if c(i) for i in 0 .. N is the net revenue from a proposed
project at the end of year i, and the (Net Present Value)
polynomial NPV = sum(c(i)*x**i) = 0 has solution X, then the
IRR is 1/X-1. Thus a project where you invest $1 today and $1 a
year from today, but get back $2 after two years and another $2
after three years, gives the equation 2*x***3 + 2*x**2 -1*x -1 = 0
which has a solution X=0.707 or IRR=0.42, a rather good payback.
People often want IRRs to compare projects and see which has better
payback.  NPV is a better method for ranking projects (for instance
suppose an alternative project would cost $1,000 today but give
back $1,100 dollars a year from now.  Its IRR of 0.10 is much less
than 0.42, but it's better to invest in something that makes $100
than something that gives a profit of $2.  Also two projects with
different time streams of revenue can rank inconsistenly between
IRR and NPV.)
  As just a programming problem, IRR consists of finding a root of
a polynomial, and probably it's a single root in the range 0.0 .. 0.5