An investment project is considered effective provided that: Investment project and its effectiveness. The procedure for selecting investment projects

Department: Finance and credit

INTRODUCTION

Introduction……………………………………………………………2

Decisions on investment projects.

Criteria and rules for their acceptance………………………………….3

Investment project. Assessment methods………………………..6

2.1 Which method is better?…………………………………………7

2.2 NPV……………………………………………………………...8

Scope and difficulties of the NPV method……………..10

2.3 PI………………………………………………………………………………..10

2.4 IRR………………………………………………………...11

Scope and difficulties of the IRR method……………...13

2.5 PP……………………………………………………………………………….14

2.6 ARR…………………………………………………………….15

Special assessment methods investment projects………15

How to choose the right discount rate … ………………………16

Conclusion……………………………………………………………..20

Appendix…………………………………………………………….22

Introduction.

Investment activity, to one degree or another, is inherent in any enterprise. It represents one of the most important aspects 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.

Meaning economic analysis for planning and implementation investment activities difficult to overestimate. At the same time, preliminary analysis, which is carried out at the stage of development of investment projects and contributes to the adoption of reasonable and informed management decisions, is of particular importance.

The degree of responsibility for the adoption of an investment project within a particular direction varies. Often decisions must be made in conditions where there are a number of alternative or mutually independent projects. In this case, it is necessary to make a choice of one or more projects based on some criteria. Obviously, there may be several such criteria, and the probability that one project will be preferable to others according to all criteria is, as a rule, significantly less than one.

Making investment decisions, like any other type of management activity, is based on the use of various formalized and informal methods. The degree of their combination is determined by various circumstances, including the extent to which the manager is familiar with the existing apparatus applicable in a particular case. In domestic and foreign practice a number of formalized methods and calculations are known, with the help of which they can serve as the basis for decision-making in the field investment policy. There is no universal method suitable for all occasions. Perhaps management is still more of an art than a science. Nevertheless, having some estimates obtained by formalized methods, even if to a certain extent conditional, it is easier to make final decisions.

The main direction of the preliminary analysis is to determine indicators of possible economic efficiency investments, i.e. returns from capital investments, which are provided for in the project. As a rule, the calculations take into account the time aspect of the value of money.

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 select the most attractive of them according to some criteria.

In connection with the above, the following issues will be considered in the work:

Basic principles underlying the analysis of investment projects;

Criteria for making an investment decision;

Criteria for assessing the economic efficiency of investment projects, including indicators of net present value, return on investment, internal rate of return;

1. Decisions on investment projects.

Criteria and rules for their acceptance.

All enterprises are to one degree or another connected with investment activities. Decision-making on investment projects is complicated by various factors: type of investment, cost of the investment project, multiplicity of available projects, limited financial resources available for investment, the risk associated with making a particular decision. In general, all solutions can be classified as follows.

Classification of common investment decisions:

1. mandatory investments, then the network are those that are necessary for the company to continue its activities:

solutions to reduce environmental harm;
improvement of working conditions to state standards.

2. solutions aimed at reducing costs:

solutions to improve the technologies used;
to improve the quality of products, works, services;
improvement of labor organization and management.

3. solutions aimed at expanding and updating the company:

investments in new construction (construction of facilities that will have the status of a legal entity);
investments in the expansion of the company (construction of facilities in new areas);
investments in the reconstruction of the company (construction and installation works on existing premises with partial replacement of equipment);
investments in technical re-equipment (replacement and modernization of equipment).

4. acquisition decisions financial assets:

decisions aimed at forming strategic alliances (syndicates, consortia, etc.);
decisions on the acquisition of companies;
decisions on the use of complex financial instruments in operations with fixed capital.

5. solutions for developing new markets and services;

6. decisions on the acquisition of intangible assets.

The degree of responsibility for the adoption of an investment project within a particular direction varies. Thus, if we are talking about replacing existing production capacities, the decision can be made quite painlessly, since the management of the enterprise clearly understands in what volume and with what characteristics new fixed assets are needed. The task becomes more complicated when it comes to investments related to the expansion of core activities, since in this case it is necessary to take into account a number of new factors: the possibility of changing the position of the company in the goods market, the availability of additional volumes of material, labor and financial resources, the possibility of developing new markets, etc. d.

Obviously, the important question is the size of the proposed investment. Thus, the level of responsibility associated with the acceptance of projects worth $100 thousand and $1 million is different. Therefore, the depth of analytical study of the economic side of the project, which precedes decision-making, must also be different. In addition, in many companies the practice of differentiating the right to make investment decisions is becoming commonplace, i.e. the maximum amount of investment within which one or another manager can make independent decisions is limited.

Often decisions must be made in conditions where there are a number of alternative or mutually independent projects. In this case, it is necessary to make a choice of one or more projects based on some criteria. Obviously, there may be several criteria, and the probability that one project will be preferable to others according to all criteria is, as a rule, significantly less than one.

Two analyzed projects are called independent if the decision to accept one of them does not affect the decision to accept the other.

Two analyzed projects are called alternative if they cannot be implemented simultaneously, i.e. acceptance of one of them automatically means that the second project must be rejected.

In conditions market economy There are plenty of investment opportunities. However, any enterprise has limited financial resources available for investment. Therefore, the task of optimizing the investment portfolio arises.

A very significant risk factor. Investment activity is always carried out under conditions of uncertainty, the degree of which can vary significantly. Thus, at the time of acquiring new fixed assets, it is never possible to accurately predict the economic effect of this operation. Therefore, decisions are often made on an intuitive basis.

Making investment decisions, like any other type of management activity, is based on the use of various formalized and informal methods and criteria. The degree of their combination is determined by various circumstances, including the extent to which the manager is familiar with the existing apparatus applicable in a particular case. In domestic and foreign practice, a number of formalized methods are known, with the help of which calculations can serve as the basis for decision-making in the field of investment policy. There is no universal method suitable for all occasions. Perhaps management is still more of an art than a science. Nevertheless, having some estimates obtained by formalized methods, even if somewhat conditional, makes it easier to make final decisions.

Criteria for making investment decisions:

1. criteria to assess the feasibility of the project:

normative criteria (legal) i.e. norms of national and international law, requirements of standards, conventions, patentability, etc.;
resource criteria, by type:

Scientific and technical criteria;

Technological criteria;

Production criteria;

Volume and sources of financial resources.

2. quantitative criteria to assess the feasibility of the project.

Compliance with the long-term goals of the project and the development goals of the business environment;
Risks and financial consequences(whether they add to investment costs or reduce expected output, price or sales);
The degree of sustainability of the project;
Probability of scenario design and state of the business environment.

3. quantitative criteria. (financial and economic), allowing you to choose from those projects whose implementation is advisable. (acceptability criteria)

project cost;
net present value;
profit;
profitability;
internal rate of return;
payback period;
sensitivity of profit to the planning horizon (term), to changes in the business environment, to errors in data assessment.

In general, making an investment decision requires the collaboration of many people with different backgrounds and different views on investing. However, the final word remains with the financial manager, who adheres to certain rules.

Rules for making investment decisions:

invest cash into production or securities only makes sense if you can get a net profit higher than from keeping money in a bank;
it makes sense to invest only if the return on investment exceeds the inflation rate;
It makes sense to invest only in the most profitable projects, taking into account discounting.

Thus, the decision to invest in a project is made if it meets the following criteria:

low cost of the project;
minimizing the risk of inflationary losses;
short payback period;
stability or concentration of revenues;
high profitability as such and after discounting;
lack of more profitable alternatives.

In practice, projects are selected not so much as the most profitable and least risky, but rather those that best fit into the company's strategy.

2. Investment project. Assessment methods.

Investment projects analyzed during the capital budgeting process have a certain logic.

It is customary to associate a cash flow (Cash Flow) with each investment project, the elements of which are either net outflows (Net Cash Outflow) or net cash inflows (Net Cash Inflow). Under the net outflow in kth year is understood to be an excess of current cash expenses for the project over current cash inflows (with the opposite ratio, there is a net inflow). A 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 year, although this limitation is not mandatory. The analysis can be carried out over equal periods of any duration (month, quarter, year, etc.). At the same time, however, it is necessary to remember the comparability of the values of the elements of cash flow, interest rate and length of the period.

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

The inflow (outflow) of funds refers to the end of the next year.

The discount factor used to value projects using discounted valuation methods should be consistent with the length of the period underlying the investment project (for example, an annual rate is taken only if the period length is a year).

It must be especially emphasized that the use of methods for assessing and analyzing projects involves a multiplicity of forecast estimates and calculations used. Plurality is determined by both the possibility of applying a number of criteria and the unconditional advisability of varying the basic parameters. This is achieved by using simulation models in a spreadsheet environment.

The criteria used in the analysis of investment activity can be divided into two groups depending on whether the time parameter is taken into account or not:

1. based on discounted valuations ("dynamic" methods):

Net present value - NPV(Net Present Value);
Return on Investment Index - P.I.(Profitability Index);
Internal rate of return - IRR(Internal Rate of Return);
Modified internal rate of return- MIRR(Modified Internal Rate of Return);
Discounted term return on investment - DPP(Discounted Payback Period).

2. based on accounting estimates (“statistical” methods):

Investment payback period - PP(Payback Period);
Investment efficiency ratio - ARR(Accounted Rate of Return).

2.1 Which method is better?

Until very recently, the calculation of the efficiency of capital investments was carried out mainly from a “production” point of view and did not meet the requirements of financial investors:

firstly, static methods were used to calculate the efficiency of investments, which did not take into account the time factor, which is of fundamental importance for financial investor;
secondly, the indicators used were aimed at identifying the production effect of investments, i.e. increasing labor productivity, reducing costs as a result of investments, the financial efficiency of which faded into the background.

Therefore, to assess the financial efficiency of a project, it is advisable to use the so-called. “dynamic” methods, based primarily on discounting the cash flows generated during the implementation of the project. The use of discounting allows us to reflect fundamental principle“tomorrow’s money is cheaper than today’s” and thereby take into account the possibility of alternative investments at the discount rate. General scheme All dynamic methods for assessing efficiency are basically the same and are based on forecasting positive and negative cash flows (roughly speaking, expenses and income associated with the implementation of the project) for the planning period and comparing the resulting balance of cash flows, discounted at the appropriate rate, with investment costs.

Obviously, this approach involves the need to make a number of assumptions, which are quite difficult to implement in practice (especially in Russian conditions). Let's consider the two most obvious obstacles.

Firstly, it is required to correctly estimate not only the volume of initial capital investments, but also current expenses and revenues for the entire period of the project. The entire conventionality of such data is obvious even in a stable economy with predictable price levels and structure and a high degree of market knowledge. In the Russian economy, the volume of assumptions that have to be made when calculating cash flows is immeasurably higher (the accuracy of the forecast is a function of the degree of systematic risk).

Secondly, to carry out calculations using dynamic methods, the premise of stability of the currency in which cash flows are assessed is used. In practice, this prerequisite is implemented by using comparable prices (with possible subsequent adjustment of the results taking into account the forecast inflation rates) or using stable prices for calculations. foreign currency. The second method is more appropriate in the case of implementing an investment project together with foreign investors.

Of course, both of these methods are far from perfect: in the first case, possible changes in the price structure remain out of sight; in the second, in addition to this, the final result is also influenced by changes in the structure of foreign exchange and ruble prices, inflation of the foreign currency itself, exchange rate fluctuations, etc.

In this regard, the question arises about the advisability of using dynamic methods for analyzing production investments in general: after all, in conditions of high uncertainty and when making various kinds of assumptions and simplifications, the results of the corresponding calculations may turn out to be even further from the truth. It should be noted, however, that the purpose of quantitative methods for assessing efficiency is not an ideal forecast of the amount of expected profit, but, first of all, to ensure the comparability of the projects under consideration in terms of efficiency, based on certain objective and re-verifiable criteria, and thereby preparing the basis for making the final solutions.

Analysis of the development and dissemination of dynamic methods for determining the effectiveness of investments proves the necessity and possibility of their use for evaluating investment projects. In highly developed industrial countries 30 years ago, the attitude towards these methods of assessing efficiency was approximately the same as in our time in Russia: in 1964 in the USA, only 16% of surveyed enterprises used dynamic calculation methods in investment analysis. By the mid-1980s, this share had risen to 86%2. In countries Central Europe(Germany, Austria, Switzerland) in 1989, more than 88% of surveyed enterprises used dynamic calculation methods to assess the effectiveness of investments. It should be taken into account that in all cases, industrial enterprises were studied, which often make investments due to technical necessity. All the more important is the dynamic analysis of investment projects in the activities of a financial institution that is profit-oriented and has numerous opportunities for alternative investment of funds.

Finally, measures to assess investment risk and the use of methods for taking into account uncertainty in financial calculations, which can 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.

Of the variety of dynamic methods for calculating the effectiveness of investments, the most well-known and often used in practice are the method of estimating the internal rate of return of a project and the method of estimating the net present value of the project. In addition, there are a number of special methods.

2.2 Net present value.( NPV )

This method is based on comparing the value of the initial investment (IC) with the total amount of discounted net cash receipts generated by it during the forecast period. Since the cash inflow is distributed over time, it is discounted using the coefficient r, established by the analyst (investor) independently based on annual percentage the return he wants or can have on the capital he invests.

Suppose a forecast is made that the investment (IC) will generate, over n years, annual income in the amount of P 1, P 2, ..., P n. The total accumulated value of discounted income (PV) and net present value (NPV) are respectively calculated using the formulas:

Obviously, if: NPV > 0, then the project should be accepted;

NPV< 0, то проект следует отвергнуть;

NPV = 0, then the project is neither profitable nor unprofitable.

When forecasting income by year, it is necessary, if possible, to take into account all types of income, both production and non-production, that may be associated with a given project. Thus, if at the end of the project implementation period it is planned to receive funds in the form of the liquidation value of equipment or the release of part of working capital, they should be taken into account as income of the corresponding periods.

If the project does not involve a one-time investment, but sequential investment of financial resources over m years, then the formula for calculating NPV is modified as follows:

where i is predicted average level inflation.

Calculation using the above formulas manually is quite labor-intensive, therefore, for the convenience of using this and other methods based on discounted valuations, special statistical tables have been developed in which the values are tabulated compound interest, discount factors, discounted value monetary unit etc. depending on the time interval and the value of the discount factor.

It should be noted that the NPV indicator reflects the forecast assessment of the change economic potential enterprises in case of acceptance of the project under consideration. This indicator is additive in the time aspect, i.e. the NPV of various projects can be summed up. This is a very important property that distinguishes this criterion from all others and allows it to be used as the main one when analyzing the optimality of an investment portfolio.

It is required to analyze an investment project with the following characteristics (million rubles): - 150, 30, 70, 70, 45. Let's consider two cases:

a) price of capital 12%;

b) the price of capital is expected to change over the years as follows: 12%, 13%, 14%, 14%.

In case a) we use formula (1): NPV = 11.0 million rubles, i.e. the project is acceptable.

B) Here NPV is found by direct calculation:

NPV= -150 + ?? + ??? + ?????? + ?????? = - 1.2 million rubles,

1,12 1,12?1,13 1,12?1,13?1,14 1,12?1,13?1,14 2

those. the project is unprofitable.

NPV-method.

Using the NPV method, you can determine not only commercial viability project, but also to calculate a number of additional indicators. Such a wide range of applications and the relative simplicity of calculations have ensured that the NPV method is widely used, and currently it is one of the standard methods for calculating investment efficiency recommended for use by the UN and the World Bank.

However, correct use of the NPV method is only possible if a number of conditions are met:

The volume of cash flows within the investment project must be assessed for the entire planning period and tied to certain time intervals. Cash flows within the investment project should be considered in isolation from the rest production activities enterprises, i.e. characterize only payments and receipts directly related to the implementation of this project. The discounting principle used in calculating net present income, from an economic point of view, implies the possibility of unlimited attraction and investment financial resources at the discount rate. Using the method to compare the effectiveness of several projects involves using a single discount rate for all projects and a single time interval (defined, as a rule, as longest period implementations from the available ones).

When calculating NPV, as a rule, a constant discount rate is used, but depending on the circumstances (for example, changes in the level of interest rates are expected), the discount rate can be differentiated by year. If during the calculations different discount rates are used, then, firstly, formulas (1) and (2) are not applicable and, secondly, the project is acceptable at constant rate discounting may become unacceptable.

This method is essentially a corollary of the net present value method. The profitability index (PI) is calculated using the formula

Obviously, if: PI > 1, then the project should be accepted;

PI< 1, то проект следует отвергнуть;

PI = 1, then the project is neither profitable nor unprofitable.

The logic of the PI criterion is as follows: it characterizes income per unit of cost; It is this criterion that is most preferable when it is necessary to organize independent projects to create an optimal portfolio in the case of an upper limit on the total investment volume.

In contrast to the net present effect, the profitability index is relative indicator. Thanks to this, it is very convenient when choosing one project from a number of alternative ones that have approximately the same NPV values. or when completing an investment portfolio with the maximum total NPV value.

2.4 Internal rate of return on investments.( IRR )

The second standard method for assessing the effectiveness of investment projects is the method of determining the internal rate of return of the project (internal rate of return, IRR), i.e. such a discount rate at which the net present value equals zero.

IRR = r, at which NPV = f(r) = 0.

The meaning of calculating this coefficient when analyzing the effectiveness of planned investments is as follows: IRR shows the maximum permissible relative level of expenses that can be associated with a given project. For example, if the project is financed entirely by a loan commercial bank, then the IRR value shows the upper limit of the acceptable level of the bank interest rate, the excess of which makes the project unprofitable.

In practice, any enterprise finances its activities, including investment, from various sources. As payment for the use of financial resources advanced into the activities of the enterprise, it pays interest, dividends, remuneration, etc., i.e. bears some reasonable expenses to maintain its economic potential. The indicator characterizing the relative level of these expenses can be called the “price” of advanced capital (CC). This indicator reflects the minimum return on capital invested in its activities at the enterprise, its profitability and is calculated using the weighted arithmetic average formula.

The economic meaning of this indicator is as follows: an enterprise can make any investment decisions, the level of profitability of which is not lower than the current value of the CC indicator (or the price of the source of funds for this project, if it has a target source). It is with this that the IRR calculated for a specific project is compared, and the relationship between them is as follows.

If: IRR > CC. then the project should be accepted;

IRR< CC, то проект следует отвергнуть;

IRR = CC, then the project is neither profitable nor unprofitable.

The practical application of this method is complicated if the analyst does not have a specialized financial calculator at his disposal. In this case, the method of successive iterations is used using tabulated values of discount factors. To do this, using tables, two values of the discount factor r 1 are selected

where r 1 is the value of the tabulated discount factor at which f(r 1)>0 (f(r 1)<0);

r 2 - the value of the tabulated discount factor at which f(r 2)<О (f(r 2)>0).

The accuracy of calculations is inversely proportional to the length of the interval (r 1 ,r 2), and the best approximation using tabulated values is achieved when the length of the interval is minimal (equal to 1%), i.e. r 1 and r 2 are the values of the discount factor closest to each other that satisfy the conditions (in the case of changing the sign of the function from “+” to “-”):

r 1 - the value of the tabulated discount factor that minimizes the positive value of the NPV indicator, i.e. f(r 1)=min r (f(r)>0);

r 2 - the value of the tabulated discount factor that maximizes the negative value of the NPV indicator, i.e. f(r 2)=max r (f(r)<0}.

By mutually replacing the coefficients r 1 and r 2, similar conditions are written for the situation when the function changes sign from “-” to “+”.

Let's take two arbitrary values of the discount factor: r = 10%, r = 20%. The corresponding calculations using tabulated values are given in Table 1.

The IRR value is calculated using the formula as follows:

IRR = 10% + ????? (20% -10%) = 16.6%.

You can clarify the obtained value. Let's assume that through several iterations we have determined the nearest integer values of the discount factor at which NPV changes sign: at r = 16% NPV = +0.05; at r = 17% NРV = -0.14. Then the adjusted IRR value will be equal to:

IRR = 16% + ????? (17% -16%) = 16.26%.

Scope and difficulties IRR-method.

When analyzing the conditions for applying the IRR method in the literature, two types of investment projects are distinguished: isolated investments, or pure investments, and mixed investments.

Net investments are understood as investments that do not require intermediate capital investments, and the funds received from the implementation of the project are used to depreciate the invested capital and as income. A normal sign of net investment is the nature of the dynamics of the balance of cash flows: up to a certain point in time, only negative balances (i.e., the excess of expenses over income), and then - only positive balances (net income), and the final balance of cash flows must be non-negative (i.e. i.e. the project must be nominally profitable).

A formal sign of mixed investments is the alternation of positive and negative cash flow balances during the implementation of the project.
An unambiguous determination of the IRR indicator becomes impossible, and the use of the IRR method for analyzing mixed investments is inappropriate. The efficiency of mixed investments is calculated using the NPV method or one of the special methods for calculating efficiency. Therefore, when speaking further about the IRR method, we will be referring to the analysis of only net investments.

To determine the effectiveness of an investment project by calculating the internal rate of return, a comparison of the obtained value with the base interest rate, which characterizes the effectiveness of the alternative use of financial resources, is used. The project is considered effective if the following inequality is satisfied:

IRR > i, where i is some base interest rate.

This criterion is also focused primarily on taking into account the possibilities of alternative investments of financial resources, since it does not show the absolute efficiency of the project as such (for this a non-negative IRR rate would be sufficient), but the relative efficiency - in comparison with operations in the financial market.

The IRR indicator can also be used to compare the effectiveness of various investment projects with each other. However, here a simple comparison of the values of the internal rate of return of the compared projects may not be enough. In particular, the results obtained when comparing the effectiveness of investment projects using NPV and IRR methods can lead to fundamentally different results. This is due to the following circumstances: to achieve absolute comparability of projects, it is necessary to use the so-called. additional investments to eliminate differences in the volume of invested capital and the timing of project implementation. When using the NPV method, it is assumed that additional investments are also discounted at the base interest rate i, while using the IRR method assumes that additional investments also have a return equal to the internal rate of return of the analyzed project and which is obviously higher than the base discount rate .

In practice, comparative analysis of investment projects is carried out in most cases using a simple comparison of the values of internal rates of return. Despite a certain theoretical incorrectness, this approach allows us to eliminate the influence of the subjective choice of the base interest rate on the results of the analysis. Indeed, the main purpose of using complementary investment tools is to try to harmonize the results comparative analysis using the NPV and IRR methods, more precisely, link the second to the first, since with this approach the net present value of the project has priority. In addition, the use of an additional investment tool is correct only in the case of a comparative analysis of alternative, or mutually exclusive, projects, which further narrows the scope of its application and makes it completely unsuitable for analyzing an investment program.

In general, compared to the NPV method, the use of the internal rate of return indicator is associated with greater limitations.

Firstly, for the IRR method all the restrictions of the NPV method are valid, i.e. the need for an isolated consideration of an investment project, the need to forecast cash flows for the entire period of project implementation, etc.

Secondly, the scope of application of the IRR method is limited only to the area of net investment.

2.5 Payback period of investment.( PP )

This method is one of the simplest and widely used in world practice; it does not imply a temporal ordering of cash receipts. The algorithm for calculating the payback period (PP) depends on the uniform distribution of projected income from the investment. If income is distributed evenly over the years, then the payback period is calculated by dividing one-time costs by the amount of annual income due to them. When a fraction is obtained, it is rounded up to the nearest whole number. If the profit is distributed unevenly, then the payback period is calculated by directly calculating the number of years during which the investment will be repaid by cumulative income. General formula calculation of the PP indicator has the form:

РР = n, at which Рк > IC.

The payback period indicator is very simple to calculate; however, it has a number of disadvantages that must be taken into account in the analysis.

First, it does not take into account the impact of recent earnings. Secondly, since this method is based on non-discounted valuations, it does not distinguish between projects with the same amount of cumulative income, but a different distribution of them over the years.

There are a number of situations in which the use of a method based on calculating the payback period may be appropriate. In particular, this is a situation when the management of an enterprise is more concerned with solving the problem of liquidity, rather than the profitability of the project - the main thing is that the investment pays off as soon as possible. The method is also good in situations where investments involve a high degree of risk, so the shorter the payback period, the less risky the project is. This situation is typical for industries or activities that are characterized by a high probability of fairly rapid technological change.

2.6 investment efficiency ratio.( ARR )

This method has two character traits: it does not involve discounting income indicators; income is characterized by the indicator net profit PN ( book profit excluding contributions to the budget). The calculation algorithm is extremely simple, which predetermines the widespread use of this indicator in practice: the investment performance ratio (ARR) is calculated by dividing the average annual profit PN by average value investments (the coefficient is taken as a percentage). The average investment value is found by dividing the initial amount of capital investment by two, if it is assumed that upon expiration of the implementation period of the analyzed project, all capital costs will be written off; if residual value (RV) is allowed to exist, then its valuation should be excluded.

ARR = _____PN ______

This indicator is compared with the return on advanced capital ratio, calculated by dividing the total net profit of the enterprise by total amount funds advanced for its activities (result of average net balance).

3.Special methods for evaluating investment projects.

The IRR and NPV methods described above are among the traditional investment valuation methods and have been used for more than three decades. In the vast majority of cases, the determination of the net present value and internal rate of return of the project is where the efficiency analysis ends. This state of affairs has an objective basis: these methods are quite simple, do not involve cumbersome calculations and can be used to evaluate almost any investment project, i.e. universal.

However reverse side This universality is the impossibility of taking into account the specifics of the implementation of some investment projects, which to a certain extent reduces the accuracy and correctness of the analysis. Special methods allow you to focus on certain moments, which can be of serious importance for a financial investor and examine the investment project as a whole in more detail. If the indicators of internal rate of return and net present value give only a general idea of what the project is, then the use of special methods allows you to get an idea of its individual aspects and thereby increase the overall level of investment analysis.

The main special methods for assessing efficiency can be divided into two groups: methods based on determining the final cost of the investment project, i.e. given not at the beginning, but at the end of the planning period, which allows us to consider separately the interest rates on attracted and invested capital. Thus, they are based on a fundamentally different approach than traditional methods; methods that are modifications of traditional calculation schemes.

4. How to choose the right discount rate.

Any financial analyst faces the problem of correctly determining the value of the discount factor (or, as it is sometimes called, the discount rate, opportunity cost or required rate of return) when calculating the present value of future cash flows. This operation must be carried out when assessing investment projects, the value of an existing business, certain types of financial assets, as well as when conducting a number of financial transactions. At the same time, the correctness of determining the discount factor is by no means a speculative category, since the final value of the current value of the cash flow depends on its choice, which, in turn, in most of the cases mentioned above is the price of the transaction. What are the main difficulties in choosing an adequate discount rate?

To answer this question, let us first recall the classic definition of the discount rate: The discount rate is the annual rate of return that would currently be received from a similar investment.. We draw readers' attention to the phrase "similar investments". As you know, investments are always characterized not only by a certain profitability, but also by a level of risk corresponding to this profitability. That is, The discount rate is a measure of not only profitability, but also risk. (R)

What are the main approaches to determining the discount rate?
First approach based on the model asset return estimates capital asset pricing model (CAPM), a theoretical model designed to explain the dynamics of securities prices and provide a mechanism by which investors can evaluate the impact of investments in prospective securities on the risk and return of their portfolio.

According to the model, the required rate of return (discount rate, opportunity costs) for any type of investment depends on the risk associated with these investments and is determined by the expression:

R = Rf + (Rm - Rf)b, where

Rf - return on risk-free assets;

Rm - average market rate of return;

b - coefficient (measurement of investment risk).

Note (this is important for further discussion) that this model derived by its author, W. Sharp, under a number of assumptions, the main ones being the assumption of the presence of an efficient capital market and perfect competition among investors.

Thus, according to this model, the required rate of return is equal to the return on alternative risk-free investments for investments with a zero level of risk (b = 0), the average market rate of return if the investment risk is equal to the average market (b = 1), and may also be more or less than Rm (at appropriate values of b).

Second approach to determine the discount rate is associated with the calculation present value of so-called debt-free cash flow(debt free cash flow), often used by investors who are analyzing the amount of cash flow a company generates that can be used to finance new projects, including the purchase or merger of debt-financed companies. To calculate it, the value of the cost of capital used by the company to finance its activities is used. Since such financing involves both own and borrowed funds, then as a value<общей>The cost of capital is the weighted average cost of capital (WACC). The weighted average cost of capital is calculated using the well-known formula:

WACC = St=1n riVi/V, where

ri is the cost of the i-th source of capital;

Vi/V is the share of the i-th source in the total attracted capital (at market value).

It is clear that the profitability of a new investment project must be higher than the WACC value (otherwise there is no point in implementing it, since it will reduce total cost company), so it is logical to use WACC as a discount rate.

And finally, when third approach To determine the value of opportunity costs, the so-called cumulative construction method is used. According to this approach, premiums for different kinds risks associated with a specific investment (country risk, risks associated with the size of the company, with dependence on a key figure, with product/geographical diversification, with clientele diversification, with financial structure, with retrospective predictability, etc.). Typically, the specific amount of the premium for each type of risk (with the exception of country risk) is determined by experts in the probable range from 0 to 5%.

So, it would seem that we are now armed with a variety of methods for determining the value of the discount rate and can easily find its value for evaluating a wide variety of projects, companies or securities. However, as Lewis Carroll's heroine said, this is where the fun begins.

Let's start in order - by determining the discount rate using the CAPM method. Suppose we evaluate the effectiveness of the implemented Russian company investment project. Then, to determine the discount rate, we must know at least three values: the return on risk-free investments, the coefficient b for the selected investment industry, and the average market return.

As a rule, the first of these values is the yield of government securities with an investment horizon similar to the project under study. It is obvious that after the events of August 17, 1998, it is unlikely that any investor would agree that investments in Russian government securities can be considered risk-free.

As for the value of coefficients b, their values are determined based on the analysis of retrospective data and are determined by the relevant statistical services of companies specializing in the market of information and analytical services (for example, Value Line). However, it is hardly possible to talk about the availability of representative databases in Russia now that would allow one to correctly identify industry risks. But even with the values of coefficient b, they can be applied correctly only if, for example, the investment project being evaluated does not go beyond the traditional activities of the company. That is, if a manufacturing company, having made a decision to create its own distribution network, implements an investment project determined by this decision, then the values of b must be looked for among the data on companies engaged in wholesale trade products of a certain type.

In a relationship market premium for risk (Rm - Rf), we note that its value is defined as the average annual excess return (the excess over the rate of return on government bonds with a maturity of 10 years) over an observation period of 5-10 years and is approximately 6-7% (USA, Canada, Japan) and 3-5% (Western European countries). For Russia, as noted above, it is not clear which assets can be considered risk-free, but a fantastic rise stock market in the first half of 1997 was replaced by an equally deep decline, which has been continuing for more than a year. Therefore, it is now simply impossible to talk about determining reasonable parameters for the average annual excess income in Russia.

How can it be applied in our conditions? CAPM model to determine the discount rate? As an alternative, it would be possible to determine the required rate of return for a Western analogue company, and then adjust this value by the amount of country risk, however, here too there is no certainty - different rating agencies assess the risk of investing in Russia differently.

Next, let’s try to imagine that a local investor wants to make the same type of investment in Russia (more precisely, one who has not yet managed to transfer his capital to Western banks and offshore companies) and a foreign investor, and from their position we will evaluate the effectiveness of upcoming investments. Investors must apply different rates of return, since it is obvious that for them, other than equal conditions the risk-free rate of return will be different (what can you do, American treasury bills or government bonds are not yet available to Russian investors!). By the way, the very difference in the risk-free rate for different investors already calls into question the correctness of using the CAPM model to determine the required rate of return, since it is the sameness of the risk-free rate for all investors that is one of the ten conditions given by its author when describing the one we have already mentioned used in its derivation assumptions about the efficiency of the capital market and the perfection of investor competition.

There are two main problems with using WACC as a discount rate:

The WACC reflects the present value of the aggregate of sources used to finance the company's normal capital investments, and when going beyond the normal limits of the organization's activities, the investment is subject to completely different risks than "normal", and therefore the WACC cannot be used as a required rate of return. since it does not take into account the difference in risks of different investments; if the scale of investment is so large that it significantly changes the structure financial sources company, then WACC cannot be used as a discount rate either.

But even if we are talking about ordinary capital investments, then in this case the investments may involve varying degrees of risk. Thus, capital investments associated with replacing equipment are usually less risky than investments made to develop new types of products. When assessing economic efficiency in this case, one can consider the weighted average cost of capital of the company as the minimum acceptable value of opportunity costs, increasing the required rate of return depending on the nature of the investment. Thus, in fact, in in this case When determining the discount rate, expert assessments are used, which introduces an element of subjectivity into this process.

Entirely based on application expert assessments The method of cumulative construction used to determine the value of the discount rate, which means that the above remark regarding the subjectivity of the resulting value of the discount rate fully applies to it (the assessment of risk factors is individual and varies among different investors).

So, it turns out that, no matter what method we try to determine the value of the discount factor, a situation can always arise (and does arise) in which this same factor is different for different investors. We have already given as a similar example the case of investing in Russian project domestic or foreign investor. You can imagine another situation: for example, financing a project by attracting borrowed capital increases the amount of financial leverage of the company and, accordingly, the amount of financial risk, so the discount rate when evaluating the same project for a lender will be greater than for a strategic investor.

Situations similar to those described arise very often, so the reader may have a legitimate question: what value of the comparison rate is considered correct and what method should be used to determine it, if all of the above methods contain an element of uncertainty?

To answer this question, let us remember what was discussed at the beginning of the article - the final value of the current value of cash flows, which is actually the price of the transaction, depends on the value of the discount factor. From here follows the criterion for the acceptability of the required rate of return - it must satisfy both parties involved in the transaction, i.e. a financial analyst, when making the appropriate calculations, must always clearly understand what criteria his counterpart will be guided by when assessing the transaction for his part.

This entails the need for a reasoned justification of the method used to determine the discount rate and the values of the parameters used, taking into account the approaches that a transaction partner may use when determining its price, as well as conducting alternative calculations of the discount rate when trying to conduct a transaction with partners for whom this the quantity can have different meanings.

To summarize our reasoning, we emphasize once again that the choice of the correct value of the discount factor should, of course, be based on the basic theoretical approaches to its determination. However, the art of a financial analyst involved in the assessment of an investment project, a package of securities or an existing business lies in his ability to take into account both the characteristic features of the specific object being assessed and the real conditions of the transaction (the nature and form<оплаты>future economic benefits acquired by the investor or lender, its opportunity costs, etc.).

Additional effort spent on elaborating these nuances will provide the analyst who performed them with a stronger position during negotiations on the transaction price with a future investor.

Conclusion.

In conclusion, I would like to once again dwell on the main points of the work.

Investing is one of the most important aspects of any dynamically developing commercial organization.

For planning and implementation of investment activities, 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 informed management decisions.

The main direction of the preliminary analysis is to determine indicators of the possible economic efficiency of investments, i.e. return on capital investments provided for by the project. As a rule, the calculations take into account the time aspect of the value of money.

When analyzing investment projects, certain assumptions are made. Firstly, it is customary to associate a cash flow with each investment project. Most often, the analysis is carried out by year. It is assumed that all investments are made at the end of the year preceding the first year of the project, although in principle they could be made over a number of subsequent years. The inflow (outflow) of funds refers to the end of the next year.

Indicators used in the analysis of investment performance can be divided into those based on discounted valuations and those based on accounting estimates.

The net present value indicator characterizes the current magnitude of the effect from the future implementation of the investment project.

Unlike the NPV indicator, the profitability index is a relative indicator. It characterizes the level of income per unit of cost, i.e. investment efficiency.

The economic meaning of the IRR criterion is as follows: IRR shows the maximum allowable relative level of costs for the project.

When assessing the effectiveness of capital investments, it is necessary to take into account the impact of inflation. This is achieved by adjusting the cash flow elements or discount factor by the inflation index. Exactly the same principle underlies the risk accounting methodology.

As the results of numerous surveys of decision-making practices in the field of investment policy in market conditions have shown, in analyzing the effectiveness of investment projects, NPV and IRR criteria are most often used. However, there may be situations where these criteria conflict with each other, for example, when evaluating alternative projects.

Quite often in investment practice there is a need to compare projects of different durations.

When drawing up a capital budget, a number of restrictions must be taken into account. For example, there are several attractive investment projects, but the enterprise, due to limited financial resources, cannot implement them all at the same time. In this case, it is necessary to select projects for implementation in such a way as to obtain maximum benefit from investing. As a rule, the main goal in such cases is to maximize the total NPV.

In a real situation, the problem of analyzing capital investments can be very difficult. It is no coincidence that studies of Western investment decision-making practice have shown that the vast majority of companies, firstly, calculate several criteria and, secondly, use the resulting quantitative estimates not as a guide to action, but as food for thought.

Therefore, to summarize, I would like to note that the use of any, even the most sophisticated, methods will not ensure complete predictability of the final result, therefore the main purpose of using the scheme proposed above is not to obtain absolutely accurate results of the effectiveness of the project implementation and its riskiness, but to compare the investment proposals proposed for consideration projects based on a unified approach, using objective and verifiable indicators whenever possible, and compiling a relatively more effective and relatively less risky investment portfolio.

Application.

Investment project of JSC<Рязанский КРЗ>

Address: 390017 Ryazan, st. Druzhnaya, 18.
Telephone: 24-20-52. Fax: 24-20-33.
Head of the enterprise: Meerevich Konstantin Nikolaevich, General Director.

BRIEF DESCRIPTION OF THE APPLICANT COMPANY

Company<Рязанский КРЗ>was created in 1992 and is the legal successor of the state cardboard and roofing felt plant, built in 1962 to provide soft roofing materials to Moscow and the central regions of Russia. The owners of the enterprise are members of the workforce and third parties individuals. Authorized capital as of the registration date - 15.88 million rubles. The enterprise is located 30 km from the center of Ryazan. The total number of employees is 1620 people. total area occupied by the enterprise land plots- 37.2 hectares. The main activities are production building materials(soft roofing, corrugated cardboard, stitched mats) and provision of services (roofing, insulation and construction work). Shipment of products for export accounts for 5% of total sales. The profit received by the enterprise in 1997 amounted to 45,777 thousand rubles. TO main advantages of the enterprise relate:

high professional training of specialists and workers;
high technological production culture;
favorable location of the enterprise in the infrastructure of the Central region of Russia.

GENERAL CONCEPT OF THE PROJECT

technological equipment for allocated funds; highly liquid The project provides for the modernization of a cardboard making machine, which will solve the problem of replacing expensive purchased semi-finished products (cardboard, paper) with self-produced semi-finished products based on waste paper. The company is not changing its scope of activity and plans to implement the project in order to reduce costs and improve product quality. The plant has production facilities and the necessary infrastructure to organize production. Corrugated cardboard is part of the company's product range. There is experience in its production, and sales of products have been established. The supplier of the necessary equipment has been identified. The project is supposed to be implemented within the existing enterprise. Selected project financing strategy- lending. The following collateral can be offered as security for borrowed funds: a block of shares of the enterprise; commercial products purchased by the enterprise.

PROJECT GOALS

Receiving a profit in the amount of 13,210 thousand rubles. in the last billing year of the project. Increasing the enterprise's share in the market of Ryazan and the Ryazan region to almost 100%.

PROJECT IMPLEMENTATION STRATEGY

Obtaining an economic effect from technological re-equipment, leading to a reduction in the cost of an already mastered product.

STATE: FORM AND DEGREE OF PARTICIPATION, REGULATION

The proposed investment project is of federal importance. The idea was supported by the administration of the Ryazan region (the administration provides significant support in resolving issues of forming a raw material base and marketing finished products).

COMPETITORS

Currently, container consumption is at Russian market increases. According to data from 1994-1997, market saturation in the CIS countries was only 15% of demand. The goods supplied as a result of the project are aimed at saturating the market of the Ryazan region. Competitors can be divided into two groups:

enterprises with modern equipment, but located in other regions and incurring more significant transportation costs;
enterprises located in this region, but using outdated resource-intensive technology, which reduces the price competitiveness of their products.

NEED FOR INVESTMENT

The total volume of required external investments is 10,890 thousand rubles.

Investment calendar

USE OF CAPITAL

The production plan assumes a smooth schedule for production to reach its design capacity.

ORGANIZATIONAL CHART OF THE PROJECT IMPLEMENTATION

The project is proposed to be implemented within the framework of an existing enterprise.

FINANCIAL PROPOSAL

Debt financing

Loan name
Amount, thousand rubles
Duration, months

FINANCIAL ASSESSMENT OF THE PROJECT

The calculation horizon is 6 years.

Forecast criteria for investment efficiency

RISKS AND THREATS

Risk factor	Possible losses	Risk prevention and reduction measure
Instability of economic legislation and the current economic situation	Loss of part of the profit	Forecasting possible changes external environment, creation of insurance cash reserves at the enterprise, insurance of contracts for the purchase of raw materials and equipment
Price reduction by competitors	Loss of profit	Reducing product costs, switching to a cost-competitive marketing strategy
Technological risk	Decline in sales volumes	Implementation of technological monitoring and consulting of the created production

Bibliography:

Kovalev V.V. Methods for evaluating investment projects. Moscow, Finance and Statistics, 2000.
Kovalev V.V. Collection of problems on financial analysis. Moscow, Finance and Statistics, 1997.
Market Valuable papers. Magazine. No. 16.1999
Stocks and bods market. Magazine. No. 9.1999
Stocks and bods market. Magazine. No. 4.1999
Northcott D. Making investment decisions. - M.: Banks and exchanges, UNITY, 1997. - 247 p.

Investment activity at an enterprise occurs in the process of implementing one or several investment projects . In economic literature the term investment project means a set of documents reflecting the economic feasibility and efficiency of investing funds (capital) in tangible and intangible entities in order to maintain and expand production. It includes justification for economic efficiency, volume and timing of capital-forming investments, and the necessary design and estimate documentation.

The investment project has three stages in its development: pre-investment(from the moment the entrepreneurial idea arises until the decision to invest), in fact investment stage and operational– beginning with the production operation of the investment object and ending with its planned liquidation. These stages constitute life cycle of an investment project.

Justification of the economic feasibility of an investment project includes determining its economic efficiency, feasibility and reliability.

A distinction is made between the effectiveness of the project as a whole and the effectiveness of participation in the project.

Project efficiency includes public (socio-economic) efficiency and commercial (general economic) efficiency. With its help, the attractiveness of the project for its possible participants is assessed and investors are searched for.

Social (socio-economic) efficiency takes into account socially - economic consequences implementation of an investment project for society as a whole. It includes not only the direct results and costs of the project, but also “external” costs and results in related sectors of the economy, environmental, social and other non-economic effects.

Commercial (overall economic) efficiency investment project takes into account the financial consequences for its participant, provided that he makes all the costs necessary for the implementation of the project from his own funds and uses all its results.

Effectiveness of participation correlates the benefits and costs of each participant (subject) of the investment project (investor, customer, contractor, user of the capital investment object) and economic structures who are not direct participants in the project. It includes:

the effectiveness of participation in the project for its participants (investors, customers, contractors, users of capital investment objects);

efficiency of investing in company shares;

the effectiveness of the project for economic structures that are not participants in the investment project, including:

regional and national economic efficiency - for individual regions and the national economy of the Russian Federation;

industry efficiency - for individual sectors of the national economy, financial and industrial groups, associations of enterprises and holding structures;

budget efficiency– for budgets of all levels and state extra-budgetary funds.

Feasibility of the investment project characterizes the possibility of its implementation given the current state of the internal and external environment of the enterprise. The most important for economic assessment is the financial component of feasibility, which means that an investment project can be implemented only if the required amount of money is available at the time when the investment is made. If the investment is financed by borrowed money then financial feasibility, in addition to the ability to take out a loan in the required amount, includes the cost of the loan. A loan that is too expensive can absorb all the benefits of an investment project and even make it unprofitable.

Economic assessment of investments carried out on the basis of indicators calculated using the discounting technique. This technique takes into account the time factor.

1) When assessing the economic efficiency of investment projects, a direct comparison of the nominal value of investments and income from them gives distorted results, since these cash flows are several years apart.

Discounting allows you to estimate at discounting date cost values related to other points in time - determine their discounted value – DS:

DS (C) = C* (1 + r) - n,

C – estimated value, rub.; DS - cost estimate on the date of discounting (reduction), rub.; r – discount rate; n – time period between date discounting and the date of existence of the assessed value (year, quarter, month).

The multiplier (1 + r) - n, with the help of which different-time values are brought to a comparable form - assessed at the discounting date, is called discount factor.

Discounted values can be summed up. This makes it possible to determine the total estimate of both expenses (for example, the costs of capital investments spread over time) and the total estimate of income.

In practice, most often the discounting date is the current point in time. The indicator characterizing such an assessment , is the current discounted value (TCV), which underlies the calculation of most indicators of economic efficiency of investments.

Net present value (NPV)- one of the main indicators of economic assessment of investments. Its calculation is based on a comparison of discounted expenses with income.

NPV =Σ TDS (D) – Σ TDS (I),

where – D – income for each period of existence of the investment project, I – expenses for each period of existence of the project.

The value of the net present value reflects the increase in the enterprise's income in the event of acceptance of the investment project. In case of refusal to implement the investment project, the funds will be used in some kind of economic circulation - in the so-called investment alternative. Under investment alternative understands the other most likely option for using funds allocated for investment. For example, instead of investing in fixed assets, funds will be placed in a bank deposit account at 10% per annum. If this 10% per annum is used as discount rates - r = 0.1, then when calculating net present value investment project, the resulting value will show how much more income from this project will be than from placing money in a bank.

A positive net present value means that during its economic life investment project:

will reimburse the costs incurred;

will provide an income of 10% - the same as from bank deposit(i.e. will receive income equal to the income from his investment alternative);

will receive additional income equal to the net present value.

When NPV = 0, the income of the investment project and its investment alternative (income from placing money in a deposit account) are the same. A negative NPV value indicates that the investment alternative is more effective, although the investment project may have some profit.

When calculating discounted indicators, the most important thing is the correct definition discount rates. As minimum value(barrier rate) discount rates apply the profitability of possible alternative uses of funds in the event of abandonment of the investment. For agricultural enterprises, an alternative to investment in most cases is the use of funds in existing production activities. The determination of the discount rate in this case is based on planned profitability taking into account inflation. Inflation is taken into account if the investment project is calculated in forecast (deflated) ) prices If current prices are used, inflation is not taken into account in the discount rate.

The most common relative indicator of the economic efficiency of investments is profitability index(IR). It characterizes how much the return on an “initial” investment (for example, capital investment) is higher than that of an investment alternative. This indicator is calculated as the ratio of the sum of current discounted income (D) to the sum of current discounted costs of investments (I).

MINISTRY OF COMMUNICATIONS OF THE RF

FAR EASTERN STATE UNIVERSITY OF COMMUNICATIONS

Test

By discipline: Economics of Investments

Khabarovsk 2002

Introduction

1.The concept of effect and efficiency. Investment project performance indicators

2. Procedure for selecting investment projects

3. Problem solving

Conclusion

List of sources used

Initial investment

Annual savings

Annual savings

Annual savings

Pure modern meaning

Investment activity, to one degree or another, is inherent in any enterprise. Making an investment decision is impossible without taking into account the following factors: type of investment, cost of the investment project, multiplicity of available projects, limited financial resources available for investment, risk associated with making a particular decision, etc.

The reasons for the need for investment may be different, but in general they can be divided into three types: updating the existing material and technical base, increasing the volume of production activities, and developing new types of activities. The degree of responsibility for the adoption of an investment project within a particular direction varies. Thus, if we are talking about replacing existing production capacities, the decision can be made quite painlessly, since the management of the enterprise clearly understands in what volume and with what characteristics new fixed assets are needed. The task becomes more complicated when it comes to investments related to the expansion of core activities, since in this case it is necessary to take into account a number of new factors: the possibility of changing the position of the company in the goods market, the availability of additional volumes of material, labor and financial resources, the possibility of developing new markets, etc. .

Obviously, the important question is the size of the proposed investment. Thus, the level of responsibility associated with the acceptance of projects worth 1 million rubles. and 100 million rubles, different. Therefore, the depth of analytical study of the economic side of the project, which precedes decision-making, must also be different. In addition, in many companies the practice of differentiating the right to make decisions of an investment nature is becoming commonplace, i.e., the maximum amount of investment within which a particular manager can make independent decisions is limited.

Often decisions must be made in conditions where there are a number of alternative or mutually independent projects. In this case, it is necessary to make a choice of one or more projects based on some criteria. Obviously, there may be several such criteria, and the probability that one project will be preferable to others according to all criteria is, as a rule, significantly less than one.

1.The concept of effect and efficiency. Investment project performance indicators

The effectiveness of the project is characterized by a system of indicators reflecting the ratio of costs and results in relation to the interests of its participants.

The following indicators of the effectiveness of an investment project differ:

· indicators of commercial (financial) efficiency, taking into account the financial consequences of the project for its direct participants;

· budget efficiency indicators reflecting the financial consequences of the project for the federal, regional or local budget;

· economic efficiency indicators that take into account the costs and results associated with the implementation of the project, going beyond the direct financial interests of the participants in the investment project and allowing value measurement. For large-scale projects (significantly affecting the interests of a city, region or all of Russia) it is recommended to evaluate the economic efficiency.

Let's consider the main performance indicators of investment projects.

An indicator of net present value.

This method is based on comparing the value of the original investment (IC) with the total discounted net cash flows it generates over the forecast period. Since the cash inflow is distributed over time, it is discounted using a factor r set by the analyst (investor) independently based on the annual percentage return that he wants or can have on the capital he invests.

Obviously, if: NPV > 0, then the project should be accepted;

NPV< 0, то проект следует отвергнуть;

NPV = 0, then the project is neither profitable nor unprofitable.

If the project does not involve a one-time investment, but sequential investment of financial resources over m years, then the formula for calculating NPV is modified as follows:

where i is the projected average inflation rate.

Internal rate of return.

The investment return rate (IRR) is understood as the value of the discount factor at which the NPV of the project is equal to zero:

IRR = r, at which NPV = f(r) = 0.

The meaning of calculating this coefficient when analyzing the effectiveness of planned investments is as follows: IRR shows the maximum permissible relative level of expenses that can be associated with a given project. For example, if a project is financed entirely by a loan from a commercial bank, then the IRR value shows the upper limit of the acceptable bank interest rate, above which the project will be unprofitable.

If: IRR > CC. then the project should be accepted;

IRR< CC, то проект следует отвергнуть;

IRR = CC, then the project is neither profitable nor unprofitable.

where r 1 is the value of the tabulated discount factor at which f(r 1)>0 (f(r 1)<0);

r 2 - the value of the tabulated discount factor at which f(r 2)<О (f(r 2)>0).

r 1 - the value of the tabulated discount factor that minimizes the positive value of the NPV indicator, i.e. f(r 1)=min r (f(r)>0);

r 2 - the value of the tabulated discount factor that maximizes the negative value of the NPV indicator, i.e. f(r 2)=max r (f(r)<0}.

By mutually replacing the coefficients r 1 and r 2, similar conditions are written for the situation when the function changes sign from “-” to “+”.

Payback period.

This method is one of the simplest and widely used in global accounting and analytical practice; it does not imply a temporal ordering of cash receipts. The algorithm for calculating the payback period (PP) depends on the uniformity of the distribution of projected income from the investment. If income is distributed evenly over the years, then the payback period is calculated by dividing one-time costs by the amount of annual income due to them. When a fraction is obtained, it is rounded up to the nearest whole number. If the profit is distributed unevenly, then the payback period is calculated by directly calculating the number of years during which the investment will be repaid by cumulative income. The general formula for calculating the PP indicator is:

PP=n, at which.

Some experts still recommend taking into account the time aspect when calculating the PP indicator. In this case, cash flows discounted according to the “price” of the advanced capital are taken into account. Obviously, the payback period is increasing.

Profitability index.

This method of assessing the effectiveness of a project is essentially a consequence of the net present value method. The profitability index (PI) is calculated using the formula

Obviously, if: P1 > 1, then the project should be accepted;

P1< 1, то проект следует отвергнуть;

P1 = 1, then the project is neither profitable nor unprofitable.

In contrast to the net present effect, the profitability index is a relative indicator. Thanks to this, it is very convenient when choosing one project from a number of alternative ones that have approximately the same NPV values. or when completing an investment portfolio with the maximum total NPV value.

Investment efficiency ratio.

This method has two characteristic features: firstly, it does not involve discounting income indicators; secondly, income is characterized by the net profit indicator PN (balance sheet profit minus contributions to the budget). The calculation algorithm is extremely simple, which predetermines the widespread use of this indicator in practice: the investment efficiency ratio (ARR) is calculated by dividing the average annual profit PN by the average investment value (the coefficient is taken as a percentage). The average investment value is found by dividing the initial amount of capital investment by two, if it is assumed that upon expiration of the implementation period of the analyzed project, all capital costs will be written off; if residual or salvage value (RV) is allowed to exist, then its valuation should be excluded.

This indicator is compared with the return on advanced capital ratio, calculated by dividing the total net profit of the enterprise by the total amount of funds advanced into its activities (the result of the average net balance).

The method based on the investment efficiency ratio also has a number of significant disadvantages, mainly due to the fact that it does not take into account the time component of cash flows. In particular, the method does not distinguish between projects with the same amount of average annual profit, but varying amounts of profit over the years, or between projects with the same average annual profit, but generated over a different number of years. and so on.

2. Procedure for selecting investment projects

All enterprises are to one degree or another connected with investment activities. Decision-making on investment projects is complicated by various factors: the type of investment, the cost of the investment project, the multiplicity of available projects, the limited financial resources available for investment, the risk associated with making a particular decision.

In a market economy, there are a lot of investment opportunities. However, any enterprise has limited financial resources available for investment. Therefore, the task of optimizing the investment portfolio arises.

When selecting investment projects, the economic efficiency of the project is taken into account based on the following main criteria:

· volume of products (in value and physical terms);

· financial results;

· availability of markets for products;

· production profitability;

· return on investment;

· volume of invested funds;

· project payback period;

· net income, internal rate of return;

· social effectiveness of the project, based on the following main criteria:

· number of new jobs;

· number of social problems being solved;

· wage level;

· environmental Safety.

For applicants for administration support Khabarovsk Territory in the form of state guarantees of the Khabarovsk Territory or regional investment resources on the basis of the “Regulations on the procedure for competitive selection and examination of investment projects, the implementation of which requires state support Administration of the Khabarovsk Territory", approved by the Resolution of the head of the Khabarovsk Territory administration dated July 26, 2001, No. 315, establishes additional criteria:

· guarantees of repayment of borrowed funds and interest for the use of borrowed funds;

· ensuring risks of irrecoverability.

When selecting investment projects, preference is given to applicants:

· having a stable financial position;

· not having debts on taxes and fees to the regional budget;

· having a certificate of a law-abiding taxpayer of the Khabarovsk Territory;

· providing for financing of the investment project from own funds in an amount of at least 20 percent;

· winners and laureates of the regional competition "Entrepreneur of the Year".

3. Problem solving

Task No. 1

Condition:

Exercise: determine the economic efficiency of the proposed equipment renewal project, calculate the internal rate of return on investment, and the repayment period for one-time costs.

Solution:

1. determination of the economic efficiency of the project.

The economic efficiency coefficient is equal to:

ARR = (3750/5) / = 1.07. Therefore, the project is effective.

2. calculation of the internal rate of return.

Table 3.1.

Initial data for calculating the IRR indicator.

Based on the calculations given in table. 3.1, we can conclude that the function NPV=f(r) changes its sign over the interval (41%,42%).

IRR = 41 + * (41 - 42) = 41.2%

3. determination of the period for repayment of one-time costs.

Investments amount to 18,530 million rubles. in the 0th year. Revenues will cover investments for 2 years. For the first year, revenues amount to 900 million rubles.

For 2 years it is necessary to cover:

1600 – 900 = 700 million rubles,

700 / 800 = 0.875, which is 10.5 months.

Task No. 2

Condition:

Exercise: To determine the cost-effectiveness of introducing self-propelled vehicles with a walkie-talkie at a technical point.

Solution:

1. Determination of economic efficiency:

Due to changing operating costs and capital investments, it is advisable to determine the efficiency of using mobile machines with a walkie-talkie by the amount of savings in the given costs using the following formula:

ΔЗ = ΔEgod + En * ΔK,

where ΔEgod is the total savings in operating costs as a result of the use of mobile machines;

En – standard of comparative economic efficiency, = 0.15;

ΔК – savings on capital investments in the locomotive fleet.

1.1. Determining total operating cost savings:

ΔEgod = ΔE + ΔFZP + ΔEo – ΔEdop,

where ΔE – annual savings in operating costs;

ΔFZP – wage fund savings;

ΔEo – reduction of part of the main general and general expenses associated with the costs of issuing, wear and tear uniforms, safety and industrial sanitation as a result of staff reduction, calculated at 300 rubles. per year for 1 person;

ΔEdop – saving additional operating costs.

ΔE = (1l-h * ΔΣt + 1b-h * ΔΣMt + bet * 1fl * ΣM + 1v-h * ΔΣt * M * m) * 365,

where 1l-h is the consumption rate for a locomotive - hour, = 5,112 rubles;

1b-h - expense rate per brigade - hour of locomotive crews, = 33.72 rubles;

1 w-hour – expense rate per car – hour, = 1,485 rubles;

1 floor – cost of 1 kWh of electricity (1 kg of fuel), = 400 rubles.

bet – hourly consumption of electricity (fuel) when the locomotive is parked, = 55 kWh;

m – train composition.

Hence, ΔE = (5.112 * 0.1 + 33.72 * 75 * 0.1 + 55 * 400 * 75 + 1.485 * 0.1 * 75 * 50) * 365 = 602545754 rub.

Determining the volume of reduction in the wage fund as a result of reducing the labor intensity of work: ΔFZP = ΔЧ * З * 12 * 1.385 * 1.1,

where 1.385 is a coefficient that takes into account social insurance contributions;

1.1 – replacement rate;

Z – average monthly salary, 1500 rubles.

ΔFZP = 15 * 1500 * 12 * 1.385 * 1.1 = 411345 rub.

ΔEo = 300 * 15 = 4500 rub.

ΔEdop = Ea + Em + Ep.

Ea – increase in depreciation charges,

Ea = (Km * Cm * a) / 100,

where Km is the number of mobile vehicles;

Cm – cost of the car, 30.5 thousand rubles;

A – depreciation rate, 9.9%.

Ea = (2 * 30.5 * 9.9) / 100 = 6000 rub.

Em - expenses for the current maintenance of machines:

Em = 2000 * 2 + 30500*0.05*2 = 7050 rub.

Ep – costs of maintaining narrow gauge tracks:

Ep = 800 * 2 * 200 = 320,000 rub.

ΔEdop = 6000 + 7050 + 320000 = 333050 rub.

Thus,

ΔEgod = 602545754 + 411345 + 4500 – 333050 = 602628549 rub. = 602.629 million rubles.

1.2. Calculation of capital investments.

In this case, the amount of capital investment savings will be:

ΔK = Kl + Kv + Kst,

Kl – savings on capital investments in the locomotive fleet:

Kl = (75/24)*1.25*820000 = 3203125 rub.

Kv – savings on capital investments in the rolling stock:

Kv = (0.10*2*50) / 24 * 1.1 * 58500 = 26812.5 rub.

Kst – savings on capital investments in the development of station tracks:

Kst = (0.10*2*50) / 24 * 16.4 * 3.5 * 0.7 * 2500 = 41854.167 rub.

ΔK = 3203125 + 26812.5 + 41854.167 = 3271792 rub.

Thus,

ΔЗ = 602628549 + 0.15 * 3271792 = 603119318 rub. = 603.12 million rubles.

Task No. 3

Condition:

The profitability standard (comparison rate is 10%), the duration of the investment process is 2 years.

Exercise: It is necessary to select a construction project.

Solution:

Project B requires a larger amount of investment compared to project A (60+5 – 20+40 = 5 million dollars). However, the income stream in project B covers the investment for 2 years, while in project A the payback period will be more than 3 years.

Moreover, within 5 years, the profit volume for project A will reach only $73 million, and for project B - $103 million.

Thus, there are objective grounds for recognizing project B as more profitable, despite the initially large amount of investment compared to project A.

CONCLUSION

In a market economy, there are quite a lot of investment opportunities. At the same time, any enterprise has limited free financial resources available for investment. Therefore, the task of optimizing the investment portfolio arises.

The risk factor is very significant. Investment activity is always carried out under conditions of uncertainty, the degree of which can vary significantly. Thus, at the time of acquiring new fixed assets, it is never possible to accurately predict the economic effect of this operation. Therefore, decisions are often made on an intuitive basis.

Making investment decisions, like any other type of management activity, is based on the use of various formalized and informal methods. The degree of their combination is determined by various circumstances, including the extent to which the manager is familiar with the existing apparatus applicable in a particular case. In domestic and foreign practice, a number of formalized methods are known, calculations with the help of which can serve as the basis for making decisions in the field of investment policy. There is no universal method suitable for all occasions. Perhaps management is still more of an art than a science. Nevertheless, having some estimates obtained by formalized methods, even if somewhat conditional, makes it easier to make final decisions.

The process of making management decisions of an investment nature is based on the assessment and comparison of the volume of proposed investments and future cash receipts. Since the compared indicators refer to different points in time, the key issue here is the problem of their comparability. It can be treated differently depending on the existing objective and subjective conditions: the inflation rate, the size of investments and generated revenues, the forecasting horizon, the level of qualifications of the analyst, etc.

LIST OF SOURCES USED

1. Winn R., Holden K. Introduction to econometric analysis. - M.: Finance and Statistics, 1991.

2. Volkov B.A. Economic efficiency of investments in railway transport in market conditions. - M.: Transport, 1999.

3. Vodyanov A.A. Investment processes in the economy transition period. (Methods of research and forecasting). - M.: IMEI, 1998.

4. Issues of state regulation of the economy: main directions and forms // Marketing in Russia and abroad, 2000. - No. 5.

5. Dontsova L.V. System of regulation of investment processes in developed countries // Marketing in Russia and abroad, 1999 - No. 4.

6. Egorova E.N., Petrov Yu.A. Comparative analysis of foreign tax systems and the development of taxation in Russia. - M.: CEMI RAS, 2000.

7. Tax policy in industrial countries. Collection of reviews. - M.: INION RAS, 1995.

8. Complete collection of codes Russian Federation. With changes and additions as of May 1, 2002. – M.: LLC “Firm Publishing House AST”, 2002.

9. Complete collection of laws of the Russian Federation. With changes and additions as of August 1, 2002. – M.: LLC “Firm Publishing House AST”, 2002.

7. Main criteria for the effectiveness of an investment project and methods for their evaluation

7. 1. general characteristics effectiveness assessment methods

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

The efficiency of using invested capital is assessed by comparing the cash flow that is generated during the implementation of the investment project and the initial investment. A project is considered effective if it provides a return on the original investment amount and the required return for investors who provided capital.
Invested capital, as well as cash flow, is reduced to the present time or to a specific accounting year (which usually precedes the start of the project).
The process of discounting capital investments and cash flows is carried out at various discount rates, which are determined depending on the characteristics of investment projects. When determining the discount rate, the structure of investments and the cost of individual components of capital are taken into account.

The essence of all assessment methods is based on the following simple scheme: Initial investments in the implementation of any project generate cash flow CF 1, CF 2, ..., CF n . Investments are considered effective if this flow is sufficient for

return of the original amount of capital investment and

ensuring the required return on invested capital.

The most common indicators of the efficiency of capital investments are:

discounted payback period (DPB).
pure modern meaning investment project (NPV),
internal rate of return (profitability, profitability) (IRR),

These indicators, as well as the corresponding methods, are used in two versions:

to determine the effectiveness of independent investment projects (the so-called absolute effectiveness), when a conclusion is made whether to accept the project or reject it,
to determine the effectiveness of mutually exclusive projects (comparative effectiveness), when a conclusion is made about which project to accept from several alternative ones.

7. 2. Discounted payback period method

Let's consider this method using a specific example of analyzing two mutually exclusive projects.

Example 1 . Let both projects involve the same investment of $1,000 and are designed for four years.

Project A generates the following cash flows: by year 500, 400, 300, 100, and project B - 100, 300, 400, 600. The cost of capital of the project is estimated at 10%. The discounted period is calculated using the following tables.

Table 7.1.
Project A

The third row of the table contains discounted values of the enterprise's cash income as a result of the implementation of the investment project. In this case, it is appropriate to consider the following interpretation of discounting: reduction sum of money at the present time corresponds to the allocation of that part of this amount that corresponds to the income of the investor, which is provided to him for the fact that he provided his capital. Thus, the remaining cash flow is intended to cover the original investment. The fourth row of the table contains the values of the uncovered portion of the original investment. Over time, the size of the uncovered portion decreases. Thus, at the end of the second year, only $214 remains uncovered, and since the discounted cash flow value in the third year is $225, it becomes clear that the investment's coverage period is two full years and some part of the year. More specifically for the project we get:

Similarly, for the second project, the calculation table and calculation of the discounted payback period are as follows.

Table 7.2.
Project V.

Based on the calculation results, it is concluded that project A is better because it has a shorter discounted payback period.

A significant disadvantage of the discounted payback period method is that it takes into account only the initial cash flows, namely those flows that fall within the payback period. All subsequent cash flows are not taken into account in the calculation scheme. So, if within the framework of the second project in the last year the flow was, for example, $1000, then the result of calculating the discounted payback period would not change, although it is quite obvious that the project will become much more attractive in this case.

7. 3. Pure modern value method (NPV method)

This method is based on the concept of Net Present Value.

Where CFi- Net cash flow,
r- the cost of capital raised for an investment project.

The term “net” has the following meaning: each amount of money is defined as the algebraic sum of input (positive) and output (negative) flows. For example, if in the second year of an investment project the volume of capital investments is $15,000, and cash income in the same year is $12,000, then the net amount of cash in the second year is ($3,000).

In accordance with the essence of the method, the modern value of all input cash flows is compared with the modern value of output flows caused by capital investments for the implementation of the project. The difference between the first and second is a pure modern value, the magnitude of which determines the decision rule.

Method procedure.

Step 1. The current value of each cash flow, input and output, is determined.

Step 2. All discounted values of cash flow elements are summed up and the NPV criterion is determined.

Step 3. A decision is made:

for a separate project: if NPV is greater than or equal to zero, then the project is accepted;
for several alternative projects: the project that has a greater NPV value is accepted, if only it is positive.

Example 2 . The company's management is going to introduce a new machine that performs operations currently performed manually. The machine costs $5,000 including installation with a service life of 5 years and zero salvage value. According to estimates from the financial department of the enterprise, the introduction of the machine due to the savings in manual labor will provide an additional input cash flow of $1,800. In the fourth year of operation, the machine will require repairs costing $300.

Is it economically feasible to introduce a new machine if the cost of capital of the enterprise is 20%.

Solution. Let us present the conditions of the problem in the form of laconic initial data.

We will make the calculation using the following table.

Table 7.3.
NPV value calculation

Name of cash flow	Monetary	Discounting multiplier 20% *	The present meaning of money
Initial investment
Input cash flow
Car repairs
Modern Net Value (NPV)

* Discount factor is determined using financial tables.

As a result of the calculations, NPV = $239 > 0, and therefore, from a financial point of view, the project should be accepted.

Now it is appropriate to dwell on the interpretation of the NPV value. Obviously, the amount of $239 represents some “margin of safety” designed to compensate possible error when forecasting cash flows. American financial managers say this is money set aside for a “rainy day.”

Let us now consider the question of the dependence of the indicator and, therefore, the conclusion made on its basis on the rate of return on investment. In other words, in this example we will answer the question, what if the return on investment (cost of capital of the enterprise) becomes greater. How should the NPV value change?

The calculation shows that when r= 24% we get NPV = ($186), that is, the criterion is negative and the project should be rejected. The interpretation of this phenomenon can be carried out as follows. What does a negative NPV mean? The fact that the initial investment does not pay off, i.e. The positive cash flows that are generated by this investment are not sufficient to compensate, taking into account the time value of money, the original amount of capital investment. Let us remember that the cost equity of a company is the return on alternative investments of its capital that the company can make. At r= 20% of the company is more profitable to invest in its own equipment, which, due to savings, generates cash flow of $1,800 over the next five years; and each of these amounts in turn is invested at 20% per annum. At r= 24% it is more profitable for a company to immediately invest its $5,000 at 24% per annum than to invest in equipment that, due to savings, will “bring” cash income of $1,800, which in turn will be invested at 24% per annum.

The general conclusion is this: with an increase in the rate of return on investments (the cost of capital of an investment project), the value of the NPV criterion decreases.

To complete the presentation of information necessary to calculate NPV, we present typical cash flows.

Typical input cash flows:

additional sales volume and increase in product price;
reduction of gross costs (reduction of the cost of goods);
residual value of the equipment cost at the end last year investment project (since the equipment can be sold or used for another project);
release of working capital at the end of the last year of the investment project (closing accounts receivable, selling remaining inventory, selling shares and bonds of other enterprises).

Typical output streams:

initial investment in the first year(s) of the investment project;
increase in working capital needs in the first year(s) of the investment project (increase in accounts receivable to attract new customers, purchase of raw materials and components to start production);
equipment repair and maintenance;
additional non-production costs (social, environmental, etc.).

It was previously noted that the resulting net cash flows are intended to provide a return invested amount money and income for investors. Let's look at how each sum of money is divided into these two parts using the following illustrative example.

Example 3. The company plans to invest money in purchasing a new device that costs $3,170 and has a service life of 4 years with zero residual value. Implementation of the fixture is estimated to provide an input cash flow of $1,000 each year. The management of the enterprise allows investments only if it leads to a return of at least 10% per year.

Solution . First, let's do the usual calculation of the net modern value.

Table 7.4.
Traditional NPV calculation

Thus, NPV=0 and the project is accepted.

Further analysis consists of dividing the $1,000 input stream into two parts:

return of some part of the original investment,
return on investment (income to the investor).

Table 7.5.
Calculation of cash flow distribution

Investment relative to a given year	Return on investment	investments	Uncoated investment at the end of the year

7. 4. The influence of inflation on the assessment of investment efficiency

Analysis of the impact of inflation can be carried out for two options

the inflation rate is different for individual components of resources (input and output),
the inflation rate is the same for different components of costs and expenses.

In the first approach, which is more representative of the real situation, especially in countries with unstable economies, the net modern method is used in its standard form, but all components of expenses and income, as well as discount rates, are adjusted according to the expected inflation rate by year. It is important to note that making a consistent forecast of different inflation rates for different types of resources seems to be an extremely difficult and practically impossible task.

As part of the second approach the influence of inflation is of a peculiar nature: inflation affects the numbers (intermediate values) obtained in the calculations, but does not affect the final result and conclusion regarding the fate of the project. Let's look at this phenomenon using a specific example.

Example 4 . The company plans to purchase new equipment at a cost of $36,000 that will provide $20,000 in cost savings (in cash flow input) per year over the next three years. During this period, the equipment will be completely worn out. The enterprise's cost of capital is 16% and the expected inflation rate is 10% per year.

First, let's evaluate the project without taking into account inflation. The solution is presented in table. 7.6.

Table 7.6.
Solution without taking into account inflation

The conclusion is obvious from the calculations: the project should be accepted, noting the high margin of safety.

Now let's take into account the effect of inflation in the calculation scheme. First of all, it is necessary to take into account the effect of inflation on the required value of the return indicator. To do this, remember the following simple reasoning. Let the enterprise plan the real profitability of its investments in accordance with interest rate 16 %. This means that if you invest $36,000 in one year, you should end up with $36,000 x (1+0.16) = $41,760. If the inflation rate is 10%, then you need to adjust this amount according to the rate: $41,760 x (1+0.10) = $45,936. The overall calculation can be written as follows

$36,000 x (1+0.16) x (1+0.10) = $45,936.

IN general case, If r r- real interest rate of profitability, and T- inflation rate, then the nominal (contractual) rate of profitability will be written using the formula

For the example under consideration, the calculation of the reduced cost of capital indicator has the form:

Let's calculate the value of the NPV criterion taking into account inflation, i.e. Let's recalculate all cash flows and discount them with a discount rate of 27.6%.

Table 7.7.
Inflation-based solution

The answers from both solutions are exactly the same. The results were the same, since we adjusted both the input money flow and the return rate for inflation.

For this reason, most firms in Western countries do not take inflation into account when calculating the efficiency of capital investments.

7. 5. Internal rate of return (IRR)

By definition, internal rate of return (sometimes called profitability) ( IRR) is the value of the discount rate at which the present value of the investment is equal to the present value of cash flows from the investment, or the value of the discount rate at which the net present value of the investment is zero.

The economic meaning of the internal rate of return is that this is the rate of return on investment at which it is equally effective for an enterprise to invest its capital at IRR interest in any financial instruments or produce real investment, which generate cash flow, each element of which is in turn invested at IRR interest.

The mathematical definition of internal rate of return involves solving the following equation

Where: CF j- input cash flow in the j-th period,
INV- the value of the investment.

Solving this equation, we find the value IRR. The decision-making scheme based on the internal rate of return method has the form:

if the IRR value is higher than or equal to the cost of capital, then the project is accepted,

if the IRR value is less than the cost of capital, then the project is rejected.

Thus, IRR is, as it were, a “barrier indicator”: if the cost of capital is higher than the IRR value, then the “capacity” of the project is not enough to ensure required refund and return of money, and therefore the project should be rejected.

In the general case, the equation for determining IRR cannot be solved in its final form, although there are a number of special cases where this is possible. Let's look at an example that explains the essence of the solution.

Example 5: You need $16,950 to buy a car. The machine will save $3,000 annually over 10 years. The residual value of the car is zero. We need to find the IRR.

Let's find the ratio of the required investment value to the annual influx of money, which will coincide with the multiplier of some (still unknown) discount factor

The resulting value appears in the formula for determining the modern value of the annuity

And, therefore, using a financial table. 4 adj. we find that for n=10 the discount rate is 12%. Let's check:

Cash flow

12% coefficient

recalculation

The present

meaning

Annual Economy

Initial investment

Thus, we found and confirmed that IRR=12%. The success of the solution was ensured by the coincidence of the ratio of the initial investment amount to the cash flow value with the specific value of the discount multiplier from the financial table. In general, you need to use interpolation.

Example 6: You need to estimate the IRR of a $6,000 investment that generates $1,500 cash flow over 10 years.

Following the previous scheme, we calculate the discount factor:

According to the table 4 adj. for n=10 years we find

This means that the IRR value is between 20% and 24%.

Using linear interpolation we find

There are more accurate methods for determining IRR, which involve the use of a special financial calculator or EXCEL electronic processor.

7. 6. Comparison of NPV and IRR methods

Unfortunately, NPV and IRR methods can conflict with each other. Let's look at this phenomenon using a specific example. Let's evaluate the comparative effectiveness of two projects with the same initial investments, but with different input cash flows. The initial data for calculating efficiency are given in the following table.

Table 7.8
Cash flows of alternative projects

For further analysis, we use the so-called NPV profile, which by definition represents the dependence of the NPV indicator on the cost of capital of the project.

Let's calculate NPV for various values of the cost of capital.

Table 7.9
NPV indicators for alternative projects

NPV profile graphs for projects will look like those shown in Fig. 7.1.

Having solved the equations that determine the internal rate of return, we obtain:

for project A IRR=14.5%,
for project B IRR=11.8%.

Thus, according to the criterion of internal rate of return, preference should be given to project A, as it has a higher IRR value. At the same time, the NPV method ambiguously gives a conclusion in favor of project A.

Rice. 7.1. NPV profiles of alternative projects

Having analyzed the ratio of NPV profiles that intersect at point , which in this case is 7.2%, we come to the following conclusion:

, the methods conflict - the NPV method accepts project B, the IRR method accepts project A.

It should be noted that this conflict occurs only when analyzing mutually exclusive projects. For individual projects, both methods give the same result, a positive NPV value Always corresponds to a situation where the internal rate of return exceeds the cost of capital.

7. 7. Decision making based on the least cost criterion

There are investment projects in which it is difficult or impossible to calculate the cash return. Projects of this kind arise at an enterprise when it intends to modify technological or transport equipment, which takes part in many diverse technological cycles and it is impossible to estimate the resulting cash flow. In this case, the criterion for deciding on the feasibility of investment is the cost of operation.

Example 7. A tractor is involved in many production processes. You need to decide to use the old one or buy a new one. The initial data for making a decision are as follows.

Let's calculate all the costs that the company will incur by accepting each of the alternatives. To make a final decision, we will bring these costs to the present moment in time (discount the costs) and choose the alternative that corresponds to the lower value of the discounted costs.

Table 7.10
Calculation of discounted purchase costs new car

	Monetary flow	Coeff. recalculation for 10%	Real meaning
Initial Investment
Residual value old tractor
Annual cost operation
Residual value new tractor
The Real Meaning of Monetary Loss

Table 7.11
Calculation of discounted costs for operating an old machine

The current value of discounted costs favors purchasing a new car. In this case, the losses will be $10,950 less .

7. 8. Assumptions made when assessing effectiveness

In conclusion, we note one important circumstance for understanding investment technologies: what assumptions are made when calculating performance indicators and to what extent they correspond to real practice.

All methods relied heavily on the following two assumptions.

Cash flows relate to the end of the accounting period. In fact, they can appear at any time during the year in question. In the framework of the investment technologies discussed above, we conditionally bring all cash income of the enterprise to the end of the corresponding year.
The cash flows that are generated by the investment are immediately invested in some other project to provide additional income on this investment. It is assumed that the return on the second project will be at least the same as the discount rate of the analyzed project.

The assumptions used, of course, do not fully correspond real situation cases, however, given the long duration of projects in general, do not lead to serious errors in assessing effectiveness.

Test questions and assignments

State the basic principles international practice assessing the effectiveness of investments.
What is the basic scheme for assessing the effectiveness of capital investments, taking into account the time value of money?
List the main performance indicators of investment projects.
What is the essence of the discounted payback period method?
How is the discounted payback period method used to compare the effectiveness of alternative capital investments?
State the basic principle of the pure modern meaning method.
What criterion is used to guide the analysis of the comparative effectiveness of capital investments using the net present value method?
What is the interpretation of the net modern meaning of the investment project?
How does the net present value change as the discount rate increases?
Which economic essence has a discount rate in the net modern value method?
List the typical cash flows in and out that should be taken into account when calculating the net present value of an investment project.
How is the enterprise's annual cash income, which is obtained through capital investment, distributed?
What two approaches are used to take into account inflation in the process of assessing the effectiveness of capital investments?
How is inflation taken into account when estimating the discount rate?
Define the internal rate of profitability of an investment project?
Formulate the essence of the internal rate of return method.
Is it generally possible to calculate the exact value of the internal rate of return?
What methods do you know for calculating the internal rate of return?
How to use the internal rate of return method for comparative analysis of the effectiveness of capital investments?
What approach should be used when comparative assessment efficiency of capital investments, when it is difficult or impossible to estimate the monetary income from capital investments?

1. The company requires a minimum return of 14 percent when investing its own funds. Currently, the company has the opportunity to purchase new equipment costing $84,900. Using this equipment will increase production volume, which will ultimately lead to an additional $15,000 per year. cash income within 15 years of equipment use. Calculate the net present value of the project, assuming a zero residual value of the equipment after 15 years.

We will carry out the calculation using the table, finding the discount factor using financial tables.

Name of cash flow	Monetary	Discount factor	The present meaning of money
Initial investment
Input cash flow
Pure modern meaning

The net present value was positive, supporting the project's acceptance.

2. The company plans new capital investments over two years: $120,000 in the first year and $70,000 in the second. The investment project is designed for 8 years with full development of the newly introduced capacities only in the fifth year, when the planned annual net cash income will be $62,000. The increase in net annual cash income in the first four years according to the plan will be 30%, 50%, 70%, 90%, respectively, for years from the first to the fourth. The company requires a minimum return of 16 percent when investing funds.

Need to determine

1. Let’s determine net annual cash income during the implementation of the investment project:

in the first year - $62,000 0.3 = $18,600;

in the second year - $62,000 0.5 = $31,000;

in the third year - $62,000 0.7 = $43,400;

in the fourth year - $62,000 0.9 = $55,800;

in all remaining years - $62,000.

2. We will calculate the net modern value of the investment project using a table.

Name of cash flow	Monetary flow	Discount factor	The present meaning of money
Investment
Investment
Cash income
Cash income
Cash income
Cash income
Cash income
Cash income
Cash income
Cash income
Net modern value of an investment project

3. To determine the discounted payback period, we calculate the values of net cash flows by year of the project. To do this, you just need to find the algebraic sum of the two cash flows in the first year of the project. It will be ($60,347) + $16,035 = ($44,312). The remaining values in the last column of the previous table are net values.

4. We will calculate the discounted payback period using a table in which we will calculate the accumulated discounted cash flow by year of the project.

	Discounted Cash Flow	Accumulated cash flow

The table shows that the number of full years of payback for the project is 7. The discounted payback period will therefore be

of the year.

3. The company has two options for investing its $100,000. In the first option, the company invests in fixed assets by purchasing new equipment, which after 6 years (the duration of the investment project) can be sold for $8,000; The net annual cash income from such an investment is estimated to be $21,000.

Under the second option, the company can invest money in working capital (inventories, increasing accounts receivable) and this will generate $16,000 in annual net cash income over the same six years. It is necessary to take into account that at the end of this period, working capital is released (inventories are sold, accounts receivable are closed).

Which option should be preferred if the company expects a 12% return on the funds it invests? Use the method of pure modern meaning.

1. Let us present the initial data of the problem in a compact form.


Investments in fixed assets...................................
Investments in working capital........................
Annual cash income...................................................
Residual value of equipment...................
Freeing up working capital..................
Project time........................................................ ....

Let us note again that working capital and equipment are planned to be sold only after 6 years.

2. Let us calculate the net modern value for the first project.

Name cash flow	Monetary flow	Discount factor	The present meaning of money
Investment
Cash income
Sale of equipment.
Pure modern meaning

3. We will carry out similar calculations for the second project

Name cash flow	Monetary flow	Discount factor	The present meaning of money
Investment
Cash income
Release
Pure modern meaning

4. Based on the calculation results, the following conclusions can be drawn:

the second project should be recognized as the best;
the first project should be rejected altogether, even without connection with the available alternative.

4. The company is planning a large investment project involving the acquisition of fixed assets and major renovation equipment, as well as investments in working capital according to the following scheme:

$130,000 - initial investment before the start of the project;
$25,000 - in the first year;
$20,000 - investment in working capital in the second year;
$15,000 - additional investment in equipment in the fifth year;
$10,000 is the cost of major renovations in the sixth year.

At the end of the investment project, the enterprise expects to sell the remaining fixed assets at their book value$25,000 and free up some of the working capital worth $35,000.

The scheme for solving the problem remains the same. We compile a table of calculated data and determine the discounted values of all cash flows.

The project should be accepted because its net contemporary value is substantially positive.

Name of cash flow	Monetary flow	Discount multiplier	The present meaning of money
Acquisition of fixed assets
Investing in working capital
Cash income in the first year
Investing in working capital
Cash income in the second year
Cash income in the third year
Cash income in the fourth year
Acquisition of fixed assets
Cash income in the fifth year
Repair of equipment
Cash income in the sixth year
Cash income in the seventh year
Cash income in the eighth year
Equipment sales
Release of working capital
Pure modern meaning

5. The company requires a minimum return of 18 percent when investing its own funds. The company currently has the opportunity to purchase new equipment costing $84,500. Using this equipment will increase production volume, which will ultimately result in $17,000 in additional annual cash income over 15 years of use of the equipment. Calculate the net present value of the project, assuming that the equipment can be sold for a residual value of $2,500 at the end of the project.

6. The company plans new capital investments over three years: $90,000 in the first year, $70,000 in the second and $50,000 in the third. The investment project is designed for 10 years with full development of the newly introduced capacities only in the fifth year, when the planned annual net cash income will be $75,000. The increase in net annual cash income in the first four years according to the plan will be 40%, 50%, 70%, 90%, respectively, for years from the first to the fourth. The company requires a minimum return of 18 percent when investing funds.

Need to determine

pure modern value of the investment project,
discounted payback period.

How will your idea of the effectiveness of the project change if the required return rate is 20%.

7. The company has two options for investing its $200,000. In the first option, the company invests in fixed assets by purchasing new equipment, which after 6 years (the duration of the investment project) can be sold for $14,000; The net annual cash income from such an investment is estimated to be $53,000.

According to the second option, the company can invest part of the money ($40,000) in the purchase of new equipment, and the remaining amount in working capital (inventories, increase in accounts receivable). This would generate $34,000 in annual net cash income over the same six years. It is necessary to take into account that at the end of this period, working capital is released (inventories are sold, accounts receivable are closed).

Which option should be preferred if the company expects a 14% return on the funds it invests? Use the method of pure modern meaning.

8. An enterprise is considering an investment project involving the acquisition of fixed assets and major repairs of equipment, as well as investments in working capital according to the following scheme:

$95,000 - initial investment before the start of the project;
$15,000 - investment in working capital in the first year;
$10,000 - investment in working capital in the second year;
$10,000 - investment in working capital in the third year;
$8,000 - additional investment in equipment in the fifth year;
$7,000 - capital repair costs in the sixth year;

At the end of the investment project, the company expects to sell the remaining fixed assets at their book value of $15,000 and free up working capital.

The result of the investment project should be the following net (i.e. after taxes) cash income:

9. A project requiring an investment of $160,000 would generate an annual income of $30,000 over 15 years. Assess the feasibility of such an investment if the discount factor is 15%.

10. A 15-year project requires an investment of $150,000. No income is expected for the first 5 years, but for the next 10 years the annual income will be $50,000. Should this project be accepted if the discount factor is 15%?

11. Projects are analyzed ($):

Rank projects according to IRR, NPV criteria, if r = 10%.

12. For each of the projects below, calculate the NPV and IRR if the discount factor is 20%.

14. Compare two projects according to NPV and IRR criteria, if the cost of capital is 13%:

15. The amount of required investment for the project is $18,000; estimated income: in the first year - $1500, in the next 8 years - $3600 annually. Assess the feasibility of accepting the project if the cost of capital is 10%.

16. An enterprise is considering the feasibility of purchasing a new production line. There are two models on the market with the following parameters ($)

Which project would you prefer?

Justification of the economic feasibility of an investment project includes determining its economic efficiency, feasibility and reliability.

A distinction is made between the effectiveness of the project as a whole and the effectiveness of participation in the project.

Social (socio-economic) efficiency takes into account the social and economic consequences of the investment project for society as a whole. It includes not only the direct results and costs of the project, but also “external” costs and results in related sectors of the economy, environmental, social and other non-economic effects.

Effectiveness of participation correlates the benefits and costs of each participant (subject) of the investment project (investor, customer, contractor, user of the capital investment object) and economic structures that are not a direct participant in the project. It includes:

the effectiveness of participation in the project for its participants (investors, customers, contractors, users of capital investment objects);

efficiency of investing in company shares;

the effectiveness of the project for economic structures that are not participants in the investment project, including:

regional and national economic efficiency - for individual regions and the national economy of the Russian Federation;

industry efficiency - for individual sectors of the national economy, financial and industrial groups, associations of enterprises and holding structures;

budgetary efficiency – for budgets of all levels and state extra-budgetary funds.

Feasibility of the investment project characterizes the possibility of its implementation given the current state of the internal and external environment of the enterprise. The most important for economic assessment is the financial component of feasibility, which means that an investment project can be implemented only if the required amount of money is available at the time when the investment is made. If investments are financed with borrowed funds, then financial feasibility, in addition to the ability to take out a loan in the required amount, includes the cost of the loan. A loan that is too expensive can absorb all the benefits of an investment project and even make it unprofitable.

Economic assessment of investments carried out on the basis of indicators calculated using the discounting technique. This technique takes into account the time factor.

Discounting allows you to estimate at discounting date cost values related to other points in time - determine their discounted value – DS:

DS (C) = C* (1 + r) - n,

The multiplier (1 + r) - n, with the help of which different-time values are brought to a comparable form - assessed at the discounting date, is called discount factor.

Net present value (NPV)- one of the main indicators of economic assessment of investments. Its calculation is based on a comparison of discounted expenses with income.

NPV =Σ TDS (D) – Σ TDS (I),

where – D – income for each period of existence of the investment project, I – expenses for each period of existence of the project.

A positive net present value means that during its economic life the investment project:

will reimburse the costs incurred;

will provide an income of 10% - the same as from a bank deposit (i.e. will receive an income equal to the income from its investment alternative);

will receive additional income equal to the net present value.

When calculating discounted indicators, the most important thing is the correct definition discount rates. As the minimum value (barrier rate) of the discount rate, the profitability of a possible alternative use of funds in the event of abandonment of investments is used. For agricultural enterprises, an alternative to investment in most cases is the use of funds in existing production activities. The determination of the discount rate in this case is based on planned profitability taking into account inflation. Inflation is taken into account if the investment project is calculated in forecast (deflated) ) prices If current prices are used, inflation is not taken into account in the discount rate.

Meaning profitability index IR > 1 means that the return on investment costs is higher than that of its full investment alternative; IR = 1.05 means that the return on investment will be 5% higher than if the same funds were placed in a bank at 10% per annum.

Investment payback period - one of the most visual and widespread in the domestic And world economic practice of investment efficiency indicators. The algorithm for calculating the payback period depends on the nature of the distribution of planned income. If they are distributed evenly over time, then the payback period is determined by simply dividing capital investments by the amount of annual income. When a fraction is obtained, it is rounded up to the nearest whole number.

If the profit is distributed unevenly, the payback period is calculated by directly counting the number of years during which the amount of income received (cumulative income) exceeds the amount of investment.

Effectiveness of participation is calculated separately for each participant (subject) of the investment project (investor, customer, contractor, user of the capital investment object) and economic structures that are not a direct participant in the project. When determining it, investment calculation models may not include all components of cash flow, but only those necessary for a given participant in the investment project. Also, discount rates for different participants may vary.

When determining feasibility investment, such indicators as the amount of reduced investment and the internal rate of return (return) are used. Amount of investments given represents the current discounted value of the costs of acquiring (constructing) an investment property. Internal rate of return(IRR) is calculated as the discount rate at which the income received becomes equal to the costs, and the net present value becomes equal to zero:

IRR = r(%), at which NPV = 0.

The value of the internal rate of return is used for conclusions of two kinds. Firstly, to assess feasibility. It shows the maximum allowable level of expenses (in percentage) for attracting financial resources that can be used for investment. For example, if an investment is financed by a loan, then the IRR value shows the upper limit of the level of interest charges on the loan, above which it becomes unprofitable. Investments with a high internal rate of return will be effective even if they are financed through “expensive” loans, as long as the interest rate on them is lower than the IRR. And if you can get a loan from a bank with an interest rate lower than the IRR, then such a project can be implemented.

Secondly, based on the internal rate of return, one can compare various options investments based on their stability to financing conditions when determining reliability. Thus, of two investment projects with values of IRR = 50% and 30%, respectively, the first is more resistant to changes in the external environment. It will make a profit even if the cost of borrowing to finance it suddenly rises to 49%. The second project becomes ineffective even when financed through a loan with a rate of 31 %.

The internal rate of return is associated not only with the cost of borrowed resources. When making investments, own funds fall out of production for a long time - they become “frozen” capital. From such a “freezing” of capital, lost profit arises, which is a kind of payment for the use of own funds - the price of advanced capital.. That is own funds are not free, they, just like borrowed ones, have a cost. Any investment decisions can be considered effective if the internal rate of return is not lower than the price of advanced capital.