# Return knowledge for lawyers

First, let’s keep the opening message in mind:

Where there is a yield on it, there is by no means a yield in it! Modern business economics long ago described return on investment as the relationship of yield (profit) to capital employed.
Thus, the result percentage indicates how the capital investment earns interest. Quite simply, the reader thinks, if I put down 100 monetary units (GE) today and get back 106 GE after one year, then I have a return of 6 percent based on my capital investment.
What’s the problem? In this constellation there is no measurement problem because only one period is measured. But how does it look if, as in the case of federal bonds, for example, nominal interest of 10 percent per year is paid for several years, let’s say five years, and the entire capital investment also flows back to the investor with the last interest instalment?
This was the example of the FAZ editor, which is currently a bit too high in terms of interest, but hits the core issue. At first glance, the superficial observer will answer the yield question in Table 1 with a 10 percent return per year on the federal bond and will be quite wrong. Surprised? Out of one hundred respondents, 97 people will give this wrong answer. Why is this wrong when it seems obvious that the return is 10 percent per year? Why should it be different?

### Basic principle of dynamic return determination without reinvestment of reflows

The answer lies in the confusion of the (nominal) interest per period (10 percent per annum) and the interest rate on the capital investment (return)? The reader must notice in Table 1 that he counts a total of only 50 GE nominal interest on his account and that he ends up with a total return of 150 GE because he only gets back the 100 GE invested.
If you invest 100 GE today, you can have 150 GE in five years. The return on his capital investment is only 8.45 percent per annum, not 10 percent per annum. This is the simple message. Apparently the “return” is 10 percent, but the interest on the capital investment is only 8.45 percent per annum? How do the differences come about, he wonders, when he could have sworn that all the business papers reported 10 percent annual returns? Where is the key to explaining the differences in return measurement?

### IRR return method with or without reinvestment premise?

In Table 1, the return on the capital invested is 8,45 %, per annum, which is the same as the return on the capital invested, because the investor also ends up with only the 150 GE that is distributed to him. The issuer gives nothing more and nothing less to the investor. Let’s do the same calculation in Table 2 at 10 percent per year and look at the final account balance of 161.05 GE.
If we assume that the returns of 10 in years 1 to 5 are used for consumption purposes and spent by the investor, he cannot reinvest them. So he only gets back a total of 150 GE and earns a return of 8.45 percent per annum.
If he does not need the returns and wants to continue saving them and keeps investing them at 10 percent per annum interest until the end of the fifth year, then he counts 161.05 GE on his account balance. How is that possible? Quite simply, he keeps receiving interest on his account balance and this compound interest amounts to exactly 11.05 GE as Table 1 shows with mathematical precision.
This additional interest comes from the compound interest effect, the nominal interest from the second column that is always reinvested. It is therefore automatically assumed that the investor always reinvests his nominal interest at 10 per cent, although in reality, according to Table 1, this is not at all provided for by the issuer of the Federal bond.
Only if the investor succeeds in finding an accumulating form of investment which, as in the case of the zero bond, automatically pays interest on the reinvestment at exactly 10 percent per annum without renewed costs, will he be able to achieve a return of 10 percent. Without reinvestment, he is left with only 8.45 percent per annum return on his capital investment.

### IRR reinvestment premise generates notional additional interest

Those who re-invest, as in Table 2, obviously have an extra GE 11,05 in interest. 161.05 financial mathematical related to the capital investment of -100 also result in the higher return of 10 percent per annum.

### Validity of IRR return also for consumers of recoveries?

If you don’t plan for reinvestment at all, you must basically feel deceived because your supposed 10 percent per annum federal bond is actually only yielding 8.45 percent per annum. Only if the fictitious additional interest from the fictitious reinvestment is attributed to him and this actually results in a reinvestment at 10 percent per annum as well, then he achieves a return in the investment network (parent investment plus reinvestments) of 10 percent on his capital investment.
If he consumes the reflows, they are no longer available for reinvestment. In this case, the parent investment yields only 8.45 percent per annum, although it earns 10 percent nominal interest per period. The reinvestment assumption is key to explaining the 10 percent federal bond yield. This brings up an interesting question. In order to achieve a 10 percent return on his capital investment, should the investor subscribe to a federal bond which itself only gives him a return of 8.45 percent per annum and he can only achieve a 10 percent return if he reinvests at the higher reinvestment interest rate of 10 percent?
This seems strange because the investor is certainly more inclined to reinvest 10 percent than to be satisfied with the 8.45 percent return per annum of the parent investment. Why shouldn’t he just turn to investments with the higher (reinvestment) interest rates of 10 percent per annum?
Without question, the internal rate of return (IRR) method is used when offering the 10 percent yield of the federal bond. The IRR method includes automatic reinvestment, as is assumed for the zero bond. In reality, the generally non-thesauration forms of investment are not automatically subject to reinvestment of the returns.

### Is the reinvestment decision made by the investor or by the IRR return method?

Whether to reinvest or consume is not decided by the return method, but solely by the investor on a case-by-case basis.

Therefore, an investor and his lawyer should pay strict attention to whether, when concluding his capital investment, the return on the assumption of reinvestment at the internal rate of return was stated or even the IRR method was stated in the prospectus or only the return on the parent investment was referred to, which does not assume reinvestment of the returns. By applying the IRR, the IRR return method anticipates the reinvestment decision.

### Legal evaluation of the IRR method

The IRR method implies factual assertions, with its application as a yield ratio:

(1) The current distributions (reflows, excluding the residual proceeds) of the investment would be automatically reinvested at the same IRR rate. This is already a deception, because in the case of distribution there is necessarily no accumulation.
(2) Since the accumulation is not anchored in the product itself, it is not an automatic reinvestment, but the IRR application implies this as a mathematically compelling or necessary condition.

(3) As a rule, products that advertise IRR returns do not include an option to reinvest the distributions in the same product in order to retain them and thus generate additional interest.(4) The fact that there are ongoing distributions forces the investor (who wants to achieve the IRR return) to take care of the reinvestment himself and to find investment opportunities that necessarily yield a return at the stated IRR interest rate.

(5) The use of the IRR misleads that it is an accumulating product and/or it misleads that the investor can necessarily invest his current distributions at the calculated IRR; in this product or in another investment product on the capital market. Generally, these reinvestment opportunities do not exist for the distributions at said IRR yield. The residual proceeds, on the other hand, will not be reinvested because they are usually returned as the final payment at the end of the investment, ending the investment period.

(6) Investors are usually implicitly led to believe that the return (ratio) on an investment calculated using the IRR method is comparable to the return on other investment opportunities. Due to the reinvestment premise and the influence of different incoming and outgoing payments (in terms of amount and timing), IRR returns are regularly not comparable in this sense.
The investor could claim damages due to the IRR deception, i.e. his asset disposition (investment decision) based on a mistake because of fraud or investment fraud: If the investor looks back, he will see that he regularly had the opportunity, neither in the investment product nor externally in any other project, to reinvest his distributions at all and at the said IRR return. The product providers also do not inform the investor that, in order to achieve the IRR return, he must reinvest all current distributions again and again at the IRR return until the scheduled end of the main investment for the remaining investment period.
Also the investor will determine retrospectively that thus the existence of additional interest was pretended to him, which is not to be obtained however regularly, because this could succeed only under strictest conditions – in the investment product conception however regularly not at all was intended.

#### A. Damages as a claim for performance

Here the consideration is to be made, what the investor actually received in current distributions and residual proceeds and what he should have received?
Example :
The IRR calculation of the ship investment in Tables 3 and 4 shows 202.73 units for the final IRR value (including reinvestment interest from the distributions at 7.32 percent per annum and the residual proceeds). Of this amount, 168 units are derived from the sum of all current distributions (excluding reinvestment) and the residual proceeds. The (notional) additional interest = 34.73 units results from the difference between the final IRR of 202.73 units and the total return without reinvestment of 168 units. Usually, prospective return statements are based on more or less non-binding forecasts. In this case, the actual distributions and residual proceeds must be subjected to a new IRR calculation and the additional interest must be claimed as compensation (lower limit) from the reduced IRR calculation.

#### C. In the event of damages arising from the reversal, the investor shall receive his equity instalments paid back in full, plus interest at the rate customary in the capital market from the beginning.

In addition, he is released from any loans and other liabilities, and returns the (in retrospect often not very profitable) capital investment.
Similarly, the users of the IRR method are liable, for example, as initiators, prospectus auditors, banks and distributors, investment advisors, tax advisors and auditors, lawyers, rating agencies and manufacturers of software for financial planning systems with IRR application or use.

### Consumers of the distributions cannot reinvest anything

If the investor was told the return according to the internal rate of return method or if this was shown in the prospectus as the only return indicator, then he was automatically and clandestinely assigned additional interest from the automatic reinvestment, which he can never achieve as a consumer of the returns, because these are only fictitiously included in the IRR and provide an incorrectly advantageous statement. In any case, the IRR yield figures are demonstrably much too high for the consumer of recoveries, as the sample calculation in Table 1 shows.
To show this also for closed-end fund investments, we use an anonymized ship investment example in Table 3, which is subject to exactly the same reinvestment assumptions when using the IRR method. The evaluation of the ship investment shows an IRR of 7.32 percent per annum, although the total of all recoveries amounts to only 168 GE.
If one reinvests all returns (equivalent to distributions) in full at 7.32 percent per annum, then one will receive 202.73 GE at the end of the investment.
However, the calculations in Tables 3, 4 and 5 show that the reinvestment generates additional interest of GE 34,73 (GE 202,73 less GE 168), which is only notional. The parent investment (reinvestment interest = 0 percent and reflux sum of 168 GE) yields only 5.32 percent per annum. Only the reinvestment of the reflows at the IRR rate of 7,32 % per annum results in 202,73 GE, of which 34,73 GE alone represents notional additional interest.
Table 4 shows the relationship once again:
In fund practice, it can be observed that over the past 20 years the internal rate of return (IRR) method has found its way into prospectuses and its results are uncritically reported there as the return of the fund offering. In its latest draft guideline ES 4 of 7.7.2005, the IdW (Institut der Wirtschaftsprüfer – Institute of Public Auditors in Germany) recommends refraining from using condensed yield ratios (e.g. IRR) in prospectus offers and “recommends” at best to use, for example, the IRR yield in the sensitivity analysis:
If the term “return” is used, it must be stated what the return refers to and how it was calculated in detail. The use of condensed return ratios (for example, internal rate of return) should be avoided because it is usually unsuitable for comparing different investments due to the different cash flows in each investment. This does not apply to the use of such condensed return ratios in the context of sensitivity analysis for the presentation of the development of the asset investment under changes in individual or several key parameters.”2
The IDW cites the lack of comparability of such return ratios as the sole justification, leaving return ratios other than IRR unnamed but not excluding them either, provided they are clearly and generally understandably defined and not used in a misleading manner3.
The IRR statement offers a high liability potential for all users because of the amount of the fictitious additional interest, which in fact cannot be achieved or can only be achieved in the very few cases of reinvestment. Anyone who uses the IRR return method and presents it to the investor automatically assumes reinvestment of the distributions, even though no investor will make a decision about that at the time. However, the reinvestment is tacitly foisted upon him. This raises the question of what conditions must be obeyed by the reinvestment that lies hidden in the IRR method?
The computational compound interest effect imposes the strict conditions of reinvestment, which we can see from Table 5. Here we again take the ship example as a basis, whose individual return flows are always invested in isolation with the internal rate of return as the reinvestment interest rate until the end of the investment of the parent investment. Table 5 shows the path of reinvestment and leads us exactly to the final account balance of 202.73 GE, which includes the fictitious reinvestment interest and therefore shows a higher fictitious return (7.32 percent per annum) in relation to the capital investment than the parent investment itself produces with 5.32 percent per annum. We see from Table 5 that over the isolated reinvestment of the first return over the remaining investment period of 9 years (10-1) at the internal rate of return of 7.32 percent per annum, a final account balance of 15.11 GE is achieved. The second return (distribution) is compounded at 7.32 percent per annum and the remaining investment term of 8 years (10-2), yielding a final account balance of 14.08 GE.
The compounding or reinvestment of the reflows is carried out up to the last reflow (here: sales proceeds with 70 plus last distribution with 14). Adding up all the final account balances gives us the total final account balance of 202.73 GE, which we had already found by another route in Table 3. Anyone who still wants to deny the reinvestment premise in the internal rate of return method is entering a total arithmetical and argumentative abyss. It cannot be stated more clearly than this.
This way of determining the notional IRR final account balance clearly shows the reinvestment conditions:
1. all recoveries must be invested without exception.
2. the reinvestment rate must always correspond to the internal rate of return of the IRR method.
3. the internal rate of return shall be valid for all reflows or reinvestment levels.
4. it must be possible to achieve it for ever shorter investment periods.
All conditions must always be fulfilled together, otherwise the IRR as a return indicator cannot be calculated: From the partly completely unrealistic reinvestment conditions, especially points 2, 3 and 4, it is easy to see even for laypersons that these will be fulfilled in practice in the rarest cases.
In reality, the reinvestment of reflows takes place on a case-by-case basis, but could be carried out strategically. Of course, this is not possible for an investor who only wants to consume the returns. The reinvestment spectrum is represented by the data set of real investment rates and forms of investment, and these are not based on the required notional rate of return of the IRR.
It is not only the investment interest rates that differ depending on the investment amounts. They also drift apart depending on the length of investment. The strongest arguments for liability because of the disclosure of a fictitious additional interest (fictitious return) in the IRR are held by investors who were not made aware in the prospectuses and sales discussions that the IRR does not apply to them in any way because they do not intend to reinvest. When using the IRR, reinvestors are expected to find investments for reinvestment whose returns (7.32 percent per annum) are supposed to be higher than the return on the parent investment (5.32 percent per annum).
Whether rating agencies take these circumstances into account when they publish and disseminate unchecked IRRs in certain circumstances? Few are not too shy to even refer to the highly controversial IRR yield method as the so-called BMF method, because it found its way into the review of the second standard example of § 2b EStG years ago by the Federal Ministry of Finance or the tax authorities.

### What is the relationship between IRR and capital commitment method or effective interest rate?

More detailed IRR presentations in the offering prospectuses correctly define IRR methodologically as the interest rate at which the balance of all present values equals zero. However, they interpret this interest rate as the rate of return on the average capital tied up, which is not only calculated fictitiously, but also obtained from another method (capital tie-up method). According to the original mathematical equation determining the IRR, the interest rate r represents the rate of return on the IRR investment expenditure over the investment period if all recoveries are reinvested at r.
Although the mathematical formal language is more daunting than affectionate, let us briefly demonstrate the connection: From the IRR-determining equation for the interest rate r, we see that the balance of the present value of all recoveries Rt, determined using r, expressed as

n
Σ Rt * (1+r)-t
t=0

and the present value of the investment expenditure, expressed as I0, at the beginning of the investment at time t0, gives the value zero. We take this condition from the IRR determination equation according to the following formula: n
NKW= Σ Rt * (1+r)-t -I0 =0
t=0
In this formula, the interest rate r is sought that compresses the net present value NKW (= balance of all present values) to zero.
We can also rewrite the simple IRR determination equation to:
n
Σ Rt *(1+r)-t =I0
t=0
So far, we have first found the values for the sum of all return present values at the beginning of the investment, and of course, with I0, we have also found the present value of the investment expenditure, which in this simple case consists of only a single value I0 = -100.
The left part of the equation represents the sum of all return cash values, which are also shown in Table 6:
Now that we have determined all the values at the beginning of the investment in t0 using the IRR formula, we can calculate the values at the end of the investment. To do this, we compound interest Rt and also I0 on the investment end tn with compound interest = (1+r)n (mathematically, “we extend”):
n
Σ Rt *(1+r)-t *(1+r)n =I0 *(1+r)n
t=0
Simplified, the final IRR value is obtained in two ways: n
Σ Rt *(1+r)n-t = I0 *(1+r)n
t=0
The left-hand side of the equation accrues interest on each return at r = 7.32 percent over the remaining investment period n-t. We applied this procedure in detail in Table 5 and obtained the final IRR value of 202.73 GE. The right-hand side of the equation represents the return on the IRR investment expenditure with r over the entire investment period n and also yields the final IRR value with 202.73 GE.
We have used this procedure in detail in Table 3. Thus, the internal rate of return r indicates the rate of return on the IRR investment expenditure I0 if all recoveries are reinvested at the investment rate r. In this context, borrowing the KBM interpretation of r as the rate of return on average capital employed (DDGK) is merely a distortion or misinterpretation of the IRR statements. The vocabulary of the KBM method has no place in IRR and yet it is incorrectly disseminated in prospectuses.
The alleged interpretation of the IRR is given a special note in the following justification: “This return is not directly comparable with the returns on other investments for which there is no change in the tied capital (for example, fixed-interest securities). A comparison is only possible by taking into account the respective average committed capital (in relation to the unfunded deposit), the total return and the investment period of the respective investment.”
Here, the author “stole” out of the IRR in the WP-approved prospectus and completely galloped into KBM. He goes on and gets completely entangled: “No assumptions are made as to how payouts will be used by the investor or from what funds the investor will make the required deposits.
In the case of a release of the respective tied-up capital determined purely by calculation, the IRR method assumes an interest on the capital then released at the internal rate of return.” Now he has done everything wrong that can only be done wrong and sees facts in the IRR method that he transplants from the KBM and MISF into the IRR method and is firmly convinced that he is still talking about the IRR method: “The IRR method is a return calculation method commonly used for closed-end funds and similar forms of capital investment, which is also used by the tax authorities to check the standard example of § 2b EStG.”
This accolade for IRR is a complete failure because he describes KBM and still thinks he is talking about IRR. The culmination culminates in the justification for non-comparability of the IRR results with other investments because, for example, there is no change in the tied capital in the case of fixed-interest securities. This is also a misconception, because the repayment of nominal interest to the investor also reduces the tied-up capital in the case of fixed-interest securities.
The cause of the error in the prospectus lies in the ignorance of how the KBM works, which in the case of fixed-interest securities and purchases at -100 and constant nominal interest rates causes a reduction in the capital tied up, while the respective mathematical capital tie-up, and this is the emphasis, remains constant. In KBM, the investment expenditure for a period is compounded at the search interest rate e and the nominal interest payment accruing to the investor is deducted. In the security example from Table 1, the compounding is carried out with e =10 percent and at the same time 10 percent nominal interest is deducted.
This procedure is continued step by step until the end of the investment and the respective arithmetic, also calculatory or pagatoric, capital commitment remains constant, but not the simple capital commitment (without interest) mentioned above. The latter is real, while the notional capital commitment is fictitious. The arithmetical average capital commitment over the term is derived from the respective arithmetical capital commitment (simple average).
It changes with every change in the value of an investment and in very few cases it coincides with the capital invested by the investor. Depending on the structure of the investment series and thus the form of investment, the average capital tied up mathematically may be far below or far above the real capital invested. This is shown by the practical investigations of the individual forms of participation in the grey capital market using the KBM method.
If the arithmetic average capital employed differs from the capital invested, this ratio will be of no use to the investor because he is interested in the return and profitability of his capital employed and not in the return on a fictitious figure such as the arithmetic average capital employed (DDGK).
It will go too far to continue the KBM at this point. We simply wanted to explain why the rationale for not comparing IRR results has nothing to do with the constancy of the arithmetic average capital commitment, as the prospectus author states.
The IRR results cannot be compared because the different IRR return results also imply different (not equal) reinvestment rates and therefore distort the original investment structure. A comparison can only be made using the return on the original series of payments for the same investment period and the same capital investment, but with a reinvestment interest rate of 0 percent. This simultaneously determines the return on the parent investment, which allows the comparison to be made. To show this, we use the formula for the IRR terminal value calculation, in which the returns Rt are compounded with the interest rate r over the respective remaining investment term n-t:
n
Σ Rt *(1+r)n-t
t=0
If the reinvestment interest rate r is set to 0 percent, then the expression (1+r)n-t and (1+0)n-t, respectively, will always equal 1, so the terminal value of the parent investment reduces to the simple sum of all recoveries. n n
Σ Rt *(1+r)n-t = Σ Rt *1
t=0 t=0
Thus, the terminal value of the parent investment (without reinvestment of the reflows) is exactly the simple sum of all reflows. This is a perplexing result, but formally and economically correct, because no reinvestment should take place. The uniformity interest rate, which links the initial value of the parent investment to the final value of the parent investment, is 5.32 percent per annum, which is below the IRR return, which was to be expected.
If we calculate the original series of payments of an alternative investment with the same investment period and the same capital investment at 0 percent reinvestment interest, then both return ratios can be compared.
In the event that capital investments and/or investment periods differ from one another, we have developed a method of making them comparable.
The question posed at the beginning of this article as to what constitutes a return on investment can be made more precise, right to the point. What is presented in the prospectuses on IRR is largely a hodgepodge of different return statements from individual return methods, without revealing the real context and presenting the investor with a clear and unambiguous return figure.
The prospectus statements on the IRR return method cannot be put into legal perspective either, because the mathematical method is unalterably fixed and there is no financial mathematical leeway for legal interpretations and interpretations. An extremely weak argument is that some recent prospectuses state that the explanations of the IRR method are “only suitable for those investors who have knowledge of financial mathematics and know how to interpret the IRR correctly”.
Which side, one wonders, are the prospect writers really on? On the side of knowledge or on the side of ignorance? Are the representatives of the IRR method really aware of the fact that the IRR promises too much return (bogus return) and thus triggers liability issues with considerable sums of damages, which at least make the investor think about whom he can turn to if the IRR return advertised in the prospectuses cannot occur at all with clever recalculation.
Who pays the investor the additional interest that the IRR automatically and notionally generates if no reinvestment is planned and who pays if the strict conditions of the IRR reinvestment cannot be met? It does no good to deny the reinvestment premise in IRR. It is there and it is working, even if it is hidden. It is easy to prove mathematically.
From the point of view of liability, not only initiators, prospectus auditors, rating agencies, banks and distributors, auditors, tax advisors and investment advisors should be aware of the differences, but also lawyers should take note of the fact that incorrect statements on returns trigger liability claims. This is particularly true for all users of the IRR method.
The users of the IRR represent a sales interest using the IRR return (IRR return as a sales catalyst) because in this method fictitious, in reality non-existent, additional interest is exploited. In reality, it is usually not possible to achieve this or it is not provided for in the product concept of the providers of closed-end funds.
Neither as external reinvestment nor as reinvestment of the distributions in the subscribed fund investment. Heinz Gerlach rightly speaks of an (inflated) “silicon yield “4 in the IRR yield valuation, which advertises inflated yield values from fictitious additional interest.
The use of the IRR yield thus constitutes investor deception within the objective elements of the offence under Section 263 of the German Criminal Code (StGB) or capital investment fraud under Section 264a of the German Criminal Code (StGB).

### Concluding remarks on the IRR yield

Using a final example from the industrial sector, we want to drastically illustrate the manipulation possibilities in the IRR methodology and switch to the maturity-based approach:
An industrial company plans to invest -20,000 units and expects a total liquidity surplus of only 250 units after fluctuating returns. Nevertheless, the IRR method shows an IRR return of 25 percent per annum. It occurs to the shrewd finance guy at the house that IRR returns could be boosted by just spreading the investment expense maturities over more than one point in time.
We see the original payment series in Table 7 in column 2. In column 3, we divide the capital expenditure of -20,000 GE into two instalments and postpone the second instalment of also -10,000 to 1.7.2005. In column 4, we again move the second installment to an even later date, 12/1/2005. Finally, in the last column, the second instalment finds its place one day before the first reflux on 30.12.2005. The other reflows remain unchanged and the simple liquidity surplus is always only 250 GE.
However : In the maturity-exact IRR yield statement, which is very easy to determine and check using the maturity-exact EXCEL formula XINTZINSFUSS, we can use it to pump up the IRR yield from 25 percent per annum to 349.548 percent per annum. The elasticity of the IRR results with respect to time shifts shows unexpected results that completely expose the manipulation possibilities of the IRR method and lead it ad absurdum. <

Authors

Johannes Fiala, lawyer, Master of Mediation (MM), banker and business economist (MBA), certified financial and investment advisor, has been advising independent financial service providers, in particular insurance brokers and agents, capital investors and distributors on the subject of consulting and prospectus liability for years. For two decades he gained experience in the fiduciary handling or administration of corporate and estate assets, real estate and securities – also by court order.

The financial analyst and financial service provider Dipl.-Kfm. Edmund J.Ranosch developed the RKRM return method from analysis results With this method, he exactly measures the return on the capital investment and takes into account how the returns can be reinvested with 0 percent (basis of the return of the parent payment series), but also with any investment interest rate. Since even investments that have fallen or even require restructuring can be properly handled with this method by introducing debit and credit interest on the RKRM current account, his method is valid and applicable to all types of investments, which cannot be said of the IRR and similar return methods at all.
Today, all investment series can be searched quickly and reliably with the RKRM and the investor can calculate all capital investments with the RKRM and compare them with each other in a mathematically and economically correct manner. This points to the basis of all the profitability and return analyses he has offered and published in his eight essays.

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Dr. Johannes Fiala
PhD, MBA, MM

Dr. Johannes Fiala has been working for more than 25 years as a lawyer and attorney with his own law firm in Munich. He is intensively involved in real estate, financial law, tax and insurance law. The numerous stages of his professional career enable him to provide his clients with comprehensive advice and to act as a lawyer in the event of disputes.