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solving payoff amount x in last period using a IRR using mysql

Posted on 2008-10-11
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Last Modified: 2013-12-13
I want to pick an IRR=r (say 15%), and determine how much would have to be paid in the last period of the cash flow sequence to achieve this IRR.
e.g.
using wikipedia e.g.
0      -100
1      40
2      59
3      55
4      x

Solving the summation equation for x
x = the amount that needs to be paid to reach an internal rate of return of 15%
r = .15
NPV = 0 = -100 + 40/(1+.15)^1 + 59/(1+.15)^2 + 55/(1+.15)^3 + x/(1+.15)^4 for x
0= -100 + 34.78261 + 44.61248 + 36.16339 + x/(1+.15)^4
0 = 15.5585 + x/(1+.15)^4
-15.5585 = x/1.749006
-15.5585*1.749006 = x
-27.2119 = x

(note: in this example the value of x is negative, but in most cases it will be positive)

please see bayparkcapital.com/topiclistE.php for progress to date
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Question by:derekstattin
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4 Comments
 
LVL 24

Expert Comment

by:mankowitz
ID: 22696408
I think I understand the problem.

Assume that your data are stored in an array like this

$seq = array(0=>-100, 1=>40, 2=>59, 3=>55);
$period_to_solve = 4;
$rate = 0.15;

//First sum everything up
for ($x=0; $x<$period_to_solve; $x++)
{
$sum += $seq[$x] * pow($rate + 1, $x);
}

// NPV = {sum} + x/(1+rate)^4
//  -{sum} * (1+rate)^4 = x
$final_period = 0 - $sum * pow(1+$rate,$period_to_solve);
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Author Comment

by:derekstattin
ID: 22696935
Thank you for the example.
It all seems to work except on little thing
The $sum should be equal to 15.5585. I ran another example using 30, 32, and 40, but the results in Excel are not the same as using the function above.
Thanks for the help,
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LVL 24

Accepted Solution

by:
mankowitz earned 500 total points
ID: 22698340
Sorry, my mistake. I think I misread the formula. Change

$sum += $seq[$x] * pow($rate + 1, $x);

to

$sum += $seq[$x] / pow($rate + 1, $x);
0
 

Author Comment

by:derekstattin
ID: 22698698
Great,  thanks so much. I should have noticed that. Now I will try to integrate this in with
www.bayparkcapital.com/G.php
I will post a couple more questions shortly.
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