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Introduction	3
1. Characteristics of investment efficiency indicators	5
1.1 Concepts and types of investment project efficiency	5
1.2 Objectives and principles for assessing the effectiveness of an investment project	6
2.Methodology for analyzing the effectiveness of investments	9
2.1 Method for calculating the net reduced effect	12
2.2 Method for calculating the return on investment index	15
2.3 Method for calculating the internal rate of return on investments	16
2.4 Method for determining the payback period of investments	18
2.5 Method for calculating the investment efficiency ratio	20
Conclusion	22
Solving investment assessment problems	25
List of used literature	28

Introduction

“Investment” is a word of foreign origin (from the Latin investire, German investition), translated as a long-term investment of capital in any enterprises, socio-economic programs, projects in one’s own country or abroad in order to generate income and social effect.

The term “investment” in Russia became widely used during the years of market reforms.

In domestic and foreign scientific literature there are a number of definitions (definitions of the concept of investment).

The most common and frequently encountered concept of investment is the following: long-term investments of cash and other capital in one’s own country or abroad in enterprises in various industries, entrepreneurial projects, socio-economic programs, innovative projects in order to generate income or achieve another beneficial effect.

And finally, in Federal law“On investment activities in the Russian Federation, carried out in the form of capital investments” dated February 25, 1999. No. 39-FZ gives the following definition to investments: “Investments are cash, securities, including property rights with a monetary value, invested in objects of entrepreneurial and (or) other activities in order to make a profit and (or) achieve another useful effect.”

In one’s own country, capital investments are made not only for the purpose of generating income, but also to meet the social needs of society.

The words “investment” and “capital investments” are close in meaning, and some authors consider them synonymous.

Investment activity is the investment of funds (investment) and the implementation of practical actions in order to generate income and achieve a beneficial effect.

Investment activities include investment and construction processes. Without them, the reproduction of fixed assets (new construction, technical re-equipment, expansion of enterprises, increase in capacity) is unthinkable.

1. CHARACTERISTICS OF INVESTMENT EFFICIENCY INDICATORS

1.1 Concept and types of efficiency of an investment project

In modern economic literature one can come across various definitions of the concept of “effectiveness of an investment project.” Some experts interpret it as a ratio of costs and results, others define the effectiveness of an investment project as a category reflecting the degree of compliance of the investment project with the goals and interests of its participants. The implementation of effective projects increases the gross domestic product available to society, which is then divided among the entities participating in the project. The income and expenses of these entities determine various types of efficiency of investment projects.

Methodological Recommendations for assessing the effectiveness of investment projects highlight the following types of project effectiveness: the effectiveness of the project as a whole and the effectiveness of participation in the project. The effectiveness of the project as a whole is assessed in order to determine the potential attractiveness of the project for possible participants and to search for sources of financing. The effectiveness of participation in the project is determined to verify its financial feasibility, as well as the interest of all its participants in it.

There are also other options for classifying the types of efficiency of an investment project. In our opinion, one of the most interesting is the classification dividing the effectiveness of the project into commercial and budgetary. This classification is based on the position from which level the investment project is assessed: macroeconomic (the effectiveness of state participation in the project in terms of income and expenditure of budgets of all levels) - budgetary efficiency is assessed or microeconomic (taking into account the consequences of the project for the participant implementing the project) - commercial effectiveness is assessed.

1.2 Objectives and principles for assessing the effectiveness of an investment project

Like any type of analysis, analysis of the effectiveness of an investment project has certain goals and objectives. Speaking about the purposes of the analysis of the effectiveness of viability, it should be noted that the main purpose of the analysis is to make a decision on the implementation of the investment project. In addition, such a strategic goal of efficiency analysis can be identified as improving the economic condition of the state, which selects the most effective projects for implementation

As for the tasks that must be solved during the analysis of the effectiveness of the project, they can be classified depending on the subject of the analysis. The subjects of analysis of the project's effectiveness can be credit institutions and other investors, financial services of the enterprise implementing the project, as well as other entities that may be involved in the project implementation process.

So, in the course of analyzing the effectiveness of an investment project, the financial service of the enterprise must solve the following tasks:

1. Conducting an aggregated analysis of design solutions and creating necessary conditions to find investors
2. Development of a project financing scheme
3. Ensuring maximum profit from the implementation of the investment project;

If borrowed funds are required to implement a project, then an analysis of the effectiveness of the investment project can be carried out by credit institutions and other investors. In this case, the tasks of analyzing the investment project will be:

1. Analysis of the compliance of the volume of funds requested by the enterprise with that volume borrowed money, which is really necessary to ensure the effectiveness of the project;
2. Minimizing the risk associated with investing in the project.
3. Selecting a project that best suits the interests of the lender

An important element of analyzing the effectiveness of an investment project are the principles on which the analysis is based. These principles can be applied to any project, regardless of its specifics:

1. The principle of considering a project at all stages of its economic cycle. This principle assumes that the assessment of the effectiveness of an investment project begins from the moment of pre-investment research and ends with the termination of the project;
2. The principle of modeling cash flows, including all cash receipts and expenses associated with the implementation of the project billing period taking into account the possibility of using different currencies;
3. The principle of comparability of comparison conditions projects involves that the analyzed investment projects are comparable in the following aspects: time, money (meaning the currency of the project), scale aspect, etc.;
4. The principle of taking into account the time factor implies that when assessing the effectiveness of an investment project, the time factor will be taken into account, that is, the dynamism of the project parameters, time gaps between production and sales of products, inequality of costs and results at different times, etc.;
5. The principle of taking into account only upcoming costs and revenues suggests that when assessing the effectiveness of an investment project, only costs and revenues that will be expected during the implementation of projects should be taken into account;
6. The principle of taking into account the presence of different project participants. This principle is especially important when analyzing efficiency, since the expected results are different for different participants in the investment project, the assessment of the cost of capital is different, and, consequently, the discount rate is different;
7. The principle of taking into account the impact of inflation and risk, as well as other principles.

All of these principles are equally important when assessing the effectiveness of a project, but the most important, in our opinion, is the principle of taking into account the presence of different project participants. This is due to the fact that the most effective project will be the one that will best meet the interests of all its participants.

2. METHODOLOGY FOR ANALYSIS OF INVESTMENT EFFICIENCY

The process of making management decisions of an investment nature is based on the assessment and comparison of the volume of proposed investments and future cash receipts. The general logic of analysis using formalized criteria is, in principle, quite obvious - it is necessary to compare the amount of required investment with projected income. Since the indicators being compared refer to different points in time, the key issue here is their comparability. It can be treated differently depending on the existing objective and subjective conditions: the inflation rate, the size of investments and generated revenues, the forecasting horizon, the level of qualifications of the analyst, etc.

Critical moments in the process of evaluating a single project or drawing up a capital budget include: a) forecasting sales volumes taking into account possible demand for products (since most projects are associated with additional production); b) inflow assessment Money on years; c) assessing the availability of required sources of financing; d) assessment of the acceptable value of the price of capital, which is also used as a discount factor.

Analysis of the possible capacity of the product sales market, i.e. forecasting sales volume is most significant, since its underestimation can lead to the loss of a certain share of the sales market, and its overestimation can lead to ineffective use of the production capacity introduced under the project, i.e. to the ineffectiveness of the investments made.

As for assessing cash inflows by year, the main problem arises in relation to the last years of the project, since the further the planning horizon, i.e. The longer the project, the more uncertain and risky cash inflows in distant years are considered. Therefore, several calculations can be performed in which reducing factors can be introduced in relation to the revenue values ​​of the last years of the project, or these revenues can be completely excluded from the analysis due to significant uncertainty.

As a rule, companies have many projects available for implementation, and the main limitation is the ability to finance them. Sources of funds vary significantly in terms of their availability - the most accessible are own funds, i.e. profit, then, according to the degree of increase in the mobilization period, come bank credits, loans, and new issues. As noted above, these sources differ not only in the length of time they are involved in the investment process, but also in the price of capital, the value of which also depends on many factors. In addition, the price of capital raised to finance a project during its implementation may change (usually upward) due to various circumstances. This means that a project accepted under some conditions may become unprofitable under others. Different projects do not respond equally to increases in the cost of capital. Thus, a project in which the bulk of the cash inflow falls in the first years of its implementation, i.e. reimbursement of investments made is carried out more intensively, and is less sensitive to the rise in price for using the source of funds. 2.3 Method for calculating the internal rate of return on investments 16
2.4 Method for determining the payback period of investments 18
2.5 Method for calculating the investment efficiency ratio 20
Conclusion 22
Solving investment assessment problems 25
List of used literature

The economic efficiency of investments is determined by comparing the effect obtained from their application with the amount of investment. For rate economic efficiency investments are used in two ways. The first method involves determining the effectiveness of investments without taking into account the time factor. In this case, depending on the goals of the analysis, the general (absolute) and comparative economic efficiency of capital investments - the main type of investment in agriculture - is determined.

Overall economic efficiency of capital investments calculated when determining the feasibility of their implementation. Its indicators are the coefficient of overall economic efficiency of capital investments and their payback period.

Coefficient of overall economic efficiency of capital investments (capital return) is measured by the ratio of the increase in profit (net output, net income) AP (PE, ND) to the capital investments K that caused this increase:

Payback period for capital investments - inverse indicator of the coefficient of overall economic efficiency, years:

Capital investments in economically are justified if the coefficient of overall economic efficiency is equal to or exceeds the value of the standard coefficient of efficiency of capital investments (0.15), and their payback period is less than 7 years.

When assessing the effectiveness of capital investments in construction, the time gap (lag) between their implementation and the receipt of the effect, which depends on the timing of construction and development of the facility, is taken into account.

Construction log represents the time required to construct the facility and install the equipment. The value of the construction lag shows the time spent in unfinished construction of the average annual amount of capital investments.

Development lag - the time required to achieve the level of return envisaged by the project from the fixed assets put into operation.

Reducing construction and development time helps to increase the economic efficiency of capital investments.

Comparative economic efficiency of capital investments is calculated by comparing several options for business decisions, i.e. determining the most effective option for capital investments.

An indicator of comparative economic efficiency of capital investments is reduced costs. Presented costs represent the sum of current production costs(cost) and capital investments reduced to the same dimension through the standard coefficient of comparative efficiency. They are calculated according to the formula, rub.:

where is TK. - current costs (product cost) by options, rub.;

K. - capital investments by options, rub.;

E n - standard investment efficiency ratio equal to 0.12.

Indicators TK and K can be applied both in relation to the total amount of capital investments and the cost of all products, and in the form of specific capital investments per unit of production and the cost of a unit of production.

The economically feasible option is the one that provides the minimum costs. At the same time, the annual economic effect from sales best option determined by the formula, rub.:

where PZ, P3 2; TZ p T3 2; K p K 2 - respectively reduced, current costs and capital investments according to options, rub.

The second way to determine the effectiveness of investments takes into account the time factor.

When assessing investment decisions It should be taken into account that a direct comparison of the amount of investment and income gives somewhat distorted results, since these values ​​are spread over several years. For example, the return on capital investments in planting an orchard will begin only 5-8 years after the main expenses for planting and caring for young plantings are made. The money will be received in the future, and capital investments in planting a garden are made in the present, so the income from investments must be assessed at the present moment - “reduced” to the value at the time of capital investments.

Income (and any other value) that will be received in the future has a present (current) value of less than its expected value. Reasons for this difference:

a) receiving a positive interest on existing capital: even

if money is not invested in production, but lies in a bank deposit account, its amount increases over time by the amount interest rate; based on this, income must be compared with investments increased by this percentage;

• b) the need to take into account inflation, which leads to the depreciation of money over time; with inflation, in a year or two the same amount of money will buy fewer goods than today;
• c) the need to take into account the risk that investments will bring less than expected income or will not pay off at all.

Due to uncertainty, 100 rubles. income expected in the future have a value less than the real 100 rubles. Today.

A special economic technique called discounting makes it possible to compare “real” money with money in the future.

Considering only the positive interest on invested capital at bank rate 10%, we can count on the fact that 100 rubles deposited in the bank today should be returned in a year in increments of 10 rubles. In other words, 110 rubles, which we expect to receive in a year, are currently equal to 100 rubles. In two years we will receive 100 rubles. (1 + 0.1) 2 = 121 rub. etc. The estimate of future income is called the current discounted value ( PDV).

where r is the discount rate;

P - the number of years for which income is summed up (the time after which the value will be obtained R).

Knowing the future value of income and the interest rate, you can determine the current (modern) discounted value of income using the formula:

The multiplier, with the help of which present and future values ​​are equalized, is called discount factor. Its calculation using the presented formulas is labor-intensive, therefore, for convenience, discount tables have been developed, which present the values ​​of discount factors depending on time intervals and values ​​of the discount rate (percentage).

For all income during the period of existence of the capital project, the value of the current discounted value is determined by summing PDV income for each year:

Where PDV(P()), PDV(P 2),..., PDV(P n) - current discounted value of income received in 1, 2,..., P years.

If investments (I) are extended over time, i.e. are carried out over several years, it is also necessary to discount the amount of investment:

The main indicators assessing the economic efficiency of investments are based on the current discounted value.

Net present value. This indicator is based on a comparison of the size of the initial investment with the total amount of discounted cash receipts from them.

Suppose there is a forecast that investments will generate annual income in the amount of P v P 2, ..., R p. The total value of discounted income is calculated using the formula:

If you compare this value with the initial investment, you get the formula for calculating net present value:

Obviously, if NPV> 0, investments will bring economic benefits; less - there will be no positive effect.

When comparing different investment options, the option with the higher net present value has greater economic efficiency.

If the project involves investment over several years, the net present value is determined as follows:

Where PDV(I)- current discounted value of investments made during P years.

Often, in the first years of implementation, a project brings losses (for technological reasons, due to lack of experience, etc.). When determining M, losses also need to be discounted.

When determining net present value, all types of receipts, both production and non-productive nature that may be associated with this investment project. So, if at the end of the project implementation period (after the expiration of the fixed assets use period) it is planned to receive funds in the form of the liquidation value of equipment or the release of part working capital, their magnitude must also be taken into account. They are accounted for as income for the corresponding periods. Moreover, in the formula NPV another element appears:

Where PDV( OS) - discounted liquidation value of equipment and the amount of released working capital.

Thus, net present value shows the enterprise's income from a particular investment project. This indicator is additive over time, i.e. The ZhRK of various projects can be summarized. This is a very important property that makes this indicator stand out and allows it to be used as the main one.

Internal rate of return (recoupment) (IRR) - important indicator economic efficiency of investments. It shows the estimated discount rate at which the income received from the project becomes equal to the costs of the project. In its simplest form, it can be defined as the interest rate at which the net present value is zero:

The internal rate of return indicator allows us to draw two conclusions regarding the effectiveness of investments.

1. The internal rate of return shows the maximum allowable level of costs for attracting financial resources that can be used in an investment project. For example, if an investment is financed by a loan, then the value IRR shows upper limit the level of interest for the loan, the excess of which makes the project unprofitable. Investments with a high internal rate of return (payback) will be effective even if they are financed through “expensive” loans - with an interest rate reaching the level IRR(%). Ineffective projects will not withstand such strict lending conditions.

The internal rate of return allows you to compare investment options based on their stability under financing conditions. IN modern conditions, characterized by instability lending rates, the internal rate of return indicator becomes particularly important. So, from two investment projects with values IRR, equal to 50 and 30%, the first is more resistant to changes in the external environment. It will make a profit even if the cost of borrowing to finance it suddenly rises to 49%. The second project becomes ineffective when financed with a loan at a rate of 31%.

2. The second conclusion about the effectiveness of investments is related to the price of capital advanced. Any enterprise finances its activities, including investment, from various sources. As a fee for using advance financial resources(own and borrowed) it pays interest, dividends, remuneration, etc. In this sense, even your own money can be likened to borrowed money, since servicing it requires certain expenses (similar to payment for a loan). The indicator characterizing the level of these expenses is called the price of advanced capital (SS). It reflects the current minimum return on invested capital at the enterprise - its minimum acceptable profitability. If profitability is below this level, the profit received will not be enough even to service the existing capital (not to mention production). The price of advanced capital, %, is calculated using the arithmetic average weighted formula of the costs of servicing all sources of money.

The economic meaning is that any investment decisions will be effective if their internal rate of return is not lower than the current value of the CC indicator (or the price of the source of funds for this project, if it is the only one). The connection between them is as follows:

• If IRR> SS, then the investments are effective, for their financing it is possible to use sources more expensive than those that the enterprise usually uses; the upper permissible limit of the cost of funds for a specific project is determined by the value IRR-,
• If The IRR effect can only be obtained with a cheap loan (cheaper than usual for the enterprise); these investments cannot be considered effective, since it is practically impossible to obtain money at an interest rate lower than usual. The internal rate of return is calculated using

computer. For quick “manual” calculations, the method of successive iterations is used. The internal rate of return is determined by a series of attempts in which NPV at different discount rates. For example, UURE is positive at a discount rate of 10% and negative at a discount rate of 20%. This means that the internal rate of return lies between 10 and 20%. If NPV at 15% is still positive, which means the internal rate of return lies between 15 and 20%. Subsequent attempts will increasingly narrow the range, and eventually the discount rate at which NPV= 0 will be found.

Return on Investment is determined by the ratio of all discounted income from the project to all discounted expenses for it:

Obviously, if R> 1, then investments in the future will pay off with a rate of return equal to R If P 1, the investment is unprofitable and, therefore, economically ineffective.

Return on investment - relative indicator. Thanks to this, it is very convenient when choosing a project from a number of alternatives that have approximately the same net present value values ​​( NPV), or when completing an investment portfolio with the maximum total value NPV

Payback period of investment. This method is the simplest; it is widely used in Russia and the world. economic practice. The algorithm for calculating the payback period depends on the uniform distribution of projected income from the investment. If the income received is distributed evenly over time, then the payback period is calculated by dividing the one-time capital investment by the amount of annual income. When receiving a fractional number, it is rounded up to the nearest whole number. If profits are distributed unevenly, the payback period is calculated by directly counting the number of years during which the amount of income received (cumulative income) exceeds the initial capital investment.

When calculating the economic efficiency of capital investments, it is necessary to take into account the origin of funds for their financing. When financed by own funds indicators are calculated based on cash flow, including expenses and income from this investment project. When financing with borrowed funds, the cash flow of the investment project should include costs associated with debt servicing.

Economic effect of investments E- This valuation increasing labor productivity, improving quality and increasing production output, reducing its cost due to investments in investment projects. The criterion (quantitative measure) of the economic effect is the increase in profit for the development option proposed in the project compared to the base (existing) option.

Efficiency is the ratio of the result of an activity to the resources spent. Efficiency is perceived as a characteristic of the system’s ability to produce an economic effect equal to the difference between the result of economic activity and the costs incurred to obtain it and use it, or operate it. Economic efficiency characterizes the effectiveness of using limited resources, that is, the extent to which needs are met with the chosen method of using resources.

Economic efficiency E investment is a relative economic effect:

E = E /I = 4,266 / 8000 = 0,00053 (3.1.1) 13

showing the share of the annual economic effect E in investments I. Reciprocal value E, represents the payback period of the investment:

Distinguish absolute economic efficiency (effect) of investments for a certain option and comparative economic efficiency of investments according to various options.

Selecting an investment discount rate

The effectiveness of long-term investments (for a period of more than a year) is assessed based on discounted cash flow analysis. Discounting operation– this is bringing the economic indicators of the project at different time intervals to a comparable level.

Discount rate (capitalization) represents the relative annual change in the value of investment resources invested in an investment project at various stages of its implementation. The discount rate reflects, firstly, the change in the cost of investment resources due to the possibility of alternative investment directions; secondly, changes in the cost of resources due to inflationary processes. The discount rate is also called opportunity costs, since it represents the profitability (efficiency) that an investor gives up by investing resources in a project rather than in other income-generating tools.

Discount rate.

Select the discount rate based on the expected growth rate of the market value of shares investor enterprises:

, (3.2.5) 15

Where d– annual dividend payments on shares of the investing enterprise,

R A– price of shares of the investor enterprise;

g– expected (predicted) rate of dividend growth.

The discount rate is:

r=16%*0.8+6%*0.2=12,8+1,2=14%

Net present value (net present value) of an investment

The net present value criterion is historically the earliest method for assessing investment performance proposed by Alfred Marshall in the work “Fundamentals of Economic Science” (1890). The method is based on comparing the value of the initial investment ( I) with the total discounted net cash flows over the forecast period T. Let's denote annual income
. Total accumulated value of discounted income PV (Present value) and net present value NPV (Net present value) are calculated using the formulas:

, (3.3.1) 17

. (3.3.2) 18

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

. (3.3.3) 19

If annual incomes are ordered streams of payments, then formulas for modern values ​​of the corresponding annuities can be used.

Net present value NPV is criterion for evaluating an investment project, because if NPV > 0 , then the project should be accepted, NPV< 0 , then the project should be rejected, NPV = 0 , then the project is neither profitable nor unprofitable.

Economic indicator NPV reflects a forecast assessment of changes in the economic potential of the enterprise in the event of project implementation; represents the income from the project if the investment is made using borrowed funds, and the loan is issued at an interest rate r. The indicator is additive, that is NPV different projects can be summarized, which allows it to be used when analyzing the optimality of an investment portfolio. Absolute value NPV depends on the choice of time of assessment. When the discount rate increases, the value NPV decreases.

Methods used in assessing the economic efficiency of investment projects can be combined into two main groups - simple (static) and complex (dynamic).

The methods of the first group use accounting ones, i.e. indicators reflected in the financial statements - investment costs, profit, depreciation.

Methods of the second group use discounted values ​​of indicators.

Simple Methods

In practice, to determine the economic efficiency of investments in a simple way, two methods are most often used: calculating the simple rate of return and the payback period.

Simple rate of return - (ROI- return on investments) calculated as a ratio net profit (Pr) for one period of time (usually a year) to the total investment costs (I):

Economically, the meaning of a simple rate of return is to estimate what portion of investment costs is recovered as profit during one planning interval. By comparing the calculated value of the simple rate of return with the minimum or average level of profitability, the investor can draw preliminary conclusions about the feasibility of these investments, as well as whether the analysis of the investment project should be continued. In addition, at this stage, an approximate estimate of the payback period of this project is possible.

In a number of cases, when calculating the simple rate of return indicator, the ratio of income (cash flow) to the amount of investment costs is actually determined:

where A is depreciation.

Investment costs in the expressions presented above mean the costs of forming fixed and working capital.

This approach does not take into account the reduction of capital investments as a result of depreciation to their residual value.

The indicator is devoid of this drawback

In this case, the ratio of income to average capital for the period of project implementation.

In most projects, the distribution of income across years of implementation is uneven. In this case, the numerator of the indicator must use average income:

In this expression, T is the period of project implementation.

Payback period - another indicator in the group of simple methods for assessing effectiveness. The payback period of a project characterizes the period of time during which the amount of one-time costs is covered by profit and depreciation charges from the project. Using this indicator, the period during which the project will work “for itself” is calculated, i.e. the entire volume of funds generated by the project, which includes profits and depreciation, is used to return the initially invested capital.

The formula for calculating the payback period can be presented as follows:

Where PP (payback period)- return on investment indicator (payback period); I0 (investment) - initial investment; R- net annual cash flow from the implementation of the investment project.

Calculation of the payback period can also be carried out by calculating the accumulated amount of depreciation charges and net profit. The period during which this amount becomes equal to the initial investment is called the payback period.

Complex Methods

The decision to invest capital is determined in most cases by the amount of income that the investor expects to receive in the future. When making such decisions, the time factor plays a very important, if not decisive, role. In this regard, the problem arises of accounting for expenses and income spread over time. To solve it, you need a correct understanding of the time value of money and the method of discounting cash flows.

The concept of time value of money can be formulated as follows: money today is worth more than the same amount we will receive in the future. This fact is due to the following circumstances.

1. Today's money can be invested and receive additional money in the form of interest.

2. The purchasing power of money may fall over time due to inflation.

3. You cannot be completely sure that you will receive money in the future.

Thus, in order to make time-effective financial decisions, it is necessary to use appropriate methods that allow take into account the time aspect of the value of money.

Transformations of cash flow elements are carried out by applying incremental and discounting operations. Accrual is the process of determining the future value of money. Discounting is the process of bringing money to its value. current value. In the first case, they move from the “present” to the future, in the second, on the contrary, from the future to the present. In both cases, using the compound interest scheme, it is possible to obtain an assessment of cash flow from the perspective of the future or “present”.

When analyzing payment flows, general indicators are used:

· increased cost;

present value;

· rate of return.

Net present value

Since funds are distributed over time, the time factor plays an important role here too.

When assessing investment projects, the calculation method is used net present value, which involves discounting cash flows: all income and costs are reduced to one point in time.

The central indicator in the method under consideration is the indicator NPV(net present value) – the current value of cash inflows minus the current value of cash outflows. This is the generalized final result of investment activity in absolute terms.

For a one-time investment, the calculation of net present value can be represented by the following expression:

Where R k – annual cash receipts during n years,

k= 1, 2, …, n;

IC– start-up investments;

i- discount rate.

An important point is the choice of discount rate, which should reflect expected average level of loan interest in the financial market.

To determine the effectiveness of an investment project by an individual company, the discount rate is used weighted average cost of capital used by the company to finance this investment project.

The NPV indicator is an absolute increase, since it estimates how much the present income covers the present costs:

· at NPV> 0 the project should be accepted;

· at NPV< 0 проект не принимается,

· at NPV= 0 the project has neither profit nor loss.

Example. The company is considering the feasibility of an investment project, the cost of which is 210 thousand dollars. Annual revenues are projected to be $55,000. The project is designed for 5 years. The required rate of return is 8%. Should this project be accepted?

Solution:

The net cost of the project is:

NPV= 55"000 (1.08)-1 + 55"000 (1.08)-2 + 55"000 (1.08)-3 + 55"000 (1.08)-4 + + 55"000 ( 1.08)-5 - 210"000 = 50"926 + 42"867 + 39"692 + 36"751 + 34"029 - 210"000 = = 204"265 - 210"000 = -5"735 dollars.

Since the net present value is -5"735 dollars, i.e. NPV< 0, то проект не может быть принят.

One of the factors determining the net present value of a project is the scale of activity, which is expressed in physical volumes of investment, production or sales. Therefore, the use of this method is limited for comparing different projects: a higher value NPV will not always correspond to more efficient use of investments. In such a situation, it is advisable to calculate the indicator return on investment(profitability index) (PI-profitability index): Formula for determining P.I. has the following form:

The return on investment (profitability) index is a relative indicator characterizing the level of income per unit of cost. The higher it is, the greater the return on investment for this project. Index P.I. used when choosing a project from a number of alternatives that have similar NPV with different amounts of investment.

A project is effective if the project's profitability index is greater than 1.

Example. Calculate the PI indicator if the initial investment is 25 million rubles, the net return at the end of the first year is 15 million rubles, at the end of the second year - 10 million rubles, and the third year - 8 million rubles. , discount rate – 12%.

PI =/25=27.05/25 = 1.08.

Payback period

To analyze investments, an indicator such as payback period(payback period method) – the length of time during which the projected cash receipts discounted at the time of completion of the investment are equal to the amount of the investment. In other words, this is the sum of years required to recoup the initial investment:

those. NPV= 0.

The payback period can be determined as the expected number of years using a simplified formula:

DPP = Number of years before the payback year + (Non-recovered cost at the beginning of the payback year / Cash inflow (discounted) during the payback year) This indicator determines the period during which the investment will be “frozen”, since real income from the investment project will only begin to flow after the payback period has expired.

Example. Calculate the payback period of a project for which the investment amount is 1 million rubles, and cash receipts over 5 years will be: 200; 500; 600; 800; 900 thousand rubles. respectively. Discount rate 15%.

Solution: Calculate discounted cash flow:

Project payback period: DPP to= 3 + 54 / 458 = 3,12

Thus, the period actually required to recoup the invested amount will be 3.12 years or 3 years and 44 days.

If income can be represented in the form of a permanent annuity, then

Internal rate of return

When analyzing the effectiveness of investment projects, the indicator is widely used internal rate of return(IRR– internal rate of return) is a discount rate that equates the amount of present income from an investment project to the amount of investment, i.e. investments pay off, but do not bring profit. The value of this rate is completely determined by the “internal” conditions characterizing the investment project.

The application of this method comes down to sequential iteration (repetition) of finding the discount factor until equality is achieved NPV= 0.

Two values ​​of the discount factor are selected at which the function NPV changes its sign, and use the formula:

The investor compares the received value IRR with the rate of attracted financial resources ( CC– Cost of Capital):

· If IRR > CC, then the project can be accepted;

· If IRR< СС , the project is rejected;

· IRR = SS the project has zero profit.

Solution: Calculation at 5% rate:

NPV= 47619 + 181406 + 388767 + 411351 + 470116 - 1200000 = 299259.

Because the NPV> 0, then the new discount rate must be greater than 5%.

Calculation at a rate of 15%:

NPV= 43478 + 151229 + 295882 + 285877 + 298306 - 1200000 = -125228.

We calculate the internal rate of return:

IRR= 5 + ] (15 - 5) = 12,05.

The internal rate of return of the project is 12.05%.

The accuracy of the calculation is the inverse of the interval between the selected interest rates, therefore, to clarify the interest rate, the length of the interval is taken as 1%.

Example. Clarify the bet amount for the previous example.

Solution: For an interest rate of 11%:

NPV= 45045 + 162324 + 329036 + 329365 + 356071 - 1200000 = 21841.

For an interest rate of 12%:

NPV= 44643 + 159439 + 320301 + 317759 + 340456 - 1200000 = -17402.

Specified value: IRR= 11 + ] (12 - 11) = 11,56.

The rate of 11.56% is the upper limit of the interest rate at which a company can recoup a loan to finance an investment project.

The IRR indicator can be used to rank projects by degree of profitability. It can also be used to assess the level of risk: the more the IRR exceeds the cost of capital, the greater the margin of safety of the project and the more insensitive to market fluctuations when estimating the value of future cash flows.

5. Investment efficiency

5.1. The concept of effect and efficiency of investments

We already know that one of the main criteria in an investor’s decision to invest capital is the profitability or profitability of the investment project. The investor is interested, first of all, in the effectiveness of his investments.

Here is a simple example: two investment projects are being considered. The implementation of the first project will bring the investor 100 million rubles in a year. net income, the second - 120 million rubles. What decision should an investor make if the risks for the projects can be considered the same?

Obviously, in order to make a decision, the investor also needs to know full amount investments for each of the projects, and only by comparing them with the amount of income, he will be able to assess the effectiveness of the project.

So, let’s now try to formulate the concepts of “effect” and “efficiency”:

EFFECT is the income (benefits) received from the implementation of any event.

INVESTMENT EFFECT is income or other benefits received from the implementation of an investment project.

As a result of the implementation of an investment project, both an economic effect, which has a cost value, and a social effect (for example, creating additional jobs, improving living conditions of the population) or environmental (improving the environment, reducing environmental damage, etc.) can be obtained. As a rule, social and environmental effects can be indirectly expressed in terms of value. For example, improving people's living conditions will ensure better reproduction of the labor force, which will ultimately manifest itself in increased labor productivity and increased incomes. Improving the ecology and improving the environment will affect the reduction in the level of morbidity among people, which will lead to a relative reduction in healthcare costs, etc. In such cases we are talking about socio-economic and socio-ecological effects.

EFFECTIVENESS is the ratio of the effect of any activity to the costs of its implementation.

EFFECTIVENESS OF AN INVESTMENT PROJECT is an indicator characterizing the ratio of the income received from the implementation of this project with the amount of investment made in this project.

It is obvious that the effect is an absolute value, efficiency is relative. In the very general case Effectiveness and efficiency indicators can be defined as follows:

, (5.2)

Where – effect from the implementation of an event or project, rub.;

– result from the implementation of an event or project, rub.;

– costs of implementing an event or project, rub.;

– effectiveness of an event or project, rub.

The result here is understood as the cost of goods produced, work performed, services rendered, i.e. revenue, and costs are the costs of the enterprise associated with the implementation of the project and reflecting cost of resources used. Thus , the effect is determined by the excess of the result over the costs, and efficiency is determined by the ratio of the effect to the costs.

In relation to assessing the effect and efficiency of investments, the result is defined as proceeds from the sale of goods produced, work performed or services provided at newly created or reconstructed enterprises, the construction or reconstruction of which was carried out as part of an investment project. In this case, the costs are included as the costs of implementing the investment project, i.e. investments (we'll call them initial costs), as well as costs associated with the implementation of production (operational) activities, i.e. current expenses:

, (5.3)

Where – investment costs associated with the implementation of an investment project - investments in construction, reconstruction, acquisition of fixed assets, formation of working capital and intangible assets, rub.;

– current costs associated with the implementation of an investment project - production (operating) costs of producing products, performing work or providing services at an enterprise created as a result of the investment project for the entire period of project implementation, rub.

The greater the effect that can be obtained per unit of costs incurred, the higher the efficiency of investment. When assessing the effectiveness of investments, the resulting effect can be compared not with the entire amount of project costs, but only with investment costs:

The effectiveness of investments is influenced by various factors (Fig. 5.1), the effects of which should be taken into account in the business plan of the investment project. For example, a change in tax legislation during the implementation of an investment project will lead to a change in the financial indicators of the enterprise, and, consequently, the net income received by the investor. When implementing similar investment projects in different economic regions that differ in natural and socio-demographic factors, different indicators of investment efficiency can also be obtained. The more carefully the influence of these factors is taken into account in the business plan, the lower the investment risks of the project.

However, the diagram we presented does not show another important factor influencing the effectiveness of investments - the time factor. We have already considered the role of this factor in the investment process in section 3.2. Below, in section 5.3, we will consider methods for taking into account the influence of the time factor on the effectiveness of investment projects.

When assessing the effectiveness of an investment project, the following performance indicators are calculated:

Indicators public (socio-economic) efficiency, taking into account the socio-economic consequences of the investment project for society as a whole. At the same time, results and costs that go beyond the direct financial interests of immediate project participants are assessed. These indicators are determined during the implementation of large investment projects of socio-economic significance.

Rice. 5.1. Factors influencing investment efficiency

Indicators regional efficiency, taking into account the socio-economic consequences of the implementation of the investment project for the region in which the investment project is being implemented. These indicators are assessed when implementing large projects of regional importance.

Indicators industry efficiency, taking into account the significance of the investment project as a whole for the industry or large industrial and financial groups.

Indicators commercial efficiency, taking into account financial consequences making investments directly for project participants. These indicators are calculated primarily for investors, their creditors, as well as for investors investing capital in the company's shares.

Indicators budget efficiency, reflecting the financial consequences of the project for budgets at various levels. Calculation of these indicators is mandatory if budgets of various levels are involved in financing the investment project.

According to the accepted methodology, both the effectiveness of the project as a whole and the effectiveness of the participation of investment process subjects in this project should be assessed (Fig. 5.2).

Rice. 5.2. Investment project performance indicators

The basis of all these investment performance indicators is principle of comparing results and costs. Various methods are used to compare the results of a project and the costs associated with its implementation. Depending on the method of measuring these indicators and taking into account the time factor, distinguish simple (static) method assessing the effectiveness of investments and discounting method (dynamic method), which we will look at in the following sections.

Methodological recommendations for assessing the effectiveness of investment projects: (Second edition). Approved Ministry of Economy of the Russian Federation, Ministry of Finance of the Russian Federation, State Construction Committee of the Russian Federation 06.21.1999 No. VK 477.; hands auto Col.: Kosov V.V., Livshits V.N., Shakhnazarov A.G. – M.: OJSC “NPO “Economy Publishing House”, 2000. – 421 p.

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