Re: IRR formula - Please help me

Re: IRR formula - Please help me

[tmoran]

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

IRR formula - Please help me

[Maurizio Incani]

Hi,

I need to implemet the IRR formula (and calculation) into
a system under development.
I don't have a clue on what is (or looks like) the IRR.
Please, help me.
My E-Mail is maurizio.incani@pixie.co.za or mi000001@pixie.co.za
Thanks
Ciao,
Maurizio

Re: IRR formula - Please help me

[Lozano Mosterin, Jesus]

	Hi, Maurizio

> I need to implemet the IRR formula (and calculation) into
> a system under development.
> I don't have a clue on what is (or looks like) the IRR.
> Please, help me.

	In short, IRR=Internal Rate of Return
	
	NetPresentValue = -Inversion(time0) + SUM from t=m to t=N
	OF net_incomes/(1+rate_of_required_return)^t
(note that t could be non integer refered to rate periodicity) 

	You can calculate it on a hand calculator or a 
spreadsheet (@IRR) BUT (!) take on account
	- Some packages are considering that the inversion was 
realized on time=1 NOT time=0, and the NPV,IRR results changes! 
	- IRR<>rate_of_required_return, but IRR its derivated 
from supposing NetPresentValue=0, and calculating this rate.
	- There are no exact computation to do this, and that 
tools uses and heuristic o aprox. calculation, usually asking you 
an initial value to search :-(
	-There are some cases (many cases) in wich the calculus 
has NO or VARIOUS solutions (related with the switch of  
net_incomes signs over the time periods)

	Resuming, the IRR could be a bad practice to evaluate bussines 
projects, especially comparing it with other methods like the calculus
of the net present value on a range of required rates or math programing
on cash flows or option's theory or... The IRR is mostly (well?) used
in banking operations, evaluating underlayed rates on multi transactions
(like more than one investment).
	I'll post you ASAP one or two algorithms to iterate in 
the heuristic calculus. They are from me, so be warned about
checking the results. I think they are quite precises, but they
had no consideration on the multiples rates problem.
	Best regards

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Re: IRR formula - Please help me

[Keith Thomas]

Maurizio Incani (maurizio.incani@pixie.co.za) wrote:
: I need to implemet the IRR formula (and calculation) into
: a system under development.
: I don't have a clue on what is (or looks like) the IRR.

Any half-reasonable economics text book should have a description of this.
Provided your costs and benefits do not have large variations, you will
normally get only one answer - although if there are large variations you
may get more than one answer. This is stretching my memory a bit as it is
a few years since I have dealt with IRR, but I seem to remember that under
particular conditions there may not be a real (non-imaginary) answer. It
is often calculated by iterative methods. 

The definition from my old 'Engineering Economy' text book is:

"the interest rate at which the present worth of the cash inflow equals 
the present worth of the cash outflow (the customary use of present 
worth amounts to determine the IRR could just as well be annual worths or 
future worths)"

KT