MINISTRY OF COMMUNICATIONS OF THE RF

FAR EASTERN STATE UNIVERSITY OF COMMUNICATIONS

Department: Finance and credit

Test

By discipline: Economics of Investments

Khabarovsk 2002

Introduction

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

2. Selection procedure investment projects

3. Problem solving

Conclusion

List of sources used

INTRODUCTION

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

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

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

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

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

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

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

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

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

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

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

An indicator of net present value.

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

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

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

NPV< 0, то проект следует отвергнуть;

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

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

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

where i is predicted average level inflation.

Internal rate of return.

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

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

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

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

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

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

IRR< CC, то проект следует отвергнуть;

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

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

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

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

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

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

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

Payback period.

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

PP=n, at which.

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

Profitability index.

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

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

P1< 1, то проект следует отвергнуть;

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

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

Investment efficiency ratio.

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

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

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

2. Procedure for selecting investment projects

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

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

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

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

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

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

· financial results;

· availability of markets for products;

· production profitability;

· return on investment;

· volume of invested funds;

· project payback period;

· net income, internal rate of return;

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

· number of new jobs;

· number of social problems being solved;

· level wages;

· environmental Safety.

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

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

· ensuring risks of irrecoverability.

When selecting investment projects, preference is given to applicants:

· having a stable financial position;

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

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

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

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

3. Problem solving

Task No. 1

Condition:

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

Solution:

1. determination of the economic efficiency of the project.

The economic efficiency coefficient is equal to:

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

2. calculation of the internal rate of return.

Table 3.1.

Initial data for calculating the IRR indicator.

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

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

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

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

For 2 years it is necessary to cover:

1600 – 900 = 700 million rubles,

700 / 800 = 0.875, which is 10.5 months.

Task No. 2

Condition:

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

Solution:

1. Determination of economic efficiency:

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

ΔЗ = ΔEgod + En * ΔK,

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

En – standard of comparative economic efficiency, = 0.15;

ΔК – savings on capital investments in the locomotive fleet.

1.1. Determining total operating cost savings:

ΔEgod = ΔE + ΔFZP + ΔEo – ΔEdop,

where ΔE – annual savings in operating costs;

ΔFZP – wage fund savings;

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

ΔEdop – saving additional operating costs.

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

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

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

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

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

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

m – train composition.

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

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

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

1.1 – replacement rate;

Z – average monthly salary, 1500 rubles.

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

ΔEo = 300 * 15 = 4500 rub.

ΔEdop = Ea + Em + Ep.

Ea – increase in depreciation charges,

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

where Km is the number of mobile vehicles;

Cm – cost of the car, 30.5 thousand rubles;

A – depreciation rate, 9.9%.

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

Em - expenses for the current maintenance of machines:

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

Ep – costs of maintaining narrow gauge tracks:

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

ΔEdop = 6000 + 7050 + 320000 = 333050 rub.

Thus,

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

1.2. Calculation of capital investments.

IN in this case the volume of capital investment savings will be:

ΔK = Kl + Kv + Kst,

Kl – savings on capital investments in the locomotive fleet:

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

Kv – savings on capital investments in the rolling stock:

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

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

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

ΔK = 3203125 + 26812.5 + 41854.167 = 3271792 rub.

Thus,

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

Task No. 3

Condition:

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

Exercise: It is necessary to select a construction project.

Solution:

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

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

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

CONCLUSION

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

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

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

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

LIST OF SOURCES USED

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

efficiency of investing in company shares;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

NPV =Σ TDS (D) – Σ TDS (I),

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

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

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

will reimburse the costs incurred;

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

will receive additional income equal to the net present value.

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

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

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

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

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

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

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

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

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

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

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

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

Making investment decisions is integral part financial policy any dynamically developing commercial organization, whose management is aimed at the well-being of the company in the long term.

An analysis of literature and practice shows that an enterprise cannot, in principle, refuse to invest, since in this case its position will significantly worsen compared to competing firms. The implementation of an investment project allows the company to adapt to macroeconomic realities and changes in the external environment. All commercial enterprises are to one degree or another connected with investment activities, but investment decision-making differs in the types of investments, the cost of projects, and the risks of making a particular decision. That is why the problem of effective investment deserves special attention.

Meaning economic analysis for planning and implementation investment activities difficult to overestimate. Wherein special role plays a role in preliminary analysis, which is carried out at the stage of development of investment projects and contributes to the adoption of reasonable and informed management decisions.

In domestic and foreign practice, when developing and examining an investment project, its assessment is carried out on the basis of an analysis of the values ​​of integral indicators, the calculations of which are devoted to a huge amount of literature.

Among the most common methods for assessing the effectiveness of investment projects, the following should be noted:

1. NPV (Net Present Value) – net present (discounted) value: the difference between discounted cash flows and initial investments;

2. IRR (Internal Rate of Return) – internal rate of return (profitability): the discount rate at which the net present value (NPV) is zero;

3. PI (Profitability Index) – profitability index: the ratio of the present income expected from investments to the amount of invested capital;

4. DPP (Discounted Payback Period) – discounted payback period: the number of years required to recoup investments with discounted net cash flows.

When making investment decisions, it should be borne in mind that the implementation of projects is carried out not only taking into account the characteristics specific enterprise, but also taking into account the conditions of the external environment in which the organization operates and the possibility of their changes. This situation leads to the fact that the set of parameters and cash flows of the project are unknown in advance and can take on different values, that is, the project has several possible implementation scenarios. In this regard, it becomes necessary to use methods that allow assessing the effectiveness and risks of a project taking into account changes in the external environment.

But, despite this, in practice, project risks are at best characterized qualitatively, that is, at the level of their listing and description. Methods for taking into account uncertainty in project assessment are not popular among enterprises, which explain this by the lack of necessary tools or the complexity of calculations. This approach is unacceptable, especially under the current conditions. Russian economy.

The purpose of risk analysis, which acts as sources of uncertainty, is to provide potential project investors with the necessary data to make a decision on the advisability of participating in it and identifying measures to protect against possible financial losses.

Risk analysis usually begins with a qualitative analysis, the purpose of which is to identify risks, which is carried out as follows:

§ identification of all possible risks characterizing the investment project;

§ description of risks;

§ classification and grouping of risks;

§ analysis of initial assumptions.

The risks inherent in investment projects can be classified based on their manifestation at one or another stage of the investment project. In accordance with this, it is possible to highlight the risks of the investment phase of the project, which may arise as a result of underfunding of projects, an increase in the cost of capital, project timing, technical impracticability of the project; risks of the production phase of the project – production and marketing; as well as complex risks, which include managerial, administrative, financial, regional, legal and other types of risks.

The second most complex stage of risk analysis is quantitative risk analysis, the purpose of which is to measure risk.

Quantitative risk analysis is a formalization of the results of qualitative analysis and determination of the degree of overall project risk.

The most common methods for assessing the risks of investment projects include the following:

§ Sensitivity analysis.

§ Scenario analysis.

§ Simulation modeling.

Sensitivity analysis consists of determining the dependence of the most important economic indicators project from changes in the basic parameters of the project, varying within certain limits. The sensitivity indicator is percentage change NPV for a one percent change in an input variable. Depending on the value of the sensitivity index, the variables are ranked from the most sensitive to the least sensitive. The higher the sensitivity, the more important the variable is for determining the efficiency indicator, which must be taken into account when predicting the variables entered for calculation and making a decision on the implementation of a particular investment project.

Some authors consider sensitivity analysis as the main, simple and widely used method for determining risk limits, as well as reducing it in the operational analysis of an enterprise's activities. However, it is not without significant drawbacks:

§ does not allow calculating the probabilities of changes, as well as probabilistic indicators of the formation of this particular and not another value of the resulting indicator. This method allows you to determine the risk of a project only at certain points;

§ In sensitivity analysis, the assumption is made that all variables except one are constant. In reality, this is impossible, since a change in some variables entails a change in others.

It is because of the above disadvantages that an investor should consider sensitivity analysis as a source of information for other methods.

To conduct an analysis with more realistic assumptions about the relationship between input variables, it is necessary to use more accurate methods, one of which is scenario analysis. This method consists of constructing scenarios for the development of events and calculating the main indicators of the economic efficiency of the project for each scenario. Conclusions are drawn based on compiling the obtained calculation results with an assessment of the likelihood of the scenario occurring. The scenario method allows you to combine the study of the sensitivity of the resulting indicator with the analysis of probabilistic estimates of its performance.

When conducting analysis using this method, it should be taken into account that scenario analysis is most effective when the number of possible values ​​of the resulting indicator is finite and relatively small. But in practice, very often there are opposite cases, characterized by an unlimited number of options for implementing an investment project. In such cases, it is more convenient to use simulation modeling, including its version of the Monte Carlo method.

Simulation modeling is one of the most powerful modern methods of analysis economic processes and systems. This method is defined as the process of constructing a model of a real system and conducting experiments on this model in order to study the behavior of the system or evaluate (within the limitations imposed by some criterion or set of criteria) various strategies that ensure the functioning of this system. The Monte Carlo method is a type of simulation modeling and allows us to take into account the impact of uncertainty on the efficiency of an investment project. This method is based on the fact that with known distribution laws of exogenous variables, using a certain technique, it is possible to obtain not a single value, but the distribution of the resulting indicator.

Compared to previously discussed methods, the Monte Carlo method has a number of significant advantages:

§ allows you to take into account the maximum possible number of factors;

§ creates additional opportunity in assessing risk by making it possible to create random scenarios;

§ the method reveals the weak points of the project and makes it possible to make amendments;

§ can be quite simply implemented in MS Excel;

§ allows you to quantify the risk of an investment project.

These and other advantages of the Monte Carlo method make it one of the best ways assessment of investment projects.

12. Statistical and dynamic methods of investment analysis: general and Comparative characteristics

The set of methods used to evaluate the effectiveness of investments can be divided into two groups: dynamic (taking into account the time factor) and static (accounting) (Fig. 8.3).

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

Return of the original amount of capital investments;

Ensuring the required return on invested capital.

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

Payback period of investment (RR);

Accounting rate of return (ARR)\

Net modern value of an investment project (NPV);

Internal rate of return (return, profitability) (IRR);

Modified internal rate of return (return, profitability) (MIRR);

Project profitability index (PF);

discounted payback period (DPP).

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 deciding whether to accept or reject the project,

To determine the effectiveness of mutually exclusive projects (comparative effectiveness), when a conclusion is made about which project to accept from several alternative ones.

Static methods. The following methods are used.

□ Payback Period- RR). This is one of the simplest and most widespread methods in world practice; it does not imply a temporal ordering of cash receipts and consists in determining the number of years required to fully reimburse the initial costs, i.e. determining the moment when the cash flow of income equals the sum of the cash flow of costs. Projects with the shortest payback periods are selected. Algorithm for calculating the payback period (RR) depends on the uniformity of the distribution of projected income from the investment. If income is distributed evenly over the years, then the payback period is calculated by dividing one-time costs by the annual income due to them. When a fraction is obtained, it is rounded up to the nearest whole number. If the profit is distributed unevenly, then the payback period is calculated by directly calculating the number of years during which the investment will be repaid by cumulative income. General formula for calculating the indicator RR looks like

Based on the example data, we will calculate the payback period of the project:

The project pays for itself in 3.4 years. If the investor is satisfied with this deadline, then the project is accepted for implementation.

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

First, it ignores cash receipts after the project's payback period expires. Secondly, since the method is based on non-discounted valuations, it does not distinguish between projects with the same amount of cumulative income, but a different distribution of them over the years. It does not take into account the possibility of reinvesting earnings and the time value of money. Therefore, projects with equal payback periods but different time structures of income are considered equivalent.

This method allows you to judge the liquidity and riskiness of the project, since long-term payback means long-term immobilization of funds (reduced liquidity of the project) and increased riskiness of the project. There are a number of situations in which the use of a method based on calculating the payback period may be appropriate. In particular, this is a situation when the management of an enterprise is more concerned with solving the problem of liquidity, rather than the profitability of the project - the main thing is that the investment pays off as soon as possible. The method is also good in situations where investments involve a high degree of risk, so the shorter the payback period, the less risky the project is considered. Method RR successfully used to quickly reject projects, as well as in conditions of strong inflation, political instability or a shortage of liquid funds: these circumstances focus the enterprise on obtaining maximum income in the shortest possible time.

□ Simple rate of return method (Accounting Rate of Return - ARR). When using this method, the average net accounting profit over the life of the project is compared with the average investment (costs of fixed and working capital) in the project.

The method is easy to understand and involves simple calculations, so it can be used to quickly reject projects. However, a significant drawback is that the non-monetary (hidden) nature of some types of costs (for example, depreciation) and the associated tax savings are ignored; income from the liquidation of old assets replaced by new ones; opportunities for reinvesting income received and the time value of money. The method does not make it possible to judge the preference of one of the projects that have the same simple accounting rate of return, but different sizes average investment:

where R b is the net accounting profit from the project;

I 0 - investment.

Dynamic methods. The international practice of assessing investment performance is based on the concept of the time value of money and is based on the following principles.

1. The efficiency of using invested capital is assessed by comparing the cash flow that is generated during the implementation of the investment project and the initial investment. A project is considered effective if it provides a return on the original investment amount and the required return for investors who provided capital.

2. Invested capital, like cash flow, is reduced to the present time or to a specific accounting year, which, as a rule, precedes the start of the project.

3. Discounting of capital investments and cash flows is carried out according to different rates discount, 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.

Dynamic methods that take into account the time factor reflect the most modern approaches to assessing the effectiveness of investments and prevail in the practice of large and medium-sized enterprises in developed countries. In the economic practice of Russia, the use of these methods is also due to high level inflation. These methods are often called discount methods, since they are based on determining the current size (i.e., discounting) cash flows associated with the implementation of the investment project.

The following assumptions are made:

Cash flows at the end (beginning) of each project period are known;

An estimate has been determined, expressed as an interest rate (discount rate), according to which funds can be invested in a given project. The average or marginal cost of capital for the enterprise is usually used as such an assessment; interest rates on long-term loans; required rate of return on invested funds, etc. The assessment is significantly influenced by inflation and risk.

Determining the discount rate. Calculations associated with investment planning show that investments generally create a stream of payments that must be compared with the initial costs. The simplest form of such flows to be analyzed is annuities, i.e. specified amounts of money paid each year over a set number of years in equal or uneven payments.

In relation to investment projects, the interest rate (discount rate) is called barrier It determines the financial return that an investor expects from his investment. According to financial management theory, this return includes two components: the risk-free rate and insurance premium. In general, this formula looks like this:

Required return = Risk free rate + Insurance premium.

The risk-free rate is the base rate. It represents the minimum acceptable return on investment in the absence of virtually all risks. This rate is usually several points above the inflation rate, which prevents erosion of the investor's capital and takes into account liquidity considerations. Investors also require an insurance premium as payment for financing a company exposed to risks in the process of implementing investment projects. The numerical expression of the risk level of an enterprise is obtained by combining the average value of the cost share capital and the cost of debt, which is defined as weighted average cost of capital- WACC). In many enterprises, the barrier rate is set by financial managers, which is constant for a certain period of time. One of the main factors influencing barrier rates is the general situation with interest rates. The financial manager must closely monitor the benchmark interest rate and, as the benchmark rises or falls, adjust the hurdle rates accordingly. Overestimated or underestimated rates lead to a deterioration in business at the enterprise.

Net Present Value (NPV). This investment evaluation criterion belongs to the group of discounted cash flow methods, or DCF methods. It is based on a comparison of the value of investment costs (/0) and total amount time-adjusted future cash flows generated by it over the forecast period. For a given discount rate (coefficient r, established by the analyst (investor) independently based on the annual percentage of return that he wants or can have on the capital he invests), it is possible to determine the current value of all outflows and inflows of funds during the economic life of the project, as well as compare them with each other. The result of such a comparison will be a positive or negative value (net inflow or net outflow of funds), which shows whether or not the project satisfies the accepted discount rate.

The net present value of the project is determined by the following formula:

Where r- discount rate;

n- number of periods of project implementation;

NCF t- net flow of payments in the period t,

Σ CIF t- total revenues from the project in period d,

Σ COF t - total payments for the project in the period t

If the net present value of the payment stream calculated in this way is greater than zero (NPV > 0), then during its economic life the project will compensate initial costs and will ensure profit generation according to a given standard G, as well as its certain reserve, equal to NPV Negative NPV shows that the given rate of profit is not ensured and the project is unprofitable. At NPV= 0 the project only covers the costs incurred, but does not generate income. However, the project NPV= 0 still has an additional argument in its favor - if the project is implemented, production volumes will increase, i.e. the company will increase in scale (which is often seen as a positive trend).

General rule For NPV: If NPV> 0, then the project is accepted, otherwise it should be rejected.

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

The method is implemented in three steps.

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 criterion is determined NPV

Step 3./7a decision is made:

For a separate project - if NPV > 0, then the project is accepted;

13. Dynamic methods for analyzing the commercial effectiveness of an investment project: the problem of justifying the project discount rate

When assessing the economic efficiency of projects or any investment in any activity, the problem of measuring the funds paid or received at different points in time constantly arises. The problem is not only that investors, having free cash, have alternative opportunities for using it and making a profit, but also in the unequal value of cash over time. So, one hundred rubles, for example, used today for production, are not identical to one hundred rubles in a year or two, three, etc. Different attitudes towards the same amount of money are caused not only by inflation or investment risk, but also by the time during which this money can bring its owner the greatest income.
To evaluate the profitability of investments over time, use discounting- the process of bringing multi-time cash flows (receipts and payments) to a single point in time. The name of the term comes from the word “discount” - a discount from the price debt obligation with advance payment of interest for using a loan.
If for a certain period of time income exceeds costs, it is usually said that net income(eng. net benefits), or positive cash flows(eng. positive cash flows); if costs exceed income, then they are usually called net costs(eng. net expenditure), or cash outflows(eng. cash outlay).

To make management decisions on the choice of an investment project, you can use the following indicators based on assessments:

· net income;

net present value ( NPV) or integral effect;

· profitability index (ID);

internal rate of return (GNI);

· payback period;

· other indicators reflecting the interests of participants or the specifics of the project.

To use indicators to compare projects, they must be brought into a comparable form.
Net undiscounted income(other names BH, NetValue,NV) is the accumulated net income (balance of real money, effect) for the billing period, calculated by the formula:

Where Ft- effect (net income, balance of real money) on m-th step, and the amount applies to all steps in the billing period.
Net present value (NPV, integral effect, net present value, NetPresentValue, NPV) - accumulated discounted net income (balance of real money, effect) for the entire billing period, calculated by the formula:

Where Ft- effect on T step; α m- discount coefficient; γ m- distribution coefficient, and the amount applies to all steps in the billing period.
If during the billing period there is no inflationary change in prices or the calculation is made in base prices, That NPV for a constant discount rate is calculated using the formula:

Where Rt- results achieved by t-th calculation step; Zt - costs incurred at the same step; T-planning and calculation horizon (equal to the number of the calculation step at which the object is liquidated); E- rate of return (discount rate); (Rt - Zt) = Et - the effect achieved by t-th step (analogue BH).
If the discount rate changes over time, then

Where P- work; Et- rate of return on t- mcalculation step.
Difference BH - NPV sometimes called project discount. If NPV investment project is positive, the project is effective (at a given discount rate) and the issue of its adoption can be considered. The more NPV, the more effective the project. If the investment project is carried out at negative NPV, the investor will suffer losses, i.e. the project is ineffective.
In practice, a modified formula is often used to determine NPV. For this purpose from the composition Zt exclude capital investments and designate them: Kt- capital investments for t- mshage; TO - the amount of discounted capital investments, i.e.:

If we accept Zt*- costs for t-step, provided that they do not include capital investments, then formula (19.30) for NPV written in the form

and expresses the difference between the sum of the given effects and capital investments. Obviously, if NPV > 0, then the project should be recommended for implementation; If NPV< 0, the project should be rejected; at NPV= 0 the project is neither profitable nor unprofitable.
If we consider several mutually exclusive projects, then the project that has NPV more. In this case, the discount rate or rate of return E should be the same for them. The profitability of each project should be determined by a condition like

Where T - calculation horizon; Et = Rt - Zt, i.e. the effects achieved on t-th calculation step; E- see formula (19.13); TO - capital investments at the zero calculation step.
In fact, the results obtained from formula (19.34) can be interpreted as bringing effects at different times to the initial step (t ³ 0). Technically it is accomplished by multiplying effects This by discount factor at, which for a constant discount rate E defined as

Where t-step number, t = 0, 1, 2, ... T.
The higher the rate or rate of return (discount) E, the more stringent conditions a project must satisfy in order to be truly effective.
If we remove the restriction according to which investments occur only at the zero point in time, accepting the postmerando flow, and assume that at This capital investments are not included ( Z*), then formula (19.34) allows for the following generalization: the project is profitable if

Where TO calculated using formula (19.32).
It should be noted that the situation with the project NPV= 0 is of some interest, since it still has an additional argument in its favor. If it is introduced, the scale of production will increase and, accordingly, the size of the enterprise will increase, which will entail additional benefits for its employees. On the other side NPV= 0 means that the investment is as profitable as placing it in others financial instruments market.
However, despite certain advantages NPV, accepted as an optimality criterion when assessing the effectiveness of investment projects, it has a number of disadvantages. First, if an error is made in the cash flow forecast or discount factor, then a project that was considered profitable may become unprofitable. Secondly, in reality, the effectiveness of a project largely depends on its scale and risk. Moreover, the dependence between NPV And E nonlinear. Therefore, when assessing the effectiveness of IP, it is necessary to calculate not only NPV, but also the profitability index ID, and internal rate of return, which, depending on the riskiness of the project, are more preferable.
In foreign economic literature, the corresponding indicator is called NetPresentValue (NPV)- net present value. It is calculated by the formula:

Where CIFt- receipt of funds for t- mcalculation step; COFT - payment of funds for t-th calculation step; T- duration of the investment period; R- rate of return.
If investments in the project are made at a time, then expression (19.36) can be presented as:

Where NCFt-net cash flow t-th calculation step; I
Positive value NPV indicates the feasibility of making a decision to finance the project. When comparing alternative projects, the project with the greatest economic effect is considered economically profitable.
Comparing the possible options for an investor’s behavior over the entire period of time, we find that his participation in the project can change the amount of funds in his accounts by an amount that is called in the literature the compounded effect (net compounded income - NCK, NetFutureValue). It can be negative in case of irrational use of resources or termination of the project and positive. Based on the negative and positive signs of the resulting compounded effect, a decision is made to participate in the project.

Return Indices (PI) represents the ratio of the sum of the given effects to the amount of capital investments. They can be calculated for discounted and undiscounted cash flows:

When assessing the effectiveness of projects, the following indices can be used:

· Cost Return Index (CRI) - This is the ratio of the amount of cash inflows (accumulated receipts) to the amount of cash outflows (accumulated payments).

· Discounted Cost Return Index (DCYI) is the ratio of the sum of discounted cash inflows to the sum of cash outflows.

· Investment Return Index (IRI) is the ratio of the sum of elements from operating activities to the absolute value of the sum of elements of cash flow from investment activities. It is equal to the value of the ratio increased by one BH to the accumulated volume of investments.

· Discounted Investment Return Index (DIRI) - is the ratio of the sum of the discounted cash flow elements from operating activities to investing activities. It is equal to the value of the ratio increased by one NPV to the accumulated discounted volume of investment.

When calculating ID And traffic police Either all capital investments for the calculation period can be taken into account, including investments in replacing retiring fixed assets, or only initial capital investments made before the enterprise is put into operation. In this case, the corresponding indicators will have different values.
As can be seen, the profitability index ID closely related to NPV. It is built from the same elements. If NPV is positive, then ID > 1 and vice versa. If ID > 1, the project is effective if ID< 1 - неэффективен.
There is also a corresponding indicator in foreign practice PtofitabilityIndex (PI), considered by the formula:

Where NCFt-net cash flow t- mcalculation step; R- rate of return; I- one-time investment in the project.
Unlike pure discounted income profitability index - relative indicator, characterizing the level of income per unit of cost. The higher the return on each ruble invested in a given project, the greater the value of this indicator. For all equal values NPV the profitability index gives grounds to choose the project that has the greatest value.
Internal rate of return or profitability (IRR) represents the discount rate Evn, at which the reduced effects are equal to the reduced capital investments. This is the discount rate at which the integral effect of the project, for example NPV, becomes equal to zero.
To obtain Evn (VIEW), the following equation needs to be solved:

If the entire project is carried out only with borrowed funds, then GNI equal to the highest percentage, under which you can take out a loan in order to be able to pay off from the proceeds from the project.
Internal rate of return value GNI reflects:

· economic inequality of costs, results and effects at different times - the benefit of making costs later and obtaining useful results earlier;

· the minimum acceptable return on invested capital at which the investor would prefer participation in the project to the alternative investment of the same funds in another project with a comparable degree of risk;

· market conditions financial market, availability of alternative and affordable investment opportunities;

· uncertainty of the conditions for the implementation of the project and, in particular, the degree of risk associated with participation in its implementation;

· the possibility of establishing limits on “concessions” in order to obtain a certain gain based on other indicators.

Advantage GNI is that the project participant should not determine his individual norm discount in advance. It defines GNI, i.e., calculates the efficiency of invested capital and then makes a decision using its value.
If we take as a basis the indicator characterizing the weighted average price of capital, as indicated earlier (see formula 19.12), GNI will consist in the fact that the enterprise can make any investment decisions, the level of profitability of which is not lower than E. Exactly with the indicator E compare GNI, calculated for a specific project.
If VND > E, then the project should be recommended for implementation; If GNI< Е the project should be rejected; at GNI= E, The project is neither profitable nor unprofitable.
At the same time, if you select projects to the maximum GNI, Projects that are beneficial from the point of view of the efficiency of the capital used, but are small and therefore have a small effect, may have advantages.
Magnitude GNI depends not only on the ratio of capital investments and income from the project, but also on their distribution over time. The longer the process of generating income is extended over time, the lower the value GNI.
There is also another drawback GNI, associated with his absence in a number of projects. On the other hand, if GNI is, then the entire dependence curve NPV from E has a “non-standard” appearance, passing through a negative value at E= 0. In such cases, there is a clear economic meaning GNI is lost, and the demand E > GNI as a positivity condition NPV becomes incorrect. Yes, and in those cases when NPV (E= 0) > 0 may be difficult to use in practice GNI, if the equation NPV (E) = O has several positive roots and the value of the first root is small.
Since in practice it is difficult to calculate the internal rate of return, the calculation method is used NPV at different discount rates. Wherein E, in which the graph will intersect the x-axis, as shown in Fig. 19.4, and determines the desired value of the internal rate of return of the project at NPV= 0, and for large values E- negative. Assessing the degree of sustainability IP determined by the difference VND - E.

An interpolation calculation formula can also be used IRR:

Where aw And en- flow increase coefficients for the upper and lower values ​​of the rates of return; A - flow increase coefficient for which the rate is determined; iв And in- or rather, the lower value of the rates of return.
The value of the internal rate of return can be obtained approximately by the iteration method.
Dependency diagram NPV from E shown in Fig. 19.5.

The function is “smoothed” using two rates E. VND calculated to the third decimal place. Curvature does not have such a strong effect on the results of profitability assessment.

There are a number of other assessment features GNI. So, when determining GNI no discount rate is needed. At the same time, the discount rate reflects the profitability of alternative investment directions. Comparison GNI with the discount rate allows us to evaluate the “margin of safety” of the project, so that a large difference between these values ​​indicates a certain stability of the project.
In foreign practice, this indicator is called InternalRateofReturn-IRR, i.e. settlement rate percent, or cost-effectiveness method. It is used as the first step in financial analysis IP. At the same time, projects are selected that have an internal rate of return of 15-20%.
In some cases, simple ranking of projects based on ratings NPV doesn't allow you to select The best decision, since the lifespan of investment projects is different. Therefore, to choose best project, uses an equivalent annuity (eng. equivalentannuity). At the same time, the method for calculating an equivalent annuity does not at all replace the method for determining NPV. It simply makes it easier to solve the problem of choosing from the compared projects the best one according to the maximum criterion NPV, which should correspond to the highest value of the annuity, i.e., all cash receipts.
In real life, other situations are quite possible when calculations of the effectiveness of investment projects require certain adjustments, associated, on the one hand, with the influence of many additional factors and conditions, and on the other hand, with insufficient information for a reliable assessment. Science and practice have developed certain rules for making decisions on investing in projects, taking into account these circumstances.

Concept, content and methodology for generating cash flows of an investment project

CASH FLOW is the difference between the income and costs of an economic entity (usually a company), expressed in the difference between payments received and payments made. Overall this is the amount retained earnings the company and its depreciation charges, saved to form its own source of funds for the future renewal of fixed capital. In other words, D. p. - net amount money actually received by the company in a given period. In many translated works this concept is expressed by the terms “cash flow” or “flow cash”, which is clearly unfortunate, since the words cash in English and “cash” in Russian are very different in the range of concepts they cover. For example, D. items include depreciation deductions or changes to entries in bank accounts firms (for non-cash payments): neither one nor the other has anything to do with cash in the generally accepted sense.

The future success of the company largely depends on how accurately the economic effect of an investment project (IP) is calculated. At the same time, one of the most difficult tasks is the correct assessment of the expected cash flow. If it is calculated incorrectly, then any method of assessing IP will give an incorrect result, which is why an effective project can be rejected as unprofitable, and an economically unprofitable one accepted as super-profitable. That is why it is important to correctly draw up a company cash flow plan. The cash flow of an investment project is understood as the receipts and payments of funds associated exclusively with the implementation of this project. Project cash flows do not include cash flows arising from the current activities of the enterprise. Cash flow investment project is the time dependence of cash receipts (inflows) and payments (outflows) during the implementation of the project, determined for the entire billing period. The effectiveness of the IP is assessed during the calculation period, covering the time interval from the start of the project to its termination. The billing period is divided into steps - segments, within which the data used to evaluate financial indicators is aggregated. At each step, the value of cash flow is characterized by: - ​​an inflow equal to the amount of cash receipts (or results in value terms) at this step; - outflow equal to payments at this step; - balance (effect) equal to the difference between inflow and outflow. Cash flow usually consists of flows from individual activities: a) cash flow from operating activities; b) cash flow from investment activities; c) cash flow from financial activities. Cash flow from operating activities includes cash receipts from the sale of goods, works and services, as well as advances from buyers and customers. Payments for raw materials, supplies, utility bills, wage payments, taxes and fees paid, etc. are shown as cash outflows. For investment activities, cash flows associated with the acquisition and sale of long-term property, that is, fixed assets and intangible assets. Financial activities involve inflows and outflows of funds from loans, borrowings, issues valuable papers etc. Net cash flow is the sum of cash flows from operating, investing and financing activities. In other words, it is the difference between the sum of all cash receipts and the sum of all payments for the same period. It is the net cash flows of various periods that are discounted when assessing the effectiveness of the project. At the initial stage of the project (investment period), cash flows, as a rule, turn out to be negative. This reflects the outflow of resources that occurs in connection with the creation of conditions for subsequent activities (for example, the acquisition non-current assets and the formation of net working capital). After the end of the investment period and the beginning of the operating period associated with the start of operation of non-current assets, the amount of cash flow, as a rule, becomes positive. Additional revenue from product sales, as well as additional production costs, arising during the implementation of the project, can be both positive and negative quantities. Technically, the task of investment analysis is to determine what the cumulative total of cash flows will be at the end of the established research horizon. In particular, it is fundamentally important whether it is positive. Cash flows can be expressed in current, forecast and deflated prices. Current prices are prices without taking into account inflation. Forecast prices are those expected (taking into account inflation) at future calculation steps. Deflated are forecast prices that are reduced to the price level at a fixed point in time by dividing by the general underlying inflation index. Along with cash flows, accumulated (cumulative) cash flow is also used when evaluating an investment project. Its characteristics are accumulated inflow, accumulated outflow and accumulated balance (cumulative effect). These indicators are determined at each step of the calculation period as the sum of the corresponding characteristics of the cash flow for this and all previous steps.

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

7. 1. general characteristics effectiveness assessment methods

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

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

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

• return of the original amount of capital investment and
• ensuring the required return on invested capital.

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

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

7. 2. Discounted payback period method

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

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

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

Table 7.1.
Project A

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

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

Table 7.2.
Project V.

.

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

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

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

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

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

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

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

Method procedure.

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

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

Step 3. A decision is made:

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

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

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

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

We will make the calculation using the following table.

Table 7.3.
NPV value calculation

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

* Discount factor is determined using financial tables.

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

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

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

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

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

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

Typical input cash flows:

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

Typical output streams:

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

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

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

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

Table 7.4.
Traditional NPV calculation

Thus, NPV=0 and the project is accepted.

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

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

Table 7.5.
Calculation of cash flow distribution

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

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

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

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

In the first approach, which is more consistent with the real situation, especially in countries with unstable economy, the net present value method is used in its standard form, but all cost and income components and discount rates are adjusted to the expected annual inflation rate. It is important to note that to produce a consistent forecast of different inflation rates for various types resources seems to be an extremely difficult and practically impossible task.

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

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

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

Table 7.6.
Solution without taking into account inflation

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

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

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

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

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

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

Table 7.7.
Inflation-based solution

Initial investment
Annual savings
Annual savings
Annual savings
Pure modern meaning

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

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

7. 5. Internal rate of return (IRR)

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

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

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

,

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

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

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

Thus, IRR is a kind of “barrier indicator”: if the cost of capital is higher than the IRR value, then the “power” 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 IRR cannot be solved in its final form, although there are a number of special cases where this is possible. Let's look at an example that explains the essence of the solution.

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

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

.

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

.

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

		Cash flow	12% coefficient recalculation	The present meaning
Annual Economy
Initial investment

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

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

Following the previous scheme, we calculate the discount factor:

.

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

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

Using linear interpolation we find

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

7. 6. Comparison of NPV and IRR methods

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

Table 7.8
Cash flows of alternative projects

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

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

Table 7.9
NPV indicators for alternative projects

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

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

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

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

Rice. 7.1. NPV profiles of alternative projects

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

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

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

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

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

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

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

Table 7.10
Calculation of discounted costs when buying a new car

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

Table 7.11
Calculation of discounted costs for operating an old machine

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

7. 8. Assumptions made when assessing effectiveness

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

All methods relied heavily on the following two assumptions.

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

Test questions and assignments

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

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

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

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

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

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

Need to determine

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

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

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

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

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

in all remaining years - $62,000.

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

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

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

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

	Discounted Cash Flow	Accumulated cash flow

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

of the year.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Need to determine

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

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

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

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

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

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

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

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

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

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

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

11. Projects are analyzed ($):

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

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

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

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

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

Which project would you prefer?

Posted on the website 05/14/2009

In the context of global economic crisis The construction sector of the Russian economy is experiencing serious difficulties, in particular, limited access to credit resources. The article discusses an example of assessing the effectiveness of an investment project for the construction of a multifunctional complex.

A.V. Zemtsov, independent expert

Criteria and methods for evaluating investment projects

Financial and economic assessment of investment projects occupies a central place in the process of justification and selection possible options investing in operations with real assets. It is largely based on design analysis. The purpose of project analysis is to determine the outcome (value) of the project. To do this, use the expression:

Project result = project price - project costs.

It is customary to distinguish between technical, financial, commercial, environmental, organizational (institutional), social, economic and other assessments of an investment project.

Predictive assessment of a project is quite a complex task, which is confirmed by a number of factors:

1) investment expenses can be made either on a one-time basis or over a fairly long period of time;

2) the period for achieving the results of the investment project may be greater than or equal to the calculated one;

3) carrying out long-term operations leads to an increase in uncertainty in assessing all aspects of investments, that is, to an increase in investment risk.

The effectiveness of an investment project is characterized by a system of indicators that reflect the ratio of costs and results depending on the interests of its participants.

Assessing the overall effectiveness of the project for the investor

Investment projects can be either commercial or non-commercial. Even with non-commercial projects, there are opportunities expended and opportunities gained.

The difference between investment projects and current activities is that costs intended for the one-time acquisition of some opportunities are not considered investments. It turns out that an investor is a person who invests his capabilities for repeated use, making them work to create new opportunities.

If there are ways to evaluate effectiveness for commercial projects, then how to evaluate the effectiveness of non-commercial projects? Efficiency in general refers to the degree of compliance with the goal 1. The goal must be set precisely, in detail and allow only an unambiguous answer - whether it has been achieved or not. At the same time, you can achieve your goal in different ways, and each path has its own costs.

To decide on the implementation of a commercial project, an assessment of its economic efficiency is carried out. In the case of a non-profit project, if it is decided to achieve a goal, then the choice is to determine the most effective way. Wherein non-financial criteria should take precedence over financial ones. But at the same time, the goal must be achieved in the least expensive way.

Also when evaluating a non-profit project:

The investor’s resilience to the implementation of the project should be taken into account - will the investor withstand the implementation of the project;

When identifying alternatives of equal quality, the cheapest one is usually chosen;

It is advisable to plan the movement of costs (investments) over time in order to calculate forces in advance, anticipate shortages and take care of attracting additional resources, if necessary.

Assessment of project externalities

The second aspect of project evaluation is that the project may have value not only for the investor. For example, investments in the knowledge of some people no longer brought benefits to themselves, but to society as a whole, which then used the discoveries and inventions of scientists for its needs. In addition to commercial significance, ordinary commercial investment projects of companies also have the following effects:

Social;

Tax;

Budget;

Ecological.

All the effects of the project for other parties are important, since the company and the project are surrounded by society, people, the state, and nature. If the project improves the environment, then it is better for the company implementing the project, because everything in the world is interconnected.

1. The social effect is assessed by the benefit of the project for the population either living around the project site or working on the project, and consists of:

In increasing the level of salaries;

Development of infrastructure and other opportunities for the population around the project site.

2. The tax effect is assessed by the volume of taxes collected from the project into the local, regional and federal budget.

3. The budgetary effect is assessed if the project is fully or partially financed from the budget (federal, regional, local). It is determined how much money the project returns to the budget through taxes, after the budget has invested in the project, over a certain number of years.

4. An environmental effect occurs if the project somehow affects the environmental situation.

Economic approach to assessing the effectiveness of an investment project

The vast majority of decisions made by market economy entities are based on preliminary assessment expected consequences. Individual assessment of the acceptability (effectiveness, value) of each investment project is carried out using various methods and taking into account certain criteria. We have analyzed Russian and foreign methods for evaluating investment projects and shown the application of these methods using practical examples.

General approaches to determining the effectiveness of investment projects

Investment decision-making is based on an assessment of the economic efficiency of investments. A market economy requires taking into account the influence on the efficiency of investment activity of environmental factors and time factors, which are not fully assessed in the calculation of these indicators.

They quite fully reflect the results of scientific research by domestic and foreign economists in the field of efficiency assessment methods. According to the Methodological Recommendations, the performance indicators of investment projects are divided into the following types 3:

Indicators of commercial efficiency, taking into account the financial consequences of the project for its direct participants;

Budget efficiency indicators reflecting the financial consequences of the project for the federal, regional or local budgets;

Indicators of economic efficiency that take into account the results and costs associated with the implementation of an investment project, going beyond the direct financial interests of the project participants and allowing for cost measurement.

The identification of such types is artificial and is associated with the determination of a single indicator of economic efficiency, but in relation to different objects and levels economic system: national economy in general (global criterion of economic efficiency), regional, sectoral, enterprise level or specific investment project.

According to methodological recommendations, investment efficiency is characterized by a system of indicators that reflect the ratio of investment-related costs and results and allow one to judge the economic advantages of some investments over others.

Investment efficiency indicators can be classified according to the following 4 criteria:

1) by type of general indicator, serving as a criterion for the economic efficiency of investments:

Absolute, in which general indicators are defined as the difference between the cost estimates of the results and costs associated with the implementation of the project;

Relative, in which generalizing indicators are defined as the ratio of cost estimates of project results to the total costs of obtaining them;

Temporary, which estimates the payback period of investment costs;

2) using the method of comparing monetary costs and results at different times:

Static, in which cash flows arising at different points in time are assessed as equivalent;

Dynamic, in which cash flows caused by the implementation of the project are reduced to an equivalent basis by discounting them, ensuring comparability of cash flows at different times.

Static methods are also called methods based on accounting estimates, and dynamic methods are called methods based on discounted estimates 5.

TO group of static methods include: payback period of investments (Payback Period, PP); investment efficiency ratio (Accounting Rate of Return, ARR).

TO dynamic methods include: net present value, net present value (Net Present Value, NPV); return on investment index (Profitability Index, PI); internal rate of return (Internal Rate of Return, IRR); modified internal rate of return (Modified Internal Rate of Return, MIRR), discounted payback period of investment (Discounted Payback Period, DPP).

It should also be noted that the assessment of the effectiveness of each investment project is carried out taking into account criteria that meet certain principles, namely:

The influence of the value of money over time;

Opportunity costs;

Possible changes in project parameters;

Carrying out calculations based on real cash flow rather than accounting indicators;

Inflation and its reflections;

Risk associated with the implementation of the project.

Let us consider the main methods for assessing the effectiveness of investment projects in more detail and find out their main advantages and disadvantages.

Static estimation methods

Payback Period (PP)

The most common static indicator for evaluating investment projects is the term payback period (PP).

The payback period is understood as the period of time from the start of the project until the operation of the facility, when the income from operation becomes equal to the initial investment (capital costs and operating costs).

This indicator answers the question: when will the full return of the invested capital occur? The economic meaning of the indicator is to determine the period within which an investor can return the invested capital.

To calculate the payback period, the elements of the payment series are summed up on an accrual basis, forming the balance of the accumulated flow, until the amount takes a positive value. The serial number of the planning interval, in which the balance of the accumulated flow takes a positive value, indicates the payback period expressed in planning intervals. The general formula for calculating the PP indicator is:

where P k is the value of the accumulated flow balance;
I 0 is the amount of initial investment.

When a fraction is obtained, it is rounded up to the nearest whole number. Often the PP indicator is calculated more accurately, that is, the fractional part of the interval (calculation period) is also considered; in this case, the assumption is made that within one step (calculation period) the balance of the accumulated cash flow changes linearly. Then the “distance” x from the beginning of the step to the moment of payback (expressed in the duration of the calculation step) is determined by the formula:

where P k- is the negative value of the balance of the accumulated flow at the step until the payback period;
P k+ is the positive value of the balance of the accumulated flow at the step after the payback moment.

As a meter, the “payback period” criterion is simple and easy to understand. However, it has significant disadvantages, which we will consider in more detail when analyzing the discounted payback period (DPP), since these disadvantages apply to both static and dynamic indicators of the payback period. The main disadvantage of the static indicator “payback period” is that it does not take into account the time value of money, that is, it does not distinguish between projects with the same balance of income flow, but with different distributions over the years.

Accounting Rate of Return (ARR)

Another indicator of static financial assessment project is the investment efficiency ratio (Account Rate of Return or ARR). This ratio is also called the accounting rate of return or the project profitability ratio.

There are several algorithms for calculating ARR.

The first calculation option is based on the ratio of the average annual profit (minus contributions to the budget) from the implementation of the project for the period to the average investment:

I av 0 - the average value of the initial investment, if it is assumed that upon expiration of the project, all capital costs will be written off.

Sometimes the profitability of a project is calculated based on the initial investment:

Calculated on the basis of the initial investment volume, it can be used for projects that create a stream of uniform income (for example, an annuity) for an indefinite or rather long period.

The second calculation option is based on the ratio of the average annual profit (minus deductions to the budget) from the implementation of the project for the period to the average investment, taking into account the residual or liquidation value of the initial investment (for example, taking into account the liquidation value of equipment upon completion of the project):

where Р r — annual average profit (minus contributions to the budget) from the implementation of the project;
I 0 is the average value (value) of the initial investment.

Dynamic estimation methods

Net present value (Net Present Value, NPV)

In modern published works, the following terms are used to name the criterion of this method: net present value 6 ; net present value 7; net present value 8 ; net present value 9 ; total financial result from the implementation of the project 10; current value 11.

The value of net present value (NPV) is calculated as the difference between the discounted cash flows of income and expenses incurred in the process of implementing the investment over the forecast period.

The essence of the criterion is to compare the current value of future cash receipts from the project with the investment costs necessary for its implementation.

The application of the method involves the sequential passage of the following stages:

1) calculation of the cash flow of the investment project;

2) selection of a discount rate that takes into account the profitability of alternative investments and the risk of the project;

3) determination of net present value.

The NPV or NPV for a constant discount rate and a one-time initial investment is determined by the following formula:

where I 0 is the amount of initial investment;

i is the discount rate.

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

The basis of calculations using this method is the premise that the value of money varies over time. The process of converting the future value of a cash flow into the current value is called discounting(from English discount- reduce).

The rate at which discounting occurs is called the rate discounting (discount), and the factor F = 1/(1 + i) t - discount factor.

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

where I t is the cash flow of the initial investment;
C t is the cash flow from the sale of investments at time t;
t — calculation step (year, quarter, month, etc.);
i is the discount rate.

The conditions for making an investment decision based on this criterion are as follows:

If NPV > 0, then the project should be accepted;

If NPV< 0, то проект принимать не следует;

If NPV = 0, then accepting the project will bring neither profit nor loss.

This method is based on following the main target set by the investor - maximizing its final state or increasing the value of the firm. Following this target setting is one of the conditions for a comparative assessment of investments based on this criterion.

A negative net present value indicates the inexpediency of making decisions on financing and implementing the project, since if the NPV< 0, то в случае принятия проекта ценность компании уменьшится, то есть владельцы компании понесут убыток и основная целевая установка не выполнится.

A positive net present value indicates the advisability of making decisions on financing and implementing a project, and when comparing investment options, the option with the highest NPV value is considered preferable, since if NPV > 0, then if the project is accepted, the value of the company, and therefore the welfare of its owners will increase. If NPV = 0, then the project should be accepted provided that its implementation will increase the flow of income from previously implemented capital investment projects. For example, extension land plot for a hotel parking lot will enhance the real estate income stream.

The implementation of this method involves a number of assumptions that must be checked for the degree of their correspondence to reality and the results that possible deviations lead to.

Such assumptions include:

The existence of only one objective function - the cost of capital;

The specified duration of the project;

Data reliability;

Payments belong to certain points in time;

Existence of a perfect capital market.

When making decisions in the investment field, you often have to deal not with one goal, but with several goals. If a cost of capital method is used, these objectives should be considered when arriving at a solution outside of the cost of capital process. In this case, methods for making multi-objective decisions can also be analyzed.

The useful life must be established in the performance analysis before applying the net present value method. For this purpose, methods for determining the optimal service life may be analyzed, unless this has not been established in advance for technical or legal reasons.

In reality, there is no reliable data when making investment decisions. Therefore, along with the proposed method for calculating the cost of capital based on predicted data, it is necessary to analyze the degree of uncertainty, at least for the most important investment objects. Methods of investing under conditions of uncertainty serve this purpose.

When forming and analyzing the method, it is assumed that all payments can be attributed to certain points in time. The time period between payments is usually one year. In reality, payments can be made at shorter intervals. In this case, you should pay attention to the compliance of the calculation period step (calculation step) with the conditions for granting the loan. For the correct application of this method, it is necessary that the calculation step be equal to or a multiple of the period for calculating interest on the loan.

The assumption of a perfect capital market, in which financial resources can be attracted or invested at any time and in unlimited quantities at a single calculated interest rate, is also problematic. In reality, such a market does not exist, and interest rates for investing and borrowing financial resources, as a rule, differ from each other. This raises the problem of determining an appropriate interest rate. This is especially important since it has a significant impact on the value of capital.

When calculating NPV, discount rates that vary from year to year can be used. In this case, it is necessary to apply individual discount factors to each cash flow, which will correspond to this calculation step. In addition, it is possible that a project acceptable at a constant discount rate may become unacceptable at a variable one.

The net present value indicator takes into account the time value of money, has clear decision criteria and allows you to select projects for the purpose of maximizing the value of the company. In addition, this indicator is absolute and has the property of additivity, which allows you to add the values ​​of the indicator for various projects and use the total indicator for projects in order to optimize the investment portfolio, that is, the following equality is valid:

NPV A + NPV B = NPV MB.

For all its advantages, the method also has significant disadvantages. Due to the difficulty and ambiguity of forecasting and generating cash flow from investments, as well as the problem of choosing a discount rate, there may be a danger of underestimating the risk of the project.

Profitability Index (PI)

The profitability index (profitability, profitability) is calculated as the ratio of the net present value of cash inflows to the net present value of cash outflows (including initial investments):

where I 0 is the enterprise’s investment at time 0;
i is the discount rate.

The profitability index is a relative indicator of the effectiveness of an investment project and characterizes the level of income per unit of cost, that is, the effectiveness of investments - the higher the value of this indicator, the higher the return monetary unit invested in this project. This indicator should be given preference when compiling an investment portfolio in order to maximize the total NPV value.

The conditions for accepting a project according to this investment criterion are as follows:

If PI > 1, then the project should be accepted;

If PI< 1, то проект следует отвергнуть;

If PI = 1, the project is neither profitable nor unprofitable. It is easy to see that when evaluating projects involving the same amount of initial investment, the PI criterion is fully consistent with the NPV criterion.

Thus, the PI criterion has an advantage when choosing one project from a number of projects with approximately the same NPV values, but different volumes of required investments. In this case, the one that provides greater investment efficiency is more profitable. In this regard, this indicator allows you to rank projects with limited investment resources.

The disadvantages of the method include its ambiguity when discounting cash inflows and outflows separately.

Internal Rate of Return (IRR)

Under internal rate of return, or internal rate of return, investment (IRR) understand the value of the discount rate at which the NPV of the project is equal to zero:

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

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

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

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

If IRR > CC, then the project should be accepted;

If IRR< СС, то проект следует отвергнуть;

0 if IRR = СС, then the project is neither profitable nor unprofitable.

Another interpretation option is to treat the internal rate of return as a possible discount rate at which the project is still profitable according to the NPV criterion. The decision is made based on comparison of IRR with standard profitability; Moreover, the higher the internal rate of return and the greater the difference between its value and the selected discount rate, the greater the margin of safety the project has. This criterion is the main guideline when an investor makes an investment decision, which does not at all detract from the role of other criteria. To calculate IRR using discount tables, two values ​​of the discount factor r are selected< i 2 таким образом, чтобы в интервале (i, …, i 2) функция NPV = f(i) меняла свое значение с «+» на «-» или с «-» на «+». Далее применяют формулу:

where r 1 is the value of the discount factor at which f (i 1) > 0 (f (i 1)< 0);
r 2 - the value of the discount factor at which f (i 1)< 0 (f (i 1) > 0).

The accuracy of the calculations is inversely proportional to the length of the interval (i 1, ..., i 2), and the best approximation is achieved in the case when i 1 and i 2 are the closest values ​​of the discount factor that satisfy the conditions.

Accurate calculation of the IRR value is only possible using a computer.

The corresponding assumption of the method for determining the internal rate (investment at the internal interest rate), as a rule, does not seem appropriate. Therefore, the method of determining the internal rate of return without taking into account specific reserve investments or other modification of conditions should not be used to assess absolute profitability if complex investments take place and thus a process of reinvestment occurs. This type of investment also poses the problem of multiple positive or negative IRRs, which can make it difficult to interpret the results obtained by the IRR method.

The method of determining the internal rate of return for assessing relative profitability should not be applied, as noted above, by comparing the internal interest rates of individual properties. Instead, the investment must be analyzed to determine the difference. If we are talking about investments made in isolation, then we can compare the internal interest rate with the calculated one to make it possible to compare profitability. If the investments for comparison of profitability are complex, then the use of the method for determining profitability is inappropriate.

The advantage of the internal rate of return method over the net present value method is the possibility of its interpretation. It characterizes the accrual of interest on capital expended (return on capital expended).

In addition, the internal interest rate can be considered as the critical interest rate for determining the absolute profitability of an investment alternative if the net present value method is used and the “hard data” assumption does not apply.

Thus, investment evaluation using this method is based on determining the maximum discount rate at which projects will break even.

NPV, IRR and PI criteria most often used in investment analysis, are actually different versions of the same concept, and therefore their results are related to each other. Thus, we can expect the following mathematical relationships to be satisfied for one project:

If NPV > 0, then IRR > CC(r); PI > 1;

If NPV< 0, то IRR < CC (r); PI < 1;

If NPV = 0, then IRR = CC (r); PI = 1.

There are techniques that adjust the IRR method for use in a particular non-standard situation. One of these methods is the modified internal rate of return (MIRR) method.

Modified Internal Rate of Return (MIRR)

The modified rate of return (MIRR) eliminates the significant shortcoming of the project's internal rate of return, which arises in the event of repeated cash outflows. An example of such repeated outflow is the purchase by installments or construction of a real estate project carried out over several years. The main difference of this method is that reinvestment is carried out at a risk-free rate, the value of which is determined based on financial market analysis.

In Russian practice, this may be the profitability of a fixed-term foreign currency deposit, offered by Sberbank of Russia. In each specific case, the analyst determines the value of the risk-free rate individually, but, as a rule, its level is relatively low.

Thus, discounting costs at a risk-free rate makes it possible to calculate their total current value, the value of which allows a more objective assessment of the level of return on investments, and is a more correct method in the case of making investment decisions with irrelevant (extraordinary) cash flows.

Discounted Payback Period (DPP)

Discounted payback period of investment (Discounted Payback Period, DPP) eliminates the disadvantage of the static payback period method and takes into account the time value of money, and the corresponding formula for calculating the discounted payback period, DPP, is:

Obviously, in the case of discounting, the payback period increases, that is, always DPP > PP.

The simplest calculations show that this technique, under conditions of a low discount rate, characteristic of a stable Western economy, improves the result by an insensible amount, but for a significantly higher discount rate, characteristic of the Russian economy, this results in a significant change in the calculated payback period. In other words, a project acceptable under the PP criterion may be unacceptable under the DPP criterion.

When using the PP and DPP criteria in assessing investment projects, decisions can be made based on the following conditions:

a) the project is accepted if payback occurs;

b) the project is accepted only if the payback period does not exceed the deadline established for a particular company.

In general, the determination of the payback period is of an auxiliary nature relative to the net present value of the project or the internal rate of return. In addition, the disadvantage of such an indicator as the payback period is that it does not take into account subsequent cash inflows, and therefore can serve as an incorrect criterion for the attractiveness of the project.

Another significant drawback of the “payback period” criterion is that, unlike the NPV indicator, it does not have the property of additivity. In this regard, when considering a combination of projects, this indicator must be handled with caution, taking into account this property.

However, the “payback period” criterion is indifferent to the amount of initial investment and does not take into account the absolute volume of investment. Thus, this indicator can only be used to analyze investments with a comparable amount of initial investment.

In some cases, the application of the payback period criterion may be critical for investment decision-making purposes. In particular, this can happen if the investment involves a high risk, and then the shorter the payback period, the more preferable such a project is. In addition, the company's management may have a certain limit on the payback period, and this is primarily due to the problem of liquidity, since the company's main goal is for investments to pay off as soon as possible. Thus, the PP and DPP criteria make it possible to judge the liquidity and riskiness of a project as follows: the shorter the payback period, the less risky the project; The more liquid project is the one that has a shorter payback period. It is advisable to apply these criteria when the company is interested in increasing liquidity, as well as in industries in which investments are associated with a high level of risk (for example, in industries with rapid changes in technology: computer systems, mobile connection etc.).

Cash flows of investment projects: analysis and assessment

Relevant cash flows

The most important stage in the analysis of an investment project is the assessment of the projected cash flow 12, which consists (in the most general form) of two elements: the required investments (outflows of funds) and cash receipts minus current expenses (inflows of funds).

In financial analysis, it is necessary to carefully consider the distribution of cash flows over time. Financial statements The income statement is not linked to cash flows and therefore does not reflect when cash inflows or outflows occur during the reporting period.

When developing cash flow, the time value of money must be taken into account.

To compare cash flow values ​​at different times, a discounting mechanism is used, with the help of which all cash flow values ​​at various stages of the investment project are brought to a certain point, called the reduction moment. Usually the moment of reduction coincides with the beginning or end of the basic stage of the investment project, but this is not prerequisite, and any stage at which it is necessary to evaluate the effectiveness of the project can be selected as the moment of reduction.

As noted above, the most important indicator project efficiency is net present value. The indicators of net present value and internal rate of return (IRR) allow you to compare different investment projects with each other in order to select the most effective one. However, such comparisons are subject to projects with comparable implementation periods, volumes of initial investments and relevant cash flows.

Relevant cash flows mean those flows in which a flow with a minus sign changes to a flow with a plus sign once. Relevant cash flows are typical for standard, typical and simplest investment projects, in which the initial investment of capital, that is, the outflow of funds, is followed by long-term receipts, that is, the inflow of funds.

Analysis of the cash flow of an investment project is not limited to studying its structure. It is also important to identify the cash flow, ensure its relevance/irrelevance, which will ultimately simplify the procedure for selecting evaluation indicators and selection criteria, as well as improve the comparability of different projects.

Irrelevant cash flows

Irrelevant cash flows are characterized by a situation where the outflow and inflow of capital alternate. In this case, some of the considered analytical indicators may change in an unexpected direction with changes in the initial parameters, that is, conclusions drawn on their basis may not always be correct.

Recalling that IRR is the root of the equation NPV = 0, and the function NPV = f(i) is an algebraic equation kth degree, where k is the number of years of project implementation, then, depending on the combination of signs and absolute values ​​of the coefficients, the number of positive roots of the equation can range from 0 to k. In particular, if cash flow values ​​alternate in sign, several values ​​of the IRR criterion are possible.

If we consider the graph of the function NPV = f (r, Pk), then it can be represented differently depending on the values ​​of the discount factor and the signs of cash flows (“plus” or “minus”). We can distinguish two most realistic typical situations (Fig. 1).

The given types of graph of a function

NPV = f (r, Pk) correspond to the following situations:

Option 1 - there is an initial investment of capital with subsequent receipts of funds;

Option 2 - there is an initial investment of capital; in subsequent years, inflows and outflows of capital alternate.

The first situation is the most typical: it shows that the function NPV = f (r) in this case is decreasing with increasing r and has a single IRR value. In the second situation, the type of graph may be different.

Project effectiveness assessment

Let's consider an example of assessing an investment project for the construction of a multifunctional complex within the third transport ring.

Assumptions

Any investment project is considered in the context of complex macro- and microeconomic processes. The process of modeling and evaluating an investment project is influenced by many, if not all, macro- and microenvironmental factors, if this concerns real investments in the construction sector that will be discussed. It is impossible to take into account absolutely everything, but there are indicators that can and even need to be taken into account: inflation, interest rate commercial loan, share of the fund’s profit, taxes, the investor’s desired profit and others. It is easy to notice that some indicators, such as inflation and taxes, are conditionally constant, that is, they quantitative characteristic can be taken as constant over a certain period of time. Others, such as the commercial loan rate, the fund's profit share, the investor's desired return and others, may vary depending on the "appetite" of the participants. To analyze the effectiveness of the proposed investment project, a model was created in which it is possible to change the indicators described above, and the computer automatically recalculates the analytical part, but for this study it is necessary to fix some indicators in the form of economic assumptions 13:

Interest rate bank loan, 27% per annum;

Bank profit share, 0%;

Copyright holder profit, 84%;

Income tax rate, 24%;

Development fee, 3% of revenue;

Marketing costs, 2% of revenue;

Land rental cost, $91,000/ha per year;

Fixed portion of operating costs, $15,000 per month.

In addition to the assumptions described above, it is worth saying that there are several strategies for the development of the proposed investment project. To minimize risks and provide a faster return on investment, we propose to consider the situation of financing the project using 100% of funds raised with the parallel sale of areas under construction as they are being built.

Logic of the study

To determine investment needs, as well as to analyze the economic efficiency of an investment project, it is necessary to go through several stages 14:

1) investment forecasting: project estimate;

2) investment forecasting: investment plan;

3) revenue forecast;

4) drawing up a cash flow report;

5) determination of net present value (NPV) and internal rate of return (IRR);

6) calculation of the investment payback period (PP), discounted payback period (DPP) and investment profitability index (PI);

7) determination of financing needs.

Let's take a closer look at the key points.

Description of the investment project

Let's consider an investment project for the construction of a multifunctional complex within the third transport ring, which is a multi-storey complex on an area of ​​1.08 hectares with underground parking, offices, retail space, a hotel, restaurant and apartments.

Project effectiveness assessment. Investment forecasting: project estimate

Let's consider specific example assessing the effectiveness of an investment project for the construction of a multifunctional complex in Moscow. Let's draw up an estimate for the project (Table 1).

Preparation of a cash flow statement

Determining Net Present Value (NPV)

To determine NPV, the profit/loss (or cash flow) line from the cash flow statement is taken. For clarity, we present a method for calculating NPV.

NPV calculation:

conclusions

In the context of the global economic crisis, the construction sector of the Russian economy is experiencing serious difficulties, in particular, access to credit resources is limited even for such large companies like Mirax Group, PIK group of companies, Glavmosstroy. Almost all developers now have to rely exclusively on their own funds, which are generally not enough to implement new and complete existing projects, not to mention those companies that carried out construction exclusively on borrowed funds.

Nevertheless, promising investment projects continue to exist on the market, and the use of the correct methodology for assessing them is still relevant. In this case, it is necessary, of course, to make amendments to the values ​​of current indicators for the cost of credit resources, exchange rates, discount rates and other indicators, and to modernize the general approach to the formation of project financing sources.

Table 1. Project estimate

Table 2. Cash flow statement

Cash flow statement
	1st year				2nd year
	I	II	III	IV	I	II	III	IV
Revenue
Sale of hotel space			$239 200 000
Sale of apartments		$54 000 000	$54 000 000	$54 000 000	$54 000 000	$54 000 000	$54 000 000	$54 000 000
Sale of parking spaces		$17 460 000		$17 460 000		$17 460 000		$17 460 000
Sale of restaurant space					$23 700 000
Sale of retail space			$3 760 000	$3 760 000	$3 760 000
Sale of office space				$5 460 000	$5 460 000	$5 460 000
Sales costs		$ (2 143 800)	$ (8 908 800)	$ (2 420 400)	$ (2 607 600)	$ (2 307 600)	$ (1 620 000)	$ (2 143 800)
Net revenue		$69 316 200	$288 051 200	$78 259 600	$84 312 400	$74 612 400	$52 380 000	$69 316 200
Expenses
Preparation of a package of documents	$125 598 000
Construction of hotel areas		$15 946 667	$15 946 667	$15 946 667
Construction of apartments					$16 800 000	$16 800 000	$16 800 000
Construction of a parking lot	$55 500 000
Construction of restaurant areas								$7 900 000
Construction of retail space		$3 760 000
Construction of office space		$4 680 000
Construction technical premises	$750 000	$750 000	$750 000	$750 000	$750 000	$750 000	$750 000	$750 000
Preparation for finishing		$628 857	$628 857	$628 857	$628 857	$628 857	$628 857	$628 857
Finishing of technical premises	$187 500	$187 500	$187 500	$187 500	$187 500	$187 500	$187 500	$187 500
Finishing of general office and retail spaces	$1 600 000
Parking lot finishing	$436 500	$436 500
Showroom organization		$900 000
Marketing costs		$1 386 324	$5 761 024	$1 565 192	$1 686 248	$1 492 248	$1 047 600	$1 386 324
Obtaining BTI								$4 402 000
Current expenses	$15 000	$15 000	$15 000	$15 000	$15 000	$15 000	$15 000	$15 000
Development Fee	$5 474 610	$908 725	$698 671	$572 796	$602 028	$596 208	$582 869	$458 090
Interest on borrowed funds		$12 687 409	$11 115 643	-	-	-	-	-
Total expenses	$187 961 610	$46 030 782	$44 012 162	$22 086 412	$23 277 233	$22 777 413	$21 631 826	$17 871 572
	$385 649 010
Total interest paid	$23 803 052
Profit Loss	$(187 961 610)	$23 285 418	$244 039 038	$56 173 188	$61 035 167	$51 834 987	$30 748 174	$51 444 628
Cumulative total	$(187 961 610)	$(164 676 192)	$79 362 846	$135 536 034	$196 571 200	$248 406 187	$279 154 361	$330 598 990

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9 - Gitmap L.J., Jonk M.D. Fundamentals of investing. - M.: Delo, 1998.

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11 - Financial analysis of the company’s activities. - M.: East service, 1994.

12 - Cash flow of an investment project is a dependence on the time of cash receipts and payments during the implementation of the project generating it, determined for the entire billing period covering the time interval from the start of the project to its termination (see: “ Guidelines on assessing the effectiveness of investment projects,” approved. Ministry of Economy of the Russian Federation, Ministry of Finance of the Russian Federation, Civil Code of the Russian Federation for Construction, Architectural and housing policy No. VK 477 dated June 21, 1999).

13 - All assumptions are based on in-depth market analysis, using data from well-known analytical companies.

14 - Mindich D.A. Finance for a growing business. - M.: JSC "Expert RA", 2007.