From: Jason Dew <Jason.Dew@...>
Date: 2008-02-11T05:51:57+09:00
Subject: Re: Internal Rate of Return (#156)

Here's my solution:

irr.rb:

require 'algebra'

class IRR

  def self.calculate(profits)
    begin
      function(profits).zero
    rescue Algebra::MaximumIterationsReached => mir
      nil
    end
  end

  private

  def self.function(profits)
    Algebra::Function.new do |x|
      sumands = Array.new
      profits.each_with_index {|profit, index| sumands <<
profit.to_f / (1 + x) ** index }
      sumands.inject(0) {|sum, sumand| sum + sumand }
    end
  end

end

puts IRR.calculate([-100, 30, 35, 40, 45])
puts IRR.calculate([-1, 1])
puts IRR.calculate([])



algebra.rb:

module Algebra

  class MaximumIterationsReached < Exception
  end

  class NewtonsMethod

    def self.calculate(function, x)
      x - function.evaluated_at(x) / function.derivative_at(x)
    end

  end

  class NewtonsDifferenceQuotient

    def self.calculate(function, x, delta=0.1)
      (function.evaluated_at(x + delta) -
function.evaluated_at(x) ).to_f / delta
    end

  end

  class Function

 
attr_accessor :differentiation_method, :root_method, :maximum_iterations, :tolerance

    def initialize(differentiation_method=NewtonsDifferenceQuotient,
root_method=NewtonsMethod, &block)
      @definition = block
      @differentiation_method, @root_method = differentiation_method,
root_method
      @maximum_iterations = 1000
      @tolerance = 0.0001
    end

    def evaluated_at(x)
      @definition.call(x)
    end

    def derivative_at(x)
      differentiation_method.calculate(self, x)
    end

    def zero(initial_value=0)
      recursive_zero(initial_value, 1)
    end

    private

    def recursive_zero(guess, iteration)
      raise MaximumIterationsReached if iteration >=
@maximum_iterations

      better_guess = @root_method.calculate(self, guess)

      if (better_guess - guess).abs <= @tolerance
        better_guess
      else
        recursive_zero(better_guess, iteration + 1)
      end
    end

  end

end

Comments welcomed.  Thanks,

On Feb 8, 9:01 am, Ruby Quiz <ja...@grayproductions.net> wrote:
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>
> -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- =-=-=
>
> 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's quiz is 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.