Thread: IRR and NPV
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[email protected] joeu2004@hotmail.com is offline
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Default IRR and NPV

tom ossieur wrote:
IRR, according to explanation in Excel, is of a similar concept with NPV.


They are __related__, not "similar". The IRR is the rate that causes
the NPV to be zero.

But if my cash flow starts from say 2009 onwards (and any cash flows between
2007-2009 are 0), IRR gives me the same result whether or not I choose cells
starting from 2007 or 2009.


There are many ways to try to explain this. Mathematically, if you
look at the formula on the Excel NPV help page, it might become
"obvious" to you. The Excel formula is:

NPV = 0 = CF1/(1+r)^1 + CF2/(1+r)^2 + CF3/(1+r)^3 + CF4/(1+r)^4 + ....

If the first k terms (e.g. CF1 through CF3 in your case) are zero, then
the IRR (r) must be chosen so that the later N-k terms sum to zero. No
matter how many zero cash flows you put in front of them, the IRR will
be the same since 0/(1+r)^x is zero for any x. Put another way, we can
multiply the equation by (1+r)^3 (if the first 3 terms are zero) to
convert it to the following equivalent equation:

NPV = 0 = CF1/(1+r)^(-2) + CF2/(1+r)^(-1) + CF3/(1+r)^0 + CF4/(1+r)^1 +
.....

Dropping the first three terms, which are zero, we get:

NPV = 0 = CF4/(1+r)^1 + ....

So the IRR is unaffect by the initial zero cash flows. In effect, the
IRR is the rate that causes the NPV to be zero, starting with the first
non-zero cash flow.

But with NPV function, the results are different.


I am not sure what you mean. The NPV can be any value you want,
depending on the rate that you choose. And yes, given the same chosen
rate, adding more initial cash flows of zero will change the NPV (if it
is non-zero) because the value of the first non-zero cash flow --
CFn/(1+r)^n -- will change.

However, there is only one rate for which the NPV will be zero. (Well,
that might be an exaggeration mathematically speaking. Perhaps I
should say that we hope there is only one __practical__ rate.)

How can I get the right
IRRs for different periods with the IRR function?


"For different periods"? The question does not make sense to me. The
IRR is "the" rate for all periods of the series of cash flows. You can
find the IRR for different series of cash flows, for example composed
of fewer and fewer consecutive periods. But I am not sure that is what
you mean.