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npv.m

## Copyright (C) 1995, 1996, 1997  Kurt Hornik
## 
## This program is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 2, or (at your option)
## any later version.
## 
## This program is distributed in the hope that it will be useful, but
## WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
## General Public License for more details. 
## 
## You should have received a copy of the GNU General Public License
## along with this file.  If not, write to the Free Software Foundation,
## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.

## usage:  npv (r, p [, i])
##
## Returns the net present value of a series of irregular (i.e., not
## necessarily identical) payments p which occur at the ends of n
## consecutive periods.  r specifies the one-period interest rates and
## can either be a scalar (constant rates) or a vector of the same
## length as p.
##
## With the optional scalar argument i, one can specify an initial
## investment.
##
## Note that rates are not specified in percent, i.e., one has to write
## 0.05 rather than 5 %.
##
## See also:  irr;  pv.
  
## Author:  KH <Kurt.Hornik@ci.tuwien.ac.at>
## Description:  Net present value of a series of payments

function v = npv (r, p, i)
  
  if ((nargin < 2) || (nargin > 3))
    usage ("npv (r, p [, i]");
  endif
  
  if !(is_vector (p))
    error ("npv:  p has to be a vector");
  else
    n = length (p);
    p = reshape (p, 1, n);
  endif
  
  if any (any (r <= -1))
    error ("npv:  all interest rates must be > -1");
  endif
  if is_scalar (r)
    d = 1 ./ (1 + r) .^ (0 : n);
  elseif (is_vector (r) && (length (r) == n))
    d = [1, 1 ./ cumprod (reshape (1 + r, 1, n))];
  else
    error (["npv:  r has be a scalar ", ...
      "or a vector of the same length as p"]);
  endif

  if (nargin == 3)
    if !is_scalar (i)
      error ("npv:  I_0 must be a scalar");
    endif
  else
    i = 0;
  endif
  
  p = [i, p];
  v = sum (d .* p);
  
endfunction

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