Is li fi a practical concept
Practical concept for the economic assessment of investments
2 Diss. No. Practical Concept for the Economic Assessment of Investments Treatise on obtaining the title of Doctor of Technical Sciences from the Swiss Federal Institute of Technology in Zurich presented by Anton N. Fritschi Dipl. Ing.ETH born on January 26, 1945 Zwingen (Bern) Accepted upon application by Prof. Dr. W. F. Daenzer, speaker Prof. Dr. 0. Angehrn, co-referee 1972, Basel, in-house printer of CIBAGEIGY AG
3 Foreword This dissertation was written over the years. For the suggestion and direction of this work, I would like to thank Prof. Dr. W.F. Thank you very much Daenzer. Prof. Dr. 0. I am indebted to them for the critical reading of the manuscript, and I also include Dipl. Kfm. H. Siebert for his valuable contributions to the discussion.
4 Summary The procedure described is a practical procedure for determining and assessing the profitability of investment projects. The explanations are very detailed in accordance with the importance of the profitability of projects that have been applied for and approved for implementation. The calculation was based on the internal rate of return method. In addition to the return on investment, the return period and the risk are determined. In order to determine and assess the profitability of investments, the exchange of information should be facilitated by evaluating the projects according to the same considerations and making the determined results comparable and generally understandable. The method presented for determining and assessing the profitability of investments can be used for investments in both tangible and financial assets. The calculation method remains the same, while the data on which the profitability calculation is based are recorded in a differentiated manner. Depending on the complexity and importance of investment projects, it is advisable to adjust the intensity of the effort required to obtain the initial data. The additional effort that is usually incurred in large projects compared to small projects is not due to the calculation method, but is almost exclusively due to the part of the data acquisition. This is also where the main problems of an investment assessment lie. It seems obvious that with complex and risky investments a higher effort for the acquisition of the data is necessary and also justified. Furthermore, it should be worthwhile in the case of extensive investment projects to fully exploit the evaluation options provided by the calculation method (determination of the scatter areas).
5 des der der der der des The procedure for determining and assessing the profitability of investments can be presented as follows: Recognition of critical conditions and investment opportunities; [Acquisition of the necessary data Determination: I Total investment amount Annual return flow of funds, duration taking into account the data acquisition guidelines; Machine or manual calculation Return on investment Refund duration Risk Investment decision on gr and from Comparing the assessment I The implementation of profitability calculations can be carried out both before and after tax. In both cases, calculations can be carried out either manually or by machine. A computer program is available for machine invoices. Investments should never be viewed in isolation. Investment decisions must always be viewed and assessed in their overall framework.
6 Table of contents PART I: The theoretical principles of investment assessment 1. Introduction, definition and meaning of the investment 1.1. Introduction S Definition and meaning of the investment General Definition of the meaning of investment types Tangible assets Financial assets 6 2. Planning of investments 2.1. Investments in the context of business planning Investment planning Organization and process of investment planning Recognizing investment needs 3.1. Requirements for identifying the best investment needs Identifying investment needs in tangible and financial assets Reasons for identifying financial investments The decision-making process Assessment methods 5.1. Presentation of assessment methods Static methods Cost comparison calculation Profit comparison calculation Return flow calculation Profitability calculation Dynamic methods Net present value method Annuity method Internal rate of return or DCF method MAPI method Modern methods (investment program) Premises and objections when applying the assessment method Alternative comparison with different capital rates Alternative comparison with different 5.3. The relationship between the capital return flow rate 6 3 and the internal rate of return for the period 67
7 6. Selection and applicability of a suitable calculation method 6.1. Selection of the suitable calculation method S Applicability of the internal rate of return method Single investments Alternative investments Investment programs Replacement investments Rationalization investments Expansion investments Tangible and financial assets 86 PART II: Investment assessment in practice 7. Data acquisition for investment assessment 7.1. General The payment series as the basis of the investment assessment Definition of the payment series The material content of the values of the payment series Type and scope of data collection (elements) for the payment series Investment expenditure Amount and type of investment expenditure for property, plant and equipment Amount and type of investment expenditure for financial assets Determination of the value for Acquisition of a company Temporal distribution of investment expenditure for tangible and financial assets Return flow of funds Return flow of funds from investments in tangible assets Return flow of funds from investments in financial assets The term of the investment Definition General guidelines for estimating the useful life of tangible assets Term of financial assets Construction of the series of payments General procedure Effects on the series of payments, if An investment made up of several sub-properties with different terms consists of an inflow of taxes on investments 113
8 8. The financial evaluation criteria of investments 8.1.
9 9. Further areas of application of the internal rate of return method 9.1. General S Leasing Isolated consideration Purchase Leasing Calculation method in leasing Numerical example (before tax) Interpretation of interdependence of financing and investment Numerical example (after tax) Machine calculation method Example leasing or purchase Development work One-off total expenditure of a project Determining the return flow of funds Conception of the profitability calculation The development process Other capital dispositions, the do not represent an investment in the narrower sense
10 1 1. Introduction, definition and importance of the investment 1.1. Introduction The importance of investments and their sensible planning is increasing steadily for the increasingly capital-intensive economy and therefore occupies a very special and important position. So it is business economists, engineers, mathematicians and economists who strive for systematic methods. They have made significant progress. The importance of the investments follows from the fact that e.g. the investment requirement for equipping a workplace can exceed the million mark. In order to fulfill the task of every economic company to provide goods of a material 2) and immaterial nature, the company management is forced to plan its future well-being in advance. However, much remains controversial and unclear, such as the consideration of financing options and the treatment of "replacement investments". The previous work in the field of investments is incomplete in that one has only dealt too much with the investment calculation, which is mostly kept in abstract mathematical language. Important questions remained neglected, such as: the recognition of investment opportunities, the necessary data and information for an investment decision and, last but not least, investment planning within the company. This may be related to the fact that systematic methods of investment calculation and investment planning have still found relatively little use in business practice. Such methods undoubtedly deserve to be used, and it is to be expected that they will be used in 20 or 30 1) Cf. Frankfurter Allgemeine Zeitung No. 55 v article: "One million DM for one job". 2) Cf. Gutenberg E .: Fundamentals of Business Administration, Berlin, Gottingen, Heidelberg 1963 p. 1 ff.
11 2 years have been used just as generally as the methods of corporate accounting are used today »3) 1.2. Definition and importance of the investment General The importance of investments and their planning is constantly increasing for the capital-intensive economy. The existence of a company is only guaranteed over a longer period of time if it is run in a sensible manner. Economic activity, however, is characterized by the fact that money is spent with the aim and expectation of a later larger return flow of funds. Good "business" means, among other things, good "investing". These two terms are largely identical. It follows that investment problems are of great importance. Investment projects must be systematically examined for their effects. A substantial part of these studies relates to the question of economic viability in order to enable the management to assess the investment project in two ways: a) Profitability of the capital employed per se b) Selection of projects with limited financial resources Definition If in general with Every expenditure of money with the aim of greater monetary income is an investment, must be limited for practical reasons: An investment project is understood as a commitment of funds in tangible and financial assets that cannot be resolved in the short term to achieve the global corporate goals set by the management. 3) See Trechsel, F .: Investment planning and investment accounting, Verlag Haupt, BernStuttgart, 196 5, p. 11.
12 Admission 3 All expenses and income associated with the investment project (including the change in the amount of current assets) must be taken into account for its assessment. The global corporate goals include technical goals as well as goals relating to sales and profitability. »These three types of goals are inextricably linked and are intended to maintain and strengthen the company. The calculation method for projects can also be used for the assessment of investments, the assessment of projects of a different nature (e.g. leasing, development, etc.) This can be achieved by: rationalizing new products in the range, increasing the market share, etc. The last two sizes have the character of an expansion. Investments provide an opportunity for necessary adjustments. Decisions about investments are effective in the long term and their economic consequences can only be corrected to a limited extent. On the other hand, the risks associated with investing should not be underestimated. Investment risk is a major component of general business risk. In particular, there is the risk of not or incomplete recovery of the medium and / or of not achieving the financial forecasted profitability used.
13 Replacement security investment 4 The need to deal explicitly with investment risks will increase, since the investment sums to be raised per project, the individual projects become more complex and the usage times tend to decrease due to the rapid technical development. Io204 Types of investment Investments in the business sense differ according to the type of their use in tangible assets and in financial assets o I.2.4.I. Tangible assets Tangible assets include land, buildings, auxiliary structures, machines and mechanical systems, movables (factory and office equipment) and, in certain cases, operating resources (fixtures, tools, etc.). They are divided into: a) Basic investment when setting up a business b) Maintenance investment (in the traditional range) = reinvestment, pure maintenance of the substance (including major repairs) Rationalization and modernization Adaptation (technical progress, cooperation, conversion) (accident prevention, stockpiling in the event of a crisis, legal regulations) Expansion investment (in existing or new range) Expansion of business activities, e.g. Eliminating bottlenecks by expanding existing plants Creating new foundations for business activities, e.g. new plants
14 Rationall 5 d) Additional investments Quantitative change in capacity (capacity expansion by adding the same elements) e) Mixed investments Combined investments from maintenance and expansion (b, c, d) f) Social investments Expenses for employees who prove useful for the company g) Security investments Investments to prevent damaging events or to limit their effects (war supplies, war provisions) h) Investments according to requirements Expenditures to comply with legal regulations (environmental pollution) For the assessment, the above types of investments are reduced to one of the four basic types, namely to expansion investments Replacement investments Other (social investments, additional investments, etc.) For the calculation procedure presented in Chapter 8, it is necessary to divide all calculable investment projects into one of the first three basic types, since the assessment procedures differentiated according to the above types and the data acquisition also takes place differently depending on the basic type (cf. also Chapter 7).
15 6 As Gutenberg also shows in a study, the pure replacement investment is very rare. Most of the time, property, plant and equipment are replaced before they are completely unusable, or they are not only replaced, but also rationalized Financial asset, if the company continues to exist independently, or a tangible asset, if it is integrated into the parent company. Financial resources that are held as a liquidity reserve are not financial assets in the sense of the above definition. 4) Gutenberg, E: Investigations into the investment decisions of industrial companies, Cologne 1959, p. 36.
16 7 2. Planning of investments 2.1. Investments within the framework of the company plan for the future must not be based on intuition. Rather, the company management should make use of a planning that is based on a careful analysis of every element of corporate events and business. Planning can be defined as a well thought-out attempt to foresee the future as well as possible and to act in such a way that an individual enterprise can at least continue to exist, but better still increase its profits and the security of its existence, and if possible to the greatest extent possible. One plan that is subordinate to the business plan of future business operations is of particular importance: the investment plan. The task of investment planning can be seen in the long-term harmonization of operational performance through the use of funds. The investment planning should take into account all changes to be made to the means of production. This includes all considerations about the necessity and expediency and the implementation of investments. The planning process for investments is carried out over 3 levels of complexity: Level of complexity I Assessment of an individual investment "II Assessment of alternative investments" III Compilation of an investment program or plan
17 8 The aim of the considerations is to draw up the investment program as a partial plan of the business plan. Complexity level I forms the basis for this. To assess the individual investments, the data for future performance and cost development are derived from the sales plan of the sales department, from the production program of the factory, from the development program of the technical departments, from the personnel planning, etc.In general, when planning investments, the data for their assessment, which are derived from the company planning, are much more well-founded than those which have to be estimated in isolation for the profitability calculation at the moment of the investment decision. Whether a given organization of investment planning is good Small projects to reduce costs and improve production methods place different demands on the organization than large projects with which the company ventures into new areas. The method and procedure, however, should not change. Small investment applications are usually created in the production departments and passed on to management or staff units for assessment and approval, while the largest projects are developed and examined by management itself. Large investments are comparatively less frequent than small investments, but they are of great importance. The assessment must be carried out by a team of specialists or senior executives. 5) Terborgh: Guide to corporate investment policy Betriebswirtschaftlicher Verlag Dr. Th. Gabler, Wiesbaden 1962, p. 49.
18 9 It is not possible to propose a generally applicable, optimally applicable organizational plan. In addition to other variables, the organizational structure has a decisive influence on: type and size of the company, condition, properties and type of production facilities and quality of the management. In order to fully and promptly forward investments to the company management and to inform them, a staff group or an employee in smaller companies should monitor the situation, collect the necessary data and forward them. It is a common illusion that investment research can be done by any intelligent person. This is a difficult and demanding task that requires experience and special training. Like any other sophisticated technology, it should be in the hands of reliable specialists. Many companies still trust in good faith and recklessly that the spontaneous suggestions for making investments made by the employees in the production departments guarantee the necessary comprehensive information. But experience shows us the opposite. Such an approach is unsystematic and random. It is not only useful to carry out this specialization in order to achieve better calculations of individual projects, but also to centralize the execution of the calculation itself. But that does not mean that all investment projects should also be carried out by specialists. Impulses and suggestions should and can come from the line, i.e. the workforce, but must run through the hands of the specialist. This carries out the formal analysis with the production people. However, he must also have the opportunity to carry out investigations and suggestions on his own initiative.
19 10 The decentralized production or line people know the operating process best, so it goes without saying that most of the ideas and suggestions for investment projects come from them. This possibility must continue to be demanded. A survey gave the following picture: 61% of plant or department heads 14% of engineers or foremen 13% of company management 7% of foremen 5% of others The ideas and suggestions from the company and applications must, however, be systematically and continuously checked by a specialist, because the line people often do not have the opportunity to assess their applications independently of their surroundings and with the necessary foresight, on the other hand they very often lack the time and necessary for such a task Attention to examine them thoroughly. The main task for a specialist, however, is to stay up to date technically, organizationally and in terms of corporate policy in order to recognize and assess the investment and its value in the overall framework with the necessary background. It is therefore necessary that there is only the closest imaginable cooperation between specialists and company employees at all levels. Cooperation with the top of the company is no less necessary, i.e. communication in both directions and mutual trust are the prerequisites for a healthy, successful investment policy. These requirements are rarely met in full, and even more rarely quickly. Time and extensive experience in the field of investments as well as in the technical field are required to develop a good organization. The success then pays off like hardly in any other area. 6) Terborgh: Guide to corporate investment policy, p.52 Betriebswirtschaftlicher Verlag Dr. Th. Gabler, Wiesbaden 62.
20 Organization and process of investment planning In order to be able to identify investment opportunities, the operating process must be subject to ongoing and systematic reviews. These investment opportunities, which are a continuously updated list of all desirable investment projects in the order of their urgency, can only be assessed using a reliable calculation method. The follow-up control of the investments made is just as important as the actual assessment. Before the actual planning work, the planning documents must be cleaned up, i.e. the latest company goals and principles as well as developments in marketing, sales and technology must be known. Before the detailed plans are created, a general planning concept must be drawn up and approved. Although the investment planning consists in achieving an optimal and all-round coordination of the investment projects with the environment, there may be deviations from an earlier partial plan to a later partial plan. As a rule, however, it is possible to keep such deviations to a minimum by creating plan reserves.
21 over over over Identifying Investment Needs 3.1. Requirements for recognizing the best investment needs Needs in the investment sector arise, among other things, from critical conditions in the company. E.g. the sales and profits of certain products are falling, an old plant is susceptible and causes production interruptions etc. is disruptive human creative achievements are assumed, which consist in the knowledge of the objectives in order to combine the present and future conditions in the company and in the environment in such a way that entrepreneurial measures that appear sensible are recognized can never be better than the best of the identified investment opportunities, a systematic approach is required when identifying them. Appropriate measures help to identify the real need for investment Nothing should be left to chance. The more intensively and systematically the search for new methods, the sooner real investment needs will be identified and economic possibilities will be found to satisfy them. This applies to all sectors, including organization and administration. 7) See also Trechsel, F .: Investment planning and investment accounting, p. 15, Haupt Verlag BernStuttgart 1966.
22 Changes, reports, observations, finding 13 It is therefore useful to get an overview of the most important signs of investment opportunities and to follow up on the following, exemplary sources of information that can be assigned to certain areas of the company: In the purchasing area: offers and brochures on new designs by the system manufacturers, evaluations of specialist journals, scientific publications, exhibitions, trade fairs, etc. with regard to new products and processes and their possible uses, records of changes in the procurement market with regard to prices, quantities and qualities of materials that are already known, documents on new types of raw materials and intermediate products, special about possible substitution possibilities in the production area: the production and capacity planning with regard to the composition and scope of the production and sales program and the sic h resulting system requirements records of frequent repairs to individual systems of defective productions, reject rates and reworking records of repeated system-related bottleneck situations and their causes of machine times after production and downtimes measurements of the capacity utilization of systems frequent missed deadlines and their causes 8) cf. also Frischmuth: data as a basis for investment decisions, p. 190, Gruyter & Co. Berlin 1969.
24 Overview reports, statistics, profitability analyzes Emfluss 15 documents on recruitment and dismissals, in particular reasons for dismissal of the workers, observation of wages and salaries development In the finance and administration area: via tax investment aids, observation of changes in assets and capital under structural and corporate policy aspects, finance, financial planning and control with regard to the possibility of raising capital and the use of liquidity peaks Evaluation of the operating accounting with regard to the composition of the job costs, machine hourly rates in the individual production departments, causes and costs of the unused resp. About employed partial capacities Results of cost unit accounting with regard to manufacturing costs of the cost unit groups, comparison between calculated and achieved prices via interior, warehouse and customer services of individual plants and procedures of customs and taxes needs to invest also due to the focus formation in the group, the business plan (production, sales , Administration), the entrepreneurial objectives, as well as the value analysis. When clarifying the investment opportunities, the company's goals must be known. On the basis of these goals, the first step is to examine the comprehensive possibilities. In practice, however, the extensive possibilities are often taken for granted and optimal solutions and possibilities are only sought on a small scale. As a result, large and lucrative investment opportunities remain untapped.
25 16 These causes can occur individually or in combination. Their very presence does not yet trigger investment activity. It depends on how they appear, i.e. on the intensity with which they influence the economic situation. This intensity of the influence of critical conditions is measured on the basis of the assessment criteria of investments, as they are presented in Chapter 8 Reasons for recognizing financial investments While under section 3.2. the recognition of investment needs in tangible and financial investments was shown, the special reasons for the initiation of financial investments should be presented here, provided that they are not already based on the above paragraph: Offer, order from outside the company or group management, evaluation of information collected, suggestions from various external bodies, suggestions various internal bodies These reasons only give general information. All possible information should be determined as completely as possible and made available for the assessment.
26 17 4. The decision-making process After the investment needs resulting from the entrepreneurial objectives have been identified and the corresponding investment projects have been drawn up and evaluated, a decision must be made as to which projects should and can be realized within the framework of the financial means. This results in the list of projects to be carried out, coordinated with the adjusted business plan. Not all needs are met with investments; in many cases, non-investments such as organizational and personnel measures are sufficient to remedy critical conditions in the company. Since in these cases there is no need to tie up funds, they are not investments either. For the decision-making process, it is irrelevant what type of investment is involved (see also Section 9.3. Development work). In the decision-making process, the profitability or profitability of the investment project is the key factor in the selection of the project, but not the only decisive factor: no anticipation of the investment decision by the profitability calculation, but only the provision of decision aids. Unquantifiable factors are often essential. Therefore, the final investment decision must be reserved for the entrepreneurial area. However, the profitability calculation is able to systematize and objectify the decision-making process. In this way, a controlled hierarchy that can be understood by third parties can be created. The investment decision and thus the entire decision-making process for investments in the company is one of the most important 9) problems of corporate policy 9) Ruhli, E .: The entrepreneurial investment decision, in: Neue Zürcher Zeitung No. 647, Betriebswirtschaftliche Beilage, Zurich 1969
27 Scarcity Long-term increase 18 This is also apparent from the following three reasons: Capital: In general, in a company neither the amount of money to be invested is fixed in advance, nor are the funds available to an unlimited extent. Therefore, the investment and financing options must be coordinated. As a rule, the capital required for investments is greater than the available capital. Bad investments should be avoided above all because they have to forego more profitable investment opportunities. Effects of the investments: The investments have a long-term effect on the success of the company. Investment decisions once made can usually not be corrected or reversed, or only with considerable financial losses. The future development of the company is strongly influenced by the investment decisions. Fixed costs through investments: The investment decisions are becoming more and more important due to the increasing capital intensity of the production process (mechanization, automation, rationalization, etc.). With every investment, more and more costs must be incurred, which are incurred regardless of the employment situation. These fixed costs can reduce the company's adaptability. Good investment decisions depend not only on appropriate material decision-making bases, but also on a suitable organization of the decision-making process, the regulation of which influences the quality of these decision-making bases 12) 11) This is presented in detail in: Albach, H .: Investment and Liquidity, Wiesbaden) Schwarz, H .: Optimal investment decisions, Munich 1967.
28 19 The organization of the decision-making process regulates the investment process and integrates investment planning, investment decision-making and investment control into the company. This is to ensure a smooth process from the suggestion through the decision to the control. The flow of the investment decision-making process can be shown schematically as a control loop: _L Decision preparation, planning, suggestions, testing, recognition, delivery of target values, investment decision, project and overall decision, setting of target values, investment implementation, procurement, commissioning, delivery of actual values, investment control, project and budget control e.g. on the size of the company, the scope of investment activity and the skills of the management. 13) Ulrich, H .: The organization of planning, in: Basic problems of business planning, Bern 1968, p. 27.
29 20 5. Assessment methods 5.1. Presentation of assessment methods For the assessment of investment projects, two primary methods can be distinguished in the literature; the older static methods and the more modern dynamic methods. In contrast to the dynamic methods, the static methods do not take into account the influence of the interest and compound interest calculation, which records the value of the time differences in the incurred expenses and income of an investment. The dynamic methods therefore take into account the changes in costs and income over the course of the investment period. The static calculations do not take into account the operational parameters that change during the investment process and thanks to the change in the process. From the standpoint of theoretical accuracy, the dynamic methods are superior to the static ones. In practice, the static methods are nevertheless used quite often, 14) has the following reasons: and it is not possible in all cases to make detailed protection of the expenses and income of an investment project for the individual periods of the life cycle.It is not always possible to determine the income generated by an investment project and assign it to the project. It is not economical in all cases to use the relatively complex dynamic calculation methods. It is not possible to say generally which calculation method or methods are most suitable for a particular company. 14) P. Wildmann: Mathematical optimization methods in investment planning, Institute for Operations Research, ETH.
30 21 In order to be able to answer this question, one must know both the special operational conditions as well as the individual processes and their possible applications and limits. The most common calculation methods are presented below. Static methods A distinction is made between the static methods: Cost comparison calculation Profit comparison calculation Return flow calculation Profitability calculation Cost comparison calculation The annual average costs of competing projects are compared using the cost comparison method. It is sufficient to compare only those costs that are different in the two methods; The following two cost components are relevant: 1. Capital costs (depreciation, interest) 2. Operating costs (personnel costs, energy, material costs, maintenance etc.) When solving the selection and replacement problems, the costs per service unit or the costs per time segment for the various Alternatives are juxtaposed to determine the most cost-effective project. In the cost comparison calculation, it is assumed that the income from the investment projects to be compared remains unchanged and the alternatives to be compared are in themselves economical, because only the best alternative is found through the cost comparison.
31 22 Example of a cost comparison calculation to choose the cheapest option by comparing the annual costs with an annual capacity utilization of 14,000 units: Version 1 Version 2 Acquisition value (CHF) Duration of the investment (years) Capacity (units / year) Capacity utilization (units) / Year) Depreciation (Fr / year) Lime »Interest (15% on 50% of the investment)" Maintenance and service "Fixed costs" Total personnel costs "Material costs" Energy "Variable costs" total total costs per year The cost comparison shows that with a annual production of stucco, variant 1 is more cost-effective than variant 2. For the investment assessment and decision it is not only necessary to determine the costs for a certain capacity utilization, but also to compare the costs taking into account variable capacity utilization. This is all the more important,
32 23 when future occupancy rates can only be estimated with difficulty and with great uncertainty. Therefore, the critical workload at which the costs per time period or per service unit are the same is determined in the following. Fr / year costs K Var 1 van K Var 2 van K, Var 2 fixed pieces / year For the above example, the critical capacity is Stuck. If the estimated utilization of the system to be procured is more than stucco / year, then variant 2 should be selected. As stated above, under Stuck / year, variant 1 is to be preferred. Determining the critical workload has the advantage that the exact workload does not have to be specified precisely. You just have to try to estimate whether it is more likely that the critical load will be exceeded or not reached. The same calculation method is used for replacement investments. By comparing the costs, it is checked whether it is economical to replace an existing system with a new one. The cost comparison calculation is easy to understand and has the advantage that the running costs are relatively easy to calculate, but on the other hand it has the disadvantage
33 24 that a cost comparison calculation cannot be used for projects of the same type (multi-purpose / single-purpose machines). Assuming that the returns of the compared investment projects are the same, the calculation leads to a meaningful result. On the other hand, only the cost comparison forms the decision criterion. There is no relationship with the investment suram. There are also potential for errors in the cost approach due to the use of the upcoming period that is regarded as representative. With the cost comparison calculation only alternative projects can be assessed. The individual cost parameters, such as the depreciation amount, can be changed by varying the investment period, and this allows a technically more popular solution to be favored. The alternatives are incorrectly formulated in the case of replacement problems, e.g. you will be asked whether it will be replaced now or at the end of its useful life. But the right question is: now or next year? The cost comparison calculation does not take into account the time difference in the occurrence of the costs Profit comparison calculation The profit growth is used as a criterion for the profit comparison calculation. Among several variants, the one that brings the greatest increase in profits is the most advantageous. Compared to the cost comparison calculation, the profit comparison calculation also contains the annual income as an additional component. In the profit comparison calculation, it is assumed that the profit growth leads to the same results on the expediency and advantageousness of expansion investments as the cost comparison calculation, because with constant income per service unit, the profit advantage must be transferred to the extended capacity together with the cost advantage. It is also assumed that
34 25 the implementation of the investment constant income} e performance unit can be achieved. The following example is used to assess an expansion investment using this method. The additional system can increase production by 50%. Existing system Additional system Total system Investment sum (Fr.) Production (piece) Unit price (Fr.) Income (Fr.) Material costs Fr / year Personnel costs, energy Maintenance "Depreciation" Interest "OOO (10% on V2 Inv.Sum) Annual costs Annual profit Fr / year With the additional system, the annual profit of the existing system can be increased from by an additional system, which has an annual profit of, to. The profit comparison has the advantage that it can be based on the accounting figures and is very understandable The disadvantage of this method is that the dynamic time sequence of the investment and its return flows are not taken into account. Even with rationalization and alternative equations, both the costs and the profit comparison calculations lead to incorrect statements, if already for a method
35 of the of the of the 26 plants are available and non-expenditure-effective costs are included. The profit comparison calculation does not represent a cash flow or profitability calculation. The profit growth is not meaningful without taking into account the investment expenditure. With the costs as well as the profit comparison calculation, the profitability depends on the capacity as well as the capacity utilization of productive plants. It enables the general assessment of systems taking into account fluctuating output quantities. Knowing the relative useful threshold is particularly important if the scope of future plant use is only determined with a large range of fluctuations. The examination can then be limited to the comparison of critical performance and probable possible performance. However, recording them is not always easy to take for granted, as it requires knowledge of the cost trend, the determination of which is often problematic. In addition to the difficulties of practical implementation, when assessing these procedures, it must be taken into account that e.g. The one-sided consideration of the capacity or capacity utilization requires the elimination of other factors that influence costs and which also have an effect on economic viability. The costs are subject to various influences such as: Prices of the cost-effective capacity change Capacity utilization of the production program structure and quality of the cost-effective goods The investigation of the cost development depending on one influencing factor requires the elimination of the other factors. The dependency of the costs on the capacity utilization is e.g. assuming constant capacity,
36 27 constant prices and quality of the cost goods as well as unchanged production programs examined return flow duration calculation The static return flow duration calculation (also known in the literature under the payback method, payoff method and repayment method) consists in determining the period of time that is required for the recovery of the capital investment. The aim of this procedure is to reduce the investment risk. When selecting alternative projects, the project with the shortest payback period had to be selected, taking into account the safety aspect. The return flow time calculation can be carried out in three ways: a) Average calculation When calculating the average return flow time of two systems, the capital employed and the average annual recovery are compared. In the case of projects with homogeneous annual income and expenditure, the investment expenditure is set in relation to the annual income surplus. The following formula applies: m = i ~ ^ ~ ä "where: m = duration of return I = investment expenditure E = annual income total A = annual expenditure total 15) Cf. also Käfer, K .: investment calculation, Zurich 1964 Trechsel, F .: investment planning and investment calculation, Bern 1966 Schindler, H .: Investment calculation in theory and practice, Meisenheim adglan 1963.
37 28 b) Cumulative calculation In contrast to the average calculation, for projects with heterogeneous annual income and expenditure, differences in the amount of annual returns over the life of a system are taken into account. Instead of the average, homogeneous mean pressure flows, the effective mean pressure flows, which are added until the amount of capital employed is reached. c) Dynamic return flow time calculation This calculation would consistently be the most accurate, taking into account the passage of time, but only complicates the procedure for practical application without the result being significantly improved. In the context of the return flow duration calculation, two methods are used to take into account the aspect of profit maximization on the one hand and risk limitation on the other hand with the help of the recovery time (= return flow duration) .The first method consists in using the criterion of the minimum return flow duration to determine the optimal type of investment becomes. The investment with the shorter return period is the cheaper. Because every investment deprives capital of a different use, it is advisable, in case of doubt, to always give preference to the shortest return period, because in this case the capital is available for a new use, with perhaps completely different earnings opportunities as soon as possible. The following investments are to be assessed using an example. 16) P. Weidmann: Math. Optimization methods in investment planning, Institute for Operations Research, ETH.
38 29 Variant 1 Variant 2 Acquisition price (CHF) Useful life (years) 6 6 Avg. Income net / year return period (years) 3 3.5 According to the above criterion, variant 1 with a return period of 3 years is to be preferred to variant 2, which requires a return period of 3.5 years. The second procedure states that when making the decision, all alternatives are subject to the condition that a certain target return duration, e.g. 3 or 4 years, not to be exceeded. A time span is set as the target return period within which one can see the development in the branch and is largely safe from surprises. Under all types of investment that meet these conditions, the alternative that promises the highest profit is then determined. This alternative is then considered to be optimal. The criterion of the minimum recovery time has long been the objection that it focuses too much on risk reduction and too little on profit maximization. If e.g. Considering the case that two different manufacturing processes can be used for a planned expansion, the following applies: Variant 1 Variant 2 Acquisition price (Fr.) Useful life (years) 8 16 Running income._ surpluses. ,,, <^ / year) Period of return (Years) 2.5 3.3
39 30 these Variant 1 is considered optimal. Under the pure aspect of profit maximization, however, 2 is more favorable, because the planned useful life has a very strong influence on the profit level here, which is twice as high as in 1. So if you consistently base your investment decisions on minimizing the amortization period, you are pursuing a very short-sighted corporate policy. This process is limited to the time required to recover the invested capital. The average calculation only makes sense if there are relatively constant annual returns, otherwise the accumulation calculation is more meaningful. Since the return flow calculation does not make any statements about the profitability of an investment, it should only be used as an additional criterion, especially for the analysis of risk and liquidity. The reflux time can be easily calculated. The length of the recovery time, to the detriment of this method, does not make any statement about the profitability of the capital rate. On the other hand, the amortization calculation is far too partial to be useful. When calculating with recovery times, each individual investment project, viewed in isolation, is always viewed as a risk-increasing measure. But that cannot be right. The profit risk is an indivisible variable that relates to the company as a whole. It can therefore only be recorded as a quantity resulting from ongoing production and the investment project in question. With such a simultaneous observation, however, one finds that it is not only risk-increasing, but also risk-reducing
40 31 there are also investments. In the last category, just think of investments to broaden the range, secure sales or procurement. The isolated risk limitation in every investment project, as it is done in the amortization calculations, thus conjures up the danger that the pursuit of security will be pushed too far at the expense of the profit level. The calculation of the capital turnover during the useful life can be combined with the return flow calculation in the form of the return flow number Z. The return flow number Z is equal to the quotient of the service life and the return flow duration. A distinction can be made between three cases: If the useful life and the capital return period are the same, the net income is sufficient to cover the capital; If the useful life is longer than the return period, an investment is to be assessed as favorable; however, if the useful life is shorter than the return flow period, the investment expenditure cannot be balanced due to the return flow and the investment results in a financial loss. The reciprocal value of the return flow time, which corresponds to the internal flow rate with a practically unlimited useful life of the investment, also gives this method an extended informative value. The shorter the period of use, the lower the Zmsfuss; it then corresponds to the rate at which the present value of the investment expenditure is equal to the present value of the funds returned with it. Profitability calculation In the profitability calculation, called the Return on Investment Method (ROI), the return on the invested capital is not specified, but is the result of the calculation. In the profitability calculation, the annual profits are set in relation to the average invested or the original capital investment.
41 32 The project data are calculated with imputed interest but not calculated on a full cost basis. The profitability of the individual projects calculated in this way becomes the decisive criterion for the assessment in comparison with the expected minimum return or with competing projects. The following formula applies: with the original kaoital income, E = annual income total K = annual monetary interest) total cost (without calcu I = original investment expenditure r = profitability of the project u with average kaoital income EK 1 rd I "0.5 where E = annual receipts K = annual monetary costs (without imputed interest) I = original investment expenditure = r profitability of the project The practical consequences of the choice of the capital investment size are not as serious as it might seem at first, because the order of preference of various investment projects is when using the The total original rate of capital is exactly the same as when the average rate of capital is used, the only difference being the absolute level of profitability.
42 33 If the Kapxtalexnsatz is assumed to be constant, then this does not correspond to reality. In reality, it decreases over the life of the company, as it usually generates profits and thus the offset depreciation flows back into the company via the income. There are a large number of versions with regard to the data to be taken into account and the quantities set in relation to one another. This method does not take into account the temporal distribution of income and expenditure and does not take into account any Zxns or Zxnseszxnsen. Different lifetimes are not taken into account with this method.If an exnemly constant average profit is expected for competing projects; and if the profit developments of the projects run in the opposite direction, then the errors that occur due to the average calculation are large temporally differentiated capital amounts. As already mentioned, this can lead to considerable errors with different service life, changing costs and yields at high rates. The payment streams of the temporally distributed expenditure and income series correctly also require the time factor to be taken into account. This takes the step into capital and interest theory. The expenses and income over the life of the investment are to be included in the calculation, which means that amounts that are in different
43 34 (I (1 (1 (1 points in time must be added together and offset against each other. The uniform time base to which the amounts refer is referred to as the calculation time Calculation methods based, shown: If a series of payments consists of a payment A at time 0. Interest is paid at p (percent) per unit of time. The interest is credited at the end of each unit of time and earns interest at the same rate. After T units of time, over the following amount A, the so-called time value, if T is an integer: 0.01p = i then the final value A. at the end of the first time unit: A, = A + A.1 = A. (1 1 ooo + l) At the end of the second time unit is: A2 = Ax + A ±. 1 = Ax. + l) = Aq. + i) 2 etc. th At the end of the T time unit is: Am = A. T o (1 + i ) tv 'If the Zmsfuss varies from time unit to time unit, so that the Zmsf uss in the first time unit i., m of the second time unit i_ etc., then: At = Aq (1 + i1) (1 + i2) (1 + i3) ... + it) ... + it) The factors (1 + i) are called addition factors or accumulation factors.
44 35 If a payment of e francs is made during T time units at the end of each time unit, after T time units interest is paid on the amounts at the rate of 1 per time unit and the interest is credited at the end of their time unit for the following amount A: AT = e (1 + i) ^ +. + e AT = (1 + J e A) T "1 i If you add: = to (1 + i) tl 1, the final value becomes: N = e. an If the payment is made at the beginning of each time unit, we get: AT = e (l + i) t + + e (l + i) AT = e (1 + i). An If the final value after T time units is to have the amount A and the interest is credited at the end of each time unit, then at the end each time unit the payment Z. Z an = AT a T The variable 1 (1 + l) t 1 is referred to as "smkmgfundfactor". A Francs that are due at time T have the value A at time o, if the Zmsfuss per unit of time is equal to i:
45 36 contmuous .. (i AT = Aq (1 + i) t AQ = AT (1 + i) "t If the Zmsfuss varies from time period to time period, you get: (1 + ix) (1 + i2). + it) T The factor (1 + i) is referred to as the deduction factor or discounting factor. The investment calculation is carried out at a point in time when a project is first being considered, ie before actual expenditure arises. It is therefore inevitable that future expenditure and revenues are discounted to the point in time of the invoice. Because expenditure and revenues are usually discounted to the present, the measured values are called present values. Investments can be characterized according to the time incurred in terms of money-related costs and income E.g. F. and V. Lutz use the structure 17) in their investment theory as follows: point mput contmuous mput point mput point output point output output for investments that are characterized by a one-off cost with e one-time use, through ongoing costs with one-time use, one-time costs with ongoing use. 17) Lutz F. and V .: The Theory of Investment of the Firm Prmceton 1951.
46 37 ~ The following example shows the basic formulas for discounting: The present value of T payments at time 0, which are due at the end of each time unit in time 1 T, is A. The rate of interest per time unit is i; the interest is credited at the end of each time unit: If e., e ...., e are the values of the series of payments, then: e2 et = A (1 + 1) (1 + l) 2 (1 + l) t T (1 + l) fc If the payments are the same size: 61 "e2 = e3 = * * = 6T" then the formula goes over to: A, e (1 + i) t 1 1 (1 + 1) T Der Expression (1 + i) T 1 is called the capital recovery factor. If the series of payments is infinite, the formula changes to: o L t = "1 (1 + L) t * A = O 1
47 38 If the first payment is due at time 0, the result is: A = e (1 + o i) The interest rate is of particular importance for the investment calculation. The question arises as to what rate of interest should be used to discount expenses and income items. The theory of the profitability calculation of systems generally knows the freely chosen calculation rate, the internal rate of return, the interest on the equity capital tied up in the investment of the entrepreneur and also the more or less objective market rate. The fact that the calculation rate is one of the objects of controversy in investment theory and calculation is due to the fact that the calculation rate is assigned various tasks: It is intended to make amounts that arise at different points in time comparable. It should make a statement as to the rate of interest at which amounts that have not yet been invested or that have already been returned are invested. It should take into account the financing options for the investment. It should possibly contain an appropriate risk premium. It should possibly take into account the effects of income tax. The calculation base can thus depend on the tasks that are in the foreground and depending on the company-specific 18) P. Wildmann: Math. Optimization Methods in Investment Planning, Institute for Operations Research, ETH.
48 39 the circumstances should be based on different types of financing or different types of supplementary or alternative investment options. Numerous authors are of the opinion that the investment calculation should also take into account the interest that would have to be paid if the project were entirely financed by outside capital, which means that the 19) loan interest rate specific to the type of investment would come into consideration. According to Schneider, the calculated interest rate must in any case be greater than the interest rate that the investor has to pay for the transfer of the borrowed capital. How big the difference between the two interest rates will be in a specific case depends on the internal rate of return the investor wishes to achieve and the risk associated with carrying out the investment. Schneider leaves the setting of the discount rate to subjective factors. It is recommended that, for external financing, a discount rate should be taken into account that is formed from the cost of borrowing, but not the nominal rate of interest on debt, but a rate that includes all costs and disadvantages associated with the increase in debt. In the case of equity financing, on the other hand, you should choose the interest that you get when the corresponding funds are loaned on the capital market. In practice, however, it is not possible to differentiate between equity and borrowed capital, as financing options and investment decisions are usually made separately from one another in terms of both location and time. The most important dynamic methods concern the calculation: 19) Schneider, E .: Profitability calculation, theory of investment, Tübingen-Zurich 1962.
49 40 Vienna Zurich of the net present value of the internal rate of return and the annuity. These common methods are related compound interest calculations of different formulations. According to Schneider, all three methods are identical and it is therefore irrelevant which of the three methods is used to carry out a profitability calculation in a specific case. The decision for one or the other method is made primarily for purpose 21) reasons of mass. In contrast, F. and V. Lutz have shown under which conditions the investment criteria correspond to the internal rate of return and the capital value method and under which do not. If the same assumptions are made, both methods deliver the same results. Contradictions between the two methods result from the different assumptions made about the interest rate 22) of the differential investments. Seelbach proves that different results of the profitability calculation, depending on the choice of calculation method, are not least due to the fact that the net present value method and the internal rate of return method are based on different objectives. He tries to prove that the selection of the investment objects according to the greatest capital value or the maximization of the capital value as a function of the investment expenditure or the investment objects means profit maximization, while the choice of the internal rate of return makes the return on capital a decision criterion. 20) Schneider, E .: Profitability calculation, theory of investment, Tubingen) Lutz, F.u.V. : The Theory of Investment of the Firm, Princeton) Seelbach, H.: Planning models in the investment calculation, Wurzburg 1967.
50 Present value 41 V Net present value method The net present value of an investment is the sum of all the income and expenses usually related to the commissioning of the plant over a certain discount rate at a valuation point, i.e. net present value of an investment = present value of the income of the expenses expressed in formulas: a ) with discontinuous interest: TK = I + Yl " 51 42 as economically sensible. If several investment variants are calculated at the same time, the variant with the highest income surplus will be the most advantageous. The net present value represents a measure of the return on the invested capital, i.e. the higher the net present value, the higher the interest rate and thus the profitability. The effective interest rate (effective interest rate = p) on the capital investment that has not yet been amortized is less than, equal to or greater than the calculated interest rate p, depending on whether the calculated net present value is negative, 0 or positive. I.e. K> 0 p> p. k o * e K = 0 * p = p, (= internal interest rate) re * k o K <0 »p 52 43 The capital market is perfect, that is, there is only one rate of interest at which the investor can borrow and borrow unlimited capital Easily determine the calculatory rate of interest. In this case, it would have to be set at the level of the market interest rate, since every investment that still has a positive capital value based on this calculation rate yields additional profit for the investor Investment risk can be chosen. The amount at which it is then also depends on the investor's willingness to take risks. In practice, the capital value method is a very useful investment calculation. However, it is disadvantageous that, due to the choice of the calculation rate, which must of course be specified, a date is required as early as the decision-making stage, the definition of which includes the scope of the investment decision. However, this "handicap" can easily be overcome by using different calculation bases and thus the presentation of the net present value function (sensitivity analysis). The reference time must be the same for all compared alternatives, as otherwise the capital values determined cannot be compared. A comparison with alternative or different projects is only possible if capital is used 53 44 and lifetime are the same. If this is not the case, this equality is to be established by forming differential investments. If the net present value of the difference investment> 0, this means that it is profitable to opt for the larger investment expenditure. If the differential investment is <0, the additional effort is not worthwhile. Since the amount of the capital value of an investment depends on the reference point, the same time base should be selected for all alternatives to be compared. In the case of investment projects to be compared, it must be possible to reinvest the return flow of funds at the calculated interest rate until the end of the useful life. It is therefore advisable to choose the discount rate with a view to this requirement. The advantage of this method is that the timing of the capital investment and the return flow of funds through interest and compounding is taken into account. The disadvantage is that this method is difficult to understand as a decision criterion. No statement is made about the recovery time. It is difficult to derive it from accounting and requires a rethink. Annuity method The mathematical content of the annuity calculation is identical to the net present value method. The series of numbers for expenditure and income are transformed into two equivalent uniform series, so that for the individual years, instead of amounts running at random, exactly the same values, i.e. expenditure and income allowances, arise. They are referred to as the average expenditure or average income per unit of time of the investment. 54 45 _ This method arose in the credit system out of the need to repay debts at constant rates. These installments therefore always contain a capital ratio (repayment contribution) and an interest ratio (interest service). If the present values are multiplied by the corresponding recovery factor read from tables based on the term and the specified minimum interest rate, the present value is converted into T annuities. T »= H Dj. i (1 + i) t = 1 (l + i) * (l + i) tl With a given discount rate, an investment makes economic sense if the average annual income is not less than the average annual expenditure, ie if the difference D becomes positive. The arithmetic operations that are additionally necessary compared to the net present value method do not lead to a significantly better statement, although the annuity method, which operates with average annual income and expenditure, corresponds best to the thinking in practice. This way of calculating the capital value of the investment is very cumbersome and impractical in this form. The advantage of this method, however, is that various derivations are possible which, despite significant computational simplifications, still provide sufficiently accurate results. 23) Schneider himself, for example, specified a so-called approximate annuity method, which 23) Schneider, E .: Introduction to the Theory of Economic Efficiency, Kiel 1964. 55 ~ 46 the splitting of the annuities into an amount calculated according to the linear method for depreciation and an amount for interest on the invested sum corresponds to the usual method in operational accounting. For the average annual output A, the approximate formula applies: I I T + 1? sr ä = + i + K T 2 T u where: = I investment expenditure o = K average operating and maintenance costs per period where the value o corresponds to the annual depreciation T I T 1 l. the average annual interest and the average annual operating and maintenance costs. The difference between the correct and the approximate annuity method depends on the rate of return and the duration of use. The greater the calculation factor and the useful life, the greater the difference between the values calculated using the correct and the approximate annuity method. Investments with a useful life of more than 10 years may no longer be assessed using the approximate annuity method, as the error would be too large. 56 A Internal Zmsfuss or DCF method 24) The DCF method is mathematically derived from the capital value method.It was developed from the idea that the effective profitability of an investment project represents a more meaningful basis than the sole determination of whether the profitability is above or below an a priori fixed calculation rate of the investor. The DCF method is based on exactly the same dimensions of the investment process as the capital value method, only the formulation of the mathematical problem is different. With the DCF method, the capital value searched for in the capital value method is set to zero from the outset (K = 0) and the Zmsfuss is kept variable. The Zmsfuss, which then satisfies the equation, is the "Internal Zmsfuss" or the DCF return. Mathematically, the problem formulated in this way can only be solved directly in special cases, e.g. In the following case: There is only one investment expenditure I at the beginning, homogeneous income E and expenditure A, i.e. the difference E is homogeneous and the investment duration is infinite. Then the formula for the internal Zmsfuss is: r = EA T 24) see also Dürr, K, investment calculation Bern 1958 Albach, H. economic calculation with uncertain expectations, Cologne 1959 Trechsel, investment planning and investment calculation, Bern 1966 Schneider, introduction m economic theory, Kiel 1964 57 1962 TübingenZürich investments, the theory of profitability calculation, E .: Schneider, cf. 26) 3/1971 Cost accounting practice investment consequences, from return calculation with interest rate multiple occurrences the Ueber W .: Ruppert, cf. 25) positive one only tried with investments, Schneider 26 ) The return on investment corresponds to this and Zmsfuss rush 25) pure only there is income ahead of the expenses that can be achieved with investments, ie investments, normal cases. be complex or occur several times, however, those of T-solutions, exactly determines algebra the fundamental theorem in 1855) (1777 Gauss already has as, equation This represents. Coefficients real and (r) unknowns of an equation with degree algebraic one represents equation above returns. Mean or net annual results = _ D1 where Q = RT + + DT ... I ^ l + r ^ + D ^ l + r ^ WjU + r) 1 "" 2 * multiplied: r) + (1 with T 0 = RT (l + r) ~ T + DT (l + r) "T + ... Io + D1 (l + r)" 1 + D2 (l + r) "2+ expressed: differently or t = lt = l" T Rm (l + r) + "AJl + r)>" E, (l + r) ^ + Iq = 0 = Kq (R ^, + At (l + r) _t y Et (l + r) _t V ^ + ro: capital value) = 0 = (K is r = Zmsfuss internal the and represent the planning period of the end at the plant the residual value of the R and investment expenditure the I if form, following in problem mathematical that arises year per A expenditure and E income heterogeneous At 48 58
51 42 as economically sensible. If several investment variants are calculated at the same time, the variant with the highest income surplus will be the most advantageous. The net present value represents a measure of the return on the invested capital, i.e. the higher the net present value, the higher the interest rate and thus the profitability. The effective interest rate (effective interest rate = p) on the capital investment that has not yet been amortized is less than, equal to or greater than the calculated interest rate p, depending on whether the calculated net present value is negative, 0 or positive. I.e. K> 0 p> p. k o * e K = 0 * p = p, (= internal interest rate) re * k o K <0 »p
52 43 The capital market is perfect, that is, there is only one rate of interest at which the investor can borrow and borrow unlimited capital Easily determine the calculatory rate of interest. In this case, it would have to be set at the level of the market interest rate, since every investment that still has a positive capital value based on this calculation rate yields additional profit for the investor Investment risk can be chosen. The amount at which it is then also depends on the investor's willingness to take risks. In practice, the capital value method is a very useful investment calculation. However, it is disadvantageous that, due to the choice of the calculation rate, which must of course be specified, a date is required as early as the decision-making stage, the definition of which includes the scope of the investment decision. However, this "handicap" can easily be overcome by using different calculation bases and thus the presentation of the net present value function (sensitivity analysis). The reference time must be the same for all compared alternatives, as otherwise the capital values determined cannot be compared. A comparison with alternative or different projects is only possible if capital is used
53 44 and lifetime are the same. If this is not the case, this equality is to be established by forming differential investments. If the net present value of the difference investment> 0, this means that it is profitable to opt for the larger investment expenditure. If the differential investment is <0, the additional effort is not worthwhile. Since the amount of the capital value of an investment depends on the reference point, the same time base should be selected for all alternatives to be compared. In the case of investment projects to be compared, it must be possible to reinvest the return flow of funds at the calculated interest rate until the end of the useful life. It is therefore advisable to choose the discount rate with a view to this requirement. The advantage of this method is that the timing of the capital investment and the return flow of funds through interest and compounding is taken into account. The disadvantage is that this method is difficult to understand as a decision criterion. No statement is made about the recovery time. It is difficult to derive it from accounting and requires a rethink. Annuity method The mathematical content of the annuity calculation is identical to the net present value method. The series of numbers for expenditure and income are transformed into two equivalent uniform series, so that for the individual years, instead of amounts running at random, exactly the same values, i.e. expenditure and income allowances, arise. They are referred to as the average expenditure or average income per unit of time of the investment.
54 45 _ This method arose in the credit system out of the need to repay debts at constant rates. These installments therefore always contain a capital ratio (repayment contribution) and an interest ratio (interest service). If the present values are multiplied by the corresponding recovery factor read from tables based on the term and the specified minimum interest rate, the present value is converted into T annuities. T »= H Dj. i (1 + i) t = 1 (l + i) * (l + i) tl With a given discount rate, an investment makes economic sense if the average annual income is not less than the average annual expenditure, ie if the difference D becomes positive. The arithmetic operations that are additionally necessary compared to the net present value method do not lead to a significantly better statement, although the annuity method, which operates with average annual income and expenditure, corresponds best to the thinking in practice. This way of calculating the capital value of the investment is very cumbersome and impractical in this form. The advantage of this method, however, is that various derivations are possible which, despite significant computational simplifications, still provide sufficiently accurate results. 23) Schneider himself, for example, specified a so-called approximate annuity method, which 23) Schneider, E .: Introduction to the Theory of Economic Efficiency, Kiel 1964.
55 ~ 46 the splitting of the annuities into an amount calculated according to the linear method for depreciation and an amount for interest on the invested sum corresponds to the usual method in operational accounting. For the average annual output A, the approximate formula applies: I I T + 1? sr ä = + i + K T 2 T u where: = I investment expenditure o = K average operating and maintenance costs per period where the value o corresponds to the annual depreciation T I T 1 l. the average annual interest and the average annual operating and maintenance costs. The difference between the correct and the approximate annuity method depends on the rate of return and the duration of use. The greater the calculation factor and the useful life, the greater the difference between the values calculated using the correct and the approximate annuity method. Investments with a useful life of more than 10 years may no longer be assessed using the approximate annuity method, as the error would be too large.
56 A Internal Zmsfuss or DCF method 24) The DCF method is mathematically derived from the capital value method.It was developed from the idea that the effective profitability of an investment project represents a more meaningful basis than the sole determination of whether the profitability is above or below an a priori fixed calculation rate of the investor. The DCF method is based on exactly the same dimensions of the investment process as the capital value method, only the formulation of the mathematical problem is different. With the DCF method, the capital value searched for in the capital value method is set to zero from the outset (K = 0) and the Zmsfuss is kept variable. The Zmsfuss, which then satisfies the equation, is the "Internal Zmsfuss" or the DCF return. Mathematically, the problem formulated in this way can only be solved directly in special cases, e.g. In the following case: There is only one investment expenditure I at the beginning, homogeneous income E and expenditure A, i.e. the difference E is homogeneous and the investment duration is infinite. Then the formula for the internal Zmsfuss is: r = EA T 24) see also Dürr, K, investment calculation Bern 1958 Albach, H. economic calculation with uncertain expectations, Cologne 1959 Trechsel, investment planning and investment calculation, Bern 1966 Schneider, introduction m economic theory, Kiel 1964
57 1962 TübingenZürich investments, the theory of profitability calculation, E .: Schneider, cf. 26) 3/1971 Cost accounting practice investment consequences, from return calculation with interest rate multiple occurrences the Ueber W .: Ruppert, cf. 25) positive one only tried with investments, Schneider 26 ) The return on investment corresponds to this and Zmsfuss rush 25) pure only there is income ahead of the expenses that can be achieved with investments, ie investments, normal cases. be complex or occur several times, however, those of T-solutions, exactly determines algebra the fundamental theorem in 1855) (1777 Gauss already has as, equation This represents. Coefficients real and (r) unknowns of an equation with degree algebraic one represents equation above returns. Mean or net annual results = _ D1 where Q = RT + + DT ... I ^ l + r ^ + D ^ l + r ^ WjU + r) 1 "" 2 * multiplied: r) + (1 with T 0 = RT (l + r) ~ T + DT (l + r) "T + ... Io + D1 (l + r)" 1 + D2 (l + r) "2+ expressed: differently or t = lt = l" T Rm (l + r) + "AJl + r)>" E, (l + r) ^ + Iq = 0 = Kq (R ^, + At (l + r) _t y Et (l + r) _t V ^ + ro: capital value) = 0 = (K is r = Zmsfuss internal the and represent the planning period of the end at the plant the residual value of the R and investment expenditure the I if form, following in problem mathematical that arises year per A expenditure and E income heterogeneous At 48
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