I think I have a solution. I would like to use a simpler example, and let you
(Noli) work out the details for IRR.
It is well known, and your links show how, to use Newton's algorithm (aka
Newton Raphson's algorithm) to find the IRR, since it's really find a root of a
polynomial (see the other post by Jeffery Kantor, which also describes the fact
that depending on the cash flows, there could be multiple solutions).
For my simpler example, suppose you wanted to find, in GLPK, the square root of
"n". This is the same as solving for the root of the function f(x) = x*x -n .
Newton's algorithm, in general, is where you begin with a reasonable
approximate, say x_0 = n/2, then iterate until convergence:
x_(k+1) = x_k - f(x_k)/f'(x_k)
In our case, f'(x) = 2x, so x - f(x)/f'(x) = x/2 + n/(2x),
It would be nice to have, after the "solve" statement, the ability to say
something like the following in GLPK (note that I hardcoded 10 iterations):
param n:=16;
param x := n/2;
for{k in 1..10} {
let x := x/2 + n/(2*x);
}
printf "Sqrt of %f = %f\n", n, x;
But GLPK doesn't allow the "let" statement. I believe that AMPL does.
So a workaround, that seems to work is:
param xx{i in 0..10} := if i=0 then n/2 else xx[i-1]/2 + n/(2*xx[i-1]);
printf "Sqrt of %f = %f\n", n, xx[10];
Again, the number of iterations is hardcoded, but hopefully you would be able
to code the Newton's iteration exactly the above.
Lastly, because of the possibility of multiple solutions, you should start (the
if i=0 then clause ) with a good first solution, mostly likely the interest
rate you used for the NPV calculation.
-Marc
-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of
Noli Sicad
Sent: Friday, September 14, 2012 11:27 AM
To: [email protected]
Subject: [Help-glpk] IRR (Internal Rate of Return) using MathProg
Hi,
I like to incorporate IRR (Internal Rate of Return) in my report (i.e.
Report Section of my LP GLPK/MathProg model). I don't how to do this using
mathprog
Linux Journal has article in IRR and programs in Java, C and Perl. You can
download the source here.
http://www.linuxjournal.com/article/2545
However, I have difficulties deciphering it.
Some discussions on various methods on how to calculate IRR.
http://finance.thinkanddone.com/irr.html
My LP model is maximizing Net Present Value (i.e. revenues / Cash flow). Here
is example of the cash flow (below).
Anybody like to have a go with this problem?
Thanks in advance.
Noli
##########################
Period (Year) Cash Flow ($)
1 39076.42996
2 21948.87949
3 21957.06148
4 21817.10073
5 22434.00213
6 25217.30759
7 28801.0362
8 33663.80729
9 39526.52516
10 47082.82071
11 52139.3562
12 55712.83969
13 54963.69578
14 54197.3533
15 53469.32228
16 52777.66322
17 52120.61624
18 51496.4058
19 50903.35207
20 50340.01419
21 49804.81457
22 49296.50083
23 48813.47914
24 48814.3007
25 48907.10984
26 49105.38398
27 49426.2852
28 49890.16458
29 50521.35707
30 51349.79884
31 52411.43084
32 53749.2502
33 54080.18986
34 53474.36278
35 53848.60448
36 54417.4497
37 55213.81919
38 56277.52781
39 57656.46566
40 57792.59562
41 56875.42409
42 57304.41377
43 56658.08866
44 55805.88753
45 55531.78289
_______________________________________________
Help-glpk mailing list
[email protected]<mailto:[email protected]>
https://lists.gnu.org/mailman/listinfo/help-glpk
________________________________
This e-mail and any attachments may be confidential or legally privileged. If
you received this message in error or are not the intended recipient, you
should destroy the e-mail message and any attachments or copies, and you are
prohibited from retaining, distributing, disclosing or using any information
contained herein. Please inform us of the erroneous delivery by return e-mail.
Thank you for your cooperation.
_______________________________________________
Help-glpk mailing list
[email protected]
https://lists.gnu.org/mailman/listinfo/help-glpk
