asked on

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

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

mankowitz

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);

derekstattin

ASKER

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,

ASKER CERTIFIED SOLUTION

mankowitz

membership

This solution is only available to members.

To access this solution, you must be a member of Experts Exchange.

Start Free Trial

derekstattin

ASKER

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.