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

Posted on 2008-10-11

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)

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