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## 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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