Returns are of central importance in the professional life of a banker. Other financial service providers, such as pension funds, financial and investment advisors and credit intermediaries are also affected. The circle of affected professions also includes the rating agency and many a tax consultant/auditor (StB/WP) who is active in connection with Basel II. Often the considerations of the parties involved are about the ability to service the debt.

The key question then is whether the borrower’s earnings provide sufficient assurance that the borrower can meet its obligations?

In particular, the �house and court reporters� in the guise of supposedly independent �analysts� have been trying for many years to create confusion about the concept of returns. All too often, the focus of their efforts is to present the so-called internal rate of return (also known as IRR or money yield or internal rate of return method) as an objective benchmark, although in fact it is at best a synthetic ratio.

The IRR does not even allow a reliable comparison between two closed investments in terms of profitability or debt service capacity.

Knowledge of the interrelationships is not only necessary for one’s own money and capital investment. On the contrary, avoidable errors can also give rise to criminal-law connecting factors’. One approach to give the IRR the quality of a means of criminal deception is the fact that in this method (as is never found in reality) the distributions or deposits outside the participation bear an identical interest rate �rentierlich�.

It is not uncommon for pension funds or private investors to then finance their capital investments, after having made a mistake about the IRR, by means of an only supposedly lower lending rate: asset losses are thus equally certain.

This also includes the banker’s duty to avoid endangering the assets of his own credit institution (§ 266 StGB) or not to participate in capital investment fraud (§264 a StGB). In civil tort law, there is often a threat of rescission in this context � including the fact that indirectly affected insurers will always refer to the fact that criminal conduct is regularly not insured or insurable. This must also be taken into account when rating.

Ratings �are often merely opinions based on assessments of a probable future development � such as creditworthiness or the certainty with which certain returns can be generated�2. In this context, it is not only the assessment of future developments that is important, but also the upstream question of whether the method of measuring returns already contains fundamental misjudgements, because the method used already implies assumptions of which the decision-maker is not aware and which, if he had known, he might have made a different decision.

� The expert is liable to the consumer if he gives wrong advice for a product decision. According to § 675 II of the German Civil Code (BGB), case law already attaches liability to a tacitly concluded contract for advice and information if (viewed objectively) the advice or information is recognisably of considerable importance for the recipient and it constitutes a basis for essential measures or decisions for the recipient. In particular, the nature, reason and purpose of the information and advice, the economic significance for the recipient, the technical and expert knowledge of the person providing the information or advice and the legal or economic interest of the parties to the contract play a role�’.

In principle, the advisor or the person providing the information has to resolve the question of the extent to which the product offered can fulfil the investment objectives and wishes of the investor or whether he must advise against purchasing the product. In doing so, he will examine the product features and confirm or reject the congruence with the investor’s expectations. As a rule, in addition to product-specific questions, he has to examine the general investment criteria such as economic, legal and tax security, the investment period, fungibility, costs, return on capital employed as well as the tax implications and inflation protection of the proposed investment alternatives. Both the advisor and product manufacturer and/or Konzeptionär and/or initiator or also the merged credit institutes avail themselves strengthened of the services the concentrated expert knowledge of the Ratingagenturen. In general, the investor wants to increase his assets with a capital investment and aims to achieve the highest possible return� at a given risk. A return method per se cannot evaluate the uncertainty or security of cash flows and only evaluates the cash flows in financial mathematical terms, whether retrospectively or prospectively. The question of certainty or uncertainty cannot be answered by the dynamic return methods to begin with.’ Here, only the answer to the question whether the in practice �indestructible� Internal Rate of Return (IRR) method, the MISF method` and the Capital Commitment Method (CBM) show the investor the right way to the return of his capital investment is examined. The investor’s way of thinking is dominated by the question of how his capital investment will earn interest so that his asset position at the end of the investment period is comparably higher than the alternatives he has chosen. Thus, in addition to the primary determination of the return on his capital investment, he unspokenly demands a central decision criterion for the comparability of the returns of alternative investments. Whether this requirement can be met with the return methods examined is left to the final considerations.

When he published the internal rate of return (IRR) method in 1930, the American economist Irving Fisher would never have dreamed of the fuss his IRR method would cause and keep generations of business administration professors busy for decades, even in German-speaking countries, trying to clarify the old controversial question of whether or not the IRR has an ‘implicit reinvestment premise’. Apart from all mathematical objections to multiple changes of sign and the occurrence of several solutions due to the polynomial equations, the question remains as to how the mathematical results can be interpreted correctly from an economic point of view and how a yield ratio can be transformed from the special discounting process and the discount rate found, which ultimately reflects the return on a capital investment. To illustrate the IRR, we use the following example in Table 1, which we also vary later.

In the simple case of compact IRR investment spending, in the first way of IRR terminal value determination, all returns R, are compounded with the IRR interest rate r and with the remaining investment period n-t in the Leibniz equation. If the final value is discounted back to the beginning by n years with the interest rate r, the initial IRR value is obtained. via the first path of reinvesting all reflows at the IRR interest rate, one obtains a final IRR value of 275,734, which exceeds the pure reflow amount by the additional interest of 65,734.

The IRR interest rate r = 10.14 percent is found by discounting all investment values whose balance results in zero. This is shown in Table 2: via discounting, the return flows are mathematically reduced by the interest income in such a way that the present values of the return flows in their sum correspond to the present value of the IRR investment expenditure and thus satisfy the IRR determination equation and the net present value = 0. This procedure corresponds to the classical approach of the internal rate of return method.

The first way also shows the transformation of the discount rate into an IRR return ratio by the reinvestment assumption (WAP) working in the background. Due to the WAP implanted in the IRR method, the reinvestment of the return flows generates the additional investments from the subsidiary investments and their return flows in turn generate additional investments of the grandchild investments, etc. until the end of the investment period of the parent investment. Mathematically, the WAP is documented in the compound interest effect with (1+r)n and (1+r)n-t, respectively. The automatic reinvestment effect is also evident via a second route that practitioners can trace in Table 3: The basic consideration is the accumulation of returns in an IRR return account, while the IRR investment expense is left out. The reflux account begins with the account beginning balance equal to the first reflux, which is credited with IRR interest at the end of the second period at the IRR interest rate of 10.14 percent per annum in the amount of 1,014. At the same time, the R account balance increases by the reflux of 10,000 as an inflow at the end of the second period to a total of 21,014. After a further period, the IRR interest of 2,130 is again credited and the reflux of the third year is added to the account balance of 33,144. This familiar posting sequence continues to the end of the investment period and the final account balance at the end of the investment period is exactly 275,734, which we have already encountered as the final IRR value in the first IRR path. Thus, the arithmetical reinvestment def’ return flows is explicitly also at the IRR interest rate r. The additional interest volume from the reinvestment in Table 3a is also 65,734 as in the first way in Table 1.

It is evident in Tables 3a and 3b that the additional interest from reinvestment lifts the reflows account to the final account balance of 275,734, which is higher than the pure reflows of 210,000 (excluding reinvestment interest) by the reinvestment interest volume of 65,734. The PIPO case9 in the mixed initial value-final value concept shows the financial mathematical connection of the initial value via the IRR interest rate r during the investment period n up to the IRR final value. We follow this third way to prove automatic reinvestment in the IRR method in Table 4:

The economic significance of the IRR rate of return r can now be derived from the development of the initial value L. in Table 4: The IRR rate of return r is the rate of return on the IRR investment expenditure up to the end of the investment if the interim returns are immediately reinvested at the interest rate r without exception’�.

All three paths to the IRR terminal value are independently irchable and work only under the reinvestment premise of the IRR method. We will spare the formal mathematical proof for reasons of space. The strict mathematical reinvestment conditions in the compound interest effect look as follows in economic implementation: Only if these arithmetical conditions of the IRR reinvestment can also be exactly fulfilled in the practice of the capital investments, the return on the capital investment succeeds at the IRR rate of return r.

In practical terms, there is only the zero bond, which reflects the reinvestment without costs with reinvestment of the interest and represents the prototype of the IRR interest because the reinvestment system is used there.

When using the IRR method, automatic reinvestment is also system. If an investor wants to meet the IRR return, he must meet the above conditions. If he does not succeed in doing so, and in practice it will be extremely difficult or even impossible, then he will not achieve the return shown in the prospectus. Logically, only a re-investor of his returns can enjoy the higher IRR “return” at all, because the IRR automatically includes additional interest as additional income in the final IRR value. Investors or investors who consume the returns sooner or later or give them away to children, grandchildren, et cetera, cannot earn reinvestment interest, even partial reinvestment, at the required rate. Thus, they do not earn the IRR rate of return shown in the prospectus.” All users and adopters of the IRR method need to be aware of this. Concealment of the unconditional IRR reinvestment requirement is to be regarded as an act of deception giving rise to liability under Section 823 of the German Civil Code, or as the concealment of adverse information in Section 264a of the German Criminal Code. Thus, every IRR user is at risk of liability.

In addition to initiators, auditors, sales pools, investment brokers, investment advisors inside and outside of banks, share-financing banks and also for the tax advisors of the investors, transparency and complete, correct clarification is necessary. Rating firms that either only take the IRR from the prospectus or from the initiator or calculate it themselves must correctly point out the weaknesses of the methods and their informative value if they do not want to fall into the liability trap. The WAP trap continues with somewhat more complicated cash flows where equity rates are spread out over time and/or share financing is also used because of the leverage effect on the IRR yield ratio.

We vary the example and allocate the compact equity rate of 50 percent to the maturity at the beginning and the other 55 percent one year later. We increase the first distribution or the return of the second year by 10,000 to 20,000 so that the total return of 210,000 remains unaffected. It is not the increase in the IRR return, triggered by the subsequent EC payment, that matters, but only the determination of the IRR investment expenditure.

The IRR method rigorously discounts all cash flows and sets all negative present values (present values) as IRR investment expense’2, which presents as a point input of -99,611. via the familiar first path of separate compounding of all positive recoveries, we arrive at the final IRR value of now 279,367. It is higher than in Table 1 because the central, sole IRR interest rate r of 10.86 percent per annum is discounted more strongly and also reflects a higher reinvestment interest rate.

In this constellation, the IRR interest rate instrumentally performs the following tasks:

1. it serves as the discount rate for determining the IRR cash value (in economic terms: IRRlnvestment expenditure).

2. it serves as a long-term reinvestment z�n rate of returns to form the IRR terminal value.

3. somewhat hidden, he also presents the short-term re-arriage rate azK = r, with whose . Help to get from the present value of the EC rates, through their compounding, exactly back to the original time-distributed EC rates. 4. 4. ultimately, the IRR rate r embodies the IRR return of the investment series as a result of the computational effort.

The interest rate r has its fifth and final instrumental effect if the investment expenditure is financed with debt capital in addition to own funds”. The variation of the investment payment series is now such that the second EK rate of -55,000 listed in Table 5 is fully financed with a five-year loan at six percent per annum nominal interest and after five years the loan is fully repaid. It is immediately apparent from Table 6 that the debt service from interest and redemption instalments cannot be fully covered by the reflows and that the investor must therefore make additional payments. How does the IRR method deal with this?

It is easy to see that the IRR ratio rises from 10.86 per cent to 12.24 per cent per annum (arithmetical leverage effect). The discount rate of 12.24 percent per annum is calculated againi. from the IRR determination equation, according to which the Sal of all present values must become zero, as can be seen in Table 7.

As a result of the financing costs of -10,284 and the repayment of the loan of -55,000 from the share financing, the return flows before share financing will be reduced from 210,000 to 154,943 (210,000 – 55,0C 10,284 + 10,228) incl. the repayment of the loan of -55,000 from the share financing. of co-payments in the years to 6 (10,228). Nonetheless, the IRR rate of return is rising because the IRR investment expense has been lowered more.

The IRR investment expenditure is calculated in the first way from all present values of all negative investments and the final IRR value results as the sum of all returns from Table 8 in the amount of v 178,600 compounded at the new IRR rate of return r = 12.24 percent per ans. The table shows that a positive return of only 154,943 can only generate reinvestment interest of 23,657 in the IRR. This is reflected in the final IRR value na share financing of 178,600 in total. The IP present value or IRR capital expenditure Table 8 is found to be -56,270. In the PIPO case, the IRR investment expenditure and the IRR terminal value combine financially to yield 12.24 percent per annum over the ten-year investment period (Leibniz equation).

In reviewing the second path to the IRR terminal value path, we consider Table 9, in which all returns are accumulated in the IRR return account, or account balance at the end of each year earns interest at the IRR rate. These are added to the account balance as reinvestment interest and reach the amount of 13,981. It is noteworthy here that at the end of the sixth year, there is a debit balance in this reflux account of -1,520, which requires IRR target interest of -186 and is based on the IRR interest rate of 12.24 percent per annum. Since there is only one central interest rate r in the IRR method, this also serves instrumentally as the lending rate (5th task of the IRR interest rate).

All investment flows (positive return flows and negative additional payments from the unit financing) add up (without interest) in the return flow account to 144,715 plus 13,981 balance of interest volume) to the final IRR value of 158,696. In terms of financial mathematics, this final value is matched by the initial equity investment of -50,000, which, compounded at the rate of return r = 12.24 percent per annum, yields exactly this IRR final value’�.

On the third path, we again achieve the IRR return rate of 12.24 percent per annum only with a different IRR investment expense of -60,228 (IRR present value is now determined with the discount rate of 12.24 percent per annum) and a different IRR terminal value of 191,158 in ten years.

In the case of unit financing, the third IRR path shows that the IRR rate of return indicates the rate of return on the IRR investment expenditure when the positive return flows and the additional payments’= are multiplied by the IRR rate of return.

The reason for equal IRR return rates at different IRR investment expenditures and IRR terminal values lies in the endogenous determination of r, which performs all fiveinterest rate tasks simultaneously and coordinates the relevant absolute values �coordinates � in the IRR iteration procedure. Such a method, which controls the arithmetic capital employed and arithmetic IRR terminal value in the background and can only be reinterpreted into a return term via the automatic WAP, is useless for measuring the return on capital employed.

The definition of IRR used throughout the prospectuses is coupled there with the KBM statement that the IRR return is the return on the average ‘arithmetically’ committed total capital. Here, the interest rate interpretation of the capital commitment method is improperly �transplanted� into the classical IRR method. In the capital commitment method, we will address the �transplantation� of interpretive statements.

Dr. Johannes Fiala

Edmund J. Ranosch

(Credit & Rating Practice 06/2005, 20-27)

Courtesy ofwww.krp.ch.

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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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