Analysis of investment projects. Basic principles for evaluating an investment project Principles for the effectiveness of investment projects

06.01.2022
Financial analysis Bocharov Vladimir Vladimirovich

8.2. Principles for evaluating investment projects

The most important stage in the process of making investment decisions is the evaluation of the effectiveness of real investments (capital investments). The timing of the return on invested capital and the prospects for the development of the enterprise depend on the correctness and objectivity of such an assessment.

Let us consider the most important principles and methodological approaches used in international practice to assess the effectiveness of capital investments.

The first of these principles is the assessment of the return on investment based on the cash flow indicator generated from profits and depreciation during the operation of the investment project. The cash flow indicator can be used to assess the effectiveness of the project with differentiation for individual years of operation of the facility or as an annual average.

The second principle of evaluation is the mandatory reduction to the present value of both the invested capital and the amount of cash flow. This is due to the fact that the investment process is not carried out all at once, but goes through a series of stages reflected in the business plan. Similarly, the amount of cash flow for individual periods of its formation should be reduced to the present value.

The third principle of evaluation is the choice of a differentiated percentage (discount) in the process of discounting the cash flow for various investment projects. The amount of income from investments (in the form of cash flow) is formed taking into account the following factors:

? average real discount rate;

? inflation (premiums for it);

? investment risk premiums;

? premiums for low liquidity of investments (for long-term investment).

Given these factors, when comparing projects with different levels of risk, unequal interest rates should be applied when discounting. A higher interest rate is usually applied to projects with a higher level of risk. Similarly, when comparing projects with different total investment periods (investment liquidity), a higher rate of interest should be applied to a project with a longer implementation period.

The fourth principle is that various variations of the forms of the interest rate used for discounting are selected based on the objectives of the assessment.

To determine various project performance indicators, the following can be selected as a discount rate:

1) average deposit or loan rate (for currency or ruble loans);

2) the individual rate of return (return) required by the investor, taking into account the rate of inflation, the level of risk and liquidity of investments;

3) rate of return on government securities (bonds of federal and subfederal loans);

4) rate of return on current (operational) activities;

5) alternative rate of return for other similar projects, etc.

The discount rate (discount rate) is expressed as a percentage or fraction of a unit. In Russian investment practice, the following discount rates are distinguished: commercial, project participant, social and budgetary.

The commercial discount rate is used in evaluating the commercial effectiveness of the project. It is determined taking into account the alternative (related to other projects) capital efficiency. The commercial efficiency of the project takes into account the financial consequences of its implementation for the participant, assuming that he bears all the costs necessary for the implementation of the project and enjoys all its results.

The discount rate of a project participant expresses the effectiveness of enterprises (or other participants) participating in the project. It is chosen by the participants themselves. In the absence of clear preferences, the commercial discount rate can be used as it. The effectiveness of participation in the project is established in order to verify the feasibility of the project and the interest in it of all its participants.

The effectiveness of participation in the project includes:

? efficiency of participation of enterprises in the project;

? the effectiveness of investing in the shares of the enterprise implementing the project;

? the effectiveness of participation in the project of structures of a higher level (regional and federal executive authorities).

The social (public) discount rate is used in the calculation of indicators of social efficiency and characterizes the minimum requirements of society for the national economic efficiency of projects. It is considered a national parameter and is determined by the federal authorities.

The budget discount rate is used in calculating the indicators of projects financed from the regional and federal budgets. It is established by the authorities (federal or regional), on the instructions of which the budgetary efficiency of investment projects is assessed.

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5.1. Methods for evaluating investment projects

MINISTRY OF EDUCATION AND SCIENCE OF THE RUSSIAN FEDERATION

federal state budgetary educational institution

higher professional education

"Transbaikal State University"

(FGBOU VPO "ZabGU")

Faculty of Additional Professional Education

Department of Construction


discipline: "Project management"

on the topic “Efficiency of investment projects. Principles of Evaluation of Efficiency»


Fulfilled Art. gr. EUNs-10

Atajanyan M.V.

Checked Ph.D., Associate Professor

Morozov V.T.




Introduction

Efficiency of investment projects

2 Economic efficiency of investment projects

Principles for evaluating the effectiveness of investment projects

Conclusion

List of sources used


INTRODUCTION


Investment activity is one of the most important aspects of the functioning of any commercial organization. The reasons for the need for investment are updating the existing material and technical base, increasing production volumes, and developing new types of activities.

The importance of economic analysis for planning and implementing investment activities can hardly be overestimated. At the same time, a preliminary analysis is of particular importance, which is carried out at the stage of development of investment projects and contributes to the adoption of reasonable and justified management decisions.

Quite often, an enterprise is faced with a situation where there are a number of alternative (mutually exclusive) investment projects. Naturally, there is a need to compare these projects and choose the most attractive of them according to some criteria.

In investment activity, the risk factor is essential. Investment is always associated with the immobilization of the financial resources of the enterprise and is usually carried out under conditions of uncertainty, the degree of which can vary significantly.

In a market economy, there are quite a lot of investment opportunities. However, the amount of financial resources of any enterprise is limited. Therefore, the relevance of the topic of the essay is to optimize investment.

The purpose of writing an essay is to study the concept of "investment projects", their effectiveness, as well as consideration of the principles of performance evaluation.

The tasks to be solved when writing an essay are familiarization with the existing methods for choosing the optimal investment project, acquiring practical analysis skills.

The abstract is set out on 29 pages of typewritten text, including a list of sources used

1. EFFICIENCY OF INVESTMENT PROJECTS


1 Characteristics of types of investment projects


As you know, fixed assets are a set of material assets used as means of labor and acting in kind for a long time both in the sphere of material production and in the non-production sphere.

In the process of operation, fixed assets morally become obsolete, physically wear out, temporarily fail. Therefore, in order to maintain and expand the production potential, an enterprise needs to ensure the reproduction of fixed assets and maintain them in working condition. The latter is achieved by carrying out current and major repairs.

The reproduction of fixed assets can be simple, extended and narrowed. In the first case, there is a simple replacement of worn-out fixed assets with fixed assets with similar technical and economic characteristics. Expanded reproduction involves an increase in production capacity in an intensive or extensive way, i.e., respectively, through improving the quality of fixed assets using the achievements of scientific and technological progress or increasing the number of fixed assets. Under the narrowed reproduction understand the lack of renewal of fixed assets and their gradual degradation.

Today, narrowed and simple reproduction of fixed assets prevails in our country, while expanded reproduction takes place only at individual enterprises in the ferrous and non-ferrous metallurgy, timber industry and in the financial and banking sector. The current situation is primarily due to the continuous decline in the volume of capital investments over 8 years and the increase in the terms of their development.

Long-term investments in fixed assets should be understood as the costs of creating and reproducing fixed assets. Investments can be made in the form of capital construction and the acquisition of fixed assets.

On the basis of interdependence, two types of investment projects can be distinguished: 1) alternative (mutually exclusive) (acceptance of one of them means the impossibility of accepting the other) and 2) independent (acceptance of one of them does not affect the decision to accept the other).


The stages of analysis of the effectiveness of investment projects are shown in Figure 1.1.


Rice. 1.1. Stages of analysis of the effectiveness of investment projects


When analyzing investment projects, certain assumptions are made. First, it is customary to associate a cash flow with each investment project, the elements of which are either net outflows or net cash inflows. Under the net outflow is understood as the excess of the current cash costs of the project over the current cash receipts. Cash flow, in which inflows follow outflows, is called ordinary. If inflows and outflows alternate, the cash flow is called extraordinary.

Most often, the analysis is carried out by years, although this limitation is not mandatory. The analysis can be carried out over equal periods of any duration. At the same time, however, it is necessary to remember about the comparability of the values ​​of the cash flow elements, the interest rate and the length of the period.

It is assumed that all investments are made at the end of the year preceding the first year of project implementation, although in principle they can be made over a number of subsequent years.

The inflow (outflow) of cash relates to the end of the next year.

The indicators used in the analysis of the effectiveness of investments can be divided into two groups depending on whether or not the time aspect of the value of money is taken into account:

a) based on discounted estimates;

b) based on accounting estimates.


1.2 Economic efficiency of investment projects


The effectiveness of investment projects implies the compliance of the project with the goals and interests of its participants. The effective implementation of projects increases the gross domestic product that is at the complete disposal of the company, which is divided among the firms participating in the project, banks, budgets of different levels, shareholders, etc. The income and costs of these entities determine the choice of various investment project efficiencies.

Types of efficiency:

1.The effectiveness of the project as a whole;

2.The effectiveness of participation in the project.

The effectiveness of the project as a whole - is evaluated to determine the possible attractiveness of the project for future participants and to find sources of funding.

It includes the public (socio-economic) and commercial effectiveness of the project.

Indicators of social efficiency - socio-economic consequences of creating an investment project for the whole society (including both direct costs and results of the project) and "external": costs and results in related sectors of the economy, social, environmental and other non-economic effects. In some cases, when these effects are very significant, in the absence of documents, the assessment of independent qualified experts can be used. The indicators of the commercial efficiency of the project take into account the financial consequences of its implementation for the participant who implements the investment project.

Project performance indicators generally characterize technological, technical and organizational aspects from an economic point of view.

The effectiveness of participation in the project lies in the interest in it of all its participants and the feasibility of the investment project.

The effectiveness of participation in the project should consist of:

1.efficiency of participation of enterprises in the project;

2.the effectiveness of participation in the project of structures of a higher level than the enterprises participating in the investment project;

.the effectiveness of investing in the company's shares;

.budgetary efficiency of the investment project.

Basic principles of efficiency:

1.consideration of the project throughout its life cycle until its termination;

2.correct distribution of cash flows, including all cash receipts and expenses related to the implementation of the project for the billing period, taking into account the possibility of using different currencies;

.comparability of different projects;

.principle of positivity and maximum effect. From the investor's point of view, in order for an investment project to be recognized as effective, it is necessary that the effect of the project implementation be with a "plus"; when comparing several alternatives of investment projects, preference should be given to the project with the highest effect value;

.taking into account the time factor. When evaluating the effectiveness of a project, it is necessary to take into account various aspects of the time factor, as well as changes in the time of the project and its economic environment; the time gap between the receipt of resources or the production of products and their payment; disparity in costs or results at different times (earlier results and later costs are preferable);

.accounting only for future receipts and expenses. When calculating performance indicators, it is necessary to take into account only the revenues and costs planned in the process of implementing the project, including costs associated with attracting previously formed production assets, as well as future losses caused by the implementation of the project (for example, from the termination of existing production in connection with the creation of place of the new one);

.taking into account all the most significant consequences of the project. When evaluating the effectiveness of an investment project, it is necessary to take into account all the consequences of its implementation. If their impact on performance is quantifiable, then it should be quantified in these cases. In other cases, this influence must be taken into account by experts;

.accounting for project participants, the conflict of their interests and different estimates of the cost of capital;

.phasing of the assessment. At different stages of the development and implementation of the project (selection of a financing scheme, justification of investments, economic monitoring), its effectiveness is re-determined with different depths of study;

.taking into account the impact on the efficiency of the investment project of the need for working capital, which is necessary for the operation of production assets created at the stages of project implementation;

.taking into account the impact of inflation (taking into account changes in resources and prices for various types of products during the project implementation period) and the possibility of using several currencies in the project implementation;

.taking into account (quantitatively) the impact of risks and uncertainties accompanying the implementation of the project.

The amount of initial information depends on the design stage at which the performance evaluation is carried out.

Initial information should include:

1. purpose of the project;

2.nature of production, general information about the technology used, type of products (works, services);

.information about the economic environment;

.conditions for the start and completion of the project, the duration of the billing period.

Before the evaluation of the effectiveness of the expert is the social significance of the project.

National economic, large-scale projects are considered socially significant.

At the initial stage, the performance indicators of the project as a whole are calculated.

The purpose of the stage is to create the necessary conditions for the search for investors and the aggregated economic evaluation of design solutions.

For local projects, only their commercial effectiveness is subject to evaluation, if it is acceptable, it is recommended to proceed directly to the next stage of evaluation.

First of all, for socially significant projects, their social effectiveness is evaluated. With poor public efficiency, such projects are not recommended for implementation and do not have the right to qualify for state support. If their public effectiveness is sufficient, their commercial effectiveness is evaluated. If a socially significant investment project has sufficient commercial efficiency, it is recommended to consider the possibility of using various forms of support to increase its commercial efficiency to the required level. If the conditions and sources of financing are already known, the evaluation of the commercial effectiveness of the project can be omitted.

After the financing scheme has been developed, the second stage of evaluation is carried out.

At this stage, the composition of participants is taken into account and the financial efficiency and feasibility of participation in the project of each of them is calculated (industry and regional efficiency, budgetary efficiency, efficiency of participation in the project of shareholders and individual enterprises, etc.).

When assessing the effectiveness of investments for certain project participants, additional information is required on the functions and composition of these participants.

For participants who simultaneously perform several heterogeneous functions in the project (for example, investors who purchase manufactured products or provide borrowed funds), these functions should be described as a whole. For those participants who have already been identified at this stage of the calculations, information is needed on their financial condition and production potential.

The production potential of an enterprise is calculated by the value of its production capacity (preferably in kind for each type of product), the wear and tear and composition of the main technical equipment, structures and buildings, the presence of intangible assets (patents, know-how, licenses), the availability and professional qualification structure of personnel .

When a project involves the creation of a new company, pre-collected information about its shareholders and the amount of the proposed share capital is necessary. Only its functions in the implementation of the project determine its other participants (for example, a lending bank, a lessor of a particular property).

Information about the economic environment of the project should include:

1.a predictive estimate of the general inflation index and a forecast of relative or absolute price changes for certain resources and products (services) for the entire period of project implementation;

2.forecast of changes in the exchange rate or the index of internal inflation of a foreign currency for the entire duration of the project (it is desirable to form various forecast scenarios for the previous and current paragraphs);

.information about the taxation system.

The forecast prices are usually determined sequentially, based on the rate of price growth at each stage.

In some cases, the dynamics of forecast prices is determined based on the need to bring the structure of these prices closer to the structure of world prices.

The source of this information is the long-term forecasts and plans of government bodies in the field of economic policy and finance, analysis of the trend in price changes and the exchange rate, analysis of the structure of prices for resources and products (services) in Russia and the world.

Information about the taxation system should contain, first of all, a more detailed list of taxes, excises, fees, duties and other similar payments (hereinafter referred to as taxes).

Particular attention should be paid to taxes that are regulated by regional legislation (taxes of federal subjects and local taxes). For each type of tax, the following information must be provided:

1.tax base;

2.tax rate;

.frequency of tax payments (payment deadlines);

.on tax benefits (in the part related to the enterprises - participants of the project). If the composition and amounts of benefits are established by federal law, you can specify the document by which they are determined. The benefits that are introduced by the subjects of the federation and local administration are described in full;

.distribution of tax payments between budgets of various levels.

The specified information is given separately for groups of taxes, and payments for them are reflected in the balance sheet of the enterprise in different ways. If information about a particular tax is established by federal law, you can only indicate the relevant document. As a result, if for the corresponding type of production or region this tax is calculated in a different order, it is necessary to bring the corresponding addition and change. The calculation of IP commercial efficiency indicators is formed on the following principles:

1.the (market) current or forecast prices for material resources, products and services provided for by the project are used;

2.cash flows are calculated in the same currencies in which the project provides for the acquisition of resources and payment for products;

.wages are included in operating costs in the amount determined by the project (including deductions);

.if the project provides for both consumption and production of certain products (for example, the production and consumption of components or equipment), the calculation takes into account only the costs of its production, but not the costs of its acquisition;

.the calculation takes into account deductions, taxes, fees, etc., provided for by law, in particular, VAT refunds for consumed resources, tax benefits established by law, etc.;

.if the project provides for full or partial binding of funds (acquisition of securities, deposit, etc.), the investment of the corresponding amounts (in the form of an outflow) is accounted for in cash flows from investment activities, and the receipt (in the form of inflow) - in cash flows from operating activities ;

.if the project provides for the simultaneous implementation of several types of operational activities, the costs for each of them are taken into account.

Tables are recommended as output forms for calculating the commercial effectiveness of the project:

1.income statement;

2.cash flows with the calculation of performance indicators.

To build a profit and loss statement, it is necessary to provide information on tax payments for each type of tax.

As an (optional) supplement, a forecast of the balance of liabilities and assets by calculation stages (balance sheet table) can also be provided. In the process of calculating performance indicators, two main aggregates are used: the amount of receipts and the amount of payments.

From the definition given in the World Bank guidelines, the amount of proceeds is the sum of the benefits received as a result of the project, and the amount of payments is the sum of the costs of the project.

In certain cases, other income from other activities, for example, financial transactions for placing free cash on deposit in a bank, may also be taken into account. That is, these are the following payments:

1.investment costs, such as the cost of building a plant;

2.production costs (bricks);

.tax payments;

.debt servicing costs, interest on loans.

Also, expenses for conducting other operations not related to the main activity (for example, financial operations with free cash resources) can be taken into account. In the list of receipts and payments, regardless of the absence of receipts in the form of own (share) or borrowed capital, there may be payments for debt service. When receiving a loan, the company actually takes money for rent, and interest is only rent payments for the use of funds.

Items of income and payments made by the bank in relation to the project:

1.income from loans issued to the project in the form of interest;

2.amounts paid to the bank as debt repayment by the company implementing the project;

.dividends from the implementation of the project (in case the bank acquires a part in the project - a block of shares of the company implementing the project);

.receipt of funds in the event that the bank sells its part (shares) of the project.

The following payments are implied:

a. costs of direct investment in the project (in case of acquisition of shares);

b. loans issued by the bank;

It should be taken into account that the conditions for participation in the project of different investors may differ from each other, for example, the bank that gave the loan and the venture fund that bought the block of shares.

Given the effectiveness of each investor's participation in the project, it is necessary to individually approach the choice of items of payments and receipts used in calculations, depending on the object of assessment.

It should also be taken into account that the discounting process already takes into account the cost of capital (resources in the bank example).

In this case, it is not necessary to take into account the amounts paid by the bank to service the debt.

Of the considered indicators, each reflects the effectiveness of the project from different angles, therefore, when evaluating any project, it is necessary to use the full set of criteria.

During the review of projects, preference should be given to those that have higher performance indicators.

Therefore, in order to make a decision on project financing in the form of key performance indicators, it is necessary to use the values ​​obtained during the calculation for the equivalent of the financial result in hard currency.

The values ​​of most criteria depend on the duration of the project.

To do this, it is necessary to take into account for what time period they were calculated.

Even the most stable monetary units can be classified as such with a certain degree of conventionality.

Having agreed among themselves on the use of certain indicators of the project's effectiveness and on quite specific methods for calculating them, the specialists, of course, had in mind that the unit of measurement of the initial data and the results obtained would meet the same basic condition, namely, constancy.

And also it should be a generally accepted monetary unit, which can be classified as conditionally stable.

It is necessary to invest in such a way that from each invested monetary unit the income is the same for each investment program.

If, on the other hand, investment costs are distributed in such a way that the increment in utility derived from the implementation of one investment program is less than from another, then the funds are used less efficiently than they could.

Therefore, utility can be increased by reducing investment in projects that generate negligible returns. An investor who wants to maximize the use of invested resources must redistribute his funds in this way and do this until the increase in utility from invested investments becomes the same in all directions.

The way that consumers of investments achieve the highest effect from them is that they must control that the marginal utility is the same for all investment programs and projects.

Investments must be used in such a way that the marginal effect is the same for all projects.

This approach should be the basis for the choice of the economy as a whole, industry, enterprise between different options for investment programs.

If all decision-makers in the national economy follow this rule, the total utility and output will be maximum.

Ignoring this provision leads to the stagnation of production, to a decline in economic growth, to a deep economic recession.

Failure to use the marginal utility leads to a deformation of the structure of investments, which are not directed to the most profitable economic sectors, which most satisfy the consumer needs of the population, chosen according to a completely different criterion.

This leads to a very deformed structure of the economy.

For prosperity to be as high as possible, it is also necessary that investment activity proceed as smoothly as possible.

In order for governments, businesses and citizens to make rational and sound investment decisions, they must have access to information about the costs and consequences of their choices. The costs of collecting information and the process of preparing for the implementation of an investment project should be very small. The higher the costs associated with the preparation of investment programs, the less efficient the investment process itself can be organized.

Economic resources are limited compared to the needs and desires of people.

Therefore, it is necessary to use them sparingly. Scarcity of resources means that people are forced to choose how to consume the resources available in order to get the most out of their use. The scarcity of resources also means that everything has a price, as there are always opportunity costs.

To get the best effect from the resources available, it is necessary to accurately balance profits and costs. At the level of a company or enterprise, the preference, return on investment, is calculated in such a way that management rarely pays attention to some effects other than those that are directly related to the economics of the company or enterprise. In the meantime, government financial calculations consider income and expenditure items included in the state budget. But the macroeconomic consequences of the decisions of the state, enterprises, companies and some citizens are more extensive. They also include aspects that do not fall directly and directly into the final settlements of the company or into the debit or credit of the state budget. Hence the need to expand the boundaries of the analysis of the consequences of certain investment decisions at the project stage, to predict the consequences, to predict the further impact on the course of the entire economic process. The value of the efficiency of investment investments is the minimum cost of resources for transportation and production as a result of these investments.

When calculating the effectiveness of investing in fixed assets, the costs of forming working capital are also added.

In addition to direct investments, related investments are also taken into account that ensure the launch of the facility into operation (power lines, access roads, engineering networks), and associated investments in the development of industries that provide this production with continuously renewable fixed assets.

The efficiency of investments over time is not the same.

This proceeds from the ratio of the increase in capital investments to the increase in national income: the greater this ratio, the greater the capital intensity of the national income, the more additional investments must be made per unit of increase in national income.

And this requires the largest share of accumulation in the national income.

The issues of choosing the volumes and directions of investments are the subject of a large number of publications and various discussions. There are several reasons for the great interest in the problem of rational investment observed recently. First of all, in the transition to market forms of organization of production, the responsibility and risk in the use of investment resources have greatly increased. In addition, in the period of a market economy, at the time of the dynamization of the life of the economy, individual volumes of investment investments increase.

The right choice of investment programs in such conditions becomes more and more responsible and difficult. It should also be said about the ongoing changes in the technical and organic composition of capital in the current era of information technology. With the progressive development and accumulation of technology and science, the share of fixed capital grows, the technical equipment of labor increases, the scale of means of labor and productivity grow. All this increases the bondage of capital in the means of labor and reduces its maneuverability.

As a result, there is growing interest in choosing the right scale and objects of investment: the stakes in the struggle for profit are too high.

Economic science is faced with the question of finding criteria for selecting extremely profitable investment projects. The main criterion for this is to achieve maximum profit. In addition to the direct benefit to date, the expected benefit is increasingly important.

The possibility of ousting competitors from the market is to be assessed, the benefits from the “secondary effect” provided by the development of subsequent investments and production, that is, benefits that go beyond the boundaries of a single company or enterprise, are determined.

The larger the enterprise, the corporation, the more capital they have, the more opportunities they have, along with investments that bring great profits, to make investments in which significant profits can be expected in the future. Incomes and expenses of the current moment of time are not equivalent to the future. Therefore, their comparison is necessary. Under market conditions, any capital invested in a firm or enterprise is defined as employed, on which interest must be paid. Even if an entrepreneur invests his own capital, in order not to be at a loss, he must take into account in his costs an interest on capital no less than that which could be received, provided that it was provided to someone on long-term credit. This percentage is usually the basis for creating companies and other objects in market conditions, comparing options and choosing the most profitable one. In addition to interest, which is, as it were, the “price of capital”, the possibility of making a profit, entrepreneurial income, is also taken into account.

Here, much depends on certain conditions of production: the supply of raw materials, energy and fuel, the availability of secure sales, the degree of use of labor power. When calculating the most profitable investments within an enterprise or company, their management resorts to various methods of calculation. In practice, a large number of individual business entities often use very rough estimates based on experience, assumptions, guesses, information about the actions of competitors, etc. Few firms use systematic methods of calculation. These are usually large firms that have a staff of specialists and the best information. The task of the former includes the development of technology, the study of market conditions, etc. If the project satisfies all the criteria for assessing economic efficiency, then it can be accepted.

2. PRINCIPLES FOR ASSESSING THE EFFICIENCY OF INVESTMENT PROJECTS


The basis for evaluating the effectiveness of investment projects<#"justify">CONCLUSION

investment project attractiveness efficiency

As a result of writing my essay on the topic “Efficiency of investment projects. Principles for evaluating investment projects” the following conclusions were made:

The effectiveness of an investment project is a category that reflects the compliance of the project with the goals and interests of its participants. In this regard, it is necessary to evaluate the effectiveness of the project as a whole, as well as the effectiveness of participation in the project of each of its participants.

The effectiveness of the project as a whole is evaluated in order to determine the potential attractiveness of the project for possible participants and search for sources of funding. It includes: socio-economic efficiency of the project; commercial viability of the project.

The effectiveness of participation in the project is determined in order to verify the feasibility of the project and the interest in it of all its participants and includes: the effectiveness of the participation of enterprises and organizations in the project; efficiency of investment in the project; the effectiveness of participation in the project of structures of a higher level, including: regional and national economic; industry; budget efficiency.
2. The most important principles for assessing the effectiveness of projects are: consideration of the project throughout its entire life cycle; cash flow modeling; comparability of conditions for comparison of various projects; the principle of positivity and maximum effect; taking into account the time factor; accounting only for future costs and receipts; comparison of states "with project" and "without project"; taking into account all the most significant consequences of the project; taking into account the presence of different project participants; multi-stage evaluation; taking into account the impact on the effectiveness of the project of the need for working capital; taking into account the impact of inflation and the possibility of using several currencies in the implementation of the project; taking into account the influence of uncertainty and risk accompanying the implementation of the project. LIST OF USED LITERATURE


1.Vilensky P.L., Livshits V.N., Smolyak S.A. Evaluation of the effectiveness of investment projects. Theory and Practice: Textbook - Delo Publishing House, Moscow, 2002.-30s.

2.Ivasenko A.G. Investments: sources and methods of financing. Textbook, publishing house "Omega-L", Moscow, 2009.-27 p.

.Mayorova T.V. Investment activity: Textbook. - Publishing House "Center for Educational Literature", Kyiv, 2004.-53 p.

.Pimenov S.V. Problems of assessing economic efficiency in the process of making investment decisions.-48 p.

.Rimer M.I., Kasatov A.D., Matvienko N.N. Economic evaluation of investments: Textbook. - St. Petersburg, 2008.-64 p.

.Tkachenko I.Yu. Investments: a textbook for students of higher educational institutions. - Publishing Center "Academy", Moscow, 2009.-55 p.


- modeling of cash flows, including all inflows and outflows of funds related to the implementation of the project for the billing period;

— comparability of conditions for comparison of different projects;

- the principle of positivity and maximum effect. In order for the IP to be recognized as effective from the point of view of the investor, it is necessary that the effect of the project implementation be positive; when comparing alternative IPs, preference should be given to the project with the highest effect value;

— taking into account the time factor. When evaluating the effectiveness of a project, the dynamism of the parameters of the project and its economic environment should be taken into account; gaps in time between the production of products or the receipt of resources and their payment; disparity in costs and/or results at different times;

- accounting only for future expenses and receipts. When calculating performance indicators, only future costs and revenues during the implementation of the project, including costs associated with attracting previously created production assets, as well as future losses directly caused by the implementation of the project, should be taken into account. Previously created resources used in a project are valued not at the cost of their creation, but at their opportunity cost, which reflects the maximum value of lost profit associated with their best possible alternative use. Past, already incurred costs that do not provide the possibility of obtaining alternative (i.e., received outside the project) income in the future (sunk costs) in
cash flows are not taken into account and do not affect the value of performance indicators;

— taking into account the most significant consequences of the project. When determining the effectiveness of an IP, all the consequences of its implementation, both directly economic and non-economic, should be taken into account;

— taking into account the presence of different project participants, the discrepancy between their interests and different estimates of the cost of capital, expressed in individual values ​​of the discount rate;

— multi-stage evaluation. At various stages of development and implementation of the project, its effectiveness is determined anew, with different depths of study;

– taking into account the impact of inflation (taking into account changes in prices for various types of products and resources during the project implementation period);

— taking into account the influence of uncertainty and risks accompanying the implementation of the project.

The international practice of assessing the effectiveness of investments is based on the concept of the time value of money and is based on the following principles:

Evaluation of the effectiveness of the use of invested capital is made by comparing the cash flow, which is formed in the process of implementing the investment project and the original investment. The project is recognized as effective if the return of the initial investment amount and the required return for the investors who provided the capital are ensured.

Invested capital, as well as cash flow, is adjusted to the present time or to a certain accounting year (which, as a rule, precedes the start of the project).

The process of discounting capital investments and cash flows is carried out at various discount rates, taking into account the structure of investments and the cost of individual components of capital.

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  • Introduction
  • 1. Concept and classification of investment projects
  • 2. Preparation of an investment project and its role in making an investment decision
  • 3. The effectiveness of the investment project
  • 4. Indicators and types of efficiency of investment projects
  • 5. Basic principles for evaluating the effectiveness of investment projects
  • Conclusion
  • Bibliography

Introduction

The condition for the development and sustainable life of any organization is the efficiency of investing in certain investment projects.

The problem of making an investment decision is to evaluate the plan of the expected development of events in terms of how the content of the plan and the likely consequences of its implementation correspond to the expected result.

The very concept of investment (from lat. investio - I dress) means capital investments in sectors of the economy within the country and abroad. Investment is something that is “put off” for tomorrow in order to be able to consume more in the future.

One part of the investment is consumer goods that are not used in the current period, but are deposited in stock (investments to increase stocks).

The other part of the investments is the resources that are directed to the expansion of production (investments in buildings, machines and structures).

Since entrepreneurial activity involves the constant implementation of projects containing innovations and activities aimed at improving production efficiency, it becomes necessary to evaluate and select them.

The feasibility study of the project is the main document that allows potential investors to analyze the attractiveness of the project and make a decision on its financing.

The purpose of this work is to determine the basic principles for evaluating the effectiveness of investment projects, as well as the scheme for evaluating the effectiveness.

To achieve this goal, the following tasks were solved in the work:

- the basic concepts and definition of an investment project, indicators and types of investment project efficiency, as well as the basic principles for evaluating the effectiveness of investment projects are given.

1. Concept and classification of investment projects

An investment project at an enterprise is considered as a set of events (proposals) deployed in time, focused on achieving established goals (commercial, social, environmental), meeting a given enterprise development strategy and requiring the expenditure (or use) of capital resources (land, capital) for its implementation or information.

Investment project (investment project) - a plan or program of investment in order to achieve the goals. Sometimes an investment project is understood as a system of organizational, legal, analytical, engineering, economic, accounting and financial documents necessary to justify and carry out the relevant work on the project.

The term "investment project" is used in two senses:

- as a matter, activity, event, involving the implementation of a complex of any actions that ensure the achievement of certain goals (obtaining certain results). Close in meaning in this case are the terms "economic event", "work (set of works)", "project";

- as a system of organizational, legal and settlement and financial documents necessary for the implementation of any actions or describing such actions.

A variety of investment projects implemented in practice can be classified depending on various characteristics. From the point of view of a general approach to the classification of investment projects, the following features can be distinguished:

- type of project - depending on the field of activity in which the project is being implemented (organizational, technological, economic, social, mixed);

- the scale of the project - a monoproject, a multiproject, a megaproject (a monoproject is a project of various types and types, a multiproject is a complex project consisting of a number of monoprojects, a megaproject is a program for the development of regions, industries, which includes a number of mono- and multiprojects);

- type of project - by the nature of the subject area of ​​the project (innovative, educational, mixed, etc.);

- project duration - according to the duration of the project cycle implementation period (short-term - up to 1 year, medium-term - 1-3 years, long-term - over 3 years).

Depending on the type, projects can be classified:

- socio-technical, aimed at increasing the productivity of workers and improving conditions on the ground;

- organizational and managerial, contributing to the improvement of production and increase in labor productivity;

- information related to the improvement of information flows and their automation;

- integrated, consisting of elements of previous projects.

In terms of the scale of implementation, projects can be implemented both at the level of the entire organization, and at the level of individual workshops, sections and individual workplaces.

According to the duration of the cycle, projects can be short-term (up to 1 year), medium-term (up to 3 years), long-term (more than 3 years).

The whole set of various investment projects can be classified depending on other features.

2. Preparation of an investment project and its role in making an investment decision

investment project efficiency solution

As noted above, in its most general form, an investment project is usually understood as a plan for investing capital in specific business objects with the aim of subsequently obtaining a profit sufficient in size to meet the requirements of the investor.

In terms of its content, such a plan includes a system of technical, technological, organizational, accounting, financial and legal, purposefully prepared materials necessary for the formation and subsequent functioning of an object of entrepreneurial activity. With the help of an investment project, an important task is solved to clarify and justify the technical feasibility and economic feasibility of creating an object of entrepreneurial activity.

In time, an investment project covers the period from the moment the idea of ​​creating or developing production was born, its transformation and until the completion of the life cycle of the object being created. This period includes three phases: pre-investment, investment and operational.

If the project is being developed in relation to an existing enterprise in the aspect of implementing an investment decision provided for by the enterprise development strategy, then the first stage of the pre-investment phase should be considered the identification of investment opportunities. As long as there is no clear understanding of the sources of funding, of potentially interested investors and the possibility of their participation in the project, there is little point in moving to the development of the project itself.

The preparation of an investment project is most often carried out in two stages: at the first stage, a preliminary feasibility study (feasibility study) of the project is developed, and at the second stage, the final one.

In terms of conceptual content, the first and second stages of the feasibility study are close. The difference lies in the depth of project development, subsequent refinement of the initial technical and economic information, information on possible sales volumes, loan costs and similar information, which ultimately affect the project's performance indicators. However, the peculiarity of the second phase is that the costs here are irreversible, and since the project is not completed, it does not yet generate income. At this stage, issues related to attracting investments are resolved: loans, issue of shares, recruitment and training of personnel.

The specificity of the investment phase, in contrast to the pre-investment phase, is that the established time frame for creating an object of entrepreneurial activity and the amount of costs provided for by the estimate must be steadily met.

Exceeding these parameters is fraught with very serious consequences, and possibly bankruptcy. Of no small importance is the monitoring of all factors and circumstances that affect the duration and costs in order to take timely measures to overcome emerging negative phenomena.

The third phase of the investment project is operational. The total duration of this phase has a significant impact on the economic efficiency of the project: the further in time the operational phase is, the greater the net income will be. This period cannot be set arbitrarily, because there are economically expedient limits for the use of fixed capital elements, which are dictated mainly by their obsolescence.

3. The effectiveness of the investment project

The effectiveness of an investment project is an indicator that reflects the compliance of the project with the goals and interests of its participants.

From the point of view of legislation, the evaluation of the effectiveness of investment projects is not mandatory, however, each investor is interested in protecting himself from the loss of invested funds and getting enough profit to compensate for the risks.

The assessment of an investment project is generally reduced to the construction and study of some economic and mathematical model of the project implementation process. The need for modeling is due to the fact that when evaluating a project, a complex and multifaceted process of its implementation has to be simplified, discarding insignificant factors and focusing on more significant ones. As a result, the object of analysis is not the project itself, but the material and cash flows associated with it. Thus, the problem boils down to “translating” project documentation into the language of cash flows, and reflecting the interests of project participants in calculation formulas that allow evaluating cash flows relative to these interests.

As a rule, when evaluating the effectiveness of investment projects, the key issues are the following: profitability of investing in a given project; payback period of investments; the degree and risk factors that have a decisive influence on the result.

When evaluating investment projects, they proceed from the information about the project that is contained in the project materials, accepting it as complete, accurate and reliable. During the examination of an investment project, the task is to find out how complete, accurate and reliable it is.

4. Indicators and types of efficiency of investment projects

Determining the level of economic efficiency of investments acceptable to the investor is the most difficult area of ​​economic calculations related to the development of a feasibility study, since here it is necessary to bring together all the many factors of various interests of potential investors, take into account difficult-to-predict changes in the external environment in relation to the project, as well as taxation systems in an unstable economy. All this becomes much more complicated due to the fact that the evaluation of efficiency should be based on relevant information for a very long calculation period.

The problem of assessing the economic efficiency of an investment project is to determine the level of its profitability in absolute and relative terms (ie, per unit of investment costs, capital), which is usually characterized as the rate of return.

Efficiency assessment is carried out according to the system of the following interrelated indicators:

- net income (NP);

- net present value (NPV) or integral effect (another name of the indicator, quite widely used abroad, is the net present (or current) value, net present value (NPV));

- profitability index (or profitability index, profitability (PI));

- payback period (term of return of non-recurring costs of RS);

- internal rate of return (or internal rate of return, profitability, internal rate of retum (IRR)).

A number of subjects take part in the implementation and implementation of the investment project: shareholders (firms, companies), banks, budgets of different levels. The income (gross domestic product) received by society from the implementation of effective projects is then divided between them.

The presence of several participants in the investment process predetermines the mismatch of their interests, different attitudes towards the priority of various project options. The income and expenses of these entities determine various types of investment project efficiency from the standpoint of each participant. At the same time, it should be borne in mind that the positions of the project participants are embodied in the initial information and the formation of specific cash flows for calculating performance indicators. Therefore, they may not have the same assessment results and decisions about their participation in the project.

At present, it can be considered generally recognized to distinguish the following types of efficiency of investment projects, presented in Fig. one.

Figure 1 - Types of efficiency of investment projects

The effectiveness of the project as a whole is evaluated for the presentation of the project and, in this regard, to determine the attractiveness of the project for potential investors.

Public efficiency characterizes the socio-economic consequences of the project as a whole, i.e. it takes into account not only the immediate results and costs of the project, but also "external" in relation to the project costs and results in related sectors of the economy, economic, social and other non-economic effects.

Social efficiency is assessed only for socially significant investment projects that affect the interests of not one country, but several.

For projects that do not require an examination of public authorities, the development of public performance indicators is not required.

The commercial efficiency of the project characterizes the economic consequences of its implementation for the initiator, based on a very conditional assumption that he incurs all the costs necessary for the implementation of the project and uses all its results. Commercial efficiency is sometimes interpreted as the effectiveness of the project as a whole. It is believed that commercial efficiency characterizes technical, technological and organizational design solutions from an economic point of view.

The most significant is the determination of the effectiveness of participation in the project. It is determined in order to check the feasibility of the investment project and the interest in it of all its participants. The effectiveness of participation is evaluated primarily for the enterprise of the project developer (or potential shareholders). This type of efficiency is also called efficiency for the equity capital of the project.

The effectiveness of participation in the project also includes such types as the effectiveness of participation in the project of higher-level structures (financial and industrial groups, holding structures), the budgetary efficiency of the investment project (the effectiveness of state participation in the project in terms of expenditures and revenues of budgets of all levels).

The system of indicators determined to evaluate the listed types of efficiency, and the methodological principles for their calculation are the same. The differences lie in the initial parameters that form the real cash flows for the project in relation to each type of efficiency.

In other words, a single and interconnected system of project parameters is embodied in performance indicators that are uniform in economic nature, depending on their area of ​​application in the economic environment that they should characterize. Some exceptions are indicators of social efficiency. "External" effects are not always possible to take into account in terms of value. In some cases, when these effects are very significant, but it is not possible to evaluate them, only a qualitative assessment of their influence is inevitable.

Assessment of future costs and results in determining the effectiveness of an investment project is carried out within the calculation period (calculation horizon). The calculation horizon is measured by the number of calculation steps. The calculation step in determining performance indicators within the calculation period can be a month, quarter or year.

The costs incurred by the participants are divided into initial, current and liquidation, which are carried out, respectively, at the stages of construction, operation and liquidation.

For the valuation of results and costs, basic, world and settlement prices can be used.

The basic prices are the prices prevailing in the national economy at a certain point in time tb. The base price for any product or resource is considered unchanged throughout the entire billing period.

Measurement of the economic efficiency of the project in basic prices is carried out at the stage of feasibility studies of investment opportunities.

At the stage of the feasibility study of an investment project, it is mandatory to calculate the economic efficiency in forecast and settlement prices. At the same time, it is recommended to carry out calculations in basic and world prices.

The forecast price Цt of a product or resource at the end of the t-th calculation step is determined by the formula:

Цt = Цб J(t,tn),

where Cb is the base price of a product or resource;

J(t,tн) - coefficient (index) of change in prices of products or resources of the corresponding group at the end of the t-th step in relation to the initial moment of calculation tн (at which prices are known).

For projects developed by order of government bodies, the values ​​of price change indices for certain types of products and resources should be set in the design assignment in accordance with the forecasts of the Ministry of Economy of the Russian Federation.

Estimated prices are used to calculate integral performance indicators if the current values ​​of costs and results are expressed in forecast prices.

This is necessary to ensure comparability of the results obtained at different levels of inflation.

Settlement prices are obtained by introducing a defiling factor corresponding to the general inflation index

When developing and comparatively evaluating several options for an investment project, it is necessary to take into account the impact of changes in sales volumes on the market price of products and the price of consumed resources.

When evaluating the effectiveness of an investment project, the comparison of multi-temporal indicators is carried out by bringing (discounting) them to the value in the initial period.

To bring the costs, results and effects at different times, the discount rate (E) is used, which is equal to the rate of return on capital acceptable to the investor.

Technically, it is convenient to bring the costs, results and effects that take place at the t-th step of calculating the implementation of the project to the basic point in time by multiplying them by the discount factor a t, determined for a constant discount rate E, as:

,

where t is the calculation step number, t = 0,1,2,...T, (T is the calculation horizon).

If the discount rate changes over time and is equal to Et at the t-th calculation step, then the discount factor is equal to:

and for t > 0.

As already noted, due to the fact that the investment project brings together several participants whose goals may not coincide, and therefore there are other performance indicators that were not reflected in this work.

Having considered the concept of the effectiveness of investment projects, let's move on to the consideration of the basic principles of efficiency assessment.

5. Basic principles for evaluating the effectiveness of investment projects

The principles for evaluating the effectiveness of investment projects and economic decisions are a set of fundamental requirements that must be met by justifying the effectiveness of the implementation of any projects and economic decisions.

In accordance with the officially approved Guidelines for evaluating the effectiveness of investment projects, the most significant of them include:

- cash flow modeling. It includes all project-related cash receipts and disbursements during the entire project cycle;

Accounting for the time factor. It is necessary to take into account the dynamics of the parameters of the project and its economic environment (changes in the exchange rate of the national currency, interest rates, etc.), as well as gaps in time between the production of products, the receipt of resources and their payment. It is important to take into account the disparity of costs and/or results at different times;

- taking into account the impact of inflation, i.e., changes in prices for various types of products and resources, during the project implementation period, taking into account the possibility of using several currencies during the project implementation;

- taking into account (in quantitative form) the impact of uncertainties and risks accompanying the implementation of the project;

- compliance with the comparability of the conditions for comparing various projects (project options);

- accounting only for future cash receipts and payments. Previously created assets are valued at the opportunity cost or maximum lost profit associated with their use as an alternative to the project under consideration;

- comparison of the scenarios "with the project" and "without the project", while paying attention to the most common mistake - replacing the scenario "without the project" with the scenario "before the project". This leads to the fact that the calculations do not take into account the damage caused by the refusal of investments;

- taking into account all the most significant consequences of the project in related areas of the economy, including social and environmental;

- taking into account the discrepancy between the interests of different project participants and various estimates of the cost of capital, expressed in individual values ​​of the discount rate.

Conclusion

Preliminary studies of investment projects make it possible to assess the practical feasibility and economic feasibility of implementing the project under consideration.

However, the use of any, even the most sophisticated, methods will not provide complete predictability of the final result, the main goal is to compare the investment projects proposed for consideration on the basis of a unified approach using, if possible, objective and verifiable indicators and compiling a relatively more effective and relatively less risky investment project analysis .

To do this, it is advisable to take into account and apply all types of project analysis, based mainly on discounting the cash flows generated during the implementation of the project.

The general scheme for all types of evaluating the effectiveness of project analysis is basically the same and is based on forecasting positive and negative cash flows (roughly speaking, expenses and income associated with the implementation of the project) for the planned period and comparing the resulting cash flow balance, discounted at the appropriate rate, with investment costs. And measures to assess the risk of investing and the use of a methodology for accounting for uncertainty in financial calculations, which make it possible to reduce the impact of incorrect forecasts on the final result and thereby increase the likelihood of a correct decision, can significantly increase the validity and correctness of the analysis results.

Bibliography

1. Ansoff I. Strategic planning. M.: Economics, - 1989.

2. Birman G., Schmidt S. Economic analysis of investment projects: Per. from English. - M.: UNITI, - 1997.

3. Bocharov V.V. Investment management. St. Petersburg: Peter, - 2000, 176p.

4. Bocharov V.V. Methods of financing the investment activity of the enterprise. M.: Finance and statistics, - 1998.

5. Vilensky P.L., Livshits V.K., Orlova E.R., Smolyan S.L. Evaluation of the effectiveness of investment projects. M.: Finance, - 1998.

6. Deeva A.I. Investments. M.: Exam 2004, 211 p.

7. M. I. Knysh, B. A. Perekatov, and Yu. Strategic planning of investment activity. St. Petersburg: Peter, - 1998.

8. Savitskaya G.V. Economic analysis textbook M.: OOO New knowledge - 2004.

9. Stoyanova E.S. Financial management. M.: Prospect 2004, 309 p.

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The efficiency of investments is determined by the ratio of the result of investments and investment costs. Since any investment activity includes the development and implementation of an investment project, we will reveal the content of the latter. The project is understood in two senses: as a design solution supported by an appropriate set of documents that form the goal of the forthcoming activity, and as a set of actions to achieve it and the set of actions itself, i.e. documentation and activities aimed at achieving the goal.

Evaluation of project effectiveness is carried out at the following stages: development of an investment proposal and a declaration of intent (express assessment of an investment proposal); development of "Investment Rationale"; development of a feasibility study; implementation of the investment project.

At all stages, the principles of performance evaluation remain the same.

The evaluation of the effectiveness of an investment project is carried out on the basis of the following principles:

For the billing period, the life cycle of the project is taken, starting from the pre-investment stage to the termination of the project;

Simulation of cash flows, i.e. all cash receipts and expenses for the billing period;

Comparability of conditions for comparative analysis of various project options;

The principle of positivity and maximum effect, which implies that for the investor the effect of the project implementation should be positive, and in case of alternative project options, preference is given to the project with the greatest effect;

Accounting for the time factor, including such aspects as: the dynamism of the parameters of the project and the external sphere; moments of time between the production of products, the receipt of resources and their payments; uneven value of multi-temporal costs and results;

Accounting for future expenses and receipts only. They take into account all costs and revenues during the implementation of the project and the costs associated with attracting the market of created production assets, as well as all losses due to the implementation of the project. Moreover, previously created resources are evaluated at the opportunity cost, i.e. by the lost profit from the best variant of their use;

Comparison of situations "with a project" and "without a project";

Comprehensive assessment of the most significant results of the project (economic and non-economic);

Accounting for the presence of different project participants through various estimates of the cost of capital (individual values ​​of the discount rate);

Multi-stage evaluation: justification of investments, feasibility study, choice of financing scheme, economic monitoring. At all stages of the development and implementation of the project, its effectiveness is determined anew:

Accounting for the impact on the efficiency of the investment project of the need for working capital;

Accounting for the impact of inflation on various types of products and resources during the project implementation period and the possibility of using several currencies;

Accounting for the influence of uncertainties and risk.

19. Cash flow of the investment project and its discounting.

The effectiveness of the project is evaluated during the calculation period, which includes the time interval (lag) from the start of the project to its termination. The settlement period is divided into steps (segments), within which the data used to evaluate financial indicators are aggregated.

Time periods in which high inflation rates are predicted (over 10% per year) should be broken down into smaller steps. Time in the billing period is measured in years or fractions of a year and is taken from a fixed moment t 0 = 0, taken as the base one.

The project, like any financial transaction related to the receipt of income and the implementation of expenses, generates cash flows . Investment project cash flow- this is the time dependence of cash receipts and payments in the implementation of any project, determined for the entire billing period.

At each calculation step, the value of the cash flow is characterized by: 1) an inflow equal to the amount of cash receipts at this step; 2) an outflow equal to payments at this step; 3) balance (net cash inflow, effect) equal to the difference between the inflow and outflow of cash.

Cash flow usually consists of private flows from certain types of activities: investment, current and financial activities.

The calculation of indicators for evaluating the profitability of real investment is based on the concept of evaluating the value of money over time.

When evaluating an investment project, it is often necessary to compare cash flows (revenues from the project and costs for its implementation) for various options for its implementation. To do this, cash flows are compared in any one period of time. For comparison, you can choose any point in time, but for convenience, take the zero period, i.e., the beginning of the project. Future cash flows must be given ( discounted) by now. For this purpose, the following formulas are used: BS

BS \u003d NS x (1 + r) t; NS = ---------- , where

BS - future amount of money (future value); HC - real (current) value of the amount of money; r - discount rate or rate of return, fractions of a unit; t- the duration of the calculation period, the number of years (months).

The future value of an investment is the amount that the money invested today will turn into after a certain period of time at a fixed interest (discount) rate. Interest can be simple or compound. Simple interest is charged only on the principal amount invested. Compound interest - on the principal amount and interest of previous periods.

The current (present) value of funds is the product of the future and the discount factor: NS - BS x CD, where

KD - discount factor, fractions of a unit.

The discount factor is always less than one, because otherwise money would be worth less today than tomorrow.

In this way, discounted cash flows is called the reduction of their multi-temporal (related to different calculation steps) values ​​to their value at a certain point in time.