
From:  Meketon, Marc 
Subject:  Re: [Helpglpk] IRR (Internal Rate of Return) using MathProg 
Date:  Sun, 16 Sep 2012 09:04:37 0500 
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[i1]/2 + n/(2*xx[i1]); 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 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 _______________________________________________ Helpglpk mailing list This email 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 email 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 email. Thank you for your cooperation. 
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