From: Carl Porth <badcarl@...>
Date: 2008-02-11T01:50:36+09:00
Subject: Re: Internal Rate of Return (#156)

Here's my binary search solution.  It can return negative values
(extra credit) and returns nil for undefined behavior.

require "enumerator"
require "rubygems"
require "facets/numeric/round"

def npv(irr, cash_flows)
  cash_flows.enum_with_index.inject(0) do |sum, (c_t, t)|
    sum + c_t / (1+irr)**t
  end
end

def irr(cash_flows, precision=10 ** -4)

  # establish an upper bound, return nil if none
  max = 1.0
  max *= 2 until npv(max, cash_flows) < 0 or max.infinite?
  return nil if max.infinite?

  # initialize search variables
  last_irr, irr, radius = max, 0.0, max

  # binary search until precision is met
  until irr.approx?(last_irr, precision/10)
    last_irr = irr

    # improve approximation of irr
    if npv(irr, cash_flows) < 0
      irr -= radius
    else
      irr += radius
    end

    # reduce the search space by half
    radius /= 2
  end

  irr.round_to(precision)
end

if __FILE__ == $PROGRAM_NAME
  puts irr(ARGV.map { |e| Float(e) }) || "Undefined"
end

On Feb 8, 6:01 am, Ruby Quiz <ja...@grayproductions.net> wrote:
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> on Ruby Talk follow the discussion.  Please reply to the originalquizmessage,
> if you can.
>
> -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- =-=-=
>
> by Harrison Reiser
>
> Internal Rate of Return (IRR -http://en.wikipedia.org/wiki/Internal_rate_of_return) is a common financial
> metric, used by investment firms to predict the profitability of a company or
> project. Finding the IRR of a company amounts to solving for it in the equation
> for Net Present Value (NPV -http://en.wikipedia.org/wiki/Net_present_value),
> another valuable decision-making metric:
>
>                N      C_t
>         NPV =  Ó  ------------
>               t=0 (1 + IRR)**t
>
> This week'squizis to calculate the IRR for any given variable-length list of
> numbers, which represent yearly cash flows, the C_t's in the formula above: C_0,
> C_1, etc. (C_0 is typically a negative value, corresponding to the initial
> investment into the project.) From the example in the Wikipedia article
> (http://en.wikipedia.org/wiki/Internal_rate_of_return), for instance, you should
> be able to produce a rate of 17.09% (to four decimal places, let's say) from
> this or a similar command:
>
>         irr([-100,+30,+35,+40,+45])
>         => 0.1709...
>
> Keep in mind that an IRR greater than 100% is possible. Extra credit if you can
> also correctly handle input that produces negative rates, disregarding the fact
> that they make no sense.