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Use Average Internal Rate of Return (AIRR) and

Don’t Use Internal Rate of Return (IRR)

Note:

This is as per my email correspondences with Prof. Carlo Alberto Magni (University of Modena

and Reggio Emilia, Italy)1 in 2015.

1 Prof. CA Magni’s personal webpage: http://morespace.unimore.it/carloalbertomagni.

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

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Karnen:

Dear Prof. Magni,

I read your paper (with Dean Altshuler, Bard Consulting LLC (Manhattan Beach, CA, USA) under

the title “Why IRR is Not the Rate of Return for Your Investment: Introducing AIRR to the

Real Estate Community”2, and am wondering as to how to get the figures under Column B as

shown in the Appendix 2A or Appendix 2B for year 1, year 2, so on? I thought it is the present

value of the next streams of cash flows , but it is not...

Note: Seems to me your idea on AIRR is interesting, but not too sure why it is not taught in many

standard corporate textbooks and it is still IRR that is preached around all those new babies in

corporate finance.

Prof. CA Magni:

Thanks for your email, Karnen.

I think you refer to the Exhibits. Column B is the IRR-implied value of the asset, so you can

compute it recursively as described in eq. (A.1), (A.2), (A.3).

For example, in Exhibit 2a, the IRR-implied value at times 1 and 2 are

100*(1+20%)+50=170

170*(1+20%)+50=254

and so on.

You can alternatively discout the prospective cash flow with the IRR and get the same results.

2 Downloadable from

http://www.bardconsulting.com/uploads/3/1/5/7/3157118/12.04.2011_why_irr_is_not_the_rate_of_return_for_your_investment_-_dean_a.pdf. Published in the Journal of Real Estate Portfolio Management 18(2), p. 219-230. 2012.

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Karnen:

Dear Prof. Magni,

I have gone through SSRN to look for your paper on IRR, yet I believe there are too many to read

through.

Can you suggest one or two of your papers that summarize the whole issues of IRR and your

suggested solution (in this AIRR) that I could read?

Prof. CA. Magni:

This one (The Internal-Rate-of-Return Approach and the AIRR Paradigm: A Refutation and A

Corroboration3) shows 18 flaws of the IRR and, a the same time, illustrate my AIRR approach and

how it overcomes the IRR's flaws:

Karnen:

Hi Prof. Magni,

I am referring to your paper (with Dean Altshuler, Bard Consulting LLC (Manhattan Beach, CA,

USA), Exhibit 2A.

What I am a bit confused is on the end of 8th year, in which you put 0 value for Column C (Actual

Market-based Values). You explained a bit in the body of the paper that the value for project once

liquidated is zero. With showing the Cash flow of US$1,204.90 under Column A, I got the

impression that the project is sold instead of liquidated, and there is a proceeds from the sale of

the project. Then why the value of project at end of 7th year (a year before the sold) doesn't factor

the Present Value of the proceeds from the sale of the project at end of 8th year? I see the

calculation of the project value (column C) for end of 7th year is pretty much only including the

annual appreciation.

3 Downloadable from http://ssrn.com/abstract=2172965. Published in the Engineering Economist, 58 (2), p.

73-111. 2013.

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By the way, you still maintain the name "Internal" for AIRR, why not Average Rate of Return or

other name? By still keeping the term "Internal", it seems to me, implicitly, the issues with standard

IRR will be carried along. However, this is just a name issue anyway.

Prof. CA Magni:

Dear Karnen,

In this example we assume that the evaluator exogenously estimate the asset’s market values.

Just for the sake of illustration, we use a 37.2% appreciation rate of the asset’s value (selling

price) until the end of 7th year; then, in the last year, there is an implicit assumption of a 31.7%

appreciation rate, so that at the end of the 8th year one sells the asset at 1204.9. Once the asset

is sold, the project is over, it is “liquidated”.

The expression “Average Internal rate of Return” is due to the following reasoning:

In finance, the sequence of holding period rates in an investment is sometimes called an “internal

return vector”: it represents a sequence of one-period internal rates of return.

The AIRR is an average of the one-period IRRs. Hence, the expression “average (of the one-

period) internal rates of return”.

The holding period rates are indeed internal, but the weights of the average are not internal (they

depend on the COC), so AIRR is not an internal rate.

I agree that this confounds things a bit, and that AIRR is a misnomer: I should have chosen

another label. “Average Rate of Return” is too generic an expression: there are many different

“average rates of return” in the literature.

In one paper, I have called it “Average Interest Rate” and one might think of keeping the acronym

AIRR while recalling it “Average Interest Rate of Return”, but “interest” and “return” are

synonymous expressions and I also fear that a change might confounds readers even more. So,

the best thing is probably to maintain the expression and clearly specify that the weights of the

mean depend on the COC, so AIRR is not internal.

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A further remark: consider that while IRR does not depend on the COC, its financial nature does:

in general, if COC changes, the financial nature of the IRR may change (from financing rate to

lending rate or vice versa).

Karnen:

Hi Prof. Magni,

I guess you might have expected it, upon reading your paper and reworking the figures in Exhibit

2A and 2B, supplying the interim investment (or market-based) values is one issue that I don’t

think it quite practical, though it is really critical to get AIRR working.

I am coming from finance practitioner background and drawn to your paper to the fact that you

touched on Akerson’s paper (1976) who used bank saving analogy to explain from where IRR

came. That’s interim period value that is interesting to me.

However, the fact that IRR is always explained in the context of “long-term” investment, it seems

to me, probably, yes, probably, as an analyst, that’s interim period value might not bring much

concern. Even if it does, I don’t think, IRR is the right tool to address it. There are a couple of tools

to consider, such as real options (as anything could happen between all those periods), or

sensitivity analysis.

I’ve seen many examples given by authors in attacking IRR by giving 3 or 4 periods’ cash flows.

This is of course, not “long-term” and we don’t even need NPV or IRR to evaluate such cash

flows.

I am not too sure whether I have ever seen analysts doing the estimate for interim investment

values. What’s the point of doing that anyway? Even if we can, I guess, we could just use simple

formula to calculate the income return from period to period, and then average all those periodical

returns using arithmetic mean.

One thing that I noted from that paper, the AIRR is not much different from IRR (20%) both in the

examples shown in Exhibit 2A and 2B.

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Prof. CA Magni:

Dear Karnen,

Thanks for your remarks. I am not sure I have understood all of your concerns, so I am not sure

whether my following remarks may be of some value to you. Anyway, the determination of the

interim values depend on the type of project and the piece of information required.

AIRR is a class of rates, each of which provides different piece of information. The shortcut

formula for an AIRR is AIRR=COC+NPV(1+COC)/capital base. [Note: COC = Cost of Capital]

In real estate assets, one can use estimated market values to find the capital base; if not available,

one can use the economic values (discounted value of prospective cash flows at the COC).

In capital investment analysis, pro forma financial statements are available to the analyst, so the

book values can be used.

For ex-post performance measurement, one can use the observed market values.

Alternatively, one can always assume that the capital depreciates uniformly so that capital at time

t -capital at time t-1 =constant=initial investment/length of the investment.

One can even set the capital base equal to the initial investment, so finding the return on initial

investment, something the IRR is not capable of computing .

The IRR is associated to a well-defined capital base as well and can certainly be used if the

assumption of capital increasing at a constant rate is appropriate.

The arithmetic mean you suggest does work only under particular circumstances (see my 2010

paper on it); in all other cases it will be inconsistent with the NPV criterion. Conversely, the

weighted mean is always consistent with the NPV.

In the example the IRR is close to the AIRR but, in general, there can be differences of many

points between the two (it depends on the cash flows and on the interim values).

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Karnen:

Hi Prof. Magni,

Your paper regarding the arithmetic mean, is this the paper: Average Internal Rate of Return

and Investment Decisions: A New Perspective (March 9, 2010)4?

Prof. CA Magni:

Yes, the section is “The simple arithmetic mean”.

This can be used only if the capital grows at the market rate

~~~~~~ ####### ~~~~~~

4 Published in the The Engineering Economist, 55(2), p. 150‒181 (“Eugene L. Grant “ Award from ASEE –

most read paper of The Engineering Economist). 2010.

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Readings:

AIRR (Average Internal Rate of Return): A New Approach to Investment Valuation and

Decision-Making. Carlo Alberto Magni’s personal webpage accessed on 15 September 2015

(http://morespace.unimore.it/carloalbertomagni).

Magni, Carlo Alberto. The Solution(s) to the Long-Standing Issue of the Internal Rate of

Return: Scientific and Educational Implications. Downloadable at

http://www.dep.unimore.it/seminari/Magni.pdf.

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