IRR vs XIRR

[Csmithers]

I have an out flow and then monthly inflows for a month. They are th
same time every month the first of the month. When I use IRR I get 18%
when I use XIRR I get 640%. If i multiply 18% by 12 I get 217% whic
seems right ,but doesn;t take into account compounding. If use thi
=(iRR(C4:C16)+1)^12-1) I get 633% which is very close to 640% but seem
way to high. I haven't even tripled my investment, which was -130,00
while making 440,00 total over the year. Can someone tell me whic
number is correct and why

 

[PJ Hooker]

Would you please list the 12 monthly cash flows

I understand that your initial cash outlay is $-130,000

It also seems you have a typo in total benefits which I assume equals
$440,000 rather that what you have posted as $440,00

I assume that the cash flows are not in equal amounts as when I
divided 440,000 by 12 the IRR values are much different than you
quoted

So unless you post your monthly cash flows, there is no way for me to
verify the result of IRR function

With that out of the way, I would like to add a few comments

You stated that the monthly benefits (+ve cash flows) occur at start
of month. That leads me to think that your XIRR results are the most
accurate here unless my assumption is incorrect that you did not add
the initial cash outlay and first monthly benefit to arrive at the
cash flow at time period 0

Thus please post the cash flows for each of the months so I can have a
look

 

[joeu2004]

I have an out flow and then monthly inflows for a month.
They are the same time every month the first of the month.
When I use IRR I get 18%, when I use XIRR I get 640%.
If i multiply 18% by 12 I get 217% which seems right ,
but doesn;t take into account compounding. If use this
=(iRR(C4:C16)+1)^12-1) I get 633% which is very close to
640%

All are right and wrong!

First, IRR returns the periodic rate. If you have monthly cash flows, IRR
returns a monthly rate.

In contrast, XIRR always returns an annual rate.

That explains why XIRR is so much larger than the (monthly) IRR.

Second, there is no general agreement on how to annualize a periodic rate.
To some degree, it depends on what financial securities you are modelling,
the industry conventions applied to those securities, and even applicable
regional laws. Sometimes it is correct to multiply a monthly IRR by 12;
sometimes it is correct to compound it over 12 periods; sometimes we
multiply by other factors.

In contrast, XIRR always compounds daily.

That partly explains why even when you compound the monthly IRR over 12
periods, it is not exactly the same as daily-compounded XIRR.

Third, by definition, IRR treats each month as the same length when using
monthly cash flows. But XIRR uses the actual number of days.

That further explains why the monthly compounded IRR over 12 periods does
not agree exactly with the XIRR.

Finally, note that neither the IRR nor the XIRR can be computed
algebraically (unless all cash flows are the same, and they occur
regularly). Instead, each function uses some algorithm to "home in on" the
rate that causes the (X)NPV to be close to zero. Microsoft documentation
indicates that starting with Excel 2003, IRR and XIRR use the Newton-Raphson
method.

But each algorithm is implemented differently, which gives rise to
differences in the results due to arithmetic anomalies (due to binary
floating-point) as well as diffences in the tolerances and the underlying
differential formulas.

That is another reason why the monthly compounded IRR over 12 period does
not agree with the XIRR.

In actual practice, it is best not to read too much into the detailed
numerical results. They are all only estimates anyway. Choose whichever
function is more appropriate for the data that you have.

PS: I might note that the Excel IRR and XIRR functions are simply two ways
to calculate the "internal rate of return" (IRR). In other words, when I
speak of "IRR", you need to decide by context whether I am speaking of the
Excel function or the financial concept.

I get 633% which is very close to 640% but seems way to
high. I haven't even tripled my investment, which was
-130,000 while making 440,00 total over the year. Can
someone tell me which number is correct and why?

Yes, that is the fallacy of annualizing periodic rates, IMHO.

For example, if the value of a security changes 1% in a day, surely you do
not believe we can expect its value has grown (will grow) at a annual rate
of 3678%. That is indeed what (1+1%)^365-1 is. But that is not a realistic
assessment of the change in value.

So even though it is common practice to annualize periodic rates, I try to
avoid it -- although there are applications of the rate of return where we
must annualize.

Instead, I prefer to specify appropriate periodic rates of return. So
instead of annualizing a periodic IRR, I prefer to "de-compound" the
annual(ized) XIRR rate. For example, (1+XIRR(...))^(1/12)-1.

Nevertheless, that monthly XIRR will not be the same as the periodic IRR
based on monthly cash flows for all of the reasons given above.

 

[Csmithers]

I have an out flow and then monthly inflows for a month.
They are the same time every month the first of the month.
When I use IRR I get 18%, when I use XIRR I get 640%.
If i multiply 18% by 12 I get 217% which seems right ,
but doesn;t take into account compounding. If use this
=(iRR(C4:C16)+1)^12-1) I get 633% which is very close to
640%-

All are right and wrong!

First, IRR returns the periodic rate. If you have monthly cash flows
IRR
returns a monthly rate.

In contrast, XIRR always returns an annual rate.

That explains why XIRR is so much larger than the (monthly) IRR.

Second, there is no general agreement on how to annualize a periodi
rate.
To some degree, it depends on what financial securities you ar
modelling,
the industry conventions applied to those securities, and eve
applicable
regional laws. Sometimes it is correct to multiply a monthly IRR by 12

sometimes it is correct to compound it over 12 periods; sometimes we
multiply by other factors.

In contrast, XIRR always compounds daily.

That partly explains why even when you compound the monthly IRR over 1

periods, it is not exactly the same as daily-compounded XIRR.

Third, by definition, IRR treats each month as the same length whe
using
monthly cash flows. But XIRR uses the actual number of days.

That further explains why the monthly compounded IRR over 12 period
does
not agree exactly with the XIRR.

Finally, note that neither the IRR nor the XIRR can be computed
algebraically (unless all cash flows are the same, and they occur
regularly). Instead, each function uses some algorithm to "home in on
the
rate that causes the (X)NPV to be close to zero. Microsof
documentation
indicates that starting with Excel 2003, IRR and XIRR use th
Newton-Raphson
method.

But each algorithm is implemented differently, which gives rise to
differences in the results due to arithmetic anomalies (due to binary
floating-point) as well as diffences in the tolerances and th
underlying
differential formulas.

That is another reason why the monthly compounded IRR over 12 perio
does
not agree with the XIRR.

In actual practice, it is best not to read too much into the detailed
numerical results. They are all only estimates anyway. Choos
whichever
function is more appropriate for the data that you have.

PS: I might note that the Excel IRR and XIRR functions are simply tw
ways
to calculate the "internal rate of return" (IRR). In other words, whe
I
speak of "IRR", you need to decide by context whether I am speaking o
the
Excel function or the financial concept.

I get 633% which is very close to 640% but seems way to
high. I haven't even tripled my investment, which was
-130,000 while making 440,00 total over the year. Can
someone tell me which number is correct and why?-

Yes, that is the fallacy of annualizing periodic rates, IMHO.

For example, if the value of a security changes 1% in a day, surely yo
do
not believe we can expect its value has grown (will grow) at a annua
rate
of 3678%. That is indeed what (1+1%)^365-1 is. But that is not
realistic
assessment of the change in value.

So even though it is common practice to annualize periodic rates, I tr
to
avoid it -- although there are applications of the rate of return wher
we
must annualize.

Instead, I prefer to specify appropriate periodic rates of return. So
instead of annualizing a periodic IRR, I prefer to "de-compound" the
annual(ized) XIRR rate. For example, (1+XIRR(...))^(1/12)-1.

Nevertheless, that monthly XIRR will not be the same as the periodic IR

based on monthly cash flows for all of the reasons given above.

Thanks for the help. Here are the monetary inputs.

1-Jan-12 (130,000)
31-Jan-12 6,685
29-Feb-12 13,133
31-Mar-12 19,262
30-Apr-12 24,986
31-May-12 30,386
30-Jun-12 35,549
31-Jul-12 40,478
31-Aug-12 45,168
30-Sep-12 49,682
31-Oct-12 54,075
30-Nov-12 58,357
31-Dec-12 62,535

I guess my follow up question now is how do I explain in laymans terms
to superiors that it is an annual 640%? When we haven't even increased
the original outlay by 640%. They seem to think that it should mean we
should make 6.4 * 130,000. for it to be a 640% return. They think that
the 217% makes the most sense.

 

[Vacuum Sealed]

Whilst you're at it:

Can you let everyone here know where we can invest our 130K, based on
your figures we can get $171.00 a day return which is approx 48% in just
12 months....

Just let me who to make the check out to....

 

[joeu2004]

I guess my follow up question now is how do I explain
in laymans terms to superiors that it is an annual 640%?
When we haven't even increased the original outlay by
640%. They seem to think that it should mean we should
make 6.4 * 130,000. for it to be a 640% return. They
think that the 217% makes the most sense.

Well, a return of 640% should mean that their return was 7.4*130000; that
is, 130000*(1+640%).

And they are correct: 640% is the wrong answer, based on how "they" appear
to be thinking.

Based on your 1-year data, the actual annual return is about 239%.

If your data are in B1:B13, your actual annual return is SUM(B2:B13)/(-B1)-1
formatted as Percentage.

That is a simple average monthly rate of about 19.9%, computed by
(SUM(B2:B13)/(-B1)-1)/12.

Alternatively, it is a compounded average monthly rate of about 10.7%,
computed by (SUM(B2:B13)/(-B1))^(1/12)-1.

The difference between these figures and the number returned by IRR (a
monthly rate of about 18.1%) is "time-value of money" -- the assumption that
it is better to have more returns earlier.

Note that if the cash flows in B2:B13 were reversed, IRR returns a different
result.

Since that does not seem to be the way "they" are thinking, I would not use
a compounded average monthly rate (10.7% or 18.1%).

 

[PJ Hooker]

'joeu2004[_2_ Wrote:

I have an out flow and then monthly inflows for a month.
They are the same time every month the first of the month.
When I use IRR I get 18%, when I use XIRR I get 640%.
If i multiply 18% by 12 I get 217% which seems right ,
but doesn;t take into account compounding.  If use this
=(iRR(C4:C16)+1)^12-1) I get 633% which is very close to
640%-

All are right and wrong!

First, IRR returns the periodic rate.  If you have monthly cash flows,
IRR
returns a monthly rate.

In contrast, XIRR always returns an annual rate.

That explains why XIRR is so much larger than the (monthly) IRR.

Second, there is no general agreement on how to annualize a periodic
rate.
To some degree, it depends on what financial securities you are
modelling,
the industry conventions applied to those securities, and even
applicable
regional laws.  Sometimes it is correct to multiply a monthly IRR by 12;

sometimes it is correct to compound it over 12 periods; sometimes we
multiply by other factors.

In contrast, XIRR always compounds daily.

That partly explains why even when you compound the monthly IRR over 12

periods, it is not exactly the same as daily-compounded XIRR.

Third, by definition, IRR treats each month as the same length when
using
monthly cash flows.  But XIRR uses the actual number of days.

That further explains why the monthly compounded IRR over 12 periods
does
not agree exactly with the XIRR.

Finally, note that neither the IRR nor the XIRR can be computed
algebraically (unless all cash flows are the same, and they occur
regularly).  Instead, each function uses some algorithm to "home in on"
the
rate that causes the (X)NPV to be close to zero.  Microsoft
documentation
indicates that starting with Excel 2003, IRR and XIRR use the
Newton-Raphson
method.

But each algorithm is implemented differently, which gives rise to
differences in the results due to arithmetic anomalies (due to binary
floating-point) as well as diffences in the tolerances and the
underlying
differential formulas.

That is another reason why the monthly compounded IRR over 12 period
does
not agree with the XIRR.

In actual practice, it is best not to read too much into the detailed
numerical results.  They are all only estimates anyway.  Choose
whichever
function is more appropriate for the data that you have.

PS:  I might note that the Excel IRR and XIRR functions are simply two
ways
to calculate the "internal rate of return" (IRR).  In other words, when
I
speak of "IRR", you need to decide by context whether I am speaking of
the
Excel function or the financial concept.

Yes, that is the fallacy of annualizing periodic rates, IMHO.

For example, if the value of a security changes 1% in a day, surely you
do
not believe we can expect its value has grown (will grow) at a annual
rate
of 3678%.  That is indeed what (1+1%)^365-1 is.  But that is not a
realistic
assessment of the change in value.

So even though it is common practice to annualize periodic rates, I try
to
avoid it -- although there are applications of the rate of return where
we
must annualize.

Instead, I prefer to specify appropriate periodic rates of return.  So
instead of annualizing a periodic IRR, I prefer to "de-compound" the
annual(ized) XIRR rate.  For example, (1+XIRR(...))^(1/12)-1.

Nevertheless, that monthly XIRR will not be the same as the periodic IRR

based on monthly cash flows for all of the reasons given above.

Thanks for the help.  Here are the monetary inputs.

1-Jan-12         (130,000)
31-Jan-12        6,685
29-Feb-12        13,133
31-Mar-12        19,262
30-Apr-12        24,986
31-May-12        30,386
30-Jun-12        35,549
31-Jul-12        40,478
31-Aug-12        45,168
30-Sep-12        49,682
31-Oct-12        54,075
30-Nov-12        58,357
31-Dec-12        62,535

I guess my follow up question now is how do I explain in laymans terms
to superiors that it is an annual 640%?  When we haven't even increased
the original outlay by 640%.  They seem to think that it should mean we
should make 6.4 * 130,000. for it to be a 640% return.  They think that
the 217% makes the most sense.

Well you made a common error in selection of the date for cash flow at
time period t=0 thus your IRR and XIRR numbers mismatched

The date for time period t = 0 would be 12/31/2011 rather than
1/1/2012

Once you make this correction the XIRR would equal 633.07% which is
the same as the annualized IRR you calculated

And the monthly IRR would equal the IRR you calculated by using Excel
IRR function

(1 + i)^12 - 1 = 633.07%
(1 + i)^12 = 6.3307 + 1
(1 + i)^12 = 7.3307
(1 + i) = (7.3307)^1/12
1 + i = 1.1805800877156739686170250080055
i = 1.18058 - 1
i = 0.18058
i = 0.1806
i = 18.06%

 

[joeu2004]

Well, a return of 640% should mean that their return
was 7.4*130000; that is, 130000*(1+640%).

Scratch that. It depends on the definition of "return".

It was an irrelevant comment in the first place. It has no bearing the rest
of my comments.

 

[joeu2004]

Here are the monetary inputs.
1-Jan-12 (130,000)
31-Jan-12 6,685
29-Feb-12 13,133
31-Mar-12 19,262
30-Apr-12 24,986
31-May-12 30,386
30-Jun-12 35,549
31-Jul-12 40,478
31-Aug-12 45,168
30-Sep-12 49,682
31-Oct-12 54,075
30-Nov-12 58,357
31-Dec-12 62,535

[....]
Well you made a common error in selection of the date
for cash flow at time period t=0 thus your IRR and XIRR
numbers mismatched

The date for time period t = 0 would be 12/31/2011 rather
than 1/1/2012

There is no "common error" if those are the actual dates of the cash flows.

But perhaps the point you intended to make is: in using the IRR with those
cash flows, we must assume the first cash flow occurs on 31-Dec-2011 (i.e.
all transactions occur at regular intervals).

And that will contribute to differences between the results of the Excel
XIRR and IRR functions.

So for an apples-to-apples comparison, we should fudge the date of the first
cash flow in the XIRR parameters.

Once you make this correction the XIRR would equal 633.07%
which is the same as the annualized IRR you calculated

Excel XIRR returns about 632.84%, whereas Excel IRR returns about 18.0617%,
which is about 633.35% when annualized by compounding.

(I wonder if the difference between PJHooker's 633.07% and Excel XIRR's
632.84% is due to the fact that Excel XIRR always uses 365 days for a year,
whereas 2012 actually has 366 days. But when I make that substitution in my
own NPV formulation, I get about 636.85%, not 633.07%; and using 633.07%
results in a large error in the NPV.)

In any case, they still are not "the same" for the other reasons that I
provided, primarily differences in cash flow frequencies (the fact that each
monthly cash flows is not the same number of days apart). There is no way
to overcome that primary difference.

But I must admit: I am surprised by the difference that 1 day makes.