The Stuttgart public prosecutor’s office, white-collar crime division, evaluates the deception of investors by misleading yield information according to the internal rate of return method, also known as IRR yield, as an objective fact of investment fraud according to § 264 a StGB. The opinion was first published in February 2005. More and more investors are being motivated to invest their money and capital in closed-end funds and investment companies.

In the last few years, investors have been increasingly deceived by initiators, financial advisors and investment brokers. In concrete terms, beautiful glossy brochures state a return that is completely unrealistic. This yield is then referred to in the fine print as the “Internal rate of return” or “IRR yield”. The enormous potential for deception is clearly illustrated by the example of a recently placed TV production fund, in which a 0.53% annual distribution turns into an IRR yield of 6.6 to 7.1% p.a.

The investor should be aware that advertising with such yield information is deceptive and misleading. Numerous German courts have already established this with legal force (see also www.ANLEGERSCHUTZAUSKUNFT.de). For the investor, this means that various persons are liable for giving incorrect advice. For example, this includes the prospectus auditor. The allegations made by deceived investors may be subject to competition, liability and criminal law. Here, there is a liability potential in the billions that is not yet time-barred. Investors can usually get their money back from placing banks and financial service providers, as the predominant claims from recent years are not yet time-barred. In addition to the financial sales companies or banks, the advisors are also regularly personally liable to the aggrieved investor.

#### The following is a brief technical information on the calculation of returns:

If the customer has been demonstrably informed about the differences, he cannot claim anything later, which reads something like this as an expert’s assignment:

**“Judicial order to provide evidence: Evidence must be obtained on the question of whether the calculation of the return on investment submitted by the defendant (intermediary) was unrealistic … by obtaining an expert opinion. The expert witness will be selected from… “.**

### 1. simple return:

This return considers the return of a single investment period. Return is the percentage growth of an investment with a one-time interest payment at the end of the investment period. In other words, change in value divided by value at the beginning of the period.

Example: 100 euros are created on a passbook on 01.01.2005. On 31.12.2005, EUR 2 interest will be credited. Yields are 2/100 = 0.02 = 2%.

### 2. tricks with the average yield:

The average return considers the return of several investment periods. If the return is to be calculated over several periods, the compound interest effect must be taken into account. If this is not done, the yield indication will be too high. This is the case when the arithmetic mean is used in the calculation instead of the geometric average, which is correct because of the compound interest effect.

#### Basic example:

An investment over 5 periods/years generated the following percentages at year-end: -16.2%, 10.5%, 55.4%, 1.0% and 18.9%.

There are no inflows or outflows of funds, but the money is reinvested.

a) The total return would be 69.6% in arithmetical terms. The arithmetic average return from the total return would be: 69.6%/5 = 13.9%

b) The geometric average return from the total return would be: 11.5%. The compound interest effect is correctly taken into account.

### 3. tricks of the trade for money inflows and outflows:

The inflows and outflows of funds are also referred to as cash flow. If there are inflows and outflows during the investment period (e.g. tax refunds, distributions, deposits through additional contributions), there are two approaches according to financial market theory: Either I adjust the cash flows or I weight the return with the invested capital. These two calculations of a cash flow return are referred to as “cash return” and “time return” respectively. The above “basic example” is taken up again here with the same annual returns.

#### The return on investment:

The cash yield is also known as the internal rate of return or internal rate of return method (abbreviated: IRR). With this “money value-weighted average return” – the achieved return is “weighted” with invested assets – and thus the result depends on the timing of the inflows and outflows !

*aa) Money yield example 1: With the above return (in percent: – 16.2%, 10.5%, 55.4%, 1.0% and 18.9%.), an initial investment of 10,000 euros was made. At the beginning of the 3rd period 3.000 Euro AB and one year later 3.000 Euro are received. Mathematically, the initial assets and all cash flows are compounded with the ONE total return to be determined, so that the final sum corresponds to the total value of the investment/portfolio. In this case, the calculated return would be 9.3%.*

*bb) Money yield example 2: At the beginning of the third period, EUR 3,000 is added and one year later EUR 3,000 is withdrawn. Let us recall that in the third year we had assumed a return of 55.4%. In this example variant, the calculated return would be 13.4%.*

### Overview:

The calculation corresponds to the internal rate of return (interest rate) of the crash flow electricity. The consequence is a dependence on the timing of cash inflows and outflows. This is justified by self-proclaimed experts in the manner of a prayer wheel, saying that it would be the “return on average capital employed”: However, this is only a cheap half-truth, because this “interest” can be represented with the so-called time yield also independently of inflows and outflows of funds.

### Criticism:

The initiator of a closed investment has it with the money yield – also called internal rate of return method – in the hand to manipulate the cash inflows and outflows of a forecast at will in order to be able to represent the “desired” yield result (above: 9.3% or 13.4%). Since the inflows and outflows in investment prospectuses and sample calculations are regularly not identical, it is not even possible to compare the yield data of two closed investments using the internal rate of return method. A small group of self-appointed experts has been trying for many years to postulate an “industry consensus” as a dogma in the interest of some initiators and distributors. In a recent “newsletter telegram”, such an expert made the following statement: It would be a mistake for the prevailing scientific opinion in business administration to dismiss the internal rate of return as merely a “theoretical value”. A villain who thinks evil of it. The investment industry pretends that the objective method of time returns does not exist.

### Time yield:

With this “time-weighted average return”, the measure of return is “adjusted” for cash flows, and thus the investment return is shown independently of inflows and outflows. The return over time is therefore “adjusted” for cash flows: it reflects exclusively the average return generated on the fluctuating asset portfolio. In concrete terms, the mathematical result of the above example, and naturally also of the above example variant, is a time yield of 11.5% (the inflows and outflows of funds have no influence on the result). You remember – the same result had already been achieved with the above “geometric return”. To put it succinctly: “Miracle oh miracle – the same will come out as in the basic example above.” The fact that the time yield is independent of cash inflows and outflows is something that initiators and so-called renowned experts are apparently quite happy to conceal “on the pay-roll of some initiators” with good reason: because, unlike the internal rate of return method, no manipulation of the result by cash inflows and outflows is possible here.

### 4th VOFI yield:

Another form of presentation of the return is the method of the complete finance plan (VOFI). This variant represents an extension of the money or time yield, since it is possible to take different interest rates for debit and credit interest into account. For presentation purposes, all payments are booked into a fictitious account – from the investor’s deposit to the initiator’s final payment.

In practical terms, this not only makes it possible to show the interest on the initial deposit, but also to make transparent those effects caused by – on the one hand, borrowing to acquire a shareholding with an often higher debit interest rate – and on the other hand, investing the distributions, tax refunds etc. with a credit interest rate that is lower in practice.

The decisive question here is which interest rates for debit and credit interest are assumed to be realistic and in line with market conditions: A typical manipulation in this area often goes so far as to assume an equally high interest rate, which of course is not realistic. In practice, this method is preferable if the investment was financed on credit. The result of this key return figure is regularly significantly lower than, for example, a so-called internal return.

### 5. cardinal error about the internal rate of return method:

It would be a fatal mistake to believe that the internal rate of return method is a good benchmark, especially for investments with staggered payments in and out. This is only conceivable in the extremely rare case where cash inflows and outflows are equal. Two extreme cases can be compared:

**Additional example 1: Investment period of 10 years. Investment 100,000 € in a zero bond. Payment after 10 years 196,715.14 €. Internal rate of return 7,0**

**Supplementary example 2: Investment of 100,000 € in a participation. Distribution of € 7,000 annually at the end of the first to ninth year, a total of € 63,000. Payment after 10 years 107,000 €.**

Total payout within 10 years 170,000.00 €. Internal rate of return 7,0 % In the first case, the investor has accumulated 196.715 € after 10 years, in the second case 170.000 €, although the internal rate of return is identical. That’s the gist of the poodle!

#### Bottom line:

The two plants are not identical in terms of cash flow. In example 1 the income is reinvested – in example 2 the distribution is made. It is a completely different side of the coin when it comes to the question of how realistic and well-founded the forecast or the planning of the distributions by the initiator was in the prospectus.

### 6. summary:

It is a completely different story that § 2b of the Income Tax Act has been defused for the initiators, in that returns based on the internal rate of return are sufficient to classify an investment as not tax-damaging. This applies analogously to the corresponding calculation of the so-called effective interest rate in accordance with the Price Indication Ordinance when granting credit. This is a political decision to promote so-called tax saving models. From the point of view of a capital investor it is important that – yield data are transparent, § 307 BGB, – and not suitable for deceiving investors, §§ 263, 264 a StGB. This has absolutely nothing to do with an “industry consensus” of the initiators. This is about the objective, complete and correct presentation, based on financial mathematical considerations.

#### Bottom line:

Anyone who uses the “internal rate of return method” (IRR) or internal rate of return method must reckon with the fact that such disclosures will be treated as investment fraud. It is therefore not sufficient to merely state “that these IRR figures are not suitable for comparison between different investment products”. Rather, it would also have to be disclosed that the inflows and outflows of funds (cash flow) assumed by the prospectus designer in his sample calculation can have a considerable (theoretically also manipulative) influence on the yield level.

It would also have to be revealed that this return calculation assumes, particularly in the case of inflows and outflows, that the capital can be reinvested on the market at the same interest rate. Since a lower interest rate is regularly paid on the market for shorter investment periods (exception: inverse interest rate structure), the “internal” return increases artificially and turns out to be unrealistic. Investors must be protected from the possibility that they might think that the internal rate of return would correspond to the interest on the amount they had invested at the beginning of their investment. The “internal rate of return” deviates even more blatantly from reality from the investor’s point of view, if he has financed the inflow of funds to the initiator for high debit interest by means of a loan, and can only earn modest credit interest on the capital market when investing released cash flows.

by Dr. Johannes Fiala

by courtesy of

www.gomopa.net (published on 23.09.2005)

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## About the author

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.

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