A firm wins a 20 year contract to supply water to N town. The initial
cash flow for the whole term the contract is:

cashflow 1:
     1              2               3              4                5
-13,309,539	-5,658,618	-148,545	612,150	        2,182,370
    6               7               8              9                10
3,965,442	5,403,716	4,729,937	3,998,399	4,174,659
    11             12              13               14              15
4,980,198	6,450,749	5,550,574	6,638,039	7,320,841	
    16             17              18              19              20
6,449,811	5,784,321	8,024,656	8,471,243	8,821,754
   21
1,903,555
 
The contract is balanced for both parties when the irr is 16.96% (irr
of cashflow 1 is: 16.96%). They agree than in case the irr changes for
any reason, they have to take the necessary actions to return the irr
to the original value.

At the 5th year, the firm is obligated to add 2.000 new customers and
make new investments (to be able to provide water to the new
customers.)

The modified cashflow is the following (including the 2,000new
customers and modified to give a irr of 16.96%)

cashflow 2:
    1              2               3               4               5
-13,309,539	-5,658,618	-148,545	612,150	        2,182,370
    6               7              8               9               10     
4,168,916	8,697,065	8,015,531	3,509,228	3,684,437	
    11              12              13              14             15
4,486,721	5,949,376	5,053,022	6,132,526	6,819,464
   16              17             18               19               20
5,940,412	5,279,390	7,511,646	7,957,840	8,305,431	
     21
1,816,124

irr of cashflow 2 (from year 1 to 21) = 16.96%

Question:

1. Explain why to correctly calculate the irr for cashflow 2 it's
necessary to take into account the cashflow results from year 1 to 21
and not only from year 5 to year 21 (when new investments and
customers where added).

- Answer should include math and theory explanation

thanks

---

Request for Question Clarification by omnivorous-ga on 03 Oct 2005 14:04 PDT

Lemontree --

By definition, the IRR is the interest rate used to discount cash
flows to zero over a multi-period term.  A change anywhere in the cash
flows, changes the discount rate because a standard IRR (not a
MODIFIED IRR) assumes re-investment of all proceeds at the same rate
--
http://invest-faq.com/articles/analy-int-rate-return.html

I don't understand what more than that you're seeking?

Best regards,

Omnivorous-GA

U can also think it as: if u calculated IRR from year 5 onwards, u
wouldnīt get to a result cuz there isnīt any negative number to which
u should discount ;)

Anyway, the fact is that u should reconsider the entire period because
the IRR is only valid for that length of time, and those values. If
you went on and calculated IRR on the fifth period, even if you didnīt
have any changes and had negative values so as to be able to discount,
you wouldnīt reach the original IRR.It simply has nothing to do with
the original IRR.

If you took, for instance, the second period on, you would be
discounting all the next ones for one period less, and not considering
a real disembursement, which was the one in the first period. Itīs
completely arbitrary and there is no way, except by mathmatical
chance, u had the same IRR.

Hope this helps.