Re: [Help-glpk] IRR (Internal Rate of Return) using MathProg

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: help-glpk-bounces+address@hidden [mailto:help-glpk-bounces+address@hidden On Behalf Of Noli Sicad
Sent: Friday, September 14, 2012 11:27 AM
To: address@hidden
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

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From:	Meketon, Marc
Subject:	Re: [Help-glpk] IRR (Internal Rate of Return) using MathProg
Date:	Sun, 16 Sep 2012 09:04:37 -0500