3 what are the methods for evaluating investment projects. Evaluation of the effectiveness of investment projects

3 what are the methods for evaluating investment projects. Evaluation of the effectiveness of investment projects

Conclusion

Conclusion

Methods estimates economic efficiency of investment projects

The meaning of the overall assessment of the investment project is to present all the information about the latter in a form that allows the decision maker to make a conclusion about the expediency (or inexpediency) of the investment. In this context, economic (commercial, financial and economic) evaluation plays a special role.

Methods for evaluating effectiveness investment projects - ways to determine the feasibility of long-term investment in various objects (projects, activities) in order to assess the prospects for their profitability and payback.

The choice of a method for evaluating the effectiveness of an investment project can be influenced by many factors: the position of the project appraiser, the comparability of the scale of the enterprise and the project, the degree to which the enterprise's assets are used in the project, the stage of project implementation, etc. The project can be evaluated by the enterprise itself, an external investor, a bank, leasing company or government agency, in case it is assumed governmental support project.

The general criteria for the commercial attractiveness of an investment project are " financial solvency"(financial evaluation), "efficiency" (economic evaluation) and alternative methods for evaluating investment projects. On fig. 2 presents the evaluation methods for each of the criteria.

In the course of its implementation, an investment project must ensure: obtaining an acceptable return on invested capital and maintaining a sustainable financial condition, which can be done with coefficients financial evaluation which are divided into three main categories:

profitability indicators: return on assets, profitability invested capital, profitability of sales, cost of sales;
· indicators of the use of investments: asset turnover, fixed capital turnover, working capital turnover;
· Indicators for assessing the financial condition: overall liquidity ratio, quick liquidity ratio, overall solvency ratio.

Among statistical methods determining the feasibility of investing capital in an investment project, as a rule, methods such as calculating a simple rate of return and calculating the payback period are used.

Simple rate of return- assessment of which part investment costs reimbursed in the form of profit within one planning interval. Comparing the calculated value of the EIT with the minimum or average level of return, a potential investor can come to a preliminary conclusion on the advisability of continuing and deepening the analysis of this investment project.

PNP = FN / FROM (1)

Payback period- determination of the duration of the period during which the project will work "for itself".

The calculation is made by gradually subtracting from the total amount of capital costs the amount of depreciation and net profit for the next planning interval (usually a year). The interval in which the remainder becomes negative means the desired "payback period".

The main disadvantage of simple methods for evaluating the effectiveness of investments is to ignore the fact that the same amounts of receipts or payments related to different periods time. Understanding and taking into account this fact is extremely important for the correct assessment of projects related to long term investment capital. This shortcoming takes into account the discounting method.

Net Present Value (NPV) obtained by discounting financial flows and determines the value of the future profit of the project at the present time for the case of a perfect capital market.

where N- the duration of the project, expressed in the number of steps of the calculation period, for example, in years or months, - the income and costs of the project for i step of the billing period, r- discount rate.

The positive value of this indicator confirms the feasibility of investing Money into the project, and negative, on the contrary, indicates the inefficiency of their use.

Index - discounted yield index (DPI) determined by the formula:

where D K is the real value cash receipts on the K-th step calculation; Z is the amount of investment at the Kth calculation step; r- discount rate; n is the number of steps in the total billing period.

If the DPI value is ? 1.0, then the project is rejected, since it will not bring additional income to the investor. Projects with DPI > 1.0 are accepted for implementation.

Discounted payback period (DPP) set according to the formula:

where Z is the amount of investments aimed at the implementation of the project; - the average amount of cash receipts from the implementation of the project in the period under review.

To use the clean method present value project, you need to pre-set the value of the comparison rate. Definition internal norm profit (IRR) is that it is the comparison rate at which the sum of discounted cash inflows equals the sum of discounted cash outflows, i.e.:

where, r a is the last highest discount rate at which NPV is positive, r b is the discount rate at which NPV is negative; while r a should be one point higher than r b (for example, if the last, highest discount rate is 17%, then r a should be equal to 18%), NPV b - net present value at the highest rate discount rate r b , at which it has a positive value, NPV a - net present value at a discount rate r a , at which it has a negative value

It should be borne in mind that the calculation of discount rates is associated with a number of assumptions. For example, the NPV method assumes that the structure and cost of capital of a firm do not change throughout life cycle investment project. For this reason, they developed alternative methods to solve these problems to some extent.

Adjusted current method cost consists in dividing the cash flow of the project into two components: real cash flow (i.e. directly related to the operating activities of the project) and “side effects” (cash flow associated with financial policy firms). The main side effect is the tax shield, since the use of debt reduces tax costs and thus increases the free cash flows from the project.

One of the most important advantages of the APV method is its flexibility: it allows you to separate cash flows and evaluate them separately discounted using appropriate rates. It is also possible to analyze various sources creating project value. Among the shortcomings of the method, they note the complexity of assessing the reduced value of various financial effects (for example, bankruptcy, guarantees, etc.), as well as the need to prepare additional information. investment risk evaluation resource

Economic value added represents monetary value value created for investors by certain period project time in excess of the expected rate of return on an investment with a similar level of risk.

Calculating EVA as a Periodic Evaluation Tool investment capital allows you to make more informed decisions to expand profitable lines of business, and also helps to identify inefficient use of funds in projects whose profitability does not cover the cost of raising capital. Since EVA is determined on the basis of accounting data, this indicator is subject to the so-called “erroneous periodization effect”, that is, the value of assets is fixed minus accumulated depreciation, the amount of capital invested in an individual project decreases over time.

F federal education agency

State educational institution of higher professional education

“M oskov state university

Instrumentation and Informatics”

		Sergiev Posad		speciality

		EF-2 “Economic Information Systems ”

Discipline		Controlling



Course work
on the topic
"Investment Appraisal Methods"


			Martyanova T.V.
	signature, date		initials and surname

	EF2-2006-01D				0611 2

					Year of admission V
Designation of the course project
			Year of protection of the work ^

The project is protected for evaluation


Project manager (work)						Koryakina E.S.
			signature, date			initials and surname
Commission members:

			signature, date			initials and surname


			signature, date			initials and surname


			signature, date			initials and surname

Sergiev Posad 2009.

Introduction……………………………………………………………………….....3

1.Methods for evaluating investments………………………………………………...5

References…………………………………………………………….31

Introduction

The current stage of Russia's development is characterized by transformations in the political, social, and economic spheres. The departure from a centrally planned economy, the introduction of market relations, a change in property relations were accompanied by a decrease in the standard of living, exacerbation of problems in the social and other spheres. Domestic industry has been significantly affected by negative factors. The reasons for this can be found in inefficient management, lack of financial resources, obsolescence of technology, and a high degree of depreciation of fixed assets.

One of the most important elements of the implementation of process innovative projects is the use of formalized methods for evaluating investments to select the best option for implementing such a project. Practice shows that at present in Russia the heads of industrial enterprises practically do not use formalized methods for evaluating investment projects for planning process innovation projects. Often, as a result of this approach, these projects are based on the option of mastering a new technology that is not cost-optimized, which leads to project failure.

It is known that risk assessment of an innovative project is a difficult task. A number of domestic economists have developed methods to assess the risks associated with investing in an innovative project. However, most of these methods are focused on assessing the risks of product innovation projects. For process innovations, the application of these methods is associated with some features, the underestimation of which can seriously complicate the assessment of the project or lead to incorrect conclusions.

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

1. Based on discounted estimates ("dynamic" methods):

net present value - NPV (Net Present Value);

ROI Index - PI(Profitability Index);

Internal rate of return - IRR (Internal Rate of Return);

Modified internal rate of return - MIRR (Modified Internal Rate of Return);

Discounted ROI - DPP (Discounted Payback Period).

2. Based on accounting estimates ("statistical" methods):

Payback period - PP (Payback Period);

Investment efficiency ratio - ARR (Accounted Rate of Return).

The use of investment assessment methods, taking into account these features, will increase the likelihood of successful implementation of innovative projects in industries, preserve the potential of Russian industry and lay the foundation for sustainable growth in industrial production and scientific and technological progress (STP).

Thus, the analysis and evaluation of the features of the application of investment assessment methods, risk accounting methods for process innovation projects relevant for the Russian economy, both in theoretical and practical aspects, especially for those industries for which the modernization of production is a necessity to reduce costs and improve the situation of enterprises. We also note that the significance of this issue is great not only for today, but also for the strategic development of the Russian economy.

Purpose and objectives of the study. The aim of the work is to study and systematize the features that must be taken into account when applying investment evaluation methods when planning process innovation projects, to develop recommendations on the application of investment project evaluation methods for planning process innovation projects.

In accordance with this goal, the following tasks are solved in the work:

Study and analysis of investment evaluation methods;

Study of the features of the evaluation of innovative projects;

Identification of specific characteristics inherent in the evaluation and selection of process innovation projects;

Analysis of the features of the application of investment assessment methods for planning process innovation projects;

Subject of research are the basic principles and features of the application of investment assessment methods for planning process innovation projects.

Object of study is the New Technological Line project.

1. Methods for evaluating investments

1.1. Based on discounted estimates ("dynamic" methods)

net present value- NPV (Net present value)

This method is based on comparing the value of the original investment (IC) with the total discounted net cash flow generated by it over the forecast period. Because cash inflows are spread over time, they are discounted by a factor r set by the analyst (investor) on their own based on the annual percentage return they want or can have on the capital they invest.

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

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

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

When forecasting income by years, it is necessary to take into account, if possible, all types of income, both industrial and non-productive, that may be associated with this project. So, if at the end of the project implementation period it is planned to receive funds in the form of the salvage 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 involves not a one-time investment, but a consistent 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.

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

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

ROI Index- PI (profitability Index)

This method is essentially a consequence of the net present value method. Profitability Index (PI) is calculated using the formula

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

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

Unlike the net present effect, the profitability index is a relative indicator. Due 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.

Internal norm arrived - IRR (Internal Rate of Return)

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

IRR = r, where NPV = f(r) = 0.

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

In practice, any enterprise finances its activities, including investment, from various sources. As a payment for the use of financial resources advanced to the activity of the enterprise, it pays interest, dividends, remuneration, etc., i.e. incurs some reasonable costs to maintain its economic potential. An indicator that characterizes the relative level of these costs can be called the "price" of advanced capital (CC). This indicator reflects the minimum return on the capital invested in its activities, its profitability, which has developed at the enterprise, and is calculated using the arithmetic weighted 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 him that the IRR indicator calculated for a specific project is compared, while the relationship between them is as follows.

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

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 applied using tabulated values of discount factors. To do this, using tables, two values of the discount factor r 1

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

r 2 is the value of the tabulated discount factor at which f(r 2)0).

The calculation accuracy 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 - the nearest to each other values of the discount coefficient that satisfy the conditions (in case of changing the sign of the function from "+" to "-"):

r 1 - the value of the tabulated discount factor, minimizing 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, maximizing the negative value of the NPV indicator, i.e. f(r 2)=max r (f(r)

By mutual replacement of the coefficients r 1 and r 2, similar conditions are written for the situation when the function changes sign from "-" to "+".

Discounted ROI - DPP (Discounted payback period)

There are a number of situations in which it may be appropriate to apply the payback method. In particular, this is a situation when the company's management 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 and as soon as possible. The method is also good in a situation where investments are associated with 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.

1.2. Based on accounting estimates ("statistical" methods)

Payback period - PP (payback period)

This method is one of the simplest and widely used in the world 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 the income is evenly distributed over the years, then the payback period is calculated by dividing the one-time costs by the amount of annual income due to them. When a fractional number is received, it is rounded up to the nearest whole number. If profits are unevenly distributed, then the payback period is calculated by directly counting the number of years during which the investment will be repaid with cumulative income. General formula calculation of the PP indicator has the form:

PP=n, at which
.

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

The payback period of an investment 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 income from recent periods. As an example, consider two projects with the same capital costs (10 million rubles), but different projected annual income: for project A - 4.2 million rubles. within three years; for project B - 3.8 million rubles. within ten years. Both of these projects during the first three years provide a return on capital investments, therefore, from the standpoint of this criterion, they are equal. However, it is clear that project B is much more profitable.

Secondly, since this method is based on undiscounted estimates, it does not distinguish between projects with the same amount of cumulative income, according to different distributions of it over the years. So, from the standpoint of this criterion, project A with annual incomes of 4000, 6000.2000 thousand rubles. and project B with annual incomes of 2000, 4000. 6000 thousand rubles. are equal, although it is obvious that the first project is more preferable, since it provides a large amount income in the first two years.

Thirdly, this method does not have the additivity property.

Coefficient efficiency investment– ARR (Accounted Rate of Return)

This method has two characteristic features: first, it does not involve discounting income indicators; secondly, income is characterized by the net profit indicator PN (balance sheet profit minus deductions 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 is found by dividing the initial amount of capital investments by two, if it is assumed that after the expiration of the analyzed project, all capital costs will be written off; if residual or salvage value (RV) is allowed, its valuation should be excluded.

This indicator is compared with the ratio of return on capital advanced, 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 drawbacks, mainly due to the fact that it does not take into account the time component cash flows. In particular, the method does not distinguish between projects with the same amount of average annual profit, but a varying amount of profit over the years, as well as between projects with the same average annual profit, but generated over a different number of years. etc.

1.3. Special Methods

The IRR- and NPV-methods described above belong to the traditional methods of investment appraisal and have been used for more than three decades. In the vast majority of cases, the definition of the net present value and the internal rate of return of the project is the end of the analysis of efficiency. 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 projects, i.e. universal.

However, the reverse side of 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 individual points that can be of serious importance for financial investor and explore 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 like, then the use of special methods allows you to get an idea of its individual aspects and thereby increase the overall level investment analysis.

The main special methods for evaluating the effectiveness can be divided into two groups: methods based on determining the final cost of an 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 a modification of traditional calculation schemes.

2. Justification of the economic feasibility of investments under the project "New technological line"

2.1. Initial data

Based on the study of the market for products that are produced at the enterprise, the possibility of increasing effective demand for it has been established. In this regard, the company is considering the feasibility of acquiring a new technological line to increase production in order to increase sales. The assessment of a possible increase in sales volume is established on the basis of an analysis of data on the potential opportunities of competitors. The cost of the line (capital investment for the project) is $18,530; service life - 5 years; profit net of tax on it from the sale of fixed assets at the end of their service life will be $926.5;. cash flows (profit minus tax on it and depreciation deductions from the cost of fixed assets put into operation at the expense of capital investments) are forecasted for the years in the following volumes: $5406, $6006, $5706, $5506, $5406. The discount rate for determining the present value of cash flows is assumed to be 12% and 15%. The threshold rate for assessing the calculated level of the internal rate of return is set at 16%. The payback period of capital investments acceptable for the enterprise, calculated according to the data on cash flows and the present value of cash flows, is 5 years. Is this project feasible for implementation?

2.2. Project evaluation by "dynamic" methods

Determination of net present value- NPV

a) At a discount rate of 12%.

b) At a discount rate of 15%.

Determination of the internal rate of return -IRR

Initial data for calculating the IRR indicator.

	Cash flows, $

Based on the calculations given in Table. 2.1, we can conclude that the function NPV=f(r) changes its sign on the interval (15%,16%).

Determination of the discounted payback period of investments -DPP.

a) At a discount rate of 12%.

The income will cover the investment for 5 years. For the first 4 years, incomes are (data taken from Table 2.1):

$4826,79 + $4787,95 + $4061,21 + $3507,01 = $17182,96

For 5 years you need to cover:

$18530 - $17182,96 = $1347,04,

$1347.04 / $3071.59 = 0.44 (approximately 5.4 months).

The total payback period is 4 years 5.4 months.

b) At a discount rate of 15%.

The income will cover the investment for 5 years. For the first 4 years, income is:

$4700,87 + $4550 + $3753,95 + $3146,29 = $16151,11

For 5 years you need to cover:

$18530 - $16151,11= $2378,89,

$2378.89 / $2689.55 = 0.88 (approximately 10.7 months).

The total payback period is 4 years 10.7 months.

Determination of return on investment indices- PI

a) At a discount rate of 12%. (data taken from Table 2.1):

PI 12% = ($4826,79 + $4787,95 + $4061,21 + $3507,01+3071,59) / $18530 = 1,09

b) At a discount rate of 15%.

PI 15% = ($4700,87 + $4550 + $3753,95 + $3146,29+2689,55) / $18530 = 1,015

2.3. Evaluation of the project by "statistical" methods

Determination of the payback period of investments -PP

The investment is $18530 in year 0. Cash flows for a five-year period are: $5406, $6006, $5706, $5506, $5406. The income will cover the investment for 4 years. For the first 3 years, income is:

$5406 + $6006 + $5706 = $17118

For 4 years you need to cover:

$18530 - $17118 = $1412,

$1412/ $5506 = 0.26 (approximately 4.1 months).

The total payback period is 3 years 4.1 months

Determination of the investment efficiency ratio -ARR

3. Conclusions on the economic feasibility of the project"New technological line"

The results obtained indicate the economic feasibility this project. Such a project can be accepted full confidence at a discount rate less than 16.6% (the maximum discount rate at which the net present value is non-negative). The lower the discount rate, the sooner the capital investment will pay off and, consequently, the enterprise that has implemented this project will receive more profit. Calculations have shown that at a lower discount rate, the net present value and profitability index increase, and the payback period decreases. So, at a discount of 15%, the investment will pay off in 4 years 10.7 months (profitability index 1.5%), and at 12% - earlier by 5.3 months (profitability index 9%). The profitability ratio of the investment project is 63.8%.

Which method is better?

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

firstly, static methods for calculating the effectiveness of investments were used, which do not take into account the time factor, which is of fundamental importance for a financial investor;

secondly, the indicators used were focused on 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 effectiveness of the 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 you to reflect the fundamental principle "tomorrow's money is cheaper than today's" and thereby take into account the possibility of alternative investments at a discount rate.

The approach is associated with the need to make a number of assumptions, which are quite difficult to fulfill in practice (especially in Russian conditions). Let's look at the two most obvious obstacles.

First, it is required to correctly estimate not only the volume of initial capital investments, but also current costs and receipts for the entire period of the project. All the conditionality of such data is obvious even in a stable economy with a predictable level and structure of prices and a high degree of market research. In the Russian economy, the amount of assumptions that have to be made when calculating cash flows is immeasurably higher (forecast accuracy is a function of the degree of systematic risk).

Secondly, for calculations using dynamic methods, the premise of currency stability is used, in which cash flows are estimated. In practice, this premise is realized through the use of comparable prices (with possible subsequent adjustment of the results taking into account inflation forecasts) or the use of a stable foreign currency for calculations. The second method is more appropriate in the case of an investment project implemented jointly 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 affected 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 of the advisability of using dynamic methods for analyzing industrial investments in general: after all, under conditions of high uncertainty and with the adoption of various kinds of assumptions and simplifications, the results of the corresponding calculations may turn out to be even more far from the truth. It should be noted, however, that the purpose of quantitative methods for evaluating efficiency is not an ideal forecast of the expected profit, but, first of all, to ensure the comparability of the projects under consideration in terms of efficiency, based on certain objective and verifiable criteria, and thereby prepare the basis for the adoption of the final solutions.

Of all the variety of dynamic methods for calculating the effectiveness of investments in practice, the method of assessing the internal rate of return of the project and the method of assessing the net present value of the project are better.

Conclusion

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

Investing is one of the most important aspects of any dynamic business organization.

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 is different. So if we are talking on the replacement of existing production capacities, the decision can be made quite painlessly, since the management of the enterprise clearly understands how much and with what characteristics new fixed assets are needed. The task becomes more complicated when it comes to investments related to the expansion of the main activity, 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 question of the size of the proposed investment is important. Thus, the level of responsibility associated with the adoption of projects worth 1 million rubles. and 100 million rubles, different. Therefore, the depth of the analytical study of the economic side of the project, which precedes the decision, should also be different. In addition, in many firms, the practice of differentiating the right to make decisions of an investment nature is becoming commonplace, i.e., the maximum amount of investment is limited, within which one or another manager can make independent decisions.

Often decisions must be made in an environment 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. It is obvious that 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, much less than one.

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.

A very significant risk factor. Investment activities always carried out under conditions of uncertainty, the degree of which can vary significantly. Thus, at the time of the acquisition of 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 decisions of an investment nature, like any other type of management activity, is based on the use of various formalized and non-formalized methods. The degree of their combination is determined by various circumstances, including those of them, as far as the manager is familiar with the available apparatus applicable in a particular case. In domestic and foreign practice, a number of formalized methods are known, calculations using 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 to a certain extent conditional, it is easier to make final decisions.

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

Criteria for making investment decisions:

criteria to assess the reality of the project:

regulatory criteria (legal) i.e. norms of national, 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.

quantitative criteria to assess the feasibility of the project.

Compliance with the project goal for the long term with the goals of developing the business environment;

Risks and financial consequences (whether they lead to additions to investment costs or reductions in expected production, prices or sales);

The degree of sustainability of the project;

Probability of scenario design and the state of the business environment.

quantitative criteria. (financial and economic), allowing you to choose from those projects, the implementation of which is appropriate. (eligibility criteria)

project cost;

net present value;

profitability;
internal rate of return;
payback period;
profit sensitivity to the planning horizon (term), to changes in the business environment, to an error in data evaluation.

In general, making an investment decision requires the collaboration of many people with different backgrounds and different views on investment. However, the financial manager has the last word, who follows certain rules.

Rules for making investment decisions:

it makes sense to invest money in production or securities only if you can get a net profit higher than from keeping money in a bank;

investing makes sense only if the return on investment exceeds the rate of inflation;

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 income;

high profitability as such and after discounting;

lack of better alternatives.

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

For the planning and implementation of investment activities, a preliminary analysis is of particular importance, which is carried out at the stage of development of investment projects and contributes to the adoption of reasonable and justified management decisions.

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

When analyzing investment projects, certain assumptions are made. First, it is customary to associate 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 project implementation, although in principle they can be made over a number of subsequent years. The inflow (outflow) of cash relates to the end of the next year.

The general criterion for the duration of the life of the project or the period of use of investments is the materiality of the cash income they generate from the point of view of the investor. So, when conducting a banking examination for a loan, the life of the project will coincide with the maturity of the debt and the further fate of the lender's investments will no longer be of interest.

The indicators used in the analysis of the effectiveness of investments can be divided into those based on discounted estimates and those based on accounting estimates.

The indicator of net present value characterizes the current value 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 costs, 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 evaluating the effectiveness of capital investments, it is imperative to take into account the effect of inflation. This is done by adjusting the cash flow elements or the discount factor for the inflation index. Exactly the same principle underlies the methodology of risk accounting.

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

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

When drawing up a budget for capital investments, a number of limitations must be taken into account. For example, there are several attractive investment projects, but the company, due to limited financial resources cannot do them all at the same time. In this case, it is necessary to select projects for implementation in such a way as to obtain the maximum benefit from the investment. 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 quite difficult. It is no coincidence that studies of Western practices of adoption investment decisions showed that the vast majority of companies, firstly, calculate several criteria and, secondly, use the obtained quantitative estimates not as a guide to action, but as information for reflection.

Therefore, summing up, I would like to note that the use of any, even the most sophisticated, methods will not provide 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 project implementation efficiency and its riskiness, but to compare the investment projects on the basis of a unified approach, using objective and verifiable indicators where possible, and compiling a relatively more efficient and relatively less risky investment portfolio.

Bibliography

Kovalev V.V. Financial analysis: Money management. Choice of investments. Reporting analysis. - M.: Finance and statistics, 2004.

Enterprise Economics: Edited by S.F. Pokropivny. Textbook. In 2 vols. v.1. - K .: "Hvilya-press", 2006.

Kovalev V.V. Methods for evaluating investment projects. Moscow, Finance and statistics, 2000

Kovalev V.V. Collection of tasks for financial analysis. Moscow, Finance and statistics, 2007

Northcott D. Making investment decisions. - M.: Banks and exchanges, UNITI, 2005. - 247 p.

Investment analysis / V.A. Chernov.; ed. M.I. Bakanov. - Moscow, UNITI, 2008

Evaluation of the effectiveness of investment projects / A.S. Volkov, A.A. Marchenko. - Moscow, RIOR, 2006.

Margolin A.M., Bystryakov A.Ya., Economic evaluation of investments: Textbook - M.: "EKMOS", 2001.

Investment in education - the most important indicator sustainable...

Methods estimates economic efficiency of investment projects
Thesis >> Finance
... investment and estimates efficiency investment led to the conclusion that there are currently a number of methods estimates... calculation, public accessibility for understanding. Static methods estimates investment can be divided into two groups...

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

7. 1. general characteristics performance evaluation 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:

Evaluation of the effectiveness of the use of invested capital is made by comparing the cash flow (cash flow), which is formed in the process of implementing the investment project and the original investment. The project is recognized as effective if the return of the initial investment amount and the required return for the investors who provided the capital are ensured.
Invested capital as well as cash flow are adjusted to the present time or to a certain settlement 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: The initial investment in the implementation of any project generates cash flow CF 1 , CF 2 , ... , CF n . Investments are recognized as effective if this flow is sufficient for

return of the initial amount of capital investments and

ensuring the required return on invested capital.

Most common the following indicators efficiency of capital investments:

discounted payback period (DPB).
net present value of the 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 efficiency), when it is concluded whether to accept the project or reject it,
to determine the effectiveness of mutually exclusive projects (comparative efficiency), when a conclusion is made about which project to accept from several alternative ones.

7. 2. Discounted payback method

Consider this method for specific example analysis of two mutually exclusive projects.

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

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

Table 7.1.
Project A

The third row of the table contains the discounted values cash income enterprises as a result of the implementation of the investment project. In this case, it is appropriate to consider the following interpretation of discounting: bringing the amount of money to the present moment of time corresponds to the allocation of this amount of that part of it that corresponds to the income of the investor, which is provided to him for providing his capital. Thus, the remaining part of the cash flow is designed to cover the original investment. The fourth row of the table contains the values of the uncovered part of the original investment. Over time, the size of the uncovered part decreases. So, by the end of the second year, only $214 remains uncovered, and since the discounted value of the cash flow in the third year is $225, it becomes clear that the investment 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 the 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 fit into the payback period. All subsequent cash flows are not taken into account in the calculation scheme. So, if in 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 would become much more attractive in this case.

7. 3. Method of pure modern value (NPV - method)

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

where CF i- Net cash flow,
r- the cost of capital raised for an investment project.

The term “pure” 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 the investment project the capital investment is $15,000 and the cash income in the same year is $12,000, then the net cash in the second year is ($3,000).

In accordance with the essence of the method, the current value of all input cash flows is compared with the current value of output flows due to capital investments for the project. The difference between the first and the 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 single project: if NPV is greater than or equal to zero, then the project is accepted;
for several alternative projects: the project with the highest NPV is accepted, provided it is positive.

Example 2 . The management of the enterprise is going to introduce a new machine that performs operations that are currently performed manually. The machine costs $5,000 with a 5-year lifespan and zero salvage value. According to the financial department of the enterprise, the introduction of the machine by saving manual labor will provide an additional input stream 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 enterprise's cost of capital is 20%.

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

We will calculate using the following table.

Table 7.3.
Calculation of the NPV value

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

* The discount multiplier 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 value of NPV. It is obvious that the amount of $239 represents some “margin of safety” designed to compensate for a possible error in forecasting cash flows. American financial managers say that this is money set aside for a “rainy day”.

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

The calculation shows that at 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 generated by this investment are not sufficient to offset, given the time value of money, the original capital investment. Recall that the cost of a company's equity is the rate of 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 a 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% of the company, it is more profitable to immediately invest its $5,000 at 24% per annum than to invest in equipment that, due to savings, will “bring” a cash income of $1,800, which in turn will be invested at 24% per annum.

The general conclusion is as follows: 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 the information necessary for calculating NPV, we present typical cash flows.

Typical input cash flows:

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

Typical output streams:

initial investment in the first year(s) of the investment project;
increase in the need for working capital 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);
repair and Maintenance equipment;
additional non-production costs(social, environmental, etc.).

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

Example 3 The company plans to invest in a new fixture that costs $3,170 and has a 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 to make investments only in the case when this leads to a return of at least 10% per year.

Solution . Let's do the usual net present value calculation first.

Table 7.4.
Traditional NPV calculation

Thus, NPV=0 and the project is accepted.

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

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

Table 7.5.
Cash flow distribution calculation

Investment in relation to the current year	Return on investment	investments	uncovered investment at the end of the year

7. 4. Influence of inflation on the assessment of investment efficiency

An analysis of the impact of inflation can be made for two options

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

As part of the first approach, which is more realistic, especially in countries with unstable economies, the net present value method is used in its standard form, but all cost and income components, as well as discount indicators, are adjusted in accordance with the expected annual inflation rate. It is important to note that to produce a consistent forecast of various inflation rates for various types resources is an extremely difficult and practically impossible task.

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

Example 4 . The company plans to purchase new equipment at a cost of $36,000 that provides $20,000 in cost savings (in cash inflow) per year over the next three years. During this period, the equipment will undergo complete wear and tear. 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 inflation into account. The solution is presented in table. 7.6.

Table 7.6.
Inflation-Free Solution

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

Now we will 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 index. For this, we recall the following simple reasoning. Let the enterprise plan the real profitability of its investments in accordance with the interest rate of 16%. This means that if you invest $36,000, in a year it should receive $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 total calculation can be written as follows

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

In general, if r p- real interest rate profitability, and T- inflation rate, then the nominal (contract) rate of return will be written using the formula

For the example under consideration, the calculation of the reduced cost of capital is as follows:

Let us 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-adjusted solution

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

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

7. 5. Internal rate of return (IRR)

By definition, the internal rate of return (sometimes called returns) ( IRR) is the value of the discount rate at which the current value of the investment is equal to the current value of cash flows from investments, 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 such a rate of return on investments at which it is equally efficient for an enterprise to invest its capital at IRR percent in any financial instruments or produce real investment, which generate cash flow, each element of which, in turn, is invested at IRR percent.

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

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

Solving this equation, we find the value IRR. The decision scheme based on the method of internal rate of return 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 is less than the cost of capital, then the project is rejected.

Thus, IRR is like a “barrier indicator”: if the cost of capital is higher than the IRR value, then the “capacity” of the project is not enough to provide the necessary return and return on money, and therefore the project should be rejected.

In the general case, the equation for determining the IRR cannot be solved in the final form, although there are a number of special cases when this is possible. Consider an example explaining the essence of the solution.

Example 5. It takes $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 us find the ratio of the required value of the investment to the annual inflow of money, which will coincide with the multiplier of some (still unknown) discount factor

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

And, therefore, with the help of the financial table. 4 app. 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 have 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 amount of cash flow with a specific value of the discount multiplier from the financial table. In general, interpolation should be used.

Example 6. You want to estimate the value of the internal rate of return of an investment of $6,000 that generates a cash flow of $1,500 over 10 years.

Following the previous scheme, we calculate the discount factor:

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

So 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 an EXCEL electronic processor.

7. 6. Comparison of NPV and IRR methods

Unfortunately NPV and IRR methods can conflict with each other. Let's consider this phenomenon on a specific example. Let's evaluate the comparative efficiency of two projects with the same initial investment, but with different input cash flows. The initial data for calculating the efficiency are placed 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 project capital.

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

Table 7.9
NPV indicators for alternative projects

Graphs of NPV profiles for projects will have the form shown in fig. 7.1.

Solving the equations that determine the internal rate of return, we get:

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 having a higher IRR value. At the same time, the NPV method gives an ambiguous conclusion in favor of project A.

Rice. 7.1. NPV profiles of alternative projects

After analyzing the ratio of NPV-profiles that have an intersection at the point , which in this case is 7.2%, we come to the following conclusion:

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

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

7. 7. Making a decision on the criterion of the least cost

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

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

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

Table 7.10
Calculation of discounted costs when buying a new car

	Monetary flow	Coeff. recalculation for 10%	Real value
Initial investment
residual value old tractor
annual cost exploitation
residual value new tractor
The real value of monetary losses

Table 7.11
Calculation of discounted costs for the operation of the old machine

The current value of discounted costs speaks in favor of buying a new car. In this case, the loss will be $10,950 less .

7. 8. Assumptions made in performance evaluation

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.

For all methods, the following two assumptions were essentially used.

Cash flows are attributed 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 the cash income of the enterprise by the end of the corresponding year.
Cash flows that are generated by investments are immediately invested in some other project to ensure additional income for these investments. 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 to the real state of affairs, however, given the long duration of projects in general, they do not lead to serious errors in the assessment of effectiveness.

Control questions and tasks

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

1. The company requires at least 14 percent return on investment of its own funds. The company currently has the option to purchase new equipment worth $84,900. The use of this equipment will increase production output, which will ultimately result in $15,000 in additional annual cash income over 15 years of equipment use. Calculate the net present value of the project, assuming zero residual value of the equipment in 15 years.

The calculation will be carried out using the table, finding the discount factor using financial tables.

Name of cash flow	Monetary	Discount multiplier	The present the value of money
Initial investment
Input cash flow
Pure modern value

The net present-day value was found to be positive, suggesting acceptance of the project.

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 newly commissioned 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 of 16 percent return on investment of cash.

Need to define

1. Determine the net annual cash income in the process of implementing 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 present value of the investment project using the table.

Name of cash flow	Monetary flow	Discount multiplier	The present the value of money
Investment
Investment
cash income
cash income
cash income
cash income
cash income
cash income
cash income
cash income
Net present value of the investment project

3. To determine the discounted payback period, we calculate the net cash flows for the years 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 rest of the values in the last column of the previous table are pure values.

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

	Discounted cash flow	Accumulated cash flow

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

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 term of the investment project) can be sold for $8,000; the net annual cash income from such an investment is estimated at $21,000.

Under the second option, the company can invest money in working capital (inventory, increase accounts receivable) and this will generate $16,000 in annual net cash income over the same six years. It should be noted 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 money it invests? Use the pure modern value method.

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


Investments in fixed assets ...............................
Investing in working capital...................................
Annual cash income ...............................................
Residual value of the equipment ..........
Release of working capital...................................
Project time .............................................................. ....

Note again that the working capital and equipment are planned to be sold only after 6 years.

2. Calculate the net present value for the first project.

Name cash flow	Monetary flow	Discount multiplier	The present the value of money
Investment
cash income
Sale of equipment.
Pure modern value

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

Name cash flow	Monetary flow	Discount multiplier	The present the value of money
Investment
cash income
Release
Pure modern value

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

the second project should be recognized as the best;
the first draft should be rejected altogether, even without regard to the available alternative.

4. The company is planning a major investment project involving the acquisition of fixed assets and overhaul 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 - Year 6 capital repairs.

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

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 present value is essentially positive.

Name of cash flow	Monetary flow	Discount multiplier	The present the value 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
Sale of equipment
Release of working capital
Pure modern value

5. The company requires at least 18 percent return on investment of its own funds. Currently, the company has the opportunity to buy new equipment worth $84,500. The use of this equipment will increase production output, which will ultimately result in $17,000 in additional annual cash income over 15 years of equipment use. Calculate the net present value of the project, assuming that the equipment can be sold at a residual value of $2,500 after the project ends.

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 the full development of newly commissioned 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 enterprise requires at least 18 percent return on investment of cash.

Need to define

net present 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 in 6 years (the term of the investment project) can be sold for $14,000; the net annual cash income from such an investment is estimated at $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 (inventory, increase in receivables). This will generate $34,000 in annual net cash income over the same six years. It should be noted 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 money it invests? Use the pure modern value method.

8. The enterprise is considering an investment project that provides for the acquisition of fixed assets and overhaul 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 - year six capital repairs;

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

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

9. The project, which requires an investment of $160,000, is expected to generate an annual income of $30,000 over 15 years. Assess the feasibility of such an investment if the discount factor is 15%.

10. The 15 year project requires an investment of $150,000. In the first 5 years, no income is expected, but in 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 the NPV, 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. The enterprise is considering the feasibility of acquiring a new production line. There are two models on the market with the following parameters ($)

Which project would you like?

An investor who decides to invest his capital in a business project, in most cases, is guided by rational arguments, which are expressed in specific numbers, terms and concepts.

business practices and economics over the entire industrial era, a solid set of tools has been accumulated that allows one to assess the prospects of almost any investment project. A variety of methods and methods for evaluating investments in modern commercial activities can be divided into two large groups according to their structure:

Fundamental analysis, which includes the study and assessment of all environmental factors associated with the implementation of an investment project, for example, market conditions, legal and social conditions, environmental impact, etc.

Technical analysis, which is based on the study and calculation of indicators of the very activity of the project or company in relation to its production, financial and technological components.

In addition, the general approach to investment appraisal is based not only on the calculation of statistical data, which for the most part takes into account past events, but also on its dynamic development, as shown in the figure below.

With such dynamic forecasting and analysis, both constant factors and variables are taken into account, which allows you to determine all changes in the market situation, calculate limit values risk, payback periods, etc. An important part of the analysis of the investment project is the sources of information and data.

Initial data for investment evaluation can be obtained:

Company financial statements(if the investment is in an existing business)
Statistical data obtained from open sources government organizations or private analytical agencies, consulting companies
Comparative studies on similar projects (benchmarking)
Expert assessments at different stages of project implementation
Own research based on information obtained from any available sources.

In addition to this, the assessment of long-term investments may also include various models or the development of scenario conditions for development, for which specialists from various applied scientific fields are involved.

AT general view According to their functional performance, all types and methods of investment assessment are divided into two large groups:

Qualitative assessment methods- include methods of analysis and development of recommendations for the investor, based on the study (forecasting) of data that cannot be expressed in quantitative parameters, for example, social or environmental effect, the degree of perception of products by the consumer, assessment of the quality of investment management (competence of management, motivation personnel). To work with such implicit qualitative data, the following are used:

Index parameters compiled on the basis of historical data, expressed in some degree of assessment, for example, negative, neutral, positive.
Scoring system, when each of the conditions or factors is expressed in a relative scoring
Expert methods of analysis and evaluation, which use the knowledge and experience of specialists on a specific project implementation problem, for example, sociologists to study the attitude of the population towards the construction of chemical production facilities.

The second large group of methods used to evaluate investments are quantitative or analytical models.

The most well-known and widely used in practice are such dynamic models (methods of taking into account inflation when evaluating investments), such as:

Net present value NPV (Net Present Value).
Internal rate of return IRR (Internal Rate of Return).
Profitability Index PI (Profitability Index).
Dynamic payback period DPP (Discounted Payback Period).

A brief description of these methods is as follows:

Net current method NPV cost(Net Present Value)

Using this method It is assumed that the goal of the company is to maximize its value. The method is based on comparing the value of the initial investment with the income streams that these investments generate over the forecast period.

Since the cash flows are distributed over time, they are discounted using the coefficient r, which is set by the investor independently, based on the annual rate (percentage) of the return on capital that he wants or can have on the capital he invests. In addition, this coefficient evaluates the impact of inflation on investment activity, since the rate of return must always be higher than the percentage of depreciation of money.

The profitability index shows the relative profitability of a project or discounted value cash receipts from the project per unit of investment:

Dynamic (discounted) payback period takes into account the time value of money.

This method consists in calculating the period of time that will be required to return the initially invested capital with a given (required) rate of return.

The second group of analytical methods is represented by non-discounted methods for evaluating investments, the most informative of which are:

is the expected recovery period for the initial investment from the net proceeds received by the project (where net proceeds are cash receipts less expenses). The method involves calculating the period during which the entrepreneur will be able to return the initially advanced capital. This determines the time during which receipts from operational activities enterprises will cover the investment costs.

The general formula for calculating the PP indicator is:

where Pk is the annual income generated by the project, IC is the size of the initial investment.

Accounting rate of return ARR (Accounting Rate of Return)

This method is based on the use of accounting characteristics of an investment project. The accounting rate of return is the ratio of the average annual profit (PN) to the invested capital (average annual investment).

This value provides information about the impact of investments on the company's financial statements. Indicators financial statements are the most important investors and shareholders in the analysis investment attractiveness companies.

Comparison of investment appraisal methods, based on the practice of their use, shows that there is no single and universal algorithm suitable for all investments. Therefore, in order to develop the most appropriate investment analysis format, an investor should, as a priority, choose those methods that consider the entire process in dynamics (i.e., with a calculation of the future perspective).

In addition to the need to analyze the project in which funds are to be invested, it also makes sense to assess the investment management system itself, i.e., the readiness of the investor or its structures to perform money management tasks over time, under conditions of uncertainty and risk.

Investments- the cost of funds aimed at the reproduction (maintenance and expansion) of fixed assets of the enterprise. Investment (investment of funds) in land, structures, production facilities is aimed at continuing and expanding production activities enterprises, generating income and profits in the future.
The need for investment is caused by several reasons. The main ones are the need to update or replace the existing material and technical base of production, its improvement or modernization due to wear and tear of production equipment, the need to increase and commission fundamentally new production capacities due to an increase in production volumes and development of new activities.
The main sources of investment are own funds (authorized capital, sinking fund, other reserve funds, accumulation fund, non-distributable profit of the enterprise).
The cheapest source of investment financing is the reinvested profit of the enterprise. Its productive application avoids additional costs associated with the payment of interest on borrowed funds, or costs associated with issuing valuable papers. The reinvestment of profits preserves the existing system of control over the activities of the enterprise, since the number of shareholders of the enterprise does not change (in contrast to their inevitable increase in the case of additional issue valuable papers).
Investment activity is carried out primarily in conditions of uncertainty. If we are talking about replacing existing production capacities, then the investment decision can be made quite simply, since the company's management clearly understands how much and with what characteristics new fixed assets (machines, machine tools, equipment, etc.) are needed. If we are talking about expanding the core business or diversifying it, then the risk factor begins to play a significant role.
At the time of acquisition of machinery and equipment, other fixed assets, it is impossible to predict with certainty the economic effect of such an operation. Investment decisions are usually made in conditions where there are several alternative projects that differ in the types and volumes of required investments, payback periods and sources of funds raised. Decision-making in such conditions involves the evaluation and selection of one of several projects based on some criteria. It is clear that there may be several criteria, their choice is arbitrary, and the probability that one project will be preferable to others in all respects is very small. Therefore, the risk associated with the adoption of an investment decision is also great.
Making investment decisions is the same art as making any other entrepreneurial (management) decisions. The intuition of the entrepreneur, his experience, and the knowledge of qualified specialists are important here. Formalized methods of evaluating investment projects known to world and domestic practice can provide some assistance.
There are several methods for evaluating investment projects (Fig. 1). All of them are based on the assessment and comparison of the volume of the proposed investment and the future cash flows due to the investment.

Payback period of investments.
One of the simplest and most widely used methods of evaluation is the method of determining the payback period of investments. The payback period is determined by counting the number of years during which the investment will be repaid from the income received (net cash receipts).
With a uniform distribution of cash receipts over the years:

If cash income (profit) is received unevenly over the years, then the payback period is equal to the period of time (number of years) for which the total net cash receipts (cumulative income) will exceed the amount of investment.
In general, the payback period n is equal to the period of time during which

where Pk is the net cash income in year k due to investments. Calculated as sum annual depreciation in k-th year and annual net profit for the k-th year; I - the amount of investment.
The method of calculating the payback period is the simplest in terms of the applied calculations and is acceptable for ranking investment projects with different terms payback. However, it has a number of significant drawbacks.
First, it does not distinguish between projects with the same amount of total (cumulative) cash income, but with a different distribution of income over the years.
This method, secondly, does not take into account the income of recent periods, i.e. periods of time after the repayment of the investment amount.
However, in a number of cases the application of this simplest method is expedient. For example, with a high degree of investment risk, when an enterprise is interested in returning the invested funds as soon as possible, with rapid technological changes in the industry or if the enterprise has liquidity problems, the main parameter taken into account when evaluating and selecting investment projects is the payback period. investment.

Investment efficiency ratio.
Another fairly simple method for evaluating investment projects is the method of calculating the investment efficiency ratio (accounting return on investment).
The investment efficiency ratio is calculated by dividing the average annual return by the average investment. The average annual net profit is taken into account (balance sheet profit minus deductions to the budget). The average investment is derived by dividing the original investment by two. If after the expiration of the analyzed project it is assumed that there is a residual value (the project term is less than the equipment depreciation period, i.e. not all the cost of the equipment is written off during the project period), then it should be excluded:

It is advisable to compare the obtained investment efficiency ratio with the efficiency ratio of the entire capital of the enterprise, which can be calculated based on the balance sheet data using the formula:

The advantages of this method include the simplicity and clarity of the calculation, the ability to compare alternative projects by one indicator. The disadvantages of the method are due to the fact that it does not take into account the time component of profit. So, for example, no distinction is made between projects with the same average annual, but in fact changing over the years, profit, as well as between projects that bring the same average annual profit, but for a different number of years.

Discounting cash flows.
To a certain extent, the shortcomings of the first two methods are reduced by methods based on the principles of discounting cash flows. In world practice, there are several similar methods, but their essence is to compare the amount of investment with the total amount of the present (discounted) future income.
Investments I for a number of years n bring a certain annual income, respectively P1, P2 ..., Pn. But, as you know, the same amount of money has a different value in the future and in the present - on financial markets any money is usually cheaper tomorrow than it is today. Income spread over different periods of time must be streamlined, brought to a single today's time estimate, since the amount of investment also has a today's estimate. It is expedient for an enterprise to compare the amount of investments not just with future income, but with the accumulated value of discounted, reduced to today's assessment, future income.
The basic principles for estimating time-adjusted cash flows are as follows:
The future value of a certain amount of today's money, bearing interest i for n periods, is calculated by the formula:

Present value - the present value of future payments, which can be received at a certain interest rate i for n periods.
Using formulas that link the present and future value of cash, you can get a formula for determining the discounted (reduced to the present, or updated) future value of cash flows generated in different years by the investment in question:

where Pk and Pk are the annual income and the reduced (discounted) annual income brought by investments in the k-th year, r is the desired annual percentage for which the funds are returned.

net present value.
The accumulated value of discounted income should be compared with the value of investments.
The total accumulated value of discounted income for n years will be equal to the sum of the corresponding discounted payments:

The difference between the total accumulated discounted income and the initial investment is the net present value (net present effect):

It is quite obvious that if the net present value is positive (a value greater than 0), then the investment project should be accepted; if it is negative, the project should be rejected. In the event that the net present value is zero, the project cannot be assessed as either profitable or unprofitable; other methods of comparison must be used. When comparing several alternative projects, preference is given to the project with a high net present value.
Manual calculation using the above formulas is quite laborious, therefore, for the convenience of using this and other methods based on discounted estimates, they resort to using special statistical tables that show the values of compound interest, discount factors, discounted value monetary unit etc. depending on the time interval and the value of the discount factor.

Return on investment.
The use of the net present value method, despite the actual difficulties of its calculation, is more preferable than the use of the method of assessing the payback period and investment efficiency, since it takes into account the time components of cash flows. The application of this method allows you to calculate and compare not only absolute indicators (net present value), but also relative indicators, which include return on investment
Obviously, if the profitability is greater than one, then the project should be accepted; if it is less than one, it should be rejected.
Return on investment as a relative indicator is extremely convenient when choosing one project from a number of alternative ones that have approximately the same values of the net present value of investments, or when completing an investment portfolio, i.e. choosing several various options simultaneous investment of funds, giving the max-th net present value.
The use of the method of net present value of investments also makes it possible to take into account the inflation factor and the risk factor, which are inherent in different projects to varying degrees, in forecasting calculations. Obviously, taking into account these factors will lead to a corresponding increase in the desired percentage at which the investment is returned, and hence the discount factor.

Criteria list method.
The essence of the method of selecting investment projects using a list of criteria is as follows: the compliance of the project with each of the established criteria is considered and the project is evaluated for each criterion. The method allows you to see all the advantages and disadvantages of the project and ensures that none of the criteria that need to be taken into account will be forgotten, even if there are difficulties with the initial assessment.
The criteria necessary for evaluating investment projects may vary depending on the specific characteristics of the organization, its industry affiliation and strategic focus. When compiling a list of criteria, it is necessary to use only those that follow directly from the goals, strategies and objectives of the organization, its orientation to long-term plans. Projects that are highly valued in terms of some goals, strategies and objectives may not be highly valued in terms of others.
The main criteria for evaluating investment projects are:
A. Organizational goals, strategy, policies and values.
1. Compatibility of the project with the organization's current strategy and long-term plan.
2. The justification for changes in the organization's strategy (if this is required by the adoption of the project).
3. Compliance of the project with the attitude of the organization to risk.
4. Compliance of the project with the attitude of the organization to innovations.
5. Compliance of the project with the requirements of the organization, taking into account the time aspect (long-term or short-term project).
6. Compliance of the project with the growth potential of the organization.
7. Sustainability of the organization.
8. The degree of diversification of the organization (i.e. the number of industries that do not have a production connection with the main industry in which the organization operates, and their share in the total volume of its production), affecting the stability of its position.
9. The influence of big financial costs and deferral of profit state of the art affairs in the organization.
10. The impact of a possible deviation of time, costs and execution of tasks from the planned ones, as well as the impact of project failure on the state of affairs in the organization.

B. Financial Criteria
1. The amount of investment (investment in production, investment in marketing; for R&D projects, the cost of conducting research and the cost of development, if the research is successful).
2. Potential annual profit.
3. Expected rate of net profit.
4. Compliance of the project with the criteria of economic efficiency of investments adopted in the organization.
5. Starting costs for the project.
6. Estimated time after which this project will begin to generate costs and revenues.
7. Availability of finance at the right time.
8. The impact of the adoption of this project on other projects requiring funding.
9. The need to attract borrowed capital (loans) to finance the project, and its share in investments.
I0. Financial risk associated with the implementation of the project.
11. Stability of income from the project (does the project provide a steady increase in the growth rate of the company's income, or will income fluctuate from year to year).
12. The period of time after which the production of products (services) will begin, and, consequently, the reimbursement of capital costs.
13. Possibilities of use tax legislation(tax benefits).
14. Return on assets, i.e. the ratio of the average annual gross income received from the project, to capital expenditure(the higher the rate of return on assets and the lower the general expenses organizations the share of fixed costs that do not depend on changes in the utilization of production capacities, and, therefore, the less will be the losses in the event of a deterioration in the economic situation; if the level of return on assets in a given organization is below the industry average, then in the event of a crisis, it is more likely to be one of the first to go bankrupt).
15. Optimal cost structure for the product included in the project (use of the cheapest and most readily available production resources).

B. Scientific and technical criteria (for R&D projects)
1. Probability of technical success.
2. Patent purity (whether the patent right of any of the patent holders has been violated).
3. Uniqueness of products (lack of analogues).
4. Availability of scientific and technical resources necessary for the implementation of the project.
5. Compliance with the draft R&D strategy in the organization.
6. Cost and development time.
7. Possible future product developments and future applications of the new generated technology.
8. Impact on other projects.
9. Patentability (is it possible to protect the project with a patent)
10. Need for consulting firms or outsourced R&D.

D. Manufacturing Criteria
1. The need for technological innovations for the implementation of the project.
2. Compliance of the project with the available production capacities (whether it will be supported high level use of available production capacity or with the adoption of the project, overhead costs will increase sharply).
3. Availability of production personnel (in terms of number and qualifications).
4. The value of production costs. Comparing it with the cost of competitors.
5. The need for additional production facilities(optional equipment).

D. External and environmental criteria.
1. Possible harmful effects of products and production processes.
2. Legal support project, its consistency with the law.
3. Possible impact of forward-looking legislation on the project.
4. Possible reaction of public opinion to the implementation of the project.

scoring method.
If it is necessary to formalize the results of the analysis of projects according to the lists of criteria (this is necessary when analyzing a large number alternative projects), a scoring of projects is used. The scoring method is as follows. The most important factors that affect the results of the project (a list of criteria is compiled). Criteria are assigned weights based on their importance. This can be achieved by a simple survey of managers, inviting them to distribute the 100 items that make up the unit over the entire group of criteria, in accordance with the relative importance of certain criteria for the overall decision.
Qualitative assessments of the project for each of the above criteria ("very good", "good", etc.) are expressed quantitatively. This can be done by experts detailed description, and then the quantitative expression of the components of the criterion. In this case, a uniform distribution of weights is not at all necessary.
If we introduce an element of stochasticity (randomness) into the main scoring scheme of the project, it is possible to facilitate the task of experts and at the same time achieve more accurate results. The fact is that it is often very difficult to decide whether one or another parameter of a given project is exactly good or satisfactory, etc., since, according to many criteria, a project with a certain probability can lead to both good and bad results. This is what is taken into account when using the stochasticity of the scoring system: for each of the criteria for considering a project, experts evaluate the probability of achieving very good, good, etc. results, which allows, among other things, to take into account the risk associated with the project.
Overall score according to this system is obtained by multiplying the weights of the ranks by the probability of reaching these ranks and thus obtaining the probabilistic weight of the criterion, which is then multiplied by the weight of the criterion; the data obtained for each criterion are summarized. However, the obtained estimates of the projects cannot be considered absolutely reliable. This is due to the subjectivity of the representations used when assigning weights to each factor, as well as when assigning numerical values to each of the ranks. Therefore, a small difference in the total score cannot be the basis for a decision. Very careful interpretation of the score value is required.

Other methods.
When choosing a project, evaluating its effectiveness, uncertainty and risk factors should be taken into account. A full study of this issue is beyond the scope of this study guide, so we will only briefly discuss them.
Uncertainty refers to the incompleteness or inaccuracy of information about the conditions for the implementation of the project, including associated costs and results. The uncertainty associated with the possibility of adverse situations and consequences arising during the implementation of the project is characterized by the concept of risk.
When evaluating projects, the following types of uncertainty and investment risks seem to be the most significant.
1. The risk associated with the instability of economic legislation and the current economic situation, investment conditions and the use of profits
2. External economic risk (the possibility of introducing restrictions on trade and supplies, closing borders, etc.)
3. Uncertainty of the political situation, the risk of adverse socio-political changes in the country or region
4. Incompleteness or inaccuracy of information about the dynamics of technical and economic indicators, parameters of new equipment and technology
5. Fluctuations in market conditions, prices, exchange rates etc.,
6. Uncertainty of natural and climatic conditions, the possibility natural Disasters
7. Production and technological risk (accidents and equipment failures, manufacturing defect etc.)
8. Uncertainty of the goals, interests and behavior of participants
9. Incomplete or inaccurate information about financial position and the business situation of participating enterprises (possibility of non-payments, bankruptcies, breaches of contractual obligations).

The most accurate method is the formalized description of uncertainty. With regard to the types of uncertainty most often encountered in the evaluation of investment projects, this method includes the following steps:
1. description of the entire set of possible conditions for the implementation of the project (either in the form of appropriate scenarios, or in the form of a system of restrictions on the values of the main technical, economic, etc. parameters of the project) and the costs that meet these conditions (including possible sanctions and costs associated with insurance and redundancy), results and performance indicators
2. transformation of the initial information about the uncertainty factors into information about the probabilities of individual implementation conditions and the corresponding performance indicators or about the intervals for their change
3. determination of project performance indicators as a whole, taking into account the uncertainty of the conditions for its implementation - indicators of expected efficiency.

Comparative characteristics some methods for evaluating investment projects are given in Table 1.
Table 1.
Basic methods for selecting investment projects

The procedure for evaluating investment projects.
In world and domestic practice, there are several standardized principles for evaluating investment projects.
First of all, a preliminary survey of the project is carried out, during which the purpose of the project and its compliance with the current and projected activities of the enterprise are determined. The preliminary survey also determines the risks associated with the project, whether the enterprise has the necessary experience to realize the opportunities created by the project. At the same stage, the criteria that will be used to evaluate the investment project are determined.
Then the feasibility of the implementation of the investment project is assessed. Typically, the evaluation is carried out in three stages:
1. calculation of baseline indicators by years (sales volume, current expenses, depreciation, net profit and net cash receipts from proposed investments)
2. calculation of analytical coefficients (calculation of the net present value of investments, return on investment, payback period and efficiency ratio of the investment project)
3. analysis of the coefficients (depending on the criteria chosen as the basis for a given enterprise, the project is either accepted or rejected, the entrepreneur can focus on one or more of the most important criteria, in his opinion, or take into account additional factors). If an investment project is adopted, specific measures are developed for its implementation.
The main indicators used to compare various investment projects (project options) and choose the best of them are indicators of the expected integral effect (economic at the level National economy, commercial at the level of an individual organization). The same indicators are used to substantiate the rational sizes and forms of reservation and insurance.
If the probabilities of various project implementation conditions are known exactly, the expected integral effect is calculated using the mathematical expectation formula:

Eozh \u003d Ei * Pi,

where Eozh is the expected integral effect of the project; Ei - integral effect under the i-th condition of implementation; Pi - the probability of the implementation of this project.
In the general case, the calculation of the expected integral effect is recommended to be carried out according to the formula:

Eozh \u003d h * Emax + (1 - h) * Emin,

where Emax and Emin - the largest and smallest of the mathematical expectations of the integral effect on admissible probability distributions; h - a special standard for taking into account the uncertainty of the effect, reflecting the system of preferences of the relevant economic entity under conditions of uncertainty. When the expected integral economic effect is found, it is recommended to take it at the level of 0.3.

There are a few things to remember and take into account general rules and principles of investment policy:
1. "Golden banking rule": the use and receipt of funds must occur in deadlines, and therefore long term investment should be financed with long-term funds.
2. The principle of solvency: investment planning must ensure the solvency of the enterprise at all times. The principle of return on investment: for all investments, it is necessary to choose the cheapest ways of financing.
3. The principle of balancing risks: the most risky investments should be financed by own funds.
4. The principle of adaptation to market needs: it is necessary to take into account market conditions and its dependence on the provision of borrowed funds.
5. The principle of marginal profitability: you should choose those investments that are most profitable.

Initial investment

Annual Savings

Annual Savings

Annual Savings

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