This is to document the email correspondences with Prof. Peter M. DeMarzo (Stanford University) and Prof. Carlo Alberto Magni with regards to Average Internal Rate of Return in Dec 2015.

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Use Average Internal Rate of Return (AIRR) and
Don’t Use Internal Rate of Return (IRR)
Part 2
Note:
This is to document my email correspondences with Prof. Carlo Alberto Magni (University of
Modena and Reggio Emilia, Italy)1
and Prof. Peter M. DeMarzo (Mizuho Financial Group
Professor of Finance, Stanford Graduate School of Business, USA)2
in December 2015 with
regards to introducing Prof. CA Magni’s idea about the superiority of the Average Internal Rate of
Return (AIRR) over “traditional” Internal Rate of Return (IRR) or even, Net Present Value (NPV).
1 Prof. CA Magni’s personal webpage: http://morespace.unimore.it/carloalbertomagni.
2
http://www.gsb.stanford.edu/faculty-research/faculty/peter-m-demarzo.
Sukarnen Suwanto
DILARANG MENG-COPY, MENYALIN,
ATAU MENDISTRIBUSIKAN
SEBAGIAN ATAU SELURUH TULISAN
INI TANPA PERSETUJUAN TERTULIS
DARI PENULIS
Untuk pertanyaan atau komentar bisa
diposting melalui website
www.futurumcorfinan.com

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Karnen:
Hi Prof. Peter,
I sent you some papers with regards to Average IRR introduced by Prof. Carlo Alberto Magni.
They are as follows:
 Hazen, G.B. A New Perspective on Multiple Internal Rates of Return. The Engineering
Economist, 2003, 48:1, 31–51.
 Altshuler D., Magni C.A. 2012. Why IRR is Not the Rate of Return on Your Investment:
Introducing the AIRR to the Real Estate Community. Journal of Real Estate Portfolio
Management 18(2), 219‒230
 Magni C.A. 2013. The Internal-Rate-of-Return approach and the AIRR Paradigm: A
Refutation and a Corroboration. The Engineering Economist, 58(2), 73‒111.
I believe what he put here is correct. IRR is indeed a rate of return on “implied interim values”.
Traditional IRR will only make sense if we want to calculate the return on a bank savings, but not
project investments (particularly real estate) in which their interim values have real world
variations in the market over project life. Something that is not new since Akerson (1976) has said
about that. Yet, Prof. CA Magni brilliantly offered his solution, called Average Internal Rate of
Return (AIRR), which could be simplified in formula into AIRR = Cost of Capital (COC) + [NPV
of Cash Flows x (1+COC)/NPV of the Interim Project Values].
To my surprise, traditional IRR is still taught intensively in many business schools and I know of
no current corporate finance textbooks that do not follow it almost religiously. Probably, because
it is so easy and quick to show how much the IRR of a project investment, just insert MS Excel
formula, IRR (or additionally, MIRR (=Meaningless IRR)) and here it is, in a blink of eyes, you will
see your IRR/MIRR. Albert Einstein once quoted saying that “Everything should be made as
simple as possible, but not simpler”.
I am a bit concerned over the fact that many business school graduates that have been preached
with that traditional IRR, is like a baby with a hammer. To a baby with a hammer, everything will
look like a nail.

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Prof. Peter:
Sukarnen --
While AIRR is an interesting metric, it is an ex-post measure, and therefore not useful for ex-ante
decision making (which is our focus as you know).
Indeed, I am not sure how the AIRR would be useful more broadly, even as an ex-post
measure. And even in cases where IRRs remain a commonly used metric (PE), investors are
often much more interested in MOMs. How would AIRRs help?
If you really want to understand ex-post performance I would think alpha or a value-added
measure would be more useful.
Karnen:
Hi Peter,
Why do you think it is an ex-post measure?
By the way, I sent one presentation materials associated with AIRR3
.
Prof. Peter:
You can't forecast the intermediate values ex ante. (Or if you did, no reason to think they are
necessarily any better than what is implicitly in IRR.) How would you use AIRR, as a ex-ante
decision making tool? It has no advantage over NPV.
Karnen:
I do not really concur with you. You "can't" or you just "don't" want?
3
Altshuler, Dean. Bard Consulting LLC. Member, NCREIF Performance Measurement Committee.
Presentation Slides: Introducing AIRR (Average IRR). July 13, 2011. Presented during the 2011 NCREIF
Summer Conference.

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Forecast is an inherent part of corporate finance, either we like it or not, it is the unpredictability
that drives the growth in finance research and study. Inherent in NPV or DCF is the forecasted
interim project value, though we might not show it explicitly in the spreadsheet.
By the way, the good thing about AIRR approach, I guess, is that approach forcing the analyst to
think hard about the interim project values (and to give numbers as reasonable as possible) as
well as the cost of capital that he/she is going to use to come up with that interim project values.
In many cases in certain investments, such as property/real estate, we could have a better idea
about that interim project value than the IRR itself.
What do you think?
Prof. Peter:
I just don't see how I would use AIRR for decision making -- NPV seems clearer and easier! I do
think it is useful to think about interim values, but again we can do that using NPV as well.
In a PE context, where practitioners are sometimes overly focused on IRR, the approach I
recommend is to compute IRR per period (rather than a single aggregate iRR). This is especially
important there, as the cost of capital typically changes over the life of the investment (so even
the AIRR is again not meaningful).
Karnen:
Hi Prof. CA Magni,
I guess your concept on AIRR should be taught to business school students. Many graduates are
not quite aware of that traditional IRR is somehow meaningless. Nobody checks on those interim
project values. They are just so focused on IRR that they got and compare it with cost of capital.

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By the way, is AIRR an ex-ante or ex-post performance measurement? Do you think it is more
appropriate for analysis on capital budgeting or project capital evaluation, compared to investors
in capital markets (e.g., for stock valuation)? This part that I feel not quite explored in your papers.
Prof. CA Magni:
Dear Karnen,
Yes: there is no need of any additional forecast of capital; the capital is the sum of the net fixed
assets and the net working capital, and these values are already used to compute the FCFs! So,
everything is already available!
This is exactly what Berk and DeMarzo themselves show in their [corporate finance] textbook.
Their eq. (8.5) in ch. 8 (p. 243 of the global edition)4
includes depreciation and capital expenditures
(i.e., changes in net fixed assets) and change in net working capital. It suffices to sum the net
fixed assets and the net working capital in each period to get the capital invested in a period.
All their examples are based, implicitly or explicitly, on estimation of capital (e.g., see pro forma
financial statements in Ideko’s example, ch. 195
). Such an estimation is necessary to compute
FCFs.
Find enclosed a spreadsheet where I compute the AIRR for Home Net’s example illustrated by
Berk and DeMarzo (chapter 8, global edition). As you will see, it is very simple.
4
Berk, Jonathan; and Peter Demarzo. Corporate Finance. Third Edition. MA (USA): Pearson Education,
Inc. 2014. Chapter 8 : Fundamentals of Capital Budgeting. Page 243.
5
Berk, Jonathan; and Peter Demarzo. Corporate Finance. Third Edition. MA (USA): Pearson Education,
Inc. 2014. Chapter 19 : Valuation and Financial Modeling: A Case Study. Page 674.

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Note that I provide two spreadsheets: one where a constant cost of capital is assumed (as in Berk
and DeMarzo’s example), and another one where time-variant costs of capital are assumed.
You can send the spreadsheet to [Peter] DeMarzo for a better understanding.
You can also take notice that
1. NPV tells us about economic profitability, but economic profitability depends on both
investment size and project efficiency: NPV says nothing about project efficiency nor
investment size. The AIRR approach enables the evaluator to decompose economic
profitability into investment size (total capital invested) and efficiency (AIRR minus COC).
The same NPV can be found by either a small investment size and a high rate of return
or a small rate of return and a high investment size.
2. NPV does not tell whether a project is a net investment or a net financing (think of
nonconventional projects with cash flows which have several changes in sign such as
engineering projects), so the analyst does not know whether value is created because
funds are invested at a rate of return which is higher than the COC (i.e. the minimum
acceptable rate of return) or, rather, because funds are borrowed at a financing rate which
is smaller than the COC (i.e., the maximum acceptable financing rate).
Therefore, the AIRR approach represents a more refined economic analysis than the NPV.
Let me add another remark: if one uses IRR to compute the project rate of return, then one incurs
a contradiction. Indeed, the IRR presupposes its own built-in interim values which contradict the
capital values (NFA and NWC) which are necessarily used to compute the FCFs.
Please, find attached.
 My 2013 paper on 18 flaws of the IRR6
.
 My 2014 paper which generalizes TRM model7
.
6
Magni C.A. 2013.The Internal-Rate-of-Return Approach and the AIRR Paradigm: A Refutation and
a Corroboration. The Engineering Economist, 58(2), 73‒111.
7
Magni C.A. 2014. Mathematical Analysis of Average Rates of Return and Investment Decisions: The
Missing Link. The Engineering Economist, 59(3), 175‒206.

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 My latest paper on AIRR, recently published on the European Journal of Operational
Research8
.
(to be continued)
~~~~~~ ####### ~~~~~~
8
Magni C.A. 2015. Investment, Financing and the Role of ROA and WACC in Value Creation.
European Journal of Operational Research, 244(3) (August), 855‒866.

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